Post on 01-Jan-2020
transcript
Financial Intermediaries and International Risk Premia
Kyriakos Chousakos∗
October 2017
Abstract
I propose a measure of adjusted leverage as a proxy for the pricing kernel of a representative financialintermediary. Using a simple theoretical framework with information production, I show that in states ofthe world where credit outstanding in the economy is low, financial leverage is not an accurate proxy forthe stochastic discount factor of financial intermediaries. Empirical evidence confirms this theoreticalfinding for an international panel of financial intermediaries. Credit outstanding arises as an importantdeterminant of the stochastic discount factor of a financial intermediary. As a result, the new proposedmeasure incorporates information on both intermediaries’ financial leverage and the amount of credit inthe economy. It is an economically meaningful state variable that is pro-cyclical and predicts financialcrises. I show that a global adjusted leverage factor prices currency portfolios and global equity portfoliosoutperforming benchmark factor models designed to price these assets.
Keywords: Asset Pricing, International Financial Markets, Financial IntermediariesJEL Classification: G2, G12, G15, G24
∗Yale University. Email: kyriakos.chousakos@yale.edu. I am grateful to my advisors Gary Gorton, Tobias Moskowitz, andJonathan Ingersoll for their guidance and invaluable comments. I thank Oliver Boguth (discussant), Robin Greenwood, TylerMuir (discussant), and Guillermo Ordoñez for helpful comments and suggestions. I also thank Thomas Bonzcek, Arun Gupta,Toomas Laarits, Avner Langut, Adriana Robertson, and participants of the 5th Annual USC Marshall PhD Conference inFinance, the PhD Session of the 2017 Northern Finance Association Annual Conference, and the PanAgora 2017 Crowell PrizeSeminar Series for useful comments. All errors remain my own.
1 Introduction
Financial intermediaries are the primary participants in capital markets. In the foreign exchange market,
international commercial banks acting as securities dealers account for more than 51% of all transactions.1
In the equities market, over the past decades households have been steadily decreasing their direct stock
holdings, while financial intermediaries have been filling the void.2 In the bond market, almost all of the
trading takes place between broker-dealers and large institutional investors in over-the-counter markets.3
Financial intermediaries are sophisticated market participants that carry out complex trading strategies, face
low transactions costs, and continuously update their strategies as new information becomes available. As
a result, financial intermediaries are ideal candidates for the role of the marginal investor in a wide array
of markets which means that their marginal value of wealth is expected to price financial assets in these
markets.4
In this paper, I improve on existing intermediary asset pricing models and study the impact of financial
intermediaries on global capital markets. More specifically, shifting the focus from U.S. only to international
financial intermediaries, I propose and test an empirical proxy for the pricing kernel of a representative global
financial intermediary. This proxy in addition to financial leverage takes into account the amount of credit in
the economy. This is motivated by a simple theoretical framework with information production in which credit
outstanding in the economy along with financial leverage arises as an important determinant of the stochastic
discount factor (SDF) of financial intermediaries. Empirical evidence presented in the paper confirms this
theoretical finding. The proposed measure is an adjusted leverage index which incorporates information
on intermediaries’ financial leverage and the availability of credit in the economy. I show that adjusted
leverage is an economically meaningful state variable that is pro-cyclical and predicts financial crises and
future consumption levels. I find that a global adjusted leverage factor prices currency portfolios and global
equity portfolios outperforming benchmark factor models designed to price these assets. A decomposition of
the global adjusted leverage factor into non-U.S. and U.S. only components reveals that non-U.S. financial
intermediaries are marginal investors in foreign exchange markets as well as in global equity markets.
To motivate the empirical work of this paper, I develop a simple theoretical framework in the spirit
of Gorton and Ordoñez (2014) and Gorton and Ordoñez (2016). The economy comprises three agents –
firms, financial institutions, and households – all of which are risk neutral with respect to lending activities1See, the foreign exchange turnover section of the triennial central bank survey conducted by the Bank for International
Settlements (BIS) in September 2016 (www.bis.org/publ/rpfx16fx.pdf).2See, e.g. Allen (2001), and Sneider et al. (2013).3See, e.g. Edwards et al. (2007) for a breakdown of the percentage of bonds traded over-the-counter and in NYSE.4A growing stream of the literature, both theoretical and empirical, studies the relation between financial intermediaries and
asset prices. I discuss the different approaches in Section 2.
1
with the exception of financial institutions which are risk averse with regard to holding firms’ equity.5 To
produce output, firms need to borrow capital from households through the financial system posting land
as collateral. Both households and financial institutions may produce information regarding the quality of
the collateral backing deposits and loans respectively with the cost of producing information for households
being significantly higher compared to that for financial institutions.6 In this setting, information production
regulates the amount of credit outstanding and deposits in the economy. Both quantities are an increasing
function of expected output and their respective rates of increase depend on the current information production
regime.
In this framework, I show that the relation between the SDF, as described in the model by the marginal
value of wealth of a financial institution, and its financial leverage is not one-to-one and strongly depends on
the level of credit outstanding. An increase in financial leverage does not necessarily indicate a decrease in the
marginal value of wealth for the financial institution. This is primarily observed in times of economic growth,
where credit outstanding is high and financial intermediaries sustain high financial leverage and low marginal
value of wealth as a result of the ample investment opportunities which they can undertake. However, this
is not the case in times of recessions or financial crises, where the amount of credit outstanding is low. In
such times both financial leverage and the marginal value of wealth of a financial institution increase as a
result of an increase in deposits not followed by a similar increase in loans and profitability. According to the
theoretical framework discussed above, it is possible that in a low credit environment an increase in leverage
is associated with an increase in the marginal value of wealth of the financial institution. This implies that
financial leverage is not an accurate empirical proxy for the SDF of a financial intermediary. A number of
empirical findings, summarized below, corroborate this theoretical proposition.
Assets that co-vary with intermediaries’ SDF are riskier and investors require higher premia to compensate
for that risk. In the literature the SDF of financial intermediaries is proxied by leverage innovations of
financial intermediaries (see, e.g. Adrian et al. (2014)) or its reciprocal capital ratio innovations (see, e.g. He
et al. (forthcoming)). I empirically show that for an international panel of countries financial leverage interacts
differently with key characteristics of financial intermediaries, such as future financial assets and stock market
returns, depending on the level of credit outstanding in the economy. When the credit outstanding is high,
financial leverage is positively correlated with the level of future assets reflecting a higher risk bearing capacity
and negatively correlated with market returns indicating lower risk for such investments. On the other hand,5This assumption is primarily motivated by the third Basel Accord (Basel III) according to which secure debt is considered
to be more liquid than equity and as a result the capital requirements for financial institutions holding equities in their balancesheets are higher compared to these for secure debt assets.
6Financial institutions possess superior technology and resources in identifying the quality of collateral posted by firmscompared to that of households.
2
when the credit outstanding in the economy is low the opposite holds true. This finding suggests that a
potential proxy for the SDF of financial intermediaries ought to take into account credit outstanding in the
economy.
I construct a proxy for intermediaries’ SDF by combining information on financial leverage of broker-
dealers with information on economy-wide credit-to-private sector. More specifically, first, I compute a
measure of global financial leverage as the aggregated country level financial leverage weighted by the level of
financial assets of each country. Second, I compute a global measure of credit-to-private sector by aggregating
country level credit-to-private sector figures again weighted by the level of financial assets of each country.
Finally, the global adjusted leverage measure is equal to the negative global leverage innovations when global
credit is less than a threshold value and equal to global leverage innovations otherwise. The threshold is set
at the 25th percentile of a rolling window on the global credit series.
This adjusted leverage measure is directly related to business cycles. Consistent with theoretical and
empirical work suggesting that the marginal value of wealth of a financial intermediary is pro-cyclical (see, e.g.
Brunnermeier and Pedersen (2009) and Adrian and Shin (2010)), adjusted leverage is positively correlated with
changes in real GDP, capital formation, and total factor productivity (TFP) at a country level. In addition,
it predicts financial crises and future levels of durables and non-durables consumption. The relation between
adjusted leverage and business cycles implies that it is an economically meaningful measure summarizing
various aspects of economic activity related to financial intermediaries’ marginal value of wealth. Based on
these properties I argue that this measure can be employed as a reasonable proxy for the SDF of financial
intermediaries.
Using a single factor model, I perform cross-sectional asset pricing tests across a set of international asset
classes. I find that excess returns of currency portfolios and international equity portfolios can be explained
by their exposure to global adjusted leverage. More specifically, the global adjusted leverage factor appears
with a significantly positive price of risk consistently across all test assets. The global adjusted factor model
outperforms benchmark models (see, e.g. Lustig et al. (2011), Menkhoff et al. (2012a), and Menkhoff et al.
(2012b)) which aim to explain the cross-section of currency portfolios, and performs similarly to standard
multifactor models, such as the Fama-French global three factor plus momentum model, which aim to explain
the cross-section of international equity portfolios. The positive price of risk across asset classes is consistent
with the theoretical framework developed in this paper where assets that co-vary with intermediaries’ SDF
are associated with a higher risk premium. My findings suggest that the marginal value of wealth of financial
intermediaries is indeed an important determinant of asset prices.
3
A common criticism of cross-sectional asset pricing tests is that mis-estimated exposures (betas) in the
time-series regressions could be explaining a spurious relationship in the cross-section of returns (see, e.g.
Lewellen et al. (2010)). I address many of the concerns voiced in Lewellen et al. (2010) by conducting a
number of robustness checks. First, I estimate the exposures of test portfolios on the global leverage factor
and find that the adjusted leverage betas increase in a pattern consistent with an increasing adjusted leverage
being associated with higher premia. Second, I construct an adjusted leverage factor-mimicking portfolio and
repeat the asset pricing tests using a longer time-series. The price of risk of the global adjusted leverage
factor remains significantly positive across all test assets with the exception of momentum portfolios. Third,
I perform beta sorts to address the potential criticism that my results only hold for portfolios used in the
tests. I estimate the exposure of country-level market portfolios and country-level financial sector portfolios
on the adjusted leverage factor-mimicking portfolio and measure the spread in average returns of these
portfolios. The resulting spread is positive, suggesting that the adjusted leverage factor is truly priced in the
cross-section. Finally, for all cross-sectional asset pricing tests, I measure the fraction of instances where
a randomly generated factor achieves an explanatory power higher than and pricing error lower than that
generated by the global adjusted leverage factor. I find that for the majority of test assets this fraction is
extremely low (less than 1%).
A number of factors aiming to capture the marginal value of wealth of financial intermediaries have
been proposed in the literature. Adrian et al. (2014) propose a single-factor intermediary SDF. The factor is
a time-series of the shocks to the leverage of securities broker-dealers and carries a large and significantly
positive price of risk. On the other hand, He et al. (forthcoming) propose as a two-factor intermediary SDF.
The first factor is the market and the second is a time-series of the shocks to the equity capital ratio of primary
dealer counterparties of the New York Federal Reserve. Using an extensive set of test assets the authors show
that it carries a consistently positive price of risk. I compare the explanatory power of the global adjusted
leverage factor against that of the factors proposed by Adrian et al. (2014) and He et al. (forthcoming). I
find that the global adjusted leverage factor appears with a consistently positive price of risk across all test
assets and that it outperforms both the leverage factor and the capital factor in the cross-section currencies
and global equities. The better performance of the adjusted leverage factor as compared to that of other
factors proposed in the literature implies that this factor is a more accurate state variable reflecting global
financial intermediaries’ SDF.
This paper is organized as follows: Section 2 discusses the related literature and the contribution of the
paper; Section 3 develops a theoretical framework that motivates the empirical work; Section 4 presents the
data sources; Section 5 presents the construction of the adjusted leverage factor and discusses its properties;
4
Section 6 discusses the empirical methodology and how it relates to theory; Section 7 shows the main findings
of the paper; Section 8 revisits the empirical findings under alternative theoretical frameworks, compares the
performance of global adjusted leverage against other measures proposed in the literature, and decomposes
global adjusted leverage into a non-U.S. and a U.S. only component; and finally Section 9 concludes the
paper.
2 Related Literature and Contribution
This paper is closely related to two main streams of the literature.
First, a large stream of literature studies the relation between financial intermediaries and asset prices.7
Financial institutions are the class of investors whose characteristics most closely align with those of a
representative investor in traditional asset pricing models, and thus the study of their marginal value of wealth
is expected to provide a more instructive stochastic discount factor (SDF).8 Models of intermediary-based
asset pricing link the marginal value of wealth to intermediaries’ funding constraints implying that marginal
utility is high when funding constraints are binding (see, e.g. Brunnermeier and Pedersen (2009), Geanakoplos
(2010), Gromb and Vayanos (2002), and Shleifer and Vishny (1997)). A common theme across these models
is a pro-cyclical intermediary leverage, which implies a positive price of risk.9 In line with this stream of
research, Gabaix and Maggiori (2015) develop a model of exchange rate determination based on capital flows
in financial markets with frictions. Empirically, Adrian and Shin (2010) show that financial intermediaries
adjust their leverage actively according to economic conditions resulting in pro-cyclical leverage. Adrian
et al. (2014) and He et al. (forthcoming) show that shocks to the leverage and capital ratios of financial
intermediaries, respectively, explain a large portion of the cross-sectional variation in the expected returns of
an array of asset classes.10 Finally, DellaCorte et al. (2016a), focusing on the currency market, show that a
global imbalance risk factor (see, e.g. Gabaix and Maggiori (2015)) explains the cross-sectional variation in
currency excess returns.
The contribution of this paper to the financial intermediation literature is twofold. On the theory side,
I deviate from the intermediary-based asset pricing models mentioned above by introducing information7Financial intermediaries play a central role in modern markets. The importance of this role and the need for additional
research has been part of past AFA presidential addresses (see, e.g. Allen (2001), Duffie (2010), Cochrane (2011)).8This approach is in contrast to conventional consumption-based asset pricing models where the marginal investor is the
household (see, e.g. Campbell and Cochrane (1999) and Bansal and Yaron (2004)). Households exhibit limited stock marketparticipation (see, e.g. Vissing-Jørgensen (2002)), pay higher transactions costs, and exhibit a lack of financial sophistication(see, e.g. Calvet et al. (2007)).
9On the other hand, He and Krishnamurthy (2013) and Brunnermeier and Sannikov (2014) propose a central role forintermediaries’ wealth and generate a countercyclical intermediary leverage (negative price of risk).
10Etula (2013), Adrian et al. (2015), Adrian et al. (2013) show that the risk-bearing capacity of U.S. securities broker-dealersis a strong predictor of asset returns (commodities, currencies, equities, and bonds).
5
production by the agents in the economy as in Gorton and Ordoñez (2014) and Gorton and Ordoñez
(2016). More specifically, I propose an alternative mechanism where information production in the economy
determines the amount of credit outstanding in the economy and subsequently the level of financial leverage
and the SDF of financial intermediaries. On the empirical side, I expand the focus from U.S. to international
financial intermediaries, and propose and test the asset pricing properties of an empirical proxy for the
SDF of a global financial intermediary. This measure captures multiple aspects of economic activity ranging
from capital formation to financial crises and future consumption. The paper establishes an economically
meaningful link between the marginal value of wealth of a global financial intermediary and asset prices, thus
relating asset prices to the macroeconomy through the financial intermediaries’ pricing kernel. I deviate from
previously used methodologies in both the dimensions of variable construction and scope of test assets. The
measure of adjusted leverage is computed by aggregating granular (balance sheet) information in tandem
with information on credit-to-private sector from a wide array of countries. This method allows me to obtain
a more accurate representation of the SDF of financial institutions on a global level, since I combine two
pieces of information (balance sheet information and aggregate credit conditions), which leads to a greater
explanatory power over the cross-section of returns.11
Second, another large stream of literature studies international assets’ excess returns. The literature
around currency excess returns has focused on portfolio strategies based on currency characteristics, such as
the interest rate differential (carry trade (see, e.g. Hansen and Hodrick (1980), Meese and Rogoff (1983),
Fama (1984), Koijen et al. (2016))), past returns (momentum and value (see, e.g. Menkhoff et al. (2012b)
and Asness et al. (2013))), and global foreign exchange volatility. Explanations for currency premia include
aggregate consumption growth risk (see, e.g. Lustig and Verdelhan (2007)), currency crash risk and peso
problems (see, e.g. Brunnermeier et al. (2008), Burnside et al. (2011a) and Burnside et al. (2011b)), global
risk (see, e.g. Lustig et al. (2011)), habits (see, e.g. Verdelhan (2010)), and rare disasters (see, e.g. Farhi and
Gabaix (2016))12 The literature around international equity excess returns has focused on documenting the
existence of size, value, and momentum premia in equity markets across the world (see, e.g. Griffin (2002) and
Fama and French (2012)). Global versions of the Fama French three-factor model can explain a large part of
variation in international equity excess returns (see, e.g. Fama and French (2012)). Alternative explanatory
factors related to funding constraints of investors in international financial markets explain cross-country11Prior empirical research uses as proxies for the marginal value of wealth of financial intermediaries the changes in the
leverage ratio (see, e.g. Adrian et al. (2014)), or a measure of the intermediary capital ratio (see, e.g. He et al. (forthcoming)without taking into account the level of the available credit in the economy. The importance of high leverage or low availablecapital varies with respect to the available level of credit in the economy. The marginal utility of an intermediary when bothleverage and credit are high is not the same as when leverage is high and credit is low. In the second case the marginal utility ofan intermediary is higher.
12Additional explanations include the term structure (see, e.g. Bansal (1997), country-specific characteristics such as per-capitaGDP and inflation (see, e.g. Bansal and Dahlquist (2000)), currency volatility (see, e.g. Menkhoff et al. (2012a) and DellaCorteet al. (2016b)), downside risk CAPM (see, e.g. Lettau et al. (2014)), and global imbalances (see, e.g. DellaCorte et al. (2016a)).
6
variation in equity premia (see, e.g Goyenko and Sarkissian (2014) and Malkhozov et al. (2017)).
This paper contributes to the international finance literature and more specifically to the above mentioned
literature on risk factors associated with risk premia in currency and equity markets. I propose an alternative
explanation based on the role of financial intermediaries as marginal investors in these markets. This
explanation is based on an economically meaningful link between the marginal value of wealth of a global
financial institution and excess returns in the cross-section of currency and international equity portfolios.
3 Theoretical Framework
In this section, I develop a two period general equilibrium framework in the spirit of Gorton and Ordoñez
(2014) and Gorton and Ordoñez (2016).
3.1 Setting
The economy comprises three agents, each with a mass 1 – firms, financial institutions, and households –
and two types of goods – capital (numeraire) and land. All agents are risk neutral, apart from the financial
institutions which are risk neutral with regard to their lending activities and risk averse with regard to
holding firms’ equity. As in Gorton and Ordoñez (2014) only firms have access to managerial labor (L∗),
which combined with numeraire (K) produce more numeraire (K ′). The production process is stochastic
with Leontief technology:
K ′ =
A min{K,L∗} with prob. q
0 with prob. (1− q),
where A is a parameter determining output when production process is successful and q is the probability that
the production process is successful. For the purposes of this model I interpret q as the level of technological
innovation. A and q combined describe the efficiency of the production process.
Production is efficient (qA > 1) which means that the optimal amount of numeraire is K∗ = L∗. In this
economy, households begin with an endowment of numeraire K̄ > K∗ which can sustain optimal production.
Financial institutions are the sole owners of firm equity, which makes them the de-facto marginal investors.
Finally, firms own land and are endowed with numeraire in period 1 (K1) but have no means of capital
in period 2. Land is not used in production however it derives its value from the amount of numeraire it
7
produces at the end of the second period. If land is “good,” it yields C units of numeraire at the end of the
second period; if it is “bad,” it does not yield anything. Only a fraction p̂ of land is good.
In this economy, output and technological innovation (q) are non-verifiable, but the quality of land is not.
This makes land valuable as collateral. To receive capital necessary for production, firms pledge a fraction of
land as collateral for the loan they receive from the financial institution. This collateral is pledged in turn by
financial institutions to facilitate deposits from households. In this setting, C > K∗ which means that land
that is “good” can support the optimal capital size (K∗).
In period 1 the agents form beliefs about the fraction of land that is of good quality. To determine
the true quality of land with certainty, households must pay γh, while financial institutions must pay γb,
where γh > γb. This reflects the fact that financial institutions have superior technology compared to that of
households in determining the quality of collateral.
3.2 Optimal Loan for a Single Firm
Firms choose between debt that causes information production about the collateral leading to information-
sensitive debt, and debt that does not induce information production leading to information-insensitive debt.
Information acquisition for the financial institution bears a cost γb. As in Gorton and Ordoñez (2014), I
determine conditions under which debt is information-sensitive or information-insensitive.
3.2.1 Information-Sensitive Debt
In this case, financial institutions discover the true value of the firms’ land at a cost γb. Financial
institutions are risk neutral when it comes to their lending activity which means that they break even:
p(qRbIS + (1− q)xbISCf −Kb) = γb, (1)
where Kb is the actual loan from the financial institution to the firm, RbIS is the face value of the debt, and
xbIS is the fraction of land posted as collateral.
The fraction of collateral that a firm posts is determined by,
RbIS = xbISCf ⇒ xbIS = pKb + γb
pCf.13
13If RbIS > xbISCf , the firm would always hand over the collateral instead of repaying the loan. On the other hand, if
8
Expected profits (net of land value) are
E(π|p, IS) = p(qAKb − xbISCf ) = pK∗(qA− 1)− γb.14 (2)
3.2.2 Information-Insensitive Debt
In this case, financial institutions do not produce information regarding the quality of firms’ land. As
financial institutions are risk neutral with respect to their lending activity and break even,
qRbII + (1− q)pxbIICf = Kb, (3)
where RbII = pxbIICf as with the previous case.
Financial institutions could potentially deviate and privately check the quality of the land prior to
lending capital. The following condition guarantees that they will not deviate since the expected payoff from
producing information is less than the cost (γb):
p(qRbII + (1− q)xbIICf −Kb) < γb ⇒ (1− p)(1− q)Kb < γb.
The financial institution lends the optimal amount of capital (K∗) if the above condition is satisfied for
Kb = K∗. However, if the above condition is not satisfied, the amount of capital is Kb = γb
(1−p)(1−q) or pCf ,
if collateral value is low. Combining the above, the loan level for information-insensitive debt is:
Kb(p, q|II) = min
{K∗,
γb
(1− p)(1− q) , pCf
}. (4)
Expected profits (net of land value) are
E(π|p, II) = pqAKb − xbIIpCf = K(p, q|II)(qA− 1). (5)
Equating profits under information-sensitive debt (equation 2) with profits under information-insensitive
debt (equation 5) allows to pin down the level of the loan under information-sensitive debt:
RbIS < xbISCf the firm would always sell the collateral and repay the loan. This means that RbIS = xbISC
f .14I assume that it is feasible to borrow the optimal amount of capital (K∗), which means that xbIS = pKb+γb
pCf ≤ 1 and thatpK∗(qA− 1) > γb. Combining the two yields the condition qA < Cf/K∗.
9
Kb(p, q|IS) = pK∗ − γb
qA− 1 . (6)
3.3 Optimal Deposits for a Financial Institution
In this setting the owners of capital are households, which deposit their wealth in financial institutions,
which in their turn lend it to firms. The banks choose between deposits that cause information production
about the ability of the bank to repay, and deposits that do not induce information production. Both banks
and households make their decisions simultaneously which means that the household cannot infer the quality
of collateral from observing the bank’s loan. The creditworthiness of the financial institution is determined by
the amount of collateral that the firm has pledged for the loan it received. The cost of information acquisition
for the household is γh.
3.3.1 Information-Sensitive Deposits
In this case, households discover the true value of the financial institution’s loans, backed by firms’ land
as collateral, by incurring the cost γh. Households are risk neutral and break even:
p(qRhIS + (1− q)xhISCb −Kh) = γh (7)
where Kh is the actual amount of deposits in the financial institution, RhIS is the face value of deposits, and
xhIS is the fraction of the financial institution’s loans posted as collateral. For the same reason as before, the
fraction of collateral that the financial institution posts is xbIS = pKh+γh
pCb . Since the collateral posted by the
financial institution is the land that has been posted by the firm to obtain its loan, Cb = Cf .
Expected profits for the financial institution are
E(πb|p, IS) = pxbISCf − pxhISCb = pKb + γb − pKh − γh.15 (8)
3.3.2 Information-Insensitive Deposits
In this contract, financial institutions attract deposits without triggering production of information
regarding their assets. Since households are risk neutral and break even:15Because of the assumption that γh > γb the bank will always produce information before the household does as both q and
p decline.
10
qRhII + (1− q)pxhIICb = Kh, (9)
where RhII = pxhIICb for the same reasons as before, which means that xhII = pKh+γh
pCb .
For the contract to be information-insensitive, no household should have an incentive to deviate. This is
guaranteed by:
p(qRhII + (1− q)xhIICb −Kh) < γh ⇒ (1− p)(1− q)Kh < γh.
As with the information-sensitive loan to the firm, the deposits contract will reach the optimal amount
of capital (K∗) if the above condition is satisfied. If it is not, the amount of deposits will either be
Kh = γh
(1−p)(1−q) , if the financial institution faces credit constraints, or pCb if the collateral value is low. Thus,
Kh(p, q|II) = min
{K∗,
γh
(1− p)(1− q) , pCb
}. (10)
Expected profits for the financial institution are
E(πb|p, II) = pxbIICf − pxhIICb = Kb −Kh. (11)
Equating profits under information-sensitive deposits (equation 8) with profits under information-
insensitive deposits (equation 11) allows to pin down the level of deposits under information-sensitive
debt:
Kh(p, q|IS) = (1− p)KbIS + γh − γb
1− p . (12)
Figure 1a shows the amount of credit in the form of deposits and loans that the household and the
financial institution respectively are willing to make depending on the probability of success of the production
process (q) keeping the fraction of land that is good (p) constant. For the remainder of this section, this
probability will represent technological innovation. The cutoffs in Figure 1a are determined as follows:
Cutoff A occurs at the level of technological innovation below which firms reduce their borrowing so that
they do not induce information production. From above:
11
K∗ = γb
(1− p)(1− q) ⇒ qb,HII = 1− γb
K∗(1− p) . (13)
Cutoff B is determined by the level of technological innovation below which financial institutions reduce
their deposits thus avoiding information production from households. As before:
K∗ = γh
(1− p)(1− q) ⇒ qh,HII = 1− γh
K∗(1− p) . (14)
Cutoff C is obtained after equalizing information-sensitive debt with information-insensitive debt:
γb
(1− p)(1− q) = pK∗ − γb
(qA− 1) . (15)
The positive root of the above quadratic equation (qbIS) is the level of technological innovation below which
financial institutions acquire information about the quality of land that firms post as collateral for their loan.
Cutoff D is obtained similarly for the case of deposits,
γh
(1− p)(1− q) = pK∗ − γb
(qA− 1) + γb − γh
(p− 1) . (16)
The above cutoffs create four distinct regions: (1) Between A and B (B(II), H(II)), both the bank and the
household are information-insensitive (II). Also, bank credit is constrained and firms cannot borrow without
triggering information production, which means that credit rationing takes place in bank lending; (2) Between
B and C (B(II), H(II)), both agents are information-insensitive (II) but credit constraints lead to rationing
in both bank lending and deposits; (3) Between C and D (B(IS), H(II)), the bank is information-sensitive
(IS) and at a cost γb discovers the true value of the land. The household is still information-insensitive and
rationing takes place in deposits; and (4) Below D (B(IS), H(II)), both agents are information-insensitive
with banks producing information about the quality of land and households producing information about the
quality of the assets of the financial institution.16
The amount of credit that is available in the economy to fund firms’ projects is a function of technological
innovation (q), the quality of land (p), and the cost of information production for financial institutions (γb)
and households (γh). For the purposes of this paper, I assume that the quality of land and the cost of16Additional regions become relevant depending on the level of the fraction of land that is good p and the value C of land.
Low collateral value can constrain the amount of deposits and subsequent loan amount, however for high enough levels of p, itbecomes irrelevant.
12
information acquisition remain constant throughout the two periods. Proposition 1 summarizes the relation
between technological innovation and the amount of credit in the economy. The proof is trivial.
Proposition 1. (Effect of technological innovation on credit.)
For fixed values of γb, γh, and p, with γb < γh and K∗ < pCf = pCb:
• Deposits are an increasing function of technological innovation (q) for q < qh,HII and independent of q
otherwise.
• Loans are an increasing function of technological innovation (q) for q < qb,HII and independent of q
otherwise.
3.4 Firm Valuation
As mentioned above, in this economy the financial institutions are the sole owners of firms. They are
risk averse with respect to their equity holdings and risk neutral with respect to their lending activity. This
assumption is motivated primarily by current banking regulation which mandates bank capital requirements
and determines internal risk-management policies. More specifically, according to the Third Basel Accord
(Basel III) equities are deemed substantially less liquid than high quality corporate debt. This means that
equities in intermediaries’ balance sheets require a higher capital provision compared to that required for high
quality corporate debt.17 I derive the stochastic discount factor (SDF) and compute the financial leverage of
financial institutions in a two period general equilibrium framework. Table 1 summarizes the timeline for this
economy. The financial institution maximizes a logarithmic utility function with two terms, a deterministic
component for the first period and a stochastic component for the second period,
max{Ct}2
t=1
Eu(C1, C2) = log(C1) + βElog(C2) (17)
Subject to:
C1 +Kb + γb + V1a1 = (π1(q1) + V1)a0 +Kh (18)
and
Kh + C2 = Kb + π2(q)a1 + pCf (19)17Basel III requires financial institutions and non-bank financial companies deemed systemically important to have enough
high-quality liquid assets (HQLA) which can be quickly liquidated to meet possible future liquidity needs. Assets are classifiedinto three groups (Level 1, Level 2A, and Level 2B) according to their liquidity properties. A total HQLA is computed as theweighted sum of the the asset value times a weight that is consistent with its liquidity group. Haircuts vary from 0% for assets inLevel 1 to 50% for assets in Level 2B. Common equity falls into Level 2B and is subject to a 50% haircut which is significantlyhigher compared to the 15% haircut of high quality (>AA- rating) corporate debt (see, e.g. www.bis.org/publ/bcbs238.pdfand www.bis.org/bcbs/publ/d406.pdf).
13
where Ct is the period t consumption, Kb the amount of the loan to the firm, Kh the amount of deposits
in the financial institution, γb the cost of information acquisition for the financial institution, at the time t
fraction of firm that is held by the financial institution, p the fraction of land that is good, C the numeraire
that land that is good delivers at the end of period 2, and πt(q) the period t firm profits as a function of
technological innovation (q).18
Market clearing requires that a0 = 1, a1 = 1, C1+Kb+γb = π1(q1)+Kh, andKh+C2 = Kb+π2(q)+pCf .
Kh and Kb are determined above.
First order conditions with respect to a1 yield:
V1 = E
(βC1
C2π2(q)
)(20)
which means that the SDF for the financial institution is:
m = Kh −Kb + π1(q1)− γb
Kb −Kh + π2(q) + pCf(21)
Financial leverage is defined as the ratio of assets to assets minus liabilities:
l = Kb + V1
Kb + V1 −Kh(22)
The relation between a financial institution’s SDF and its financial leverage depends on the level of
information acquisition from the household and the financial institution, which in turn is directly related to
the level of technological innovation that the economy experiences. Technological innovation is also directly
related to the level of credit outstanding in the economy (Proposition 1). Hence any relation between a
financial institution’s SDF and its financial leverage across levels of technological innovation holds across
levels of credit outstanding. Proposition 2 summarizes this relation for different “regimes” of information
production defined by the level of technological innovation.19
Proposition 2. (Stochastic discount factor and financial leverage.)
The relation between the SDF of a financial intermediary and its financial leverage depends on the level
of technological innovation (q) and information acquisition from the household and the financial intermediary:18π1(q1) = Aq1K1, and π2(q) = Kb(p, q|II)(qA−1) when bank loans are information-insensitive and π2(q) = pK∗(qA−1)−γb
when bank loans are information-sensitive.19The proof can be found in the appendix.
14
• Bank loans and household deposits are information-insensitive with no credit constraints present (B(II),
H(II)): Leverage is constant and SDF a negative function of technological innovation.
• Bank loans and household deposits are information-insensitive, but credit constraints are present (B(II),
H(II)): Leverage is positively and SDF negatively correlated with technological innovation.
• Bank loans and household deposits are information-insensitive, but deposit and credit constraints are
present (B(II), H(II)): Leverage is positively and SDF negatively correlated with technological innovation.
• Bank loans are information-sensitive and household deposits are information-insensitive with deposit
constraints present (B(IS), H(II)): Both leverage and SDF a positive function of technological innovation
• Bank loans and household deposits are information-sensitive (B(IS), H(IS)): Leverage is positively and
SDF negatively correlated with technological innovation.
Figure 1b provides an illustration of Proposition 2. For a high level of technological innovation and
credit outstanding, the relationship between SDF and financial leverage is negative. An increase in financial
leverage is associated with a decrease in the SDF of the financial institution. This usually represents times
of economic growth where the financial institution is able to sustain a relatively high level of leverage due
to the availability of a large number of profitable investment opportunities and the high level of funding it
secures from the household. However, when technological innovation and credit outstanding is at a relatively
low level and the household does not yet produce information, the relationship between the two variables is
the opposite.20 An increase in financial leverage is associated with an increase in the SDF of the financial
institution. The change in the relationship between the two variables is caused by the fact that the rate of
increase in deposits is higher than that in loans and the valuation of the firm. The increase in funding from
households does not keep up with the improvement in the profitability of investment opportunities in the
economy leading to an increasing leverage ratio and an increasing SDF. This usually represents times of
economic recession or financial crises where the financial institution may have sufficient funding, but not
enough investment opportunities leading to high levels of leverage.
Both Proposition 2 and Figure 1b underline the point that financial leverage is not always an accurate
measure of the SDF of a financial institution. In times when credit is low the relation between the two
variables reverses and a more accurate proxy of the marginal value of wealth of financial institutions should
take that into account. When credit is high, assets that co-vary with leverage are riskier and as a result
should earn higher premia. On the other hand, when credit is low, assets that co-vary with leverage are less20Usually the household does not produce information about the quality of the assets of the financial institution, unless there
is widespread uncertainty about the health of the financial system. Which makes the last case of Proposition 2 less likely to beobserved in the data.
15
risky and should earn lower premia.21 In the following section, I propose an empirical measure that takes
this point directly into account and combines information from both credit and financial leverage.
4 Data
This section describes the data used in the empirical analysis. I provide details on the construction of
the adjusted leverage factor, currency excess returns, currency portfolios, and the macroeconomic variables
used in the empirical tests.
4.1 Leverage Ratio
Intermediary asset pricing models suggest that financial intermediaries are sophisticated investors who
play a leading role in capital markets. They are considered marginal investors which means that their pricing
kernel is relevant for pricing the cross-section of risky assets.22 Motivated by the theoretical framework
developed above, I construct a proxy for the marginal value of wealth which takes into account the leverage
ratios of financial intermediaries and the credit conditions in the economy. I compute leverage ratios for
financial institutions that act as broker-dealers for an international panel (Table 2) using data from Thomson
Reuters WorldScope.23 I delete duplicate entries and data on ADRs. Leverage ratios are computed as follows:
Leverage = log
(Assets
Assets− Liabilities
)(23)
4.2 Assets Portfolios
For the purposes of the asset pricing tests of Section 7.1 I use currency and global equity portfolios.
I construct six forward discount portfolios following the methodology of Lustig et al. (2011). I rank21This relation can reverse if financial institutions face a higher cost of information acquisition on the firms’ assets than
households do (γb > γh). However, this does not seem to be the case in modern economies where financial institutions have aplethora of resources at their disposal to research and identify the quality of the posted collateral.
22There are two approaches to modeling an intermediary pricing kernel each of which has a different theoretical motivation.The first uses intermediary leverage as a proxy for the SDF (see, e.g. Brunnermeier and Pedersen (2009), while the second usesintermediary wealth (see, e.g. He and Krishnamurthy (2013) and Brunnermeier and Sannikov (2014)). Throughout this paper Ifollow the first approach.
23The actual WorldScope industry codes for financial firms used in the analysis are: 4310 for Commercial Banks - Multi-BankHolding Companies (used only for international financial institutions), 4394 for Securities Brokerage Firms, and 4395 forMiscellaneous Financial. Financial institutions classified as commercial banks in the database serve as broker-dealers in manycountries. Commercial Banks - Multi-Bank Holding Companies (4310, U.S only data), Commercial Banks - One Bank HoldingCompanies (4320), Investment Companies (4350), Commercial Finance Companies (4360), Insurance Companies (4370), Landand Real Estate (4380), Personal Loan Company (4390), Real Estate Investment Trust Companies, including Business Trusts(4391), Rental & Leasing (4392), and Savings & Loan Holding Companies (4393) are not included.
16
currencies from low to high interest rates such that portfolio 1 contains currencies with the lowest forward
discounts, and portfolio 6 contains the currencies with the highest forward discounts. The strategy that is
long on portfolio 6 and short on portfolio 1 represents carry trade and constitutes the carry factor (CAR)
that I use in the following asset pricing tests. Currency momentum portfolios are constructed using the
methodology of Menkhoff et al. (2012b). Each month I form six portfolios on the basis of excess currency
returns of the previous n months. Portfolio 1 contains currencies with the lowest prior n month returns,
while portfolio 6 comprises of currencies with the highest prior n month returns. I construct two types of
momentum portfolios, long-term momentum (n = 12 months) and short-term momentum (n = 1 month). The
strategy that is long on short-term momentum portfolio 6 and short on portfolio 1 constitutes the momentum
factor (MOM). I construct value portfolios following the methodology in Asness et al. (2013). As with
currency momentum, I form six portfolios based on the lagged five-year excess return of the currency of
each country in the sample. I assign the lowest lagged returns to portfolio 1 and the highest to portfolio 6.
Global equities portfolios comprise twenty-five international size and value sorted portfolios and the
twenty-five international size and momentum portfolios all obtained from Kenneth French’s online
data library.24
4.3 Macroeconomic Data
In Section 5, I explore the properties of the adjusted leverage measure with respect to macroeconomic
variables. Annual Real GDP and capital formation are from the Penn World Tables (PWT), domestic credit
to private sector, credit to households and credit to corporates are from the World Bank World Development
Indicators. Financial crisis episodes are from Valencia and Laeven (2012). Global imbalances are defined
as the difference between assets and liabilities denominated in the same currency. I construct the measure
of total global imbalances, which is the sum of global imbalances issued in domestic and foreign currency
standardized for the GDP of a country. For additional details see Bénétrix et al. (2015).25 Market returns are
the average market returns at a country level, financial intermediaries returns are the average financial sector
returns at a country level, and global volatility is the average market volatility among an international set of
countries (see, e.g. Chousakos et al. (2016)). In addition, and only for the U.S. economy, I collect data on
credit spreads, per capita consumption on durables, non-durables, and private investment from the Federal
Reserve Economic Data (FRED) maintained by the St. Louis FED. Table 3 summarizes the data used in this
paper.24http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html#International.25The dataset can be found at Philip Lane’s website http://www.philiplane.org/BLSJIE2015data.htm.
17
5 Adjusted Leverage
In the literature the marginal value of wealth of financial institutions is proxied by their financial leverage
and more specifically by seasonally adjusted changes in the level of broker-dealer leverage (see, e.g. Adrian et
al. (2014)). This could be potentially problematic because as discussed in Section 3 financial leverage or its
reciprocal capital ratio does not fully characterize the risk-bearing capacity of financial intermediaries across
all states of the economy. An increase in financial leverage does not necessarily indicate a decrease in the
marginal value of wealth for the financial institution. This could be true in times of economic growth, where
credit outstanding is high and the financial system can sustain high levels of leverage as financial intermediaries
are able to pursue profitable investments and at the same time raise capital if needed. However, this is not
the case in times of recessions or financial crises, where the amount of credit outstanding is low. According
to the theoretical framework discussed above, it possible that in a low credit environment an increase in
leverage is associated with an increase in the marginal value of wealth of the financial institution due to a
lack of profitable investment opportunities. A number of empirical findings, summarized below, suggest that
financial leverage interacts differently with key characteristics of financial intermediaries depending on the
level of credit outstanding in the economy.
The level of assets of financial intermediaries reflects among other factors their risk-bearing capacity.
A high level of assets in intermediaries’ balance sheets is usually the result of higher risk-bearing capacity.
If the financial leverage of an intermediary is a good proxy for its risk-bearing capacity, then the relation
between leverage and the level of future assets is expected to be positive across all states of the economy (see
e.g. Adrian et al. (2014)). The following regression specification provides a test of the above claim:
assetsn,t+q = αn + αt+q + β′Xn,t + γassetsn,t + εn,t+q (24)
where assetsn,t+q is the logarithm of the financial assets of country n at time t + q quarters, Xn,t =
(fin.leveragen,t, fin.leveragen,t × 1(Creditn,t > 75%), fin.leverage× 1(Creditt < 25%))′, fin.leveragen,t
is the logarithm of financial leverage of country n at time t, 1(Creditn,t > 75%) is a dummy variable
representing instances where credit-to-private sector of a given country is higher than the 75th percentile
of the cross-section of credit outstanding values at a given time, 1(Creditn,t < 25%) is a dummy variable
representing instances where credit-to-private sector of a given country is lower than the 25th percentile of
the cross-section of credit outstanding values at a given time, αn represents country fixed effects, and αt+q
time fixed effects.
18
Table 4 shows that the relation between leverage and the level of future assets is not consistently positive
across all states of the economy for an international panel of financial institutions aggregated at the country
level. More specifically, when interacted with the dummy variable 1(Creditn,t > 75%), and the dummy
variable 1(Creditt < 25%), the relationship between financial leverage and future assets is not consistently
positive. In the first case, financial leverage and future levels of assets are positively correlated, suggesting a
higher risk-bearing capacity, while in the second case a negative correlation suggests a lower risk-bearing
capacity leading to lower future levels of assets.26 Figure 2 confirms the above findings using country level
time-series regressions. When credit is low compared to the historical credit series for the country, the
majority of countries exhibits a negative correlation between leverage and future levels of assets, while the
opposite holds true when credit is high.
Another variable that reflects the risk-bearing capacity of financial institutions is intermediaries’ future
stock returns. According to traditional finance theory, higher expected returns usually reflect riskier
investments. Financial intermediaries that are perceived to be riskier usually face tighter funding constraints
and their risk-bearing capacity is limited. To test this claim I repeat the previous exercise, but now I replace
future assets with future returns. The regression specification is as follows:
rfinn,t+q = αn + αt+q + β′Xn,t + γrfinn,t + εn,t+q (25)
where rfinn,t+q is the logarithm of the market returns of financial intermediaries of country n at time t + q
quarters. Table 5 shows that on an aggregate level, financial intermediaries with high financial leverage
operating in a high credit environment consistently earn lower returns, while similar financial institutions
operating in a low credit environment earn consistently higher returns. This finding suggests that financial
leverage alone does not fully capture intermediaries’ risk-bearing capacity. Financial leverage viewed in
tandem with credit-to-private sector can be considered as a more accurate proxy for the marginal value of
wealth of financial intermediaries.27 As with the case of future assets, Figure 3 confirms the panel regression
findings using country level time-series regressions.
Motivated by the above findings, I propose a measure of a global adjusted leverage, which in addition to
financial leverage takes into account the level of credit-to-private sector at a global level. This measure serves
as a proxy for the marginal value of wealth of financial intermediaries and it is used in the asset pricing
tests of Section 7. I construct the global adjusted leverage index as follows: First, I compute a measure of26The same pattern holds true when focusing only on the U.S. economy (table can be found at the internet appendix).27The same pattern holds true when focusing only on the U.S. economy (Table can be found at the accompanying internet
appendix).
19
global financial leverage (Figure 4a) as the aggregated country level financial leverage weighted by the level
of financial assets of each country,
Global Leveraget =N∑c=1
wc,tLeveragec,t
where Leveragec,t is the country level financial leverage computed by aggregating firm level financial leverage,
wc,t = Assetsc,t∑N
c=1Assetsc,t
, and Assetsc,t =∑Mi=1 Assetsc,i,t. Second, I compute a global measure of credit-to-
private sector (Figure 4b) by aggregating the country level credit-to-private sector again weighted by the
level of financial assets of each country,
Global Creditt =N∑c=1
wc,tCreditc,t
Finally, the global adjusted leverage measure is equal to the residuals of an AR(1) process on global leverage
when credit-to-private sector is higher than the 25th percentile of a 12 quarter rolling window and equal
to the negative residuals of the same AR(1) process when credit-to-private sector is lower than the 25th
percentile of a 12 quarter rolling window (Figure 4c).28 The AR(1) process is,
Global Leveraget = α+ βGlobal Leveraget−1 + εt
The Adjusted leverage measure is,
Adjusted Leveraget =
−ε̂t if 1(Credit < 25th Percentile) = 1
+ε̂t otherwise.(26)
The rolling window guarantees no forward looking bias in the computation of the measure. Figure 5 shows
how the global adjusted leverage measure compares to innovations in global financial leverage. The correlation
between the two measures is 52.9%.
The risk-bearing capacity of financial intermediaries is associated with the state of the macroeconomy. It
is pro-cyclical, which suggests that favorable funding conditions are usually observed in periods with higher
credit outstanding, capital formation, and aggregate output. Adjusted leverage as a proxy for intermediaries’
risk-bearing capacity is expected to exhibit such a pro-cyclical behavior. Using an international panel28An alternative way to derive the adjusted leverage measure would be to compute the residuals of an AR(1) process on the
product of leverage and credit-to-private sector. In results which are available upon request, I show that this alternative adjustedleverage measure shares most of the properties of the adjusted leverage measure discussed above, however the explanatory powerof the second is significantly higher.
20
of observations, I perform a set of country level regressions of macroeconomic variables on the adjusted
leverage measure. Figures 6 and 7 summarize the results. Adjusted leverage is positively correlated with
contemporaneous changes in real GDP, capital formation, total factor productivity (TFP), and future financial
assets. This finding confirms that adjusted leverage is a pro-cyclical measure. In addition, adjusted leverage
is positively correlated with contemporaneous changes in credit to households, while the opposite holds true
for the case of credit-to-corporate entities. An increase in the global risk-bearing capacity is immediately
reflected in credit-to-households, but not in credit-to-corporate entities possibly due to the fact that corporate
loans require a longer assessment period. Total global imbalances are, in general, negatively correlated with
adjusted leverage suggesting that an increase in the global risk-bearing capacity of financial institutions leads
to a net loss of capital to advanced countries such as the U.S., France, and Denmark.29
The adjusted leverage measure incorporates, by construction, information about credit conditions in
the economy. Schularick and Taylor (2012) document that credit growth is a strong predictor of financial
crises. This finding motivates the following tests of the predictive power of adjusted leverage over financial
crises. Using an international panel, I regress the occurrence of a financial crisis on a set of lagged adjusted
leverage observations. I employ both a linear probability model and a logistic regression specification. Table
7 shows that 6-month lagged observations of adjusted leverage negatively predict financial crises. This finding
suggests that, prior to financial crises, financial institutions exhibit a lower risk-bearing capacity. This lower
risk-bearing capacity suggests that financial institutions could potentially adjust their activity to better
prepare themselves for an imminent financial crisis.
The U.S economy is no exception to the above mentioned patterns presented in Figures 6 and 7. Global
adjusted leverage is a pro-cyclical measure, positively correlated to changes in credit-to-households, real
GDP, capital formation, and TFP, while negatively correlated with the occurrence of financial crises and
credit spreads. Figure 8 looks at the relation between adjusted leverage, future per-capita consumption, and
future private investments on an expanding window reaching five years into the future. More specifically,
an increase in adjusted leverage is associated with a short term (1-year) increase in per-capita consumption
both in durables and non-durables, while an increase in adjusted leverage is associated with a medium term
(4,5-year) increase in private investments. This finding further supports the pro-cyclical nature of adjusted
leverage and shows that an increase in the risk-bearing capacity of the financial sector leads to an increase in
lending activity, both in the short- and in the long-term.
From the above findings, I conclude that adjusted leverage can be used as a reasonable proxy for the
marginal value of wealth of a financial intermediary. Adjusted leverage is high when credit conditions are29And possibly to other countries not in the current sample of countries.
21
favorable and low when credit conditions are adverse and leverage is high. It is pro-cyclical (positively
correlated with other measures of credit, real GDP, capital formation, and TFP), which is a characteristic of
marginal value of wealth that is consistent with theory (see, e.g. Brunnermeier and Pedersen (2009)), predicts
financial crises, and correlates with future consumption of durables and non-durables. The pro-cyclical nature
of adjusted leverage implies that this measure increases in good times when funding constraints are lax. In
the following sections, I test the asset pricing properties of this measure for both currency and global equity
portfolios.
6 Adjusted Leverage Factor in an Asset Pricing Setting
In this section I propose a pricing model which attempts to more accurately capture financial intermedi-
aries’ marginal value of wealth. I discuss how it relates to the theoretical framework of Section 3 and describe
the empirical methodology used to test its asset pricing properties.
6.1 Adjusted Leverage as Stochastic Discount Factor
In Section 3, I derived the stochastic discount factor of a financial institution in a two period economy
and discussed its relation with financial leverage across different levels of credit outstanding and technological
innovation, which define a set of information production regimes. More specifically, I show that when
both loans and deposits are information-insensitive, the relation between the stochastic discount factor
of the financial institution and financial leverage is negative, with the first decreasing while the second
increasing as credit outstanding in the economy increases. These information production regimes occur
when credit outstanding and technological innovation in the economy are at a relatively high level. The
increase in financial leverage is associated with a decrease in the marginal value of wealth of the financial
institution mainly due to the increase in the profitability of the firm. On the other hand, when loans are
information-sensitive and deposits are information-insensitive, the relation between the stochastic discount
factor of the financial institution and financial leverage is positive. This information production regime occurs
when credit outstanding and technological innovation are at relatively low levels. Both measures increase as
credit increases due to the fact that the increase in deposits is higher than that of the profitability of the firm.
This means that if SDFt ≈ α− bcLeveraget, then when credit is sufficiently high, assets that co-vary
with leverage are risky and earn a higher risk premium (bc > 0), while when credit is sufficiently low, assets
that co-vary with leverage are less risky and earn a lower risk premium (bc < 0). The proposed global adjusted
22
leverage measure addresses exactly this point by incorporating information from both credit outstanding
and financial leverage. Hence, SDFt ≈ a− b ·Adjusted Leveraget. In Section 7 I discuss the asset pricing
properties of adjusted leverage and show how consistent these properties are with this theoretical framework.
6.2 Empirical Methodology
In this section, I propose a linear factor model which consists of the global adjusted leverage factor. Using
a cross-section of asset returns, I test for the asset pricing properties of this factor using the methodology
proposed by Lewellen et al. (2010). The proposed SDF is linear in the global adjusted leverage factor:
SDFt = 1− b ·Adjusted Leveraget (27)
In the absence of arbitrage opportunities, asset j’s excess return has a price of zero and satisfies the Euler
equation:
E0[Rej,tSDFt
]= 0 (28)
Combining equations 28 and 27 we obtain:
E0[Rej,t
]= bCov
(Rej,t, Adjusted Leveraget
)= λAdj.Levβj,Adj.Lev (29)
where λAdj.Lev = bV ar(Adj.Lev) and βj,Adj.Lev = Cov(Rej,t, Adj.Levt
)/V ar(Adj.Lev). λAdj.Lev is the cross-
sectional price of risk for the global adjusted leverage factor, and βj,Adj.Lev is the exposure of asset j to the
risk-bearing capacity of financial intermediaries.
To test the above model, I employ two-pass regressions. First, I estimate the exposure of each asset j
(βj,f ) to the factors of interest (f) using the following time-series regression specification,
Rej,t = aj + β′j,fft + εi,t
where aj is the constant for asset j; εj,t is a vector of the estimation errors for asset j at time t. Second,
I estimate the price of risk exposure (λf ) to the factors of the model (f) using the following cross-section
regression specification,
E[Rej ] = λ0 + β′i,fλf + αj
where λ0 is the constant of the regression; αi are the estimation errors for asset i.30 I estimate the coefficients30I choose to include the intercept (λ0) since I do not want to impose extra structure into this linear model. I acknowledge a
23
using an OLS specification.
At a minimum level, an asset pricing model is expected to produce small (both economically and
statistically) values for λ0, a statistically significant price of risk exposure (λf ), and pricing errors (αi) close
to zero. I assess the size of pricing errors (i) by computing an adjusted R2 for the cross-sectional regression
performed on the test assets, (ii) by computing the mean absolute pricing error (MAPE), the maximum
pricing error (MAX) and the sum of MAPE and λ0 (TOTAL), and (iii) by testing whether a weighted sum of
squared pricing errors (α′cov(α)−1α ∼ χ2N−K) is statistically different from zero.31 32 I estimate t-statistics
for the price of risk using both the Fama and MacBeth (1973) and Shanken (1992) methodologies.
Lewellen et al. (2010) provide a critique of the robustness of traditional cross-sectional asset pricing
models. They contend that the commonly used asset pricing tests set the bar too low and offer supporting
evidence by generating high values for R2 and low pricing errors (α) by using random noise factors whose
actual explanatory power is zero. In their paper they suggest a number of tests designed to improve the
arsenal of evaluation techniques for asset pricing models. Many of the suggested improvements for model
testing are incorporated into the asset pricing tests that follow.
In the spirit of Lewellen et al. (2010), using bootstrapping I construct confidence intervals for the true
value of the adjusted R2 of the models considered in the analysis.33 Lewellen et al. (2010) motivate this
method by making the observation that even in cases where the actual R2 of a model is zero, it is possible
that the sample adjusted R2 is relatively large, and the opposite, that even when the actual R2 of a model is
one, it is possible that the sample adjusted R2 is significantly less than one. Finally, I estimate and report
the probability that the cross-sectional R2, the mean absolute pricing error (MAPE), and the pricing errors
(α) of the asset pricing models considered in the analysis are higher and lower respectively compared to those
of artificial factors which are constructed by randomly drawing from the empirical distribution of the actual
factors with replacement.34
potential loss in efficiency, but I choose not to sacrifice the robustness of the model by imposing no intercept to it and forcing itto fit the data. This approach allows the model to provide additional information about the data (see, e.g. Cochrane (2005)).
31MAPE = 1N
∑i
|αi|.
32K is the number of factors considered in the model when I estimate cov(α) using the Shanken (1992) correction, and K is 1when we estimate cov(α) using the Fama and MacBeth (1973) approach.
33For the exact details of the method I refer the reader to Lewellen et al. (2010).34I construct 100,000 such factors and compare their performance against that of the actual factors.
24
7 Empirical Findings
7.1 Cross-Sectional Analysis
This section presents the main finding of this paper. Excess returns of international asset portfolios
(international equities and currencies) can be understood by their exposure to the global adjusted leverage
factor. The portfolios that I employ for international equities are the 25 global portfolios formed on size and
book-to-market and the 25 global portfolios formed on size and momentum. Table 8 summarizes the results
for the 25 global size and book-to-market portfolios. Panel A summarizes the cross-sectional prices of risk,
Panel B shows a number of specification tests, and Panel C tests the asset pricing properties of the proposed
model against a set of random pricing factors.35 The global adjusted leverage factor appears with a positive
price of risk and outperforms the market factor and the Fama-French three factor model across all metrics.
More specifically, the global adjusted leverage factor model exhibits an adjusted R2 of 71% which is one of
the highest across all other models considered. In addition, the χ2 value the lowest the p-value of the test
does not reject the null of jointly zero pricing errors. The adjusted leverage model performs better than the
Fama-French three factor model in terms of the p-value of the χ2 test; equally well regarding the adjusted
R2, MAPE, and MAX figures; and worse in terms of the value of the intercept. Figure 9 summarizes the
predicted versus realized average returns for the four models considered in Table 8. Figure 9a confirms the
good explanatory power of the global adjusted leverage factor model which is comparable only with that of
the Fama-French factor models (9d).
Focusing next on the 25 global size and momentum portfolios, I again compare the global adjusted
leverage factor model against the market model, the Fama-French three factor model, and the Fama-French
three factor plus momentum model. Table 9 summarizes the results. The findings are almost identical to
the ones presented for currency portfolios and the 25 global size and book-to-market portfolios. The global
adjusted leverage factor appears with a significantly positive price of risk, and outperforms the market model
and the Fama-French three factor model across all metrics. The overall performance of the global adjusted
leverage factor is comparable to that of the Fama-French three factor plus momentum model. Figure 10
confirms the results from Table 9. The predicted versus realized average returns for the test assets of the
global adjusted leverage factor model line up closely on the 45-degree line (10a).
Having tested for the explanatory power of the global adjusted leverage factor in the cross-section of
equity portfolios, I turn to another large set of global assets, that of currencies. Table 10 presents the35The tables summarizing the results of the cross-sectional asset pricing tests follow a format similar to that of Adrian et al.
(2014).
25
results of asset pricing tests using as test assets 24 currency portfolios (6 carry trade, 6 short-term currency
momentum, 6 long-term currency momentum, and 6 currency value portfolios). The factors tested are the
long/short carry portfolio (CAR), a measure of global volatility (VOL), the long/short short-term currency
momentum portfolio (MOM), and the global adjusted leverage factor (Lev.Adj).36 The first three columns of
Table 10 summarize the results of asset pricing tests using factors already proposed in the literature. All
three factors factors appear with statistically significant prices of risk, however the overall explanatory power
of these models is generally low (the highest R2 is that of the momentum factor model and is equal to 47%),
and the null hypothesis of the χ2 test, which tests whether pricing errors are jointly zero, is rejected at the
5% level. Overall, neither of the above three models can sufficiently explain the cross-section of returns
of currency portfolios. The fourth column shows the results for an asset pricing factor model with global
adjusted leverage as the only factor. The price of risk is positive and statistically significant. The adjusted
R2 is 57% with a confidence interval of [0.43, 0.86], and the TOTAL MAPE is 3%. Both metrics are an
improvement compared to those of the models of columns 1 through 3. The χ2 value is significantly lower
compared to that of the other models and the null of pricing errors being jointly zero is not rejected. The
results remain essentially invariable even after the addition of the carry factor into the model (column 5).
Figure 11 confirms the findings of Tables 8 and 9. The realized versus predicted mean returns using the
global adjusted leverage factor model align closely on the 45-degree line (Figure 11a) yielding the best fit,
followed by that of the momentum factor model (Figure 11a). This comes as no surprise since the global
adjusted leverage factor model exhibits the highest adjusted R2, and the lowest χ2 among all of the models
considered in this exercise.37
Overall, the global adjusted leverage factor explains a large amount of variation in the cross-section of
expected returns of currency and international equities portfolios. It outperforms currency factors, the global
market factor, and the global Fama-French three factor model, whereas it performs equally well with the
global four Fama-French three factor plus momentum model. The price of risk of the global adjusted leverage
factor is positive and of the same order of magnitude across similar test assets. This finding is consistent
with theory and reenforces the argument that the marginal value of wealth of financial intermediaries is an
important component of the determination of asset prices.36See, e.g. Lustig et al. (2011) for the carry trade factor; Menkhoff et al. (2012a), Ang et al. (2006), Adrian and Rosenberg
(2008) for the asset pricing properties of volatility for currencies and equities respectively; Menkhoff et al. (2012b) for momentum.37The low explanatory power of carry, volatility, and momentum seems to be at odds with the asset pricing properties
attributed to them in the literature (see, e.g. Lustig et al. (2011) for carry trade factor; Menkhoff et al. (2012a) for volatility andcarry trade, Menkhoff et al. (2012b) for momentum). This discrepancy is explained by the fact that these factors explain verywell the cross-section of returns of portfolios relevant to the specific strategies from which they were derived. When tested fortheir explanatory power using a wider set of currency portfolios, their explanatory power is lower compared to that of globaladjusted leverage.
26
7.2 Time-Series Analysis
Figure 12 summarizes the results of time-series regressions of the test portfolios’ excess returns on the
adjusted leverage factor. The figures report the estimated coefficients along with a 95% confidence interval,
and the R2 values of the time-series regression for each test portfolio. Figure 12a shows the coefficients for
currency portfolios. The adjusted leverage betas increase in a pattern from left to right as the expected
returns of the currency portfolios increase. This pattern is consistent with the theoretical motivation behind
the construction of the adjusted leverage factor. A portfolio with a higher exposure to adjusted leverage is
expected to earn a higher premium.
Figure 12b reports the results for the time-series regressions of the 25 global size and book-to-market
portfolios on the adjusted leverage factor. As with the case of currency portfolios, the adjusted leverage
betas follow an increasing pattern within each size bracket, which is consistent with the positive relation
between the adjusted leverage factor and asset returns. However, the statistical significance of the estimated
betas is fairly low, primarily reflecting noise or measurement error in the adjusted leverage factor. Figure
12c reports the same findings for the time-series regressions of the 25 global size and momentum portfolios.
Again, the coefficients exhibit a decreasing pattern within each size bracket, but the statistical significance of
the estimates and explanatory power of the model is low.
The low explanatory power of the adjusted leverage factor in the time-series regressions of international
equity portfolios is a common challenge documented in the literature. It is usually attributed to noise or
measurement error of the explanatory factor, especially when the factor is not tradable.38 The concern
with low explanatory power is that when betas are not well estimated they could be capturing a spurious
relationship in the cross-section of returns. I address this concern first by using the Shanken (1992) correction
to control for the fact that betas are estimated, and second by simulating a randomly generated factor, or
set of factors, and measuring the fraction of instances where this randomly generated factor achieves an
explanatory power higher than, and pricing errors lower than the ones generated by the factors considered in
the asset pricing models tested in this paper. As reported in Section 7.1, the fraction of instances in which
this is the case for the global adjusted leverage factor is extremely low. This finding alleviates concerns about
a potential spurious relationship in the data reflected in the cross-sectional test results.38See, e.g. the discussion in p.2581 of Adrian et al. (2014)
27
7.3 Factor-Mimicking Portfolio
In this section I construct an adjusted leverage factor-mimicking portfolio and repeat the asset pricing
tests of Section 7.1. The factor-mimicking portfolio enables the use of longer time-series. This technique
allows us to test whether the relation between adjusted leverage and asset returns is a recent phenomenon.
The factor-mimicking portfolio is a traded portfolio which is constructed by projecting the adjusted leverage
factor onto the space of traded returns. The loadings of the factor onto the portfolios that summarize the
return space are estimated using the following regression specification:
Adjusted Leverage t = α+ b′[CAR, V ALLS ,Mkt,HML,SMB,MOM ]t + εt (30)
where CAR is the long/short currency carry portfolio, V ALLS is the long/short currency value portfolio,
Mkt is the global market portfolio, HML is the global high-minus-low book-to-market portfolio, SMB is the
global small-minus-big size portfolio, and MOM is the global momentum portfolio. The factor-mimicking
portfolio is computed as follows:
Adjusted Leverage FMPt = b̂′[CAR, V ALLS ,Mkt,HML,SMB,MOM ]t (31)
where b̂ = (−0.29,−0.33,−0.19, 1.23, 0.59,−0.01) are the estimates of b in equation 30. The correlation
between the adjusted leverage factor and its factor-mimicking portfolio is 60.8%, which implies that the
resulting factor-mimicking portfolio explains a large part of the adjusted leverage factor variation. Figure 13
visually confirms the high correlation between the two series.
In what follows, I test for the pricing properties of the factor-mimicking portfolio by replacing the global
adjusted leverage factor of the pricing kernel with the factor-mimicking portfolio. As in Section 7.1 I use
currency and global equity portfolios as test assets. The performance of the mimicking portfolio is comparable
to that of the adjusted leverage factor for the case of global equity portfolios. Column 1 of Tables 11a and
11b summarizes the results for the 25 global size and book-to-market portfolios over two time frames, from
1991-Q1 until 2014-Q1 and from 2001-Q1 until 2014-Q1 respectively. The mimicking portfolio appears with a
significantly positive price of risk and its performance is comparable to that of the Fama-French global three
factor model. Testing against a randomly generated factor shows that a very low percentage (less than 1% of
such factors) outperforms the adjusted leverage factor-mimicking portfolio.
Regarding the 25 global size and momentum portfolios, the mimicking portfolio does not explain the
28
cross-section of returns over the extended period of the test (1991-Q1 - 2014-Q1). Repeating the test over
the period for which adjusted leverage data is available, yields that the factor-mimicking portfolio has a
positive price of risk with an overall performance comparable to that of the Fama-French global three factors
plus momentum model. Column 2 of Tables 11a and 11b summarizes the results. The finding that the
factor-mimicking portfolio does not perform well over the extended period is explained by the low exposure
of the adjusted leverage factor on the global momentum factor prior to 2001-Q1. This suggests that either
the relation between adjusted leverage and expected returns for this set of portfolios is a recent finding, or
that the factor-mimicking portfolio is not an accurate proxy for the leverage factor prior for the period from
1991-Q1 until 2001-Q1.
The performance of the mimicking portfolio is comparable to that of the adjusted leverage factor for the
case of currency portfolios as well. Column 3 of Tables 11a and 11b summarizes the results. The price of
risk of the mimicking portfolio is significantly positive over both the extended period of the test (1991-Q1 -
2014-Q1) and the main period of the paper (2001-Q1 - 2014-Q1), and the explanatory power of the asset
pricing model is significantly higher compared to that of benchmark models. Testing against randomly
generated factors reveals that less than 1% of the random models yield higher adjusted R2 and lower MAPE.
Overall, the above findings suggest that, with the exception of the 25 global size and momentum portfolios,
the empirical results of Section 7.1 hold well over a time horizon which is double that of the paper. The
adjusted leverage factor-mimicking portfolio outperforms benchmark factors for currency portfolios and
performs comparably to the Fama-French 3 factor model for global equities.
7.4 Placebo Tests
As a placebo test, I construct two alternative adjusted leverage measures and repeat the cross-sectional
tests of Section 7.1. The first alternative measure (Lev.Adj(OthFin)) is constructed using all firms which
are classified as financial by WorldScope, but were not included in the computation of the original global
adjusted measure.39 The second alternative measure (Lev.Adj(Oth)) is constructed using data only from
non-financial firms.40 Table 12 summarizes the findings of cross-sectional asset pricing tests using these
alternative measures of adjusted leverage in tandem with the original measure. The original adjusted leverage
measure remains statistically significant with a positive price of risk across all test assets. On the other hand,39The WorldScope industry codes of financial firms used in the construction of this measure are: Commercial Banks -
Multi-Bank Holding Companies (4310, U.S only data), Commercial Banks - One Bank Holding Companies (4320), InvestmentCompanies (4350), Commercial Finance Companies (4360), Insurance Companies (4370), Land and Real Estate (4380), PersonalLoan Company (4390), Real Estate Investment Trust Companies, including Business Trusts (4391), Rental & Leasing (4392),and Savings & Loan Holding Companies (4393) are not included.
40These are firms with a general industry clasification from WorldScope of 1 through 3.
29
the other two measures are not statistically significant, with the exception of the non-financial firms’ adjusted
leverage (Lev.Adj(Oth)) which appears with a significantly negative price of risk for the case of currency
portfolios. This is a finding consistent with the fact that most non-financial firms hedge their exposure to
foreign currency. This means that high currency returns occur when such firms experience high marginal
value of wealth.
7.5 Portfolios Based on Adjusted Leverage
Beta sorts are a method commonly used in the asset pricing literature to identify risk premia.41 As an
additional robustness check for the asset pricing properties of the adjusted leverage factor, I form market-cap
weighted portfolios of international equities (expressed by market-wide returns) and international financial
firms (expressed by sector-wide returns) according to their exposure to the factor-mimicking portfolio and
measure the spread in the average returns of these portfolios. The use of individual country returns addresses
potential criticism that the results of Section 7.1 hold only for the portfolios used in the tests. More specifically,
both equity markets and financial firms are grouped into portfolios on the basis of preranking betas, which
are estimated using a rolling window of 36 months.42 Portfolios are rebalanced every 3 months. Figure 14
summarizes average annualized returns and beta exposures for currency and financial firms portfolio excess
returns.
The figure shows that investing in markets/financial sectors with low adjusted leverage beta yields
a significantly lower return (7.19%/7.68%) compared to investing in markets/financial sectors with high
adjusted leverage beta (11.74%/20.25%). The spread between portfolio 1 (low adjusted leverage beta) and
portfolio 5 (high adjusted leverage beta) is 4.55%/12.57% per annum and the average returns exhibit an
increasing pattern from portfolio 1 to portfolio 5. The resulting spread is consistent with the empirical
findings presented above and with theoretical arguments that risk premia of assets that co-vary with financial
intermediaries’ marginal value of wealth should reflect that risk. The evidence from the cross-section of equity
markets and financial firms suggests that the adjusted leverage factor is indeed priced.43
41See, e.g. Fama and French (1993), Pástor and Stambaugh (2003), Ang et al. (2006), and Lustig et al. (2011).42To avoid the influence of outliers, I winsorize both market level returns and financial sector returns.43In the online appendix I repeat this exercise for the remainder of economic sectors as classified by Thomson/Reuters.
The sectors of focus are Technology, Utilities, Basic Materials, Industrials, Telecommunications, Healthcare, Energy, CyclicalConsumer Goods, and Non-Cyclical Consumer Goods. The observed increasing pattern in risk premia is observed in theTechnology, Utilities, and Basic Materials sectors.
30
8 Discussion
In this section, I discuss how the empirical findings of Section 7 are consistent with alternative theoretical
frameworks (see, e.g. Brunnermeier and Pedersen (2009) and Gabaix and Maggiori (2015)); I compare the
performance of global adjusted leverage against that of related measures proposed in the literature (see, e.g.
the leverage factor of Adrian et al. (2014) and the capital ratio factor of He et al. (forthcoming)); and finally
I decompose global adjusted leverage into a non-U.S. and a U.S. only component, and test their respective
asset pricing properties for a cross-section of international portfolios.
8.1 Alternative Theoretical Frameworks
As I mentioned above there is a long strand of theoretical literature which incorporates financial
intermediaries’ marginal value of wealth into an asset pricing framework.44 In the following paragraphs, in
addition to the theoretical framework presented in Section 3, I explain how global adjusted leverage enters
the pricing kernel using two popular frameworks whose assumptions closely describe modern capital markets.
The first is that of Brunnermeier and Pedersen (2009) and the second is that of Gabaix and Maggiori (2015).
Brunnermeier and Pedersen (2009) propose a theoretical framework where the pricing kernel depends
on future funding liquidity conditions, φ1 (following their notation, φ1 is the shadow cost of capital of the
intermediary at time t = 1). The intermediary maximizes its expected utility E0 [φ1W1], where W1 is wealth
at time 1. If the speculator does not face constraints at time t = 0, then the first-order condition for their
holdings in security j is E0
[φ1(pj1 − p
j0)], which means that the SDF takes the functional form of φ1
E0[φ1] and
the price of security j is as follows:
pj0 = E0
[pj1
]+Cov0
[φ1, p
j1
]E0 [φ1] (32)
As a result, the expected excess return of security j at time 0 is:
E0
[Re,j1
]= −
Cov0
[φ1, R
e,j1
]E0 [φ1] (33)
Equation 33 shows that the expected returns at time-0 depend on the covariance of future returns with the
funding liquidity conditions at time-1. The time-0 expected return or a security is higher if the covariance44See, e.g. Brunnermeier and Pedersen (2009), Geanakoplos (2010), Gromb and Vayanos (2002), and Shleifer and Vishny
(1997).
31
term is negative, which means that the security has a low payoff in states of the nature when funding liquidity
conditions are tight (i.e. φ1 is high).
In the context of Brunnermeier and Pedersen (2009), adjusted leverage is a measure of funding liquidity
conditions. When adjusted leverage is high, as discussed above, this is an indication of high availability
of credit implying lax funding liquidity constraints. On the other hand, when adjusted leverage is low,
availability of credit is low and leverage of intermediaries is high, implying tight liquidity conditions. Hence,
φ1 ≈ a− b ·Adjusted Leverage1.
Gabaix and Maggiori (2015) propose a theory of financial intermediation and exchange rate dynamics.
In their model, exchange rates are determined by capital flows and financial intermediaries’ risk-bearing
capacity in an imperfect financial markets setting. More specifically, countries maintain trade imbalances
and intermediaries are exposed to currency risk since they have long positions in the debtor country and
short positions in the creditor country. Intermediaries are also financially constrained which means that their
participation in the currency markets is determined by their risk-bearing capacity. As a result, in equilibrium,
an imbalance that requires intermediaries to enter into a long position in a currency will be followed by an
increase in the expected return of this currency to incentivize the intermediary to sustain the imbalance.
According to the model, the expected currency excess return (see Proposition 6, p.1398) is:
E0
[Rfx1
]= Γ
R∗
R E0 [ι1]− ι0(R∗ + Γ)ι0 + R∗
R E0 [ι1](34)
where R∗
R is the interest rate differential between the foreign and the home country, ι denotes the preference
parameter towards foreign goods (the difference E0 [ι1]− ι0 can be thought of as the evolution of net exports
(see, e.g. DellaCorte et al. (2016a))), and Γ is inversely related to the risk-bearing capacity of the intermediary
(Γ increases when the risk-bearing capacity decreases).
In the context of Gabaix and Maggiori (2015), global adjusted leverage can be interpreted as a proxy for
the risk-bearing capacity of the financiers. When global adjusted leverage is high, risk-bearing capacity is
high as well, reflecting high levels of credit-to-private sector, and expected premia of assets that negatively
co-vary with Γ are low. On the other hand, when global adjusted leverage is low, risk-bearing capacity is low,
consistent with low levels of credit-to-private sector and high levels of leverage, and expected premia of assets
are high.
Under all three frameworks discussed in this paper, the negative relation between global adjusted leverage
and marginal value of wealth of financial intermediaries implies that assets positively correlated with global
adjusted leverage are more risky and, as a result, earn a higher risk premium. The empirical findings of
32
Section 7 corroborates this theoretical prediction.
8.2 Comparison with Other Measures
As mentioned in the literature review, this paper is closely related to Adrian et al. (2014) and He et
al. (forthcoming). Both papers test the asset pricing properties of measures related to the marginal value
of wealth of financial intermediaries, and both find supporting evidence in favor of their proposed factors,
but their findings are seemingly contradictory. More specifically, Adrian et al. (2014) propose a single-factor
intermediary SDF. The factor is a time-series of shocks to the financial leverage of securities broker-dealers
and is constructed using data from the Federal Reserve Flow of Funds. They conduct a number of asset
pricing tests and find that the proposed factor carries a large and significant positive price of risk.45 On the
other hand, He et al. (forthcoming) propose a different factor which comprises shocks to the equity capital
ratio of primary dealer counterparties of the New York Federal Reserve and, using an extensive set of test
assets, show that this factor has a consistently positive and of similar magnitude price of risk.46 This finding
is at odds with that of Adrian et al. (2014). The leverage ratio proposed by Adrian et al. (2014) is inversely
related to the capital ratio of He et al. (forthcoming). As mentioned in He et al. (forthcoming) the seemingly
puzzling results could be attributed to the different theoretical underpinnings of the two papers.47 In the
framework of Adrian et al. (2014), leverage is pro-cyclical while in the framework of He et al. (forthcoming)
leverage is counter-cyclical.
To better understand the properties of the above mentioned measures and how they relate to the measure
of adjusted leverage, I study their explanatory power over financial intermediaries’ future returns and levels
of their balance sheet assets across credit regimes defined as in Section 5.48 Tables 13a and 13b summarize
the results. The correlation of both the leverage factor and the capital risk factor with both intermediaries’
returns and future assets varies depending on the credit regime. When credit-to-private sector is low (less than
the 25th percentile of its historical time-series), the leverage factor is positively correlated/uncorrelated and
the capital risk factor is seemingly uncorrelated with intermediaries’ returns/future assets, while this pattern
reverses in periods where credit-to-private sector is high (higher than the 75th percentile of its historical45The test assets used in the analysis are 25 size and book-to market portfolios, 25 size and momentum portfolios, 10
momentum portfolios, and 6 Treasury bond portfolios.46They consider a wide set of test assets including 25 size and book-to-market portfolios, 10 government bond portfolios,
10 corporate bond portfolios, 6 sovereign bond portfolios, 18 options portfolios, 12 foreign exchange portfolios, 23 commodityportfolios, and 20 CDS portfolios.
47Adrian et al. (2014) construct and test a measure corresponding to the theoretical work of Brunnermeier and Pedersen(2009), Geanakoplos (2010), Gromb and Vayanos (2002), and Shleifer and Vishny (1997). Meanwhile, He et al. (forthcoming)construct and test a measure which corresponds to the theoretical work of He and Krishnamurthy (2013) and Brunnermeier andSannikov (2014).
48Stock market returns usually reflect the risk of an investment and future levels of assets are a result of previous risk-bearingcapacity for financial institutions.
33
time-series).49 The findings once again suggest that the marginal value of wealth of financial institutions is
related to the amount of credit outstanding in the economy. The opposite signs between leverage factor and
capital risk factor are consistent with the theoretical motivation of the two measures and reinforce the puzzle
mentioned above regarding their price of risk in the cross-section of financial assets.
To further identify whether the above mentioned factors capture the same information, I compute
correlation coefficients among them. I find that the global adjusted leverage factor is essentially uncorrelated
to the leverage and capital ratio factors. Over the period of 2001-Q1 until 2014-Q1, the leverage factor is
weakly positively correlated to the capital ratio factor (19.7%), a figure that is comparable to that reported
in He et al. (forthcoming) (14%) referring to the period of 1970-Q1 until 2012-Q4. The estimated correlation
coefficients suggest that the three factors summarize different aspects of information related to financial
intermediaries’ funding constraints. The low pairwise correlations between the adjusted leverage factor and
the leverage and capital risk factors are not surprising since the last two measures include information only
on broker-dealers’ balance sheets and do not take into account the credit conditions in the economy.
In what follows, I measure the extent to which the above factors are priced in the cross-section of
both U.S. and global assets, when included simultaneously in a linear factor model. Using international
assets portfolios (currencies and global equities portfolios), I find that the global adjusted leverage factor
consistently exhibits a significantly positive price of risk which is of similar magnitude among all test assets.
Table 14 summarizes the results. More specifically, the adjusted leverage factor outperforms the leverage
ratio factor and the capital ratio factor in the cross-section of global equity portfolios and remains strongly
statistically significant in the cross-section of currency portfolios. An interesting finding is that the price of
risk of the other two factors is significantly negative in the cross-section of currency portfolios, which is at
odds with previous empirical findings on the price of risk of these factors and with the theoretical motivation
behind them. The superior performance of the global adjusted leverage factor comes as no surprise since it
incorporates information about the funding constraints of financial institutions operating on a global scale.50
Using a global measure along with two U.S. specific measures in a linear factor model and testing it
against portfolios of international assets could potentially give an unfair advantage to the global measure. To
address concerns that this measure does not outperform the other two measures when these measures are49The leverage factor is negatively/positively correlated and the capital risk factor is positively/negatively correlated with
intermediaries’ returns/future assets.50In an accompanying internet appendix, I repeat the above exercise, but I use U.S. only asset portfolios as test assets. More
specifically, I use the same set of assets employed in the asset pricing tests of He et al. (forthcoming) (The data are available onAsaf Manela’s website http://apps.olin.wustl.edu/faculty/manela/data.html. In comparison to the other two measures, theglobal adjusted leverage factor shows a higher level of significance when tested against option and CDS portfolios. No measureconsistently explains U.S. asset portfolios. This implies that thus far we do not have an accurate measure of the marginal valueof wealth of the representative investor in these assets. This remains an open question, an answer to which can lead to theconstruction of a more accurate proxy for the funding constraints of financial intermediaries
34
computed using international data, I repeat the above exercise using a two factor linear model which includes
the global adjusted leverage measure and global financial leverage innovations as computed in Section 5.
Table 15 summarizes the findings. Once again, the addition of a another factor does not change significance
of the price of risk of the global adjusted leverage factor.
In sum, the global adjusted leverage factor outperforms a number of other factors proposed in the
literature when jointly used in a linear pricing model and tested in the cross-section of international equity
and currency portfolios. The better performance of the adjusted leverage factor in the cross-section of equities
and currencies implies that this factor can be considered as a state variable that more accurately reflects
financial intermediaries’ funding constraints. The pro-cyclical nature of the adjusted leverage factor, its
predictive power over financial crises, and consumption measures provide a strong economic justification for
the use of this factor as a state variable for the funding constraints of financial intermediaries.51
8.3 Global Versus U.S. Adjusted Leverage
In this section, motivated by the strong explanatory power of the global adjusted leverage ratio, I address
the question of whether the explanatory power of adjusted leverage is due to non-U.S., or due to U.S. financial
intermediaries. With this exercise I attempt to identify the country of origin of the marginal investors in
international capital markets. I decompose the global adjusted leverage factor into two factors, one related
only to the adjusted leverage of non-U.S. financial intermediaries and one related only to the adjusted leverage
of U.S. financial firms. The U.S adjusted leverage series is computed according to equation 26, but only using
U.S. data. The non-U.S. adjusted leverage series is equal to the residuals of a regression of the U.S. series on
the global series,
Global Adjusted Leveraget = α+ βU.S Adjusted Leveraget + εt
which means that,
Ex-U.S Adjusted Leveraget = ε̂t
Figure 15 shows the time-series evolution of the two measures. Non-U.S. adjusted leverage is less volatile that
the U.S. adjusted leverage, and the correlation between the two series is -12% suggesting that the funding
constraints of non-U.S. financial intermediaries are not the same with these of U.S. financial intermediaries.
Focusing on international assets portfolios, I construct a two factor asset pricing model consisting of the51In Section 5 I discuss in detail the relation between the adjusted leverage factor and the macroeconomy.
35
Ex-U.S. and the U.S. adjusted leverage and test for the asset pricing properties of the two factors. Table
16 shows that the Ex-U.S. adjusted leverage factor appears with a significantly positive price of risk in the
cross-section of all asset portfolios. These findings suggest that international intermediaries are the marginal
investors in currency markets and international equity markets and that U.S. financial intermediaries are
playing a lesser role in global markets. The price of risk of the Ex-U.S. adjusted leverage factor remains
essentially unchanged even after adding the leverage factor of Adrian et al. (2014) and the capital ratio factor
of He et al. (forthcoming) into the linear factor model.52 Non-U.S. financial intermediaries are the marginal
investors in international equity markets, and in currency markets.
9 Conclusion
In this paper, I introduce a global adjusted leverage factor as a proxy for the pricing kernel of a
representative global financial intermediary. Using a simple theoretical framework, I show that when credit in
the economy is low, financial leverage is not an accurate proxy for the stochastic discount factor of financial
intermediaries. Empirical evidence confirms this theoretical finding. The level of credit outstanding in the
economy arises as an important determinant of the risk-bearing capacity of a financial intermediary. As a
result, the proposed measure of adjusted leverage incorporates information on both the financial leverage of
intermediaries and the availability of credit in the economy. Adjusted leverage is high when credit-to-private
sector is high, and low when credit-to-private sector is low and financial leverage is high. This measure is
pro-cyclical, and predicts financial crises and future consumption, all traits of an economically meaningful
measure of the funding constraints of financial intermediaries.
I test for the asset pricing properties of the adjusted leverage factor in the cross-section of a wide array
of test assets and find that, consistent with the theoretical framework discussed in the paper, it is associated
with a positive price of risk. A global adjusted leverage single factor model outperforms benchmark factors
in the cross-section of currency portfolios and performs comparably to the Fama-French three factors plus
momentum model in the cross-section of international equity portfolios. In a comparison with the leverage
factor of Adrian et al. (2014) and the capital risk factor of He et al. (forthcoming), the global adjusted leverage
factor exhibits a significantly negative price of risk in the cross-section of global equities and international
asset portfolios. Finally, I decompose the global adjusted leverage factor into a non-U.S. and a U.S. only
component and find that non-U.S. financial intermediaries are marginal investors in global and domestic
equities markets and in currency markets.52These tables can be found in the internet appendix.
36
The results of this paper underline the importance of financial intermediaries’ marginal value of wealth
for the determination of asset prices. I show that broker-dealers are the marginal investors in global equities
and in currency markets. However, there are markets for which the broker-dealers do not seem to be the
marginal investors. Further research is required both on a theoretical and on an empirical level to uncover
the exact relation between financial intermediaries’ funding constraints and asset prices.
37
References
Adrian, Tobias and Hyun Song Shin, “Liquidity and Leverage,” Journal of Financial Intermediation,
2010, 19 (3), 418 – 437. Risk Transfer Mechanisms and Financial Stability.
and Joshua Rosenberg, “Stock Returns and Volatility: Pricing the Short-Run and Long-Run Compo-
nents of Market Risk,” The Journal of Finance, 2008, 63 (6), 2997–3030.
, Emanuel Moench, and Hyun Song Shin, “Dynamic Leverage Asset Pricing,” Staff Reports 625,
Federal Reserve Bank of New York 2013.
, Erkko Etula, and Hyun Song Shin, “Risk Appetite and Exchange Rates,” Staff Reports 750, Federal
Reserve Bank of New York December 2015.
, , and Tyler Muir, “Financial Intermediaries and the Cross-Section of Asset Returns,” The Journal
of Finance, 2014, 69 (6), 2557–2596.
Allen, Franklin, “Do Financial Institutions Matter?,” The Journal of Finance, 2001, 56 (4), 1165–1175.
Ang, Andrew, Robert Hodrick, Yuhang Xing, and Xiaoyan Zhang, “The Cross-Section of Volatility
and Expected Returns,” Journal of Finance, 2006, 61 (1), 259–299.
Asness, Clifford S., Tobias J. Moskowitz, and Lasse Pedersen, “Value and Momentum Everywhere,”
Journal of Finance, 2013, 68 (3), 929–985.
Bansal, Ravi, “An Exploration of the Forward Premium Puzzle in Currency Markets,” Review of Financial
Studies, 1997, 10 (2), 369–403.
and Amir Yaron, “Risks for the Long Run: A Potential Resolution of Asset Pricing Puzzles,” The
Journal of Finance, 2004, 59 (4), 1481–1509.
and Magnus Dahlquist, “The Forward Premium Puzzle: Different Tales from Developed and Emerging
Economies,” Journal of International Economics, 2000, 51 (1), 115 – 144.
Bénétrix, Agustin S., Philip R. Lane, and Jay C. Shambaugh, “International Currency Exposures,
Valuation Effects and the Global Financial Crisis,” Journal of International Economics, 2015, 96, Supplement
1, S98 – S109.
Brunnermeier, Markus K. and Lasse Heje Pedersen, “Market Liquidity and Funding Liquidity,”
Review of Financial Studies, 2009, 22 (6), 2201–2238.
38
and Yuliy Sannikov, “A Macroeconomic Model with a Financial Sector,” American Economic Review,
February 2014, 104 (2), 379–421.
, Stefan Nagel, and Lasse H. Pedersen, “Carry Trades and Currency Crashes,” NBER Macroeconomics
Annual 2008, 2008, 23, 313–347.
Burnside, Craig, Martin Eichenbaum, and Sergio Rebelo, “Carry Trade and Momentum in Currency
Markets,” Annual Review of Financial Economics, 2011, 3 (1), 511–535.
, , Isaac Kleshchelski, and Sergio Rebelo, “Do Peso Problems Explain the Returns to the Carry
Trade?,” Review of Financial Studies, 2011, 24 (3), 853–891.
Calvet, Laurent E., John Y. Campbell, and Paolo Sodini, “Down or Out: Assessing the Welfare
Costs of Household Investment Mistakes,” Journal of Political Economy, 2007, 115 (5), 707–747.
Campbell, John and John Cochrane, “Force of Habit: A Consumption-Based Explanation of Aggregate
Stock Market Behavior,” Journal of Political Economy, 1999, 107 (2), 205–251.
Chousakos, Kyriakos, Gary Gorton, and Guillermo Ordonez, “Aggregate Information Dynamics,”
Working Paper, Yale University 2016.
Cochrane, John H., Asset Pricing: (Revised Edition), Princeton University Press, 2005.
, “Presidential Address: Discount Rates,” The Journal of Finance, 2011, 66 (4), 1047–1108.
DellaCorte, Pasquale, Steven J. Riddiough, and Lucio Sarno, “Currency Premia and Global Imbal-
ances,” Review of Financial Studies, 2016.
, Tarun Ramadorai, and Lucio Sarno, “Volatility Risk Premia and Exchange Rate Predictability,”
Journal of Financial Economics, 2016, 120 (1), 21 – 40.
Duffie, Darrell, “Presidential Address: Asset Price Dynamics with Slow-Moving Capital,” The Journal of
Finance, 2010, 65 (4), 1237–1267.
Edwards, Amy K., Lawrence E. Harris, and Michael S. Piwowar, “Corporate Bond Market Trans-
action Costs and Transparency,” The Journal of Finance, 2007, 62 (3), 1421–1451.
Etula, Erkko, “Broker-Dealer Risk Appetite and Commodity Returns,” Journal of Financial Econometrics,
2013, 11 (3), 486.
Fama, Eugene and Kenneth French, “Common Risk Factors in the Returns on Stocks and Bonds,”
Journal of Financial Economics, 1993, 33 (1), 3–56.
39
Fama, Eugene F., “Forward and Spot Exchange Rates,” Journal of Monetary Economics, 1984, 14 (3), 319
– 338.
and James D. MacBeth, “Risk, Return, and Equilibrium: Empirical Tests,” Journal of Political
Economy, 1973, 81 (3), 607–636.
and Kenneth R. French, “Size, Value, and Momentum in International Stock Returns,” Journal of
Financial Economics, 2012, 105 (3), 457 – 472.
Farhi, Emmanuel and Xavier Gabaix, “Rare Disasters and Exchange Rates,” Quarterly Journal of
Economics, 2016, 131 (1), 1–52. Lead Article.
Gabaix, Xavier and Matteo Maggiori, “International Liquidity and Exchange Rate Dynamics,” The
Quarterly Journal of Economics, 2015, 130 (3), 1369–1420.
Geanakoplos, John, “The Leverage Cycle,” NBER Macroeconomics Annual 2009, Volume 24, April 2010,
pp. 1–65.
Gorton, Gary and Guillermo Ordoñez, “Collateral Crises,” American Economic Review, February 2014,
104 (2), 343–78.
and , “Good Booms, Bad Booms,” Working Paper 22008, National Bureau of Economic Research
February 2016.
Goyenko, Ruslan and Sergei Sarkissian, “Treasury Bond Illiquidity and Global Equity Returns,” Journal
of Financial and Quantitative Analysis, 10 2014, 49, 1227–1253.
Griffin, John M., “Are the Fama and French Factors Global of Country Specific?,” Review of Financial
Studies, 06 2002, 15, 783–803.
Gromb, Denis and Dimitri Vayanos, “Equilibrium and Welfare in Markets with Financially Constrained
Arbitrageurs,” Journal of Financial Economics, 2002, 66 (2–3), 361 – 407.
Hansen, Lars and Robert Hodrick, “Forward Exchange Rates as Optimal Predictors of Future Spot
Rates: An Econometric Analysis,” Journal of Political Economy, 1980, 88 (5), 829–53.
He, Zhiguo and Arvind Krishnamurthy, “Intermediary Asset Pricing,” American Economic Review,
April 2013, 103 (2), 732–70.
, Bryan Kelly, and Asaf Manela, “Intermediary Asset Pricing: New Evidence from Many Asset Classes,”
Journal of Financial Economics, forthcoming.
40
Koijen, Ralph S. J., Tobias J. Moskowitz, Lasse Heje Pedersen, and Evert B. Vrugt, “Carry,”
Working Paper, 2016.
Lettau, Martin, Matteo Maggiori, and Michael Weber, “Conditional Risk Premia in Currency
Markets and Other Asset Classes,” Journal of Financial Economics, 2014, 114 (2), 197 – 225.
Lewellen, Jonathan, Stefan Nagel, and Jay Shanken, “A Skeptical Appraisal of Asset Pricing Tests,”
Journal of Financial Economics, 2010, 96 (2), 175 – 194.
Lustig, Hanno and Adrien Verdelhan, “The Cross Section of Foreign Currency Risk Premia and
Consumption Growth Risk,” American Economic Review, March 2007, 97 (1), 89–117.
, Nikolai Roussanov, and Adrien Verdelhan, “Common Risk Factors in Currency Markets,” Review
of Financial Studies, 2011.
Malkhozov, Aytek, Philippe Mueller, Andrea Vedolin, and Gyuri Venter, “International Illiquidity,”
Working Paper, 2017.
Meese, Richard and Kenneth Rogoff, “Empirical Exchange Rate Models of the Seventies: Do they Fit
out of Sample?,” Journal of International Economics, 1983, 14 (1-2), 3–24.
Menkhoff, Lukas, Lucio Sarno, Maik Schmeling, and Andreas Schrimpf, “Carry Trades and Global
Foreign Exchange Volatility,” The Journal of Finance, 2012, 67 (2), 681–718.
, , , and , “Currency Momentum Strategies,” Journal of Financial Economics, 2012, 106 (3),
660–684.
Newey, Whitney K. and Kenneth D. West, “A Simple, Positive Semi-Definite, Heteroskedasticity and
Autocorrelation Consistent Covariance Matrix,” Econometrica, 1987, 55 (3), 703–708.
and , “Automatic Lag Selection in Covariance Matrix Estimation,” The Review of Economic Studies,
1994, 61 (4), 631.
Schularick, Moritz and Alan M. Taylor, “Credit Booms Gone Bust: Monetary Policy, Leverage Cycles,
and Financial Crises, 1870-2008,” American Economic Review, April 2012, 102 (2), 1029–1061.
Shanken, Jay, “On the Estimation of Beta-Pricing Models,” Review of Financial Studies, 1992, 5 (1), 1–33.
Shleifer, Andrei and Robert W. Vishny, “The Limits of Arbitrage,” The Journal of Finance, 1997, 52
(1), 35–55.
41
Sneider, Amanda, David J. Kostin, Stuart Kaiser, Ben Snider, Peter Lewis, and Rima Reddy,
“An Equity Investor’s Guide to the Flow of Funds Accounts,” Portfolio Strategy Research, Goldman Sachs,
2013.
Ľuboš Pástor and Robert F. Stambaugh, “Liquidity Risk and Expected Stock Returns,” Journal of
Political Economy, 2003, 111 (3), 642–685.
Valencia, Fabian and Luc Laeven, “Systemic Banking Crises Database; An Update,” IMF Working
Papers 12/163, International Monetary Fund June 2012.
Verdelhan, Adrien, “A Habit-Based Explanation of the Exchange Rate Risk Premium,” The Journal of
Finance, 2010, 65 (1), 123–146.
Vissing-Jørgensen, Annette, “Limited Asset Market Participation and the Elasticity of Intertemporal
Substitution,” Journal of Political Economy, 2002, 110 (4), 825–853.
White, Halbert, “A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for
Heteroskedasticity,” Econometrica, 1980, 48 (4), 817–838.
42
Appendices
A Proofs
Proposition 2. (Stochastic discount factor and financial leverage.)
The relation between the SDF of a financial intermediary and its financial leverage depends on the level
of technological innovation (q) and information acquisition from the household and the financial intermediary:
• Bank loans and household deposits are information-insensitive with no credit constraints present (B(II),
H(II)): Leverage is constant and SDF a negative function of technological innovation.
• Bank loans and household deposits are information-insensitive, but credit constraints are present (B(II),
H(II)): Leverage is positively and SDF negatively correlated with technological innovation.
• Bank loans and household deposits are information-insensitive, but deposit and credit constraints are
present (B(II), H(II)): Leverage is positively and SDF negatively correlated with technological innovation.
• Bank loans are information-sensitive and household deposits are information-insensitive with deposit
constraints present (B(IS), H(II)): Both leverage and SDF a positive function of technological innovation
• Bank loans and household deposits are information-sensitive (B(IS), H(IS)): Leverage is positively and
SDF negatively correlated with technological innovation.
Proof. The proof is organized into five sections, one for each of the statements made in the proposition.
(A) When both the household and the financial institution are information insensitive and borrowing is
not informationally constrained (B(II), H(II)), the marginal utility of consumption for the financial institution
is,
m = Kh −Kb + π1
Kb −Kh + π2 + pCf= K∗ −K∗ +Aq1K1
K∗ −K∗ +K∗(q2A− 1) + pCf= Aq1K1
K∗(q2A− 1) + pCf. (35)
Taking first order conditions with respect to technological innovation of period 2 (q2) it follows that,
∂m
∂q2= − A2q1K1K
∗
(K∗(q2A− 1) + pCf )2 . (36)
Which means that for the region where q2 > qb,HII the stochastic discount factor of the financial is a negative
function of q2.
43
Financial leverage for this region of technological innovation is computed as,
l = Kb + V1
Kb + V1 −Kh=K∗ + Aq1K1
K∗(q2A−1)+pCf (K∗(Aq2 − 1) + pCf )Aq1K1
K∗(q2A−1)+pCf (K∗(Aq2 − 1) + pCf )= K∗ +Aq1K1
Aq1K1. (37)
Taking first order conditions with respect to technological innovation of period 2 (q2) it follows that,
∂l
∂q2= 0, (38)
which means that leverage is constant.
(B) When both the household and the financial institution are information insensitive, borrowing
informationally constrained for the financial institution (B(II), H(II)), the marginal utility of consumption
for the financial institution is,
m = Kh −Kb + π1
Kb −Kh + π2 + pCf=
K∗ − γb
(1−p)(1−q2) +Aq1K1γb
(1−p)(1−q2) −K∗ + γb
(1−p)(1−q2) (q2A− 1) + pCf⇒
m = (1− p)(1− q2)(K∗ +Aq1K1)− γb
γbq2A+ (pCf −K∗)(1− p)(1− q2) . (39)
Taking first order conditions with respect to technological innovation of period 2 (q2) it follows that,
∂m
∂q2= γb(A2q1K1(p− 1) +A(γb +K∗(p− 1)) + (p− 1)(pCf −K∗))
(γbq2A+ (pCf −K∗)(1− p)(1− q2))2 , (40)
which is negative when γb +K∗(p− 1) ≤ 0 which means that γb
K∗ ≤ 1− p. 53
Financial leverage for this region of technological innovation is computed as,
l = Kb + V1
Kb + V1 −Kh=
γb
(1−p)(1−q2) +m( γb
(1−p)(1−q2) (q2A− 1) + pCf )γb
(1−p)(1−q2) +m( γb
(1−p)(1−q2) (q2A− 1) + pCf )−K∗. (41)
Taking first order conditions with respect to technological innovation of period 2 (q2) it follows that,
∂l
∂q2= −K∗
γb(1−p)(1+mA)((1−p)(1−q2))2 + ∂m
∂q2( γb(q2A−1)
(1−p)(1−q2) + pCf )
( γb
(1−p)(1−q2) +m( γb
(1−p)(1−q2) (q2A− 1) + pCf )−K∗)2, (42)
which means that leverage is an increasing function of technological innovation since γb(1−p)(1+mA)((1−p)(1−q2))2 +
53This condition is not satisfied for very high values of p (p > 0.95 for a cost of producing information that is higher than 5%of the optimal loan size).
44
∂m∂q2
( γb(q2A−1)(1−p)(1−q2) + pCf ) < 0 for q2 between cutoff points A and B.
(C) When both the household and the financial institution are information insensitive, and borrowing
is informationally constrained for both (B(II), H(II)), the marginal utility of consumption for the financial
institution is,
m = Kh −Kb + π1
Kb −Kh + π2 + pCf=
γh
(1−p)(1−q2) −γb
(1−p)(1−q2) +Aq1K1γb
(1−p)(1−q2) −γh
(1−p)(1−q2) + γb
(1−p)(1−q2) (q2A− 1) + pCf⇒
m = γh − γb +Aq1K1(1− p)(1− q2)γbq2A− γh + pCf (1− p)(1− q2) . (43)
Taking first order conditions with respect to technological innovation of period 2 (q2) it follows that,
∂m
∂q2= − AK1q1(1− p)
Aq2γb + pCf (1− p)(1− q2) −(Aγb − pCf (1− p))(AK1q1(1− p)(1− q2) + γh − γb)
(Aq2γb + pCf (1− p)(1− q2))2 , (44)
which is negative when (γb − γh)(Aγb + pCf (p− 1)) +AK1q1(p− 1)(Aγb − γh) < 0.
Financial leverage for this region of technological innovation is computed as,
l = Kb + V1
Kb + V1 −Kh=
γb
(1−p)(1−q2) +m( γb
(1−p)(1−q2) (q2A− 1) + pCf )γb
(1−p)(1−q2) +m( γb
(1−p)(1−q2) (q2A− 1) + pCf )− γh
(1−p)(1−q2)
. (45)
Taking first order conditions with respect to technological innovation of period 2 (q2) it follows that,
∂l
∂q2=− γh
(1− p)(1− q2)
γb(1−p)(1+mA)((1−p)(1−q2))2 + ∂m
∂q2( γb(q2A−1)
(1−p)(1−q2) + pCf )
( γb
(1−p)(1−q2) +m( γb
(1−p)(1−q2) (q2A− 1) + pCf )− γh
(1−p)(1−q2) )2
+ γh
(1− p)(1− q2)2
( γb
(1−p)(1−q2) +m( γb
(1−p)(1−q2) (q2A− 1) + pCf ))2
( γb
(1−p)(1−q2) +m( γb
(1−p)(1−q2) (q2A− 1) + pCf )− γh
(1−p)(1−q2) )2
, (46)
which means that leverage is an increasing function of technological innovation since γb(1−p)(1+mA)((1−p)(1−q2))2 +
∂m∂q2
( γb(q2A−1)(1−p)(1−q2) + pCf ) < 0 for q2 between cutoff points B and C.
(D) When the household is information insensitive, and the financial institution information sensitive
(B(IS), H(II)), the marginal utility of consumption for the financial institution is,
m = Kh −Kb + π1 − γb
Kb −Kh + π2 + pCf=
γh
(1−p)(1−q2) − pK∗ + γb
Aq2−1 +Aq1K1 − γb
pK∗ + γb − γh
(1−p)(1−q2) + pK∗(Aq2 − 1)− γb + pCf⇒
45
m =γh
(1−p)(1−q2) − pK∗ + γb
Aq2−1 +Aq1K1 − γb
pK∗Aq2 − γh
(1−p)(1−q2) + pCf. (47)
Taking first order conditions with respect to technological innovation of period 2 (q2) it follows that,
∂m
∂q2=
( γh
(1−p)(1−q2)2 − γbA(Aq2−1)2 )(pK∗Aq2 − γh
(1−p)(1−q2) + pCf )
(pK∗Aq2 − γh
(1−p)(1−q2) + pCf )2
−( γh
(1−p)(1−q2) − pK∗ + γb
Aq2−1 − γb)(pK∗A− γh
(1−p)(1−q2)2 )
(pK∗Aq2 − γh
(1−p)(1−q2) + pCf )2
(48)
which is positive since Aq1K1( γh
(1−p)(1−q2)2 −pK∗A) + γhAAq2−1 ( γh
1−q2−pK∗Aq2−pCf ) ≥ 0 for q2 between cutoff
points C and D.
Financial leverage for this region of technological innovation is computed as,
l = Kb + V1
Kb + V1 −Kh=
pK∗ − γb
Aq2−1 +m(pK∗(q2A− 1)− γb + pCf )
pK∗ − γb
Aq2−1 +m(pK∗(q2A− 1)− γb + pCf )− γh
(1−p)(1−q2)
. (49)
Taking first order conditions with respect to technological innovation of period 2 (q2) it follows that,
∂l
∂q2=− γh
(1− p)(1− q2)
γbA(Aq2−1)2 + ∂m
∂q2(pK∗(q2A− 1)− γb + pCf ) +mpK∗A
(pK∗ − γb
Aq2−1 +m(pK∗(q2A− 1)− γb + pCf )− γh
(1−p)(1−q2) )2
+ γh
(1− p)(1− q2)2
(pK∗ − γb
Aq2−1 +m(pK∗(q2A− 1)− γb + pCf )
(pK∗ − γb
Aq2−1 +m(pK∗(q2A− 1)− γb + pCf )− γh
(1−p)(1−q2) )2,
, (50)
which means that leverage is an increasing function of technological innovation since γbA(Aq2−1)2 + ∂m
∂q2(pK∗(q2A−
1)− γb + pCf ) +mpK∗A < 0 for q2 between cutoff points C and D.
(E): The proof follows the same logic.
46
B Figures
Figure 1: Amount of credit and relation between pricing kernel and financial leverage. Thisfigure summarizes the evolution of credit as a function of technology (q), and the relation between thestochastic discount factor and financial leverage of the representative financial institution. The quality of land(p) is set at 60%, managerial labor (L∗) and optimal capital (K∗) at 7, the endowment numeraire for thefirm (K1) at 5, the production parameter (A) at 3, the proceeds from land ownership (C) at 15, and the costof producing information for the financial institution (γb) is set at 0.35 and for the household (γh) at 0.5.
DC
B A
B(II),H(II)B(II),H(II)B(IS),H(II)B(IS),H(IS)
45
67
Ava
ilabl
e C
redi
t
.65 .7 .75 .8 .85 .9Technology (q)
Financial Institution Household
(a) Credit
B(II),H(II)B(II),H(II)B(IS),H(II)B(IS),H(IS)
1.45
1.5
1.55
1.6
1.65
1.7
Leve
rage
.5.6
.7.8
.91
SD
F
.65 .7 .75 .8 .85 .9Technology (q)
SDF Leverage
(b) SDF vs. Leverage
47
Figure 2: Financial Leverage and Financial Intermediaries’ Future Assets Across CreditRegimes (Individual Country Series). The figure summarizes the relation between future asset levels offinancial intermediaries and global financial leverage across different credit regimes: (i) a high credit regimedefined as instances where credit-to-private sector of a given country is higher than the 75th percentile ofits historical credit series, and (ii) a low credit regime defined as instances where credit-to-private sectorof a given country is lower than the 25th percentile of its historical credit series. The regression specifi-cation is: assetst+1 = α + β′Xt + γassetst + εt+1, where Xt = (fin.leverage, fin.leverage × 1(Creditt >75%), fin.leverage × 1(Creditt < 25%))′. Lowercase variables are log variables. Data are quarterly fromDataStream, WorldScope, and the World Development Indicators database, and span a period from 2001until 2014. Standard errors are heteroskedasticity- (White (1980)) and autocorrelation-robust (Newey andWest (1987) and Newey and West (1994)).
−1
−.5
0.5
Coe
ffici
ent
Aus
tria
Bel
gium
Bra
zil
Bul
garia
Can
ada
Chi
leC
olom
bia
Cro
atia
Cyp
rus
Che
ch R
epub
licD
enm
ark
Fin
land
Fra
nce
Ger
man
yG
reec
eH
ong
Kon
gH
unga
ryIc
elan
dIn
done
sia
Isra
elIta
lyJa
pan
Kaz
akhs
tan
Ken
yaS
outh
Kor
eaK
uwai
tM
alay
sia
Mex
ico
Net
herla
nds
New
Zea
land
Nor
way
Om
anP
akis
tan
Per
uP
hilip
pine
sP
olan
dP
ortu
gal
Qat
arR
oman
iaR
ussi
aS
audi
Ara
bia
Sin
gapo
reS
lova
kia
Slo
veni
aS
pain
Sw
eden
Sw
itzer
land
Tha
iland
Ukr
aine
UA
EU
nite
d K
ingd
omU
nite
d S
tate
sV
enez
uela
Country
(a) fin.leverage× 1(Creditt < 25%)
−.2
0.2
.4.6
.8C
oeffi
cien
t
Aus
tria
Bel
gium
Bra
zil
Bul
garia
Can
ada
Chi
leC
olom
bia
Cro
atia
Cyp
rus
Che
ch R
epub
licD
enm
ark
Fin
land
Fra
nce
Ger
man
yG
reec
eH
ong
Kon
gH
unga
ryIc
elan
dIn
done
sia
Isra
elIta
lyJa
pan
Kaz
akhs
tan
Ken
yaS
outh
Kor
eaK
uwai
tM
alay
sia
Mex
ico
Net
herla
nds
New
Zea
land
Nor
way
Om
anP
akis
tan
Per
uP
hilip
pine
sP
olan
dP
ortu
gal
Qat
arR
oman
iaR
ussi
aS
audi
Ara
bia
Sin
gapo
reS
lova
kia
Slo
veni
aS
pain
Sw
eden
Sw
itzer
land
Tha
iland
Ukr
aine
UA
EU
nite
d K
ingd
omU
nite
d S
tate
sV
enez
uela
Country
(b) fin.leverage× 1(Creditt > 75%)
−20
−10
010
Coe
ffici
ent
Aus
tria
Bel
gium
Bra
zil
Bul
garia
Can
ada
Chi
leC
olom
bia
Cro
atia
Cyp
rus
Che
ch R
epub
licD
enm
ark
Fin
land
Fra
nce
Ger
man
yG
reec
eH
ong
Kon
gH
unga
ryIc
elan
dIn
done
sia
Isra
elIta
lyJa
pan
Kaz
akhs
tan
Ken
yaS
outh
Kor
eaK
uwai
tM
alay
sia
Mex
ico
Net
herla
nds
New
Zea
land
Nor
way
Om
anP
akis
tan
Per
uP
hilip
pine
sP
olan
dP
ortu
gal
Qat
arR
oman
iaR
ussi
aS
audi
Ara
bia
Sin
gapo
reS
lova
kia
Slo
veni
aS
pain
Sw
eden
Sw
itzer
land
Tha
iland
Ukr
aine
UA
EU
nite
d K
ingd
omU
nite
d S
tate
sV
enez
uela
Country
(c) fin.leverage
−1
−.5
0.5
11.
5C
oeffi
cien
t
Aus
tria
Bel
gium
Bra
zil
Bul
garia
Can
ada
Chi
leC
olom
bia
Cro
atia
Cyp
rus
Che
ch R
epub
licD
enm
ark
Fin
land
Fra
nce
Ger
man
yG
reec
eH
ong
Kon
gH
unga
ryIc
elan
dIn
done
sia
Isra
elIta
lyJa
pan
Kaz
akhs
tan
Ken
yaS
outh
Kor
eaK
uwai
tM
alay
sia
Mex
ico
Net
herla
nds
New
Zea
land
Nor
way
Om
anP
akis
tan
Per
uP
hilip
pine
sP
olan
dP
ortu
gal
Qat
arR
oman
iaR
ussi
aS
audi
Ara
bia
Sin
gapo
reS
lova
kia
Slo
veni
aS
pain
Sw
eden
Sw
itzer
land
Tha
iland
Ukr
aine
UA
EU
nite
d K
ingd
omU
nite
d S
tate
sV
enez
uela
Country
(d) financial assets
48
Figure 3: Financial Leverage and Financial Intermediaries’ Future Returns (Individual Coun-try Series). The figure summarizes the relation between future market returns of financial intermediariesand global financial leverage across different credit regimes: (i) a high credit regime defined as instances wherecredit-to-private sector of a given country is higher than the 75th percentile of its historical credit series, and(ii) a low credit regime defined as instances where credit-to-private sector of a given country is lower than the25th percentile of its historical credit series. The regression specification is: rfint+1 = α+ β′Xt + γrfint + εt+1,where Xt = (fin.leverage, fin.leverage× 1(Creditt > 75%), fin.leverage× 1(Creditt < 25%))′. Lowercasevariables are log variables. Data are quarterly from DataStream, WorldScope, and the World DevelopmentIndicators database, and span a period from 2001 until 2014. Standard errors are heteroskedasticity- (White(1980)) and autocorrelation-robust (Newey and West (1987) and Newey and West (1994)).
−.5
0.5
Coe
ffici
ent
Aus
tria
Bel
gium
Bra
zil
Bul
garia
Can
ada
Chi
leC
olom
bia
Cro
atia
Cyp
rus
Che
ch R
epub
licD
enm
ark
Fin
land
Fra
nce
Ger
man
yG
reec
eH
ong
Kon
gH
unga
ryIc
elan
dIn
dia
Indo
nesi
aIs
rael
Italy
Japa
nJo
rdan
Kaz
akhs
tan
Ken
yaS
outh
Kor
eaK
uwai
tM
alay
sia
Mex
ico
Net
herla
nds
New
Zea
land
Nor
way
Om
anP
akis
tan
Per
uP
hilip
pine
sP
olan
dP
ortu
gal
Qat
arR
oman
iaR
ussi
aS
audi
Ara
bia
Sin
gapo
reS
lova
kia
Slo
veni
aS
pain
Sw
eden
Sw
itzer
land
Tha
iland
Ukr
aine
UA
EU
nite
d K
ingd
omU
nite
d S
tate
sV
enez
uela
Country
(a) fin.leverage× 1(Creditt < 25%)
−1
−.5
0.5
1C
oeffi
cien
t
Aus
tria
Bel
gium
Bra
zil
Bul
garia
Can
ada
Chi
leC
olom
bia
Cro
atia
Cyp
rus
Che
ch R
epub
licD
enm
ark
Fin
land
Fra
nce
Ger
man
yG
reec
eH
ong
Kon
gH
unga
ryIc
elan
dIn
dia
Indo
nesi
aIs
rael
Italy
Japa
nJo
rdan
Kaz
akhs
tan
Ken
yaS
outh
Kor
eaK
uwai
tM
alay
sia
Mex
ico
Net
herla
nds
New
Zea
land
Nor
way
Om
anP
akis
tan
Per
uP
hilip
pine
sP
olan
dP
ortu
gal
Qat
arR
oman
iaR
ussi
aS
audi
Ara
bia
Sin
gapo
reS
lova
kia
Slo
veni
aS
pain
Sw
eden
Sw
itzer
land
Tha
iland
Ukr
aine
UA
EU
nite
d K
ingd
omU
nite
d S
tate
sV
enez
uela
Country
(b) fin.leverage× 1(Creditt > 75%)
−5
05
Coe
ffici
ent
Aus
tria
Bel
gium
Bra
zil
Bul
garia
Can
ada
Chi
leC
olom
bia
Cro
atia
Cyp
rus
Che
ch R
epub
licD
enm
ark
Fin
land
Fra
nce
Ger
man
yG
reec
eH
ong
Kon
gH
unga
ryIc
elan
dIn
dia
Indo
nesi
aIs
rael
Italy
Japa
nJo
rdan
Kaz
akhs
tan
Ken
yaS
outh
Kor
eaK
uwai
tM
alay
sia
Mex
ico
Net
herla
nds
New
Zea
land
Nor
way
Om
anP
akis
tan
Per
uP
hilip
pine
sP
olan
dP
ortu
gal
Qat
arR
oman
iaR
ussi
aS
audi
Ara
bia
Sin
gapo
reS
lova
kia
Slo
veni
aS
pain
Sw
eden
Sw
itzer
land
Tha
iland
Ukr
aine
UA
EU
nite
d K
ingd
omU
nite
d S
tate
sV
enez
uela
Country
(c) fin.leverage
−.5
0.5
1C
oeffi
cien
t
Aus
tria
Bel
gium
Bra
zil
Bul
garia
Can
ada
Chi
leC
olom
bia
Cro
atia
Cyp
rus
Che
ch R
epub
licD
enm
ark
Fin
land
Fra
nce
Ger
man
yG
reec
eH
ong
Kon
gH
unga
ryIc
elan
dIn
dia
Indo
nesi
aIs
rael
Italy
Japa
nJo
rdan
Kaz
akhs
tan
Ken
yaS
outh
Kor
eaK
uwai
tM
alay
sia
Mex
ico
Net
herla
nds
New
Zea
land
Nor
way
Om
anP
akis
tan
Per
uP
hilip
pine
sP
olan
dP
ortu
gal
Qat
arR
oman
iaR
ussi
aS
audi
Ara
bia
Sin
gapo
reS
lova
kia
Slo
veni
aS
pain
Sw
eden
Sw
itzer
land
Tha
iland
Ukr
aine
UA
EU
nite
d K
ingd
omU
nite
d S
tate
sV
enez
uela
Country
(d) returns
49
Figure 4: Global Leverage, Credit, and Adjusted Leverage Innovations (Broker-Dealers). Globalleverage is the assets weighted leverage of broker-dealers (WorldScope industry classification: 4394, 4395 forthe U.S. economy, and 4310, 4394, 4395 for all other countries). Leverage is the log of the ratio of assets toassets minus liabilities (Leverage = log(assets/(assets − liabilities))). Global Credit-to-Private-Sector isthe assets weighted credit-to-private sector aggregated from the country level. The Global Adjusted LeverageInnovations are equal to the residuals of an AR(1) regression of global leverage when Credit-to-Private-Sectoris higher than the 25th percentile of a 12 quarter rolling window and equal to the negative residuals whenCredit-to-Private-Sector is lower than the 25th percentile of a 12 quarter rolling window. The data are fromthe World Bank Development Indicators. All data are quarterly and span 2001 until 2014.
2.8
33.
23.
4Le
vera
ge
2000−Q1 2005−Q1 2010−Q1 2015−Q1Date
Credit<25th Percentile Global Leverage
(a) Global Financial Leverage
120
130
140
150
Cre
dit
2000−Q1 2005−Q1 2010−Q1 2015−Q1Date
Credit<25th Percentile Global Credit−to−Private Sector
(b) Global Credit-to-Private Sector
−.2
0.2
.4G
loba
l Lev
erag
e F
acto
r
2000−Q1 2005−Q1 2010−Q1 2015−Q1Date
Credit<25th Percentile Global Leverage Factor
(c) Global Adjusted Leverage Innovations
50
Figure 5: Global Leverage Innovations vs. Adjusted Leverage Innovations (Broker-Dealers).Global leverage Innovations are the residuals of an AR(1) regression of global leverage. Global AdjustedLeverage Innovations are equal to the residuals of an AR(1) regression of global leverage when Credit-to-Private-Sector is higher than the 25th percentile of a 12 quarter rolling window and equal to the negativeresiduals when Credit-to-Private-Sector is lower than the 25th percentile of a 12 quarter rolling window. Thedata are from WorldScope (industry classification: 4394, 4395 for the U.S. economy, and 4310, 4394, 4395 forall other countries) and the World Bank Development Indicators. All data are quarterly and span 2001 until2014.
−.4
−.2
0.2
.4Le
vera
ge F
acto
r
2000−Q1 2005−Q1 2010−Q1 2015−Q1Date
Credit<25th Percentile Global Leverage Factor
Leverage Innovations
51
Figure6:
AdjustedLe
verage
andMacroecon
omic
Activity(C
ountry
Level,Broker-Dealers).
The
figuresummarizes
theexplan
atory
powe
rof
glob
alAdjustedLe
verage
onloga
rithm
icchan
gesin
real
GDP
(rGDP),
capitalformation(INV),
totalfactorprod
uctiv
ity(TFP),
andtotal
finan
cial
assets
(Fin.Assets).The
regressio
nspecificatio
nis:
∆Econom
icVariable t
=α
+βAdj.Levt+ε t,w
hereEconom
icVariable t
=log(rGDP
) t,
log(INV
) t,T
FPt+
1,an
dFin.Assets t
+1.
Dataarefrom
WorldSc
ope,
World
Develop
mentIndicators,a
ndVa
lenc
iaan
dLa
even
(2012)
andspan
ape
riodfrom
2001
until
2014.Stan
dard
errors
arehe
terosked
astic
ity-(
White
(1980))an
dau
tocorrelation-robu
st(N
ewey
andWest(1987)
andNew
eyan
dWest(1994)). −10123
Coefficient
AustriaBelgium
BrazilCanada
DenmarkFinlandFrance
GermanyGreece
Hong KongHungary
IndiaIndonesia
IsraelItaly
JapanMalaysia
MexicoNetherlands
New ZealandNorwayPoland
PortugalRussia
Saudi ArabiaSingapore
SpainSweden
SwitzerlandThailand
United KingdomUnited States
Cou
ntry
(a)real
GDP
−2−1012Coefficient
AustriaBelgium
BrazilCanada
DenmarkFinlandFrance
GermanyGreece
Hong KongHungary
IndiaIndonesia
IsraelItaly
JapanMalaysia
MexicoNetherlands
New ZealandNorwayPoland
PortugalRussia
Saudi ArabiaSingapore
SpainSweden
SwitzerlandThailand
United KingdomUnited States
Cou
ntry
(b)Cap
italF
ormation
−.20.2.4.6Coefficient
AustriaBelgium
BrazilCanada
DenmarkFinlandFrance
GermanyGreece
Hong KongHungary
IndiaIndonesia
IsraelItaly
JapanMalaysia
MexicoNetherlands
New ZealandNorwayPoland
PortugalRussia
Saudi ArabiaSingapore
SpainSweden
SwitzerlandThailand
United KingdomUnited States
Cou
ntry
(c)TFP
−10−50510Coefficient
AustriaBelgium
BrazilCanada
DenmarkFinlandFrance
GermanyGreece
Hong KongHungary
IndiaIndonesia
IsraelItaly
JapanMalaysia
MexicoNetherlands
New ZealandNorwayPoland
PortugalRussia
Saudi ArabiaSingapore
SpainSweden
SwitzerlandThailand
United KingdomUnited States
Cou
ntry
(d)Fina
ncialA
ssets
52
Figure7:
AdjustedLe
verage
andMacroecon
omic
Activity(C
ountry
Level,Broker-Dealers).
The
figuresummarizes
theexplan
atory
power
ofglob
alAdjustedLe
verage
onlogarit
hmic
chan
gesin
househ
oldcred
it(H
H.Cr),c
orpo
rate
cred
it(Corp.Cr),a
ndtotalg
loba
limba
lanc
es(GI(Total)).
The
regressio
nspecificatio
nis:
∆Econom
icVariable t
=α
+βAdj.Levt+ε t,w
hereEconom
icVariable t
=(log
(HH.Cr)t,log
(Corp.Cr)t,
andlog(GI(Total)
) t).
Dataarefrom
WorldSc
opean
dWorld
Develop
mentIndicators,a
ndspan
ape
riodfrom
2001
until
2014
.Stan
dard
errors
are
heterosked
astic
ity-(
White
(1980))an
dau
tocorrelation-robu
st(N
ewey
andWest(1987)
andNew
eyan
dWest(1994)).
−.2−.10.1.2.3Coefficient
AustriaBelgium
BrazilCanada
DenmarkFinlandFrance
GermanyGreece
Hong KongHungary
IndiaIndonesia
IsraelItaly
JapanMalaysia
MexicoNetherlands
New ZealandNorwayPoland
PortugalRussia
Saudi ArabiaSingapore
SpainSweden
SwitzerlandThailand
United KingdomUnited States
Cou
ntry
(a)Hou
seho
ldCredit
−.4−.20.2.4Coefficient
AustriaBelgium
BrazilCanada
DenmarkFinlandFrance
GermanyGreece
Hong KongHungary
IndiaIndonesia
IsraelItaly
JapanMalaysia
MexicoNetherlands
New ZealandNorwayPoland
PortugalRussia
Saudi ArabiaSingapore
SpainSweden
SwitzerlandThailand
United KingdomUnited States
Cou
ntry
(b)Corpo
rate
Credit
−60−40−20020Coefficient
AustriaBelgium
BrazilCanada
DenmarkFinlandFrance
GermanyGreece
Hong KongHungary
IndiaIndonesia
IsraelItaly
JapanMalaysia
MexicoNetherlands
New ZealandNorwayPoland
PortugalRussia
Saudi ArabiaSingapore
SpainSweden
SwitzerlandThailand
United KingdomUnited States
Cou
ntry
(c)Globa
lImba
lances
(Total)
53
Figure 8: Adjusted Leverage, Future Consumption (Non-Durables, Durables), and Future Pri-vate Investments (U.S. Economy). This figure summarizes the predictive power of global AdjustedLeverage on (a) future logarithmic changes of non-durables consumption (log(Cndt+q/Cndt )), (b) future logarith-mic changes of durables consumption (log(Cdt+q/Cdt )), and (c) future private investment (log(INVt+q/INVt))for the U.S. economy. The regression specification is: log(Xt+q/Xt) = αt+q + βAdj.Levt + εt+q whereXt = (Cndt , Cdt , INVt). The data are quarterly and span a period from 2001-Q1 until 2014-Q1. Standarderrors are heteroskedasticity- (White (1980)) and autocorrelation-robust (Newey and West (1987) and Neweyand West (1994)).
−.1
0.1
.2.3
Coe
ffici
ent
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Quarters from time t (k)
(a) Non-Durables (Coefficient)
0.0
5.1
.15
R−
Squ
ared
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Quarters from time t (k)
(b) Non-Durables (R-Squared)
−.2
0.2
.4.6
Coe
ffici
ent
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Quarters from time t (k)
(c) Durables (Coefficient)
0.0
2.0
4.0
6.0
8R
−S
quar
ed
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Quarters from time t (k)
(d) Durables (R-Squared)
−.2
0.2
.4.6
.8C
oeffi
cien
t
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Quarters from time t (k)
(e) Investments (Coefficient)
0.0
5.1
.15
R−
Squ
ared
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Quarters from time t (k)
(f) Investments (R-Squared)54
Figure 9: Realized vs. Predicted Mean Returns. This figure summarizes the realized averageannualized returns of 25 value-weighted Fama-French global equity portfolios sorted on size and book-to-marketagainst the average returns predicted by four linear pricing models (Adjusted Leverage, Global Market,Global Fama-French Factors, and Global Fama-French Factors & Momentum) with an intercept. Thedata are quarterly and span a period from 2001-Q1 until 2014-Q1. All returns are annualized.
−0.04 −0.02 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22 0.24−0.04
−0.02
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.22
0.24
S1B1
S1B2
S1B3S1B4
S1B5
S2B1
S2B2 S2B3
S2B4
S2B5
S3B1
S3B2
S3B3S3B4
S3B5
S4B1
S4B2S4B3 S4B4S4B5
S5B1
S5B2S5B3S5B4
S5B5
Predicted Expected Return
Rea
lized
Mea
n R
etur
n
(a) Adjusted Leverage
−0.04 −0.02 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22 0.24−0.04
−0.02
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.22
0.24
S1B1
S1B2
S1B3S1B4
S1B5
S2B1
S2B2 S2B3
S2B4
S2B5
S3B1
S3B2
S3B3S3B4
S3B5
S4B1
S4B2S4B3 S4B4S4B5
S5B1
S5B2S5B3S5B4
S5B5
Predicted Expected Return
Rea
lized
Mea
n R
etur
n
(b) Global Market
−0.04 −0.02 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22 0.24−0.04
−0.02
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.22
0.24
S1B1
S1B2
S1B3S1B4
S1B5
S2B1
S2B2 S2B3
S2B4
S2B5
S3B1
S3B2
S3B3S3B4
S3B5
S4B1
S4B2S4B3 S4B4S4B5
S5B1
S5B2S5B3S5B4
S5B5
Predicted Expected Return
Rea
lized
Mea
n R
etur
n
(c) Global Fama-French Factors
−0.04 −0.02 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22 0.24−0.04
−0.02
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.22
0.24
S1B1
S1B2
S1B3S1B4
S1B5
S2B1
S2B2 S2B3
S2B4
S2B5
S3B1
S3B2
S3B3S3B4
S3B5
S4B1
S4B2S4B3S4B4S4B5
S5B1
S5B2S5B3S5B4
S5B5
Predicted Expected Return
Rea
lized
Mea
n R
etur
n
(d) Global Fama-French Factors & Momentum
55
Figure 10: Realized vs. Predicted Mean Returns. This figure summarizes the realized averageannualized returns of 25 value-weighted Fama-French global equity portfolios sorted on size and momentumagainst the average returns predicted by four linear pricing models (Adjusted Leverage, Global Market,Global Fama-French Factors, and Global Fama-French Factors & Momentum) with an intercept. Thedata are quarterly and span a period from 2001-Q1 until 2014-Q1. All returns are annualized.
−0.04 −0.02 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22 0.24−0.04
−0.02
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.22
0.24
S1M1
S1M2
S1M3
S1M4
S1M5
S2M1
S2M2S2M3
S2M4
S2M5
S3M1S3M2
S3M3S3M4
S3M5
S4M1
S4M2
S4M3S4M4
S4M5
S5M1
S5M2S5M3
S5M4S5M5
Predicted Expected Return
Rea
lized
Mea
n R
etur
n
(a) Adjusted Leverage
−0.04 −0.02 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22 0.24−0.04
−0.02
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.22
0.24
S1M1
S1M2
S1M3
S1M4
S1M5
S2M1
S2M2S2M3
S2M4
S2M5
S3M1S3M2
S3M3S3M4
S3M5
S4M1
S4M2
S4M3S4M4
S4M5
S5M1
S5M2S5M3
S5M4S5M5
Predicted Expected Return
Rea
lized
Mea
n R
etur
n
(b) Global Market
−0.04 −0.02 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22 0.24−0.04
−0.02
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.22
0.24
S1M1
S1M2
S1M3
S1M4
S1M5
S2M1
S2M2S2M3
S2M4
S2M5
S3M1S3M2
S3M3S3M4
S3M5
S4M1
S4M2
S4M3S4M4
S4M5
S5M1
S5M2S5M3
S5M4S5M5
Predicted Expected Return
Rea
lized
Mea
n R
etur
n
(c) Global Fama-French Factors
−0.04 −0.02 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22 0.24−0.04
−0.02
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.22
0.24
S1M1
S1M2
S1M3
S1M4
S1M5
S2M1
S2M2S2M3
S2M4
S2M5
S3M1S3M2
S3M3S3M4
S3M5
S4M1
S4M2
S4M3S4M4
S4M5
S5M1
S5M2S5M3
S5M4S5M5
Predicted Expected Return
Rea
lized
Mea
n R
etur
n
(d) Global Fama-French Factors & Momentum
56
Figure 11: Realized vs. Predicted Mean Returns. This figure summarizes the realized averageannualized returns of 6 carry trade portfolios, 6 currency momentum portfolios (short-term), 6 currencymomentum portfolios (long-term), and 6 currency value portfolios against the average returns predictedby four linear pricing models (Adjusted Leverage, Carry, Global V olatility, and Momentum) with anintercept. The data are quarterly and span a period from 2001-Q1 until 2014-Q1. All returns are annualized.
−0.1 −0.08 −0.06 −0.04 −0.02 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18−0.1
−0.08
−0.06
−0.04
−0.02
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
CT1CT2
CT3
CT4CT5
CT6
MOM1MOM2
MOM3
MOM4
MOM5
MOM6
LT MOM1
LT MOM2
LT MOM3
LT MOM4
LT MOM5
LT MOM6
VAL1
VAL2
VAL3
VAL4
VAL5
VAL6
Predicted Expected Return
Rea
lized
Mea
n R
etur
n
(a) Adjusted Leverage
−0.1 −0.08 −0.06 −0.04 −0.02 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18−0.1
−0.08
−0.06
−0.04
−0.02
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
CT1CT2
CT3
CT4CT5
CT6
MOM1MOM2
MOM3
MOM4
MOM5
MOM6
LT MOM1
LT MOM2
LT MOM3
LT MOM4
LT MOM5
LT MOM6
VAL1
VAL2
VAL3
VAL4
VAL5
VAL6
Predicted Expected Return
Rea
lized
Mea
n R
etur
n
(b) Carry
−0.1 −0.08 −0.06 −0.04 −0.02 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18−0.1
−0.08
−0.06
−0.04
−0.02
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
CT1 CT2
CT3
CT4CT5
CT6
MOM1MOM2
MOM3
MOM4
MOM5
MOM6
LT MOM1
LT MOM2
LT MOM3
LT MOM4
LT MOM5
LT MOM6
VAL1
VAL2
VAL3
VAL4
VAL5
VAL6
Predicted Expected Return
Rea
lized
Mea
n R
etur
n
(c) Global Volatility
−0.1 −0.08 −0.06 −0.04 −0.02 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18−0.1
−0.08
−0.06
−0.04
−0.02
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
CT1CT2
CT3
CT4CT5
CT6
MOM1MOM2
MOM3
MOM4
MOM5
MOM6
LT MOM1
LT MOM2
LT MOM3
LT MOM4
LT MOM5
LT MOM6
VAL1
VAL2
VAL3
VAL4
VAL5
VAL6
Predicted Expected Return
Rea
lized
Mea
n R
etur
n
(d) Momentum
57
Figure 12: Time-Series Regressions - Exposure to Adjusted Leverage (International Assets).This figure summarizes the beta exposure of international asset portfolios (Currencies, 25 Global SBM, and25 Global SMOM) on the global adjusted leverage factor. Currency portfolios comprise six carry portfoliosranked on forward discounts (CAR# 1 through 6), six short-term momentum portfolios ranked on past1-month excess currency returns (MOM# 1 through 6), six long-term momentum portfolios ranked on past12-month excess currency returns (MOM_LT# 1 through 6), and six value portfolios ranked on lagged 5-yearexcess currency returns (VAL# 1 though 6). Global equity portfolios comprise twenty-five equity portfoliosdouble-sorted on size (S# 1 through 5) and value (BM# 1 through 5) and twenty-five global equity portfoliosdouble-sorted on size (S# 1 through 5) and momentum (MOM# 1 through 5). The data are quarterlyand span a period from 2001-Q1 until 2014-Q1. Standard errors are heteroskedasticity- (White (1980)) andautocorrelation-robust (Newey and West (1987) and Newey and West (1994)).
−.1
5−
.1−
.05
0.0
5.1
Coe
ffici
ent
CA
R1
CA
R2
CA
R3
CA
R4
CA
R5
CA
R6
MO
M1
MO
M2
MO
M3
MO
M4
MO
M5
MO
M6
MO
M_L
T1
MO
M_L
T2
MO
M_L
T3
MO
M_L
T4
MO
M_L
T5
MO
M_L
T6
VA
L1
VA
L2
VA
L3
VA
L4
VA
L5
VA
L6
Country
(a) Currencies
−.3
−.2
−.1
0.1
Coe
ffici
ent
S1B
M1
S1B
M2
S1B
M3
S1B
M4
S1B
M5
S2B
M1
S2B
M2
S2B
M3
S2B
M4
S2B
M5
S3B
M1
S3B
M2
S3B
M3
S3B
M4
S3B
M5
S4B
M1
S4B
M2
S4B
M3
S4B
M4
S4B
M5
S5B
M1
S5B
M2
S5B
M3
S5B
M4
S5B
M5
Portfolio
(b) 25 Global SBM
−.3
−.2
−.1
0.1
Coe
ffici
ent
S1M
OM
1S
1MO
M2
S1M
OM
3S
1MO
M4
S1M
OM
5S
2MO
M1
S2M
OM
2S
2MO
M3
S2M
OM
4S
2MO
M5
S3M
OM
1S
3MO
M2
S3M
OM
3S
3MO
M4
S3M
OM
5S
4MO
M1
S4M
OM
2S
4MO
M3
S4M
OM
4S
4MO
M5
S5M
OM
1S
5MO
M2
S5M
OM
3S
5MO
M4
S5M
OM
5
Portfolio
(c) 25 Global SMOM
58
Figure 13: Global Adjusted Leverage vs. Factor-Mimicking Portfolio. This figure summarizes thetime-series evolution of Global Adjusted Leverage factor versus its Factor-Mimicking Portfolio. The mimickingportfolio is computed as Adjusted Leverage FMPt = b̂′(CAR, V AL,Mkt,HML,SMB,MOM)t, whereb̂ = (−0.29,−0.33,−0.19, 1.23, 0.59,−0.01) and the tradable portfolios are the carry portfolio, the currencyvalue portfolio, the global equities market, high-minus-low book-to-market, the small-minus-big size, andmomentum portfolio respectively. The data are quarterly and span a period from 2001-Q1 until 2014-Q1, butreturns are annualized.
−.1
0.1
.2.3
Adj
uste
d Le
vera
ge
−.2
0.2
.4F
acto
r−M
imic
king
Por
tfolio
2000−Q1 2005−Q1 2010−Q1 2015−Q1Date
Global Adjusted Leverage Factor−Mimicking Portfolio
59
Figure 14: Beta Sorted Portfolios - Market and Financials Returns. The figures summarize averagereturns of portfolios formed on the basis of the exposure of market-cap weighted market and financialsportfolios on the factor-mimicking portfolio of the adjusted leverage factor. The country-level portfoliosare sorted with respect to their beta exposure and three bins are formed. The figures also report the betaloadings and a 95% confidence interval. The data are monthly from 1991-Q1 until 2014-Q1. All returns areannualized.
−.6
−.5
−.4
−.3
−.2
−.1
Bet
as
−.05
0
.05
.1
.15
.2
Ret
urns
1 2 3Beta Bins (1−3)
Average Returns High End/Low End
Average Betas
(a) Returns - Market
−.05
0
.05
.1
Ret
urns
2−1 3−1Beta Spreads (Q−1)
Average Returns High End/Low End
(b) Spread - Market
−.4
−.3
−.2
−.1
0.1
Bet
as
0
.1
.2
.3
Ret
urns
1 2 3Beta Bins (1−3)
Average Returns High End/Low End
Average Betas
(c) Returns - Financials
.05
.1
.15
.2
Ret
urns
2−1 3−1Beta Spreads (Q−1)
Average Returns High End/Low End
(d) Spread - Financials
60
Figure 15: Ex-U.S. Adjusted Leverage vs. U.S. Adjusted Leverage. This figure summarizes thetime-series evolution of the Global Adjusted Leverage excluding the U.S. financial system versus the AdjustedLeverage series of the U.S.. The data are quarterly and span a period from 2001-Q1 until 2014-Q1.
−.2
−.1
0.1
.2U
S A
djus
ted
Leve
rage
−.6
−.4
−.2
0.2
.4E
x−U
S A
djus
ted
Leve
rage
2000−Q1 2005−Q1 2010−Q1 2015−Q1Date
Ex−US Adjusted Leverage US Adjusted Leverage
61
C Tables
Tab
le1:
Tim
elineof
theecon
omy.
The
tablesummarizes
thetim
elineof
thede
cisio
nsmad
eby
thethreeagents
ofthe
econ
omy(hou
seho
lds,
bank
s,an
dfirms).It
describ
esthede
cisio
nmak
ingprocessthat
takesplacein
perio
d1an
d2.
Period1
Period2
Hou
seho
ldan
dba
nkha
veform
edbe
liefs
regard-
ingthequ
ality
ofcolla
teral(p)an
deffi
cien
cyof
prod
uctio
n(q)
Firm
prod
uces
usingnu
meraire
(Kb)
Hou
seho
ldis
endo
wedwith
numeraire
(K)enou
gh
tosustainprod
uctio
n
Firm
repa
ysloan
toba
nk
Firm
appliesforaloan
from
theba
nkBan
kreceives
profi
tsfrom
firm
ownership(π
2)
Hou
seho
ldan
dba
nkde
cide
(sim
ultane
ously
)on
whe
ther
toprod
uceinform
ationat
acostγhan
d
γb,a
ndon
thelevelo
fdep
osit(K
h)an
dloan
(Kb)
Ban
krepa
ysloan
toho
useh
old
Firm
prod
uces
usingendo
wmentnu
meraire
(K1)
andba
nkreceives
proceeds
(π1)
Ban
kcolle
ctsland
output
(pC)
Ban
k,ho
useh
oldconsum
eforpe
riod1(cb,1,ch,1)
Ban
k,ho
useh
oldconsum
eforpe
riod2(cb,2,ch,2)
62
Table 2: Credit-to-Private Sector and Financial Leverage Data - Countries. The table summarizesthe countries for which data is available on credit-to-private sector and broker-dealers’ financial leverage.Data are quarterly from WorldScope and the World Development Indicators database; the start date is statedon the table, and the end date is Mar-2014.
Country Year Quarter Country Year Quarter1 Austria 2001 1 29 Malaysia 2005 42 Belgium 2001 4 30 Mexico 2001 13 Brazil 2004 3 31 Netherlands 2001 44 Bulgaria 2007 1 32 New Zealand 2005 15 Canada 1999 1 33 Norway 2001 16 Chile 2004 3 34 Oman 2004 37 Colombia 2004 3 35 Pakistan 2004 38 Croatia 2007 1 36 Peru 2004 39 Cyprus 2005 1 37 Philippines 2001 110 Czech Republic 2001 4 38 Poland 2002 411 Denmark 2001 1 39 Portugal 2001 112 Finland 2001 1 40 Qatar 2005 113 France 2002 1 41 Romania 2009 214 Germany 2001 1 42 Russian Federation 2005 115 Greece 2001 4 43 Saudi Arabia 2003 116 Hong Kong SAR, China 2001 4 44 Singapore 2002 217 Hungary 2002 4 45 Slovak Republic 2009 118 Iceland 2004 3 46 Slovenia 2009 119 India 2001 4 47 Spain 2001 120 Indonesia 2007 3 48 Sweden 2001 121 Israel 2004 3 49 Switzerland 2001 222 Italy 2001 1 50 Thailand 2001 123 Japan 2001 4 51 Ukraine 2006 124 Jordan 2004 3 52 United Arab Emirates 2003 225 Kazakhstan 2005 1 53 United Kingdom 2001 126 Kenya 2005 1 54 United States 1998 127 Korea (South) 2002 3 55 Venezuela 2004 328 Kuwait 2003 1
Table 3: Summary Statistics. The table summarizes descriptive statistics for the variables used in thepaper. The data are quarterly from 2001-Q1 until 2014-Q1.
Count Mean St.Dev Min MaxrGDP (in bn.) 568 1023.849 2293.663 11.408 16800INV (% of rGDP ) 551 22.808 4.850 13.008 46.811TFP 166 623.416 113.213 260.759 823.585Credit to Priv.(% of rGDP ) 573 87.873 53.368 15.499 241.044Credit to Corp.(% of rGDP ) 1435 80.318 35.197 11.800 211.600Credit to Hhld.(% of rGDP ) 1435 56.259 30.487 4.200 140.100Global Imbalances 297 -7.337 63.824 -127.637 252.845∆ rGDP 345 0.078 0.101 -0.264 0.329∆ INV 340 -0.003 0.081 -0.308 0.317∆ TFP 166 -0.002 0.026 -0.098 0.113∆Credit to Priv. 1334 0.006 0.028 -0.132 0.173∆Credit to Hhld. 1334 0.010 0.022 -0.097 0.167Financial Assets (in bn.) 2257 834.171 1589.500 0.040 8292.429Financial Leverage 2257 14.897 8.771 1.128 44.735Adjusted Leverage 2168 -0.003 0.229 -2.275 2.237Global Adjusted Leverage 64 0.010 0.136 -0.373 0.434Global F inancial Leverage Innovations 64 0 0.136 -0.434 0.345Currency Returns (Quarterly) 2257 0.422 4.639 -69.316 41.569Intermediaries′ Returns (Quarterly) 1459 0.340 0.735 -1.292 2.954
63
Table 4: Financial Leverage and Financial Intermediaries’ Future Assets Across CreditRegimes. The table summarizes the relation between future asset levels of financial intermediaries andfinancial leverage across different credit regimes: (i) a high credit regime defined as instances wherecredit-to-private sector of a given country is higher than the 75th percentile of the cross-section creditvalues, and (ii) a low credit regime defined as instances where credit-to-private sector of a given coun-try is lower than the 25th percentile of the cross-section credit values. The regression specification is:assetsn,t+q = αn+αt+q+β′Xn,t+γassetsn,t+εn,t+q, whereXn,t = (fin.leverage, fin.leverage×1(Creditt >75%), fin.leverage × 1(Creditt < 25%))′. Lowercase variables are log variables. Data are quarterly fromDataStream, WorldScope, and the World Development Indicators database, and span a period from 2001until 2014. Robust t-statistics adjusted for country-level clustering are reported in parentheses.
(1) (2) (3) (4) (5) (6) (7) (8)att+1 att+1 att+2 att+2 att+3 att+3 att+4 att+4
fin.leveraget -0.056 -0.103 0.089 0.045 0.135 0.062 0.297 0.247(-0.29) (-0.63) (0.47) (0.28) (0.51) (0.28) (1.23) (1.12)
total assetst 0.650∗∗∗ 0.659∗∗∗ 0.613∗∗∗ 0.634∗∗∗ 0.481∗∗∗ 0.499∗∗∗ 0.586∗∗∗ 0.601∗∗∗(5.13) (4.99) (6.55) (5.88) (3.99) (3.63) (5.20) (5.26)
fin.leveraget × 1(Creditt < 25%) -0.092∗ -0.104∗ -0.123∗ -0.080+
(-2.14) (-2.11) (-2.43) (-1.98)
fin.leveraget × 1(Creditt > 75%) 0.146+ 0.148∗ 0.207∗ 0.138∗(1.80) (2.14) (2.14) (2.01)
N 2148 2148 2074 2074 2008 2008 1946 1946R2 0.92 0.92 0.93 0.93 0.92 0.92 0.94 0.94FE (country) YES YES YES YES YES YES YES YESFE (quarter) YES YES YES YES YES YES YES YESt-statistics in parentheses+ p < 0.10, ∗ p < 0.05, ∗∗ p < 0.01, ∗∗∗ p < 0.001
Table 5: Financial Leverage and Financial Intermediaries’ Future Returns. The table summarizesthe relation between future stock returns of financial intermediaries and financial leverage across differentcredit regimes: (i) a high credit regime defined as instances where credit-to-private sector of a given countryis higher than the 75th percentile of the cross-section credit values, and (ii) a low credit regime definedas instances where credit-to-private sector of a given country is lower than the 25th percentile of thecross-section credit values. The regression specification is: rfinn,t+q = αn + αt + β′Xn,t + γrfinn,t + εn,t+q,where Xn,t = (fin.leverage, fin.leverage× 1(Creditn,t > 75%), fin.leverage× 1(Creditn,t < 25%))′. Stockreturns are the average total holding period returns per country. Data are quarterly from DataStream,WorldScope, and the World Development Indicators database, and span a period from 2001 until 2014.Robust t-statistics adjusted for time- and country-level clustering are reported in parentheses.
(1) (2) (3) (4) (5) (6) (7) (8)rfin
t+1 rfint+1 rfin
t+2 rfint+2 rfin
t+3 rfint+3 rfin
t+4 rfint+4
fin.leveraget 0.003 0.003 0.006 0.005 0.010+ 0.011+ 0.010+ 0.009(0.85) (0.59) (1.30) (0.95) (1.91) (1.80) (1.91) (1.23)
rfint 0.123+ 0.123+ 0.124∗∗ 0.121∗∗ -0.006 -0.010 -0.006 0.052
(1.89) (1.89) (2.89) (2.75) (-0.13) (-0.23) (-0.13) (1.30)
fin.leveraget × 1(Creditt < 25%) 0.001 0.016∗∗ 0.022∗ 0.019+
(0.07) (3.08) (2.25) (1.69)
fin.leveraget × 1(Creditt > 75%) 0.001 -0.000 -0.004 -0.005(0.14) (-0.03) (-0.66) (-0.84)
N 1371 1371 1327 1327 1286 1286 1286 1247R2 0.49 0.49 0.49 0.49 0.49 0.50 0.49 0.50FE (country) YES YES YES YES YES YES YES YESFE (quarter) YES YES YES YES YES YES YES YESt-statistics in parentheses+ p < 0.10, ∗ p < 0.05, ∗∗ p < 0.01, ∗∗∗ p < 0.001
64
Table 6: Adjusted Leverage and Macroeconomic Activity (U.S. Economy, Broker-Dealers). Thetable summarizes the explanatory power of global Adjusted Leverage (Adj.Lev) and leverage innovations(Lev.Inn) on logarithmic changes in household credit (HH.Cr), corporate credit (Corp.Cr), instances offinancial crises (Crisis), logarithmic changes in real GDP (rGDP ), capital formation (INV ), credit spread(Cr.Sprd), and total factor productivity (TFP ). The regression specification is: Economic V ariablen,t =αn + αt + βAdj.Levn,t + γLev.Innn,t + εn,t, where Economic V ariablen,t = (HH.Crn,t, Corp.Crn,t,rGDP , INV , Cr.Sprdn,t, TFPn,t), and Pr(Crisisn,t = 1|Xn,t) = 1/(1 + e−(αn+β′Xn,t)), where Xn,t =(Adj.Levn,t, Lev.Innn,t). Data are quarterly from WorldScope, World Development Indicators, and Valenciaand Laeven (2012) and span a period from 2001 until 2014. Standard errors are heteroskedasticity- (White(1980)) and autocorrelation-robust (Newey and West (1987) and Newey and West (1994)).
(1) (2) (3) (4) (5) (6) (7)HH.Cr Corp.Cr Crisis rGDP INV Cr.Sprd TFP
Adj.Levt 0.033∗∗∗ -0.001 -23.271∗ 0.118∗∗ 0.467∗ -1.185∗ 0.188∗∗(6.06) (-0.12) (-2.11) (3.43) (2.63) (-2.58) (4.73)
Lev.Innt 0.062∗∗∗ 0.021 -8.188 0.167∗∗∗ 0.101 0.402 0.057(5.28) (1.05) (-0.78) (4.65) (0.94) (0.67) (1.10)
N 53 53 40 13 12 39 10R2 0.28 0.05 0.51 0.44 0.06 0.61t-statistics in parentheses+ p < 0.10, ∗ p < 0.05, ∗∗ p < 0.01, ∗∗∗ p < 0.001
Table 7: Adjusted Leverage and Financial Crises. The table summarizes the predictive powerof country level Adjusted Leverage on Financial Crises. The regression specification is: (A) a lin-ear probability model (columns (1) and (2)): 1(Crisisn,t) = αn + β′Xn,t + εn,t, and (B) a logitmodel (columns (3) and (4)): Pr(Crisisn,t = 1|Xn,t) = 1/(1 + e−(αn+β′Xn,t)), where Xn,t =(Adj.Levn,t, Adj.Levn,t−1, Adj.Levn,t−2, Creditn,t, Creditn,t−1, Creditn,t−2). Data are from WorldScope,World Development Indicators, and Valencia and Laeven (2012) and span a period from 2001 until 2014.
(1) (2) (3) (4)LPM LPM LOGIT LOGIT
Adj.Levt 0.012 0.009 0.042 -3.605(0.07) (0.07) (0.05) (-0.99)
Adj.Levt−1 0.006 0.068 -0.041 -4.408(0.05) (1.04) (-0.05) (-0.83)
Adj.Levt−2 -0.189∗ -0.113+ -1.231 -10.664+
(-2.02) (-1.76) (-1.37) (-1.74)
Creditt -0.005 -0.002 -0.025 0.329(-0.66) (-0.30) (-0.63) (0.97)
Creditt−1 0.009 0.007 0.043 0.356(0.72) (1.19) (0.72) (1.37)
Creditt−2 -0.001 0.017∗∗∗ -0.003 0.723+
(-0.14) (4.73) (-0.09) (1.86)
N 113 113 113 78R2 0.13 0.60FE (country) NO YES NO YESt-statistics in parentheses+ p < 0.10, ∗ p < 0.05, ∗∗ p < 0.01, ∗∗∗ p < 0.001
65
Table 8: Cross-Sectional Asset Pricing Tests (25 Fama-French Global Size and Book-to-MarketPortfolios). The table shows the price of risk (λ) and asset pricing tests estimated for 25 value-weightedFama-French global equity portfolios sorted on size and book-to-market using the cross-sectional regressionE [Re] = λ0 + β′λ. Adjusted Leverage is a proxy for the risk bearing capacity of the global financial system,Market is the global market factor, SMB is the global small-minus-big factor, HML is the global high-minus-lowfactor, and Momentum is a global momentum factor, from Kenneth French’s database. Panel A summarizesthe prices of risk along with their Shanken (1992) and Fama and MacBeth (1973) t-statistics. Panel Bshows the results of a number of additional tests including mean absolute pricing errors (MAPE), adjustedR2 values with confidence intervals (Lewellen et al. (2010)), χ2 statistic tests of jointly zero pricing errors.Panel C reports the percentage of times that randomly generated factors produce adjusted R2 values andalphas (α) higher and lower respectively compared to the models considered in the analysis. The data arequarterly and span a period from 2001-Q1 until 2014-Q1. All returns and risk premia are annualized.
PANEL A: Estimates and t-Statistics of Risk PremiaLev.Adj Lev.Adj,Mkt Mkt FF FF,MOM
Intercept 0.11 0.15 0.20 0.18 -0.03t-FM 1.86 2.68 3.28 3.87 -0.51t-Shanken 1.54 2.22 3.20 3.53 -0.38Adj.Lev 0.28 0.27t-FM 2.89 2.85t-Shanken 2.52 2.49Mkt -0.08 -0.11 -0.11 0.10t-FM -1.01 -1.32 -1.60 1.18t-Shanken -0.90 -1.30 -1.53 0.98SMB 0.03 0.03t-FM 1.71 1.61t-Shanken 1.71 1.59HML 0.05 0.05t-FM 2.14 2.26t-Shanken 2.14 2.24MOM 0.23t-FM 3.00t-Shanken 2.42
PANEL B: Cross-Sectional R2s and Specification TestsMAPE 0.01 0.01 0.02 0.01 0.01MAX 0.03 0.03 0.07 0.04 0.03TOTAL 0.12 0.16 0.22 0.19 -0.02Adj.R2 0.71 0.72 0.09 0.73 0.82C.I.Adj.R2 [ 0.66 , 0.92 ] [ 0.72 , 1 ] [ 0 , 0.66 ] [ 0.79 , 1 ] [ 1 , 1 ]χ2N−K 6.83 31.36 39.79 36.12 20.31
p-value 1.00 0.09 0.02 0.02 0.44PANEL C: Test Against Random Factor
Adj.R2 0.01 0.01 0.55 0.01 0.00MAPE 0.02 0.01 0.53 0.00 0.00Adj.R2, α 0.01 0.01 0.53 0.01 0.00
66
Table 9: Cross-Sectional Asset Pricing Tests (25 Fama-French Global Size and MomentumPortfolios). The table shows the price of risk (λ) and asset pricing tests estimated for 25 value-weightedFama-French global equity portfolios sorted on size and momentum using the cross-sectional regressionE [Re] = λ0 + β′λ. Adjusted Leverage is a proxy for the risk bearing capacity of the global financial system,Market is the global market factor, SMB is the global small-minus-big factor, HML is the global high-minus-lowfactor, and Momentum is a global momentum factor, from Kenneth French’s database. Panel A summarizesthe prices of risk along with their Shanken (1992) and Fama and MacBeth (1973) t-statistics. Panel Bshows the results of a number of additional tests including mean absolute pricing errors (MAPE), adjustedR2 values with confidence intervals (Lewellen et al. (2010)), χ2 statistic tests of jointly zero pricing errors.Panel C reports the percentage of times that randomly generated factors produce adjusted R2 values andalphas (α) higher and lower respectively compared to the models considered in the analysis. The data arequarterly and span a period from 2001-Q1 until 2014-Q1. All returns and risk premia are annualized.
PANEL A: Estimates and t-Statistics of Risk PremiaLev.Adj Lev.Adj,Mkt Mkt FF FF,MOM
Intercept 0.12 0.14 0.18 0.19 0.05t-FM 2.23 1.91 2.50 2.32 1.08t-Shanken 1.61 1.40 2.47 2.08 0.96Adj.Lev 0.39 0.37t-FM 2.84 3.54t-Shanken 2.13 2.77Mkt -0.07 -0.08 -0.12 0.01t-FM -0.77 -0.86 -1.28 0.22t-Shanken -0.62 -0.86 -1.18 0.21SMB 0.04 0.05t-FM 2.14 2.58t-Shanken 2.10 2.54HML 0.04 0.06t-FM 1.05 1.41t-Shanken 0.98 1.30MOM 0.05t-FM 1.23t-Shanken 1.22
PANEL B: Cross-Sectional R2s and Specification TestsMAPE 0.01 0.01 0.02 0.02 0.01MAX 0.04 0.04 0.09 0.06 0.04TOTAL 0.14 0.15 0.20 0.21 0.06Adj.R2 0.75 0.75 0.18 0.62 0.81C.I.Adj.R2 [ 0.71 , 0.93 ] [ 0.79 , 1 ] [ 0 , 0.72 ] [ 0.56 , 1 ] [ 0.98 , 1 ]χ2N−K 1.88 12.71 34.14 33.71 26.43
p-value 1.00 0.94 0.06 0.04 0.15PANEL C: Test Against Random Factor
Adj.R2 0.01 0.01 0.45 0.04 0.00MAPE 0.01 0.01 0.33 0.03 0.00Adj.R2, α 0.01 0.01 0.42 0.04 0.00
67
Table 10: Cross-Sectional Asset Pricing Tests (Currency Portfolios). The table shows the priceof risk (λ) and asset pricing tests estimated for 6 carry trade portfolios, 6 currency momentum portfolios(short-term), 6 currency momentum portfolios (long-term), and 6 currency value portfolios using the cross-sectional regression E [Re] = λ0 +β′λ. Adjusted Leverage is a proxy for the risk bearing capacity of the globalfinancial system, Carry is the carry trade portfolio, Volatility is the global 1/V ol measure, and Momentum is along/short portfolio on currency momentum. Panel A summarizes the prices of risk along with their Shanken(1992) and Fama and MacBeth (1973) t-statistics. Panel B shows the results of a number of additionaltests including mean absolute pricing errors (MAPE), adjusted R2 values with confidence intervals (Lewellenet al. (2010)), χ2 statistic tests of jointly zero pricing errors. Panel C reports the percentage of timesthat randomly generated factors produce adjusted R2 values and alphas (α) higher and lower respectivelycompared to the models considered in the analysis. The data are quarterly and span a period from 2001-Q1until 2014-Q1. All returns and risk premia are annualized.
PANEL A: Estimates and t-Statistics of Risk PremiaLev.Adj Lev.Adj,CAR CAR VOL MOM
Intercept 0.11 0.10 0.00 0.08 0.02t-FM 5.53 5.44 0.17 4.43 1.17t-Shanken 1.29 1.30 0.16 2.69 0.87LEV.Adj 1.66 1.61t-FM 8.11 7.46t-Shanken 1.95 1.84CAR 0.11 0.09t-FM 4.08 3.31t-Shanken 2.03 3.24VOL 0.31t-FM 4.28t-Shanken 2.77MOM 0.19t-FM 5.75t-Shanken 5.22
PANEL B: Cross-Sectional R2s and Specification TestsMAPE 0.03 0.03 0.04 0.04 0.03MAX 0.09 0.09 0.13 0.13 0.08TOTAL 0.14 0.13 0.04 0.12 0.05Adj.R2 0.53 0.52 0.05 0.20 0.47C.I.Adj.R2 [ 0.43 , 0.86 ] [ 0.41 , 1 ] [ 0.03 , 0.63 ] [ 0.01 , 0.72 ] [ 0.36 , 0.84 ]χ2N−K 6.24 9.56 101.82 55.74 34.85
p-value 1.00 0.98 0.00 0.00 0.04PANEL C: Test Against Random Factor
Adj.R2 0.12 0.12 0.65 0.43 0.16MAPE 0.17 0.16 0.46 0.45 0.15Adj.R2, α 0.11 0.11 0.17 0.37 0.07
68
Tab
le11
:Cross-Section
alAsset
Pricing
Tests
(Portfoliosof
Internationa
lAssets)
-Fa
ctor-M
imicking
Portfolio.The
tableshow
sthe
priceof
risk(λ)an
dassetpricingtestsestim
ated
forinternationa
lportfolios(SizeandBook-to-Market,S
izeandMom
entum,a
ndCurrencies)
usingthecross-sectiona
lregressionE
[Re]=
λ0
+β′ λ.AdjustedLe
verage
isthefactor-m
imicking
portfolio
oftheglob
alad
justed
leverage
factor,
Marketis
theglob
almarketfactor,S
MB
istheglob
alsm
all-m
inus-big
factor,H
MLis
theglob
alhigh
-minus-lo
wfactor,a
ndMom
entum
isaglob
almom
entum
factor,from
Ken
neth
Fren
ch’s
databa
se.Pan
elA
summarizes
theprices
ofris
kalon
gwith
theirSh
anken(199
2)an
dFa
maan
dMacBeth
(197
3)t-statist
ics.Pan
elB
show
stheresults
ofanu
mbe
rof
additio
naltests
includ
ingmeanab
solute
pricingerrors
(MAPE
),ad
justed
R2values
with
confi
denc
eintervals(L
ewellenet
al.(20
10)),χ
2statist
ictestsof
jointly
zero
pricingerrors.Pan
elC
repo
rtsthepe
rcentage
oftim
esthat
rand
omly
gene
ratedfactorsprod
ucead
justed
R2values
andalph
as(α
)high
eran
dlower
respectiv
elycompa
redto
themod
elsconsidered
inthean
alysis.
The
data
arequ
arterly
,Tab
le11aspan
sape
riodfrom
1991-Q
1un
til2014-Q
1,an
dTa
ble11bspan
sape
riodfrom
2001-Q
1un
til20
14-Q
1.Allreturnsan
dris
kprem
iaarean
nualized
. (a)1991Q1-2014Q1
PANEL
A:E
stim
ates
andt-Statist
icsof
Risk
Prem
iaSM
BSM
OM
CUR
Intercep
t0.09
0.08
0.01
t-FM
2.49
1.97
0.55
t-Shanken
2.43
1.97
0.19
Adj.Lev
0.07
-0.04
0.78
t-FM
2.20
-0.77
9.77
t-Shanken
2.19
-0.77
3.72
PANEL
B:C
ross-Sectio
nalR
2 san
dSp
ecificatio
nTe
sts
MAPE
0.01
0.03
0.02
MAX
0.04
0.11
0.06
TOTA
L0.10
0.11
0.03
Adj.R
20.68
-0.01
0.72
C.I.Adj.R
2[0
.59,0
.91]
[0,0
.54]
[0.66,0
.92]
χ2 N−K
10.49
25.61
7.77
p-value
0.99
0.32
1.00
PANEL
C:T
estAgainst
Ran
dom
Factor
Adj.R
20.01
0.84
0.01
MAPE
0.01
0.84
0.01
Adj.R
2 ,α
0.01
0.30
0.01
(b)2001Q1-2014Q1
PANEL
A:E
stim
ates
andt-Statist
icsof
Risk
Prem
iaSM
BSM
OM
CUR
Intercep
t0.11
0.13
0.03
t-FM
1.85
2.33
1.47
t-Shanken
1.73
1.94
0.81
Adj.Lev
0.10
0.16
0.37
t-FM
2.79
2.84
6.02
t-Shanken
2.75
2.49
3.71
PANEL
B:C
ross-Sectio
nalR
2 san
dSp
ecificatio
nTe
sts
MAPE
0.01
0.01
0.03
MAX
0.04
0.05
0.11
TOTA
L0.12
0.14
0.06
Adj.R
20.69
0.74
0.48
C.I.Adj.R
2[0
.63,0
.91]
[0.69,0
.93]
[0.36,0
.85]
χ2 N−K
9.32
2.54
18.74
p-value
0.99
1.00
0.66
PANEL
C:T
estAgainst
Ran
dom
Factor
Adj.R
20.02
0.01
0.16
MAPE
0.01
0.01
0.15
Adj.R
2 ,α
0.01
0.01
0.08
69
Tab
le12
:Cross-Section
alAsset
Pricing
Tests
(Finan
cials,
Other
Finan
cials,
andNon
-Finan
cials).The
tableshow
sthepriceof
risk(λ)
andassetpricingtestsestim
ated
forasetof
internationa
lasset
portfolio
s(Currencies,SizeandBook-to-Market,a
ndSizeandMom
entum)using
thecross-sectiona
lregressionE
[Re]=
λ0
+β′ λ.AdjustedLe
verage
(Other
Fina
ncials)
iscompu
tedwith
outtaking
into
accoun
tfin
ancial
institu
tions
othe
rthan
commercial
bank
san
dbroker-dealers,A
djustedLe
verage
(Non
-Finan
cials)
iscompu
tedusingda
taon
lyon
Non
-Finan
cial
Firm
s.Pan
elA
summarizes
theprices
ofris
kalon
gwith
theirSh
anken(1992)
andFa
maan
dMacBeth(1973)
t-statist
ics.Pan
elB
show
stheresults
ofanu
mbe
rof
additio
nalt
ests
includ
ingmeanab
solute
pricingerrors
(MAPE
),an
dad
justed
R2values
with
confi
denc
eintervals(L
ewellenet
al.(
2010)).Pan
elC
repo
rtsthepe
rcentage
oftim
esthat
rand
omly
generatedfactorsprod
ucead
justed
R2values
andalph
as(α
)high
eran
dlower
respectiv
elycompa
red
tothemod
elsconsidered
inthean
alysis.
The
data
arequ
arterly
andspan
ape
riodfrom
2001
-Q1un
til2014
-Q1.
Allreturnsan
dris
kprem
iaare
annu
alized
.
PANELA:E
stim
ates
and
t-Statistic
sof
RiskPremia
CUR
CUR
CUR
SBM
SBM
SBM
SMOM
SMOM
SMOM
Intercep
t0.11
0.11
0.10
0.11
0.09
0.08
0.12
0.13
0.13
t-FM
5.53
5.82
5.27
1.86
1.84
2.03
2.23
2.57
2.58
t-Shanken
1.29
1.76
1.64
1.54
1.49
1.67
1.61
1.86
1.78
LEV.Adj
1.66
1.26
0.52
0.28
0.27
0.25
0.39
0.39
0.31
t-FM
8.11
6.91
3.85
2.89
2.68
2.43
2.84
2.74
2.56
t-Shanken
1.95
2.18
1.29
2.52
2.28
2.09
2.13
2.06
1.87
LEV.Adj(O
thFin)
0.01
-0.03
0.11
0.09
0.07
0.14
t-FM
0.05
-0.29
1.52
1.27
0.75
1.98
t-Shanken
0.02
-0.09
1.26
1.08
0.56
1.44
LEV.Adj(O
th)
-2.22
0.12
-0.46
t-FM
-6.93
0.39
-1.40
t-Shanken
-2.27
0.33
-1.00
PANELB:C
ross-Sectio
nalR
2san
dSp
ecificatio
nTe
sts
MAPE
0.03
0.03
0.02
0.01
0.01
0.01
0.01
0.01
0.01
MAX
0.09
0.07
0.04
0.03
0.03
0.03
0.04
0.04
0.03
TOTA
L0.14
0.15
0.11
0.12
0.10
0.09
0.14
0.15
0.15
Adj.R
20.53
0.57
0.85
0.71
0.72
0.71
0.75
0.75
0.78
C.I.Adj.R
2[0
.42,0
.86]
[0.46,1
][1
,1]
[0.65,0
.92]
[0.73,1
][0
.73,1
][0
.7,0
.93]
[0.8
,1]
[0.89,1
]χ
2 N−K
6.24
10.06
6.83
1.88
p-value
1.00
0.98
1.00
1.00
PANELC:T
estAgainst
Ran
dom
Factor
Adj.R
20.11
0.09
0.00
0.01
0.01
0.01
0.01
0.01
0.01
MAPE
0.17
0.16
0.00
0.02
0.02
0.01
0.01
0.01
0.01
Adj.R
2,α
0.11
0.08
0.00
0.01
0.01
0.01
0.01
0.01
0.01
70
Table 13: Adjusted Leverage, Leverage Factor, and Capital Ratio Across Credit Regimes (U.S.Economy). Table 13a summarizes the relation between future returns of financial intermediaries and theLeverage Factor of Adrian et al. (2014), the capital ratio factor of He et al. (forthcoming) and financialleverage across credit regimes. Table 13b repeats the exercise for the case of aggregate financial assets. Thedata are quarterly and span a period from 2001-Q1 until 2012-Q4. Standard errors are heteroskedasticity-(White (1980)) and autocorrelation-robust (Newey and West (1987) and Newey and West (1994)).
(a) Future Returns
(1) (2) (3) (4) (5)rfin
t+1 rfint+1 rfin
t+1 rfint+1 rfin
t+1Leverage Factort -0.040 -0.060 0.139
(-0.18) (-0.28) (1.22)Leverage Factort × 1(Creditt < 25%) -0.044 0.097 0.377+
(-0.16) (0.43) (2.02)Leverage Factort × 1(Creditt > 75%) -1.717∗∗∗ -1.619∗∗∗ -0.748∗
(-4.37) (-4.03) (-2.41)Capital Risk Factort 1.029 1.047 1.467∗
(1.22) (1.30) (2.26)Capital Risk Factort × 1(Creditt < 25%) -0.307 -0.326 -0.207
(-0.41) (-0.59) (-0.66)Capital Risk Factort × 1(Creditt > 75%) 2.552∗ 2.351∗ 1.474∗∗∗
(2.53) (2.38) (3.91)Financial Leveraget -0.504∗∗ -0.442∗
(-3.29) (-2.46)Financial Leveraget × 1(Creditt < 25%) 0.167∗∗∗ 0.188∗∗
(3.59) (3.54)Financial Leveraget × 1(Creditt > 75%) -0.018 -0.017
(-0.91) (-0.67)rfin
t -0.048 -0.368 -0.227∗∗ -0.363 -0.702∗(-0.45) (-1.23) (-2.78) (-1.14) (-2.43)
N 48 48 52 48 48R2 0.04 0.10 0.23 0.14 0.38t-statistics in parentheses+ p < 0.10, ∗ p < 0.05, ∗∗ p < 0.01, ∗∗∗ p < 0.001
(b) Future Assets
(1) (2) (3) (4) (5)assetst+1 assetst+1 assetst+1 assetst+1 assetst+1
Leverage Factort 0.035 -0.003 0.046(0.40) (-0.04) (0.67)
Leverage Factort × 1(Creditt < 25%) 0.143 0.157+ 0.111(1.57) (1.77) (1.42)
Leverage Factort × 1(Creditt > 75%) 0.672∗∗∗ 0.681∗∗∗ 0.441∗∗(4.94) (4.83) (3.26)
total assetst 0.895∗∗∗ 0.925∗∗∗ 0.722∗∗∗ 0.900∗∗∗ 0.719∗∗∗(23.26) (30.34) (10.99) (27.41) (7.55)
Capital Risk Factort 0.190∗ 0.183 0.122(2.29) (1.61) (1.49)
Capital Risk Factort × 1(Creditt < 25%) -0.383∗∗∗ -0.300∗ -0.151(-4.20) (-2.41) (-1.36)
Capital Risk Factort × 1(Creditt > 75%) -0.638∗∗ -0.644 -0.485∗(-2.77) (-1.59) (-2.51)
Financial Leveraget 0.157 0.120(1.65) (0.81)
Financial Leveraget × 1(Creditt < 25%) -0.013 -0.005(-0.56) (-0.16)
Financial Leveraget × 1(Creditt > 75%) 0.035∗ 0.033+
(2.38) (1.71)
N 48 48 52 48 48R2 0.86 0.86 0.88 0.87 0.89t-statistics in parentheses+ p < 0.10, ∗ p < 0.05, ∗∗ p < 0.01, ∗∗∗ p < 0.001
71
Table 14: Cross-Sectional Asset Pricing Tests (Portfolios of International Assets). The tableshows the price of risk (λ) and asset pricing tests estimated for a set of International asset portfolios(Currencies, Size and Book-to-Market, and Size and Momentum) using the cross-sectional regressionE [Re] = λ0 + β′λ. Adjusted Leverage is a proxy for the risk bearing capacity of the global financial system,HKM is the intermediary capital factor of He et al. (forthcoming), and AEM is the leverage factor of Adrianet al. (2014). Panel A summarizes the prices of risk along with their Shanken (1992) and Fama and MacBeth(1973) t-statistics. Panel B shows the results of a number of additional tests including mean absolute pricingerrors (MAPE), adjusted R2 values with confidence intervals (Lewellen et al. (2010)), χ2 statistic tests ofjointly zero pricing errors. Panel C reports the percentage of times that randomly generated factors produceadjusted R2 values and alphas (α) higher and lower respectively compared to the models considered in theanalysis. The data are quarterly and span a period from 2001-Q1 until 2012-Q4. All returns and risk premiaare annualized.
PANEL A: Estimates and t-Statistics of Risk PremiaCUR SBM SMOM
Intercept 0.11 0.15 0.08t-FM 5.28 2.80 1.77t-Shanken 1.88 2.23 1.39LEV.Adj 0.90 0.29 0.30t-FM 6.21 2.99 3.00t-Shanken 2.38 2.55 2.53HKM -0.55 -0.13 -0.04t-FM -4.43 -1.31 -0.30t-Shanken -2.00 -1.19 -0.26AEM -47.47 -6.07 -13.65t-FM -2.94 -0.27 -0.73t-Shanken -1.17 -0.22 -0.60PANEL B: Cross-Sectional R2s and Specification TestsMAPE 0.03 0.01 0.01MAX 0.07 0.05 0.03TOTAL 0.14 0.16 0.09Adj.R2 0.58 0.69 0.81C.I.Adj.R2 [ 0.5 , 1 ] [ 0.68 , 0.98 ] [ 0.98 , 1 ]
PANEL C: Test Against Random FactorAdj.R2 0.09 0.01 0.00MAPE 0.14 0.01 0.00Adj.R2, α 0.08 0.01 0.00
72
Table 15: Cross-Sectional Asset Pricing Tests (Portfolios of International Assets). The tableshows the price of risk (λ) and asset pricing tests estimated for a set of international asset portfolios(Currencies, Size and Book-to-Market, and Size and Momentum) using the cross-sectional regressionE [Re] = λ0 + β′λ. Adjusted Leverage is a proxy for the risk bearing capacity of the global financial systemand Leverage Innovations are the residuals of an AR(1) regression of global financial leverage. Panel Asummarizes the prices of risk along with their Shanken (1992) and Fama and MacBeth (1973) t-statistics.Panel B shows the results of a number of additional tests including mean absolute pricing errors (MAPE),and adjusted R2 values with confidence intervals (Lewellen et al. (2010)). Panel C reports the percentageof times that randomly generated factors produce adjusted R2 values and alphas (α) higher and lowerrespectively compared to the models considered in the analysis. The data are quarterly and span a periodfrom 2001-Q1 until 2014-Q1. All returns and risk premia are annualized.
PANEL A: Estimates and t-Statistics of Risk PremiaSBM SBM SMOM SMOM CUR CUR
Intercept 0.11 0.12 0.12 0.12 0.12 0.10t-FM 1.86 1.96 2.23 1.99 5.48 4.99t-Shanken 1.54 1.47 1.61 1.44 1.28 0.97Adj.Lev 0.28 0.27 0.39 0.39 1.66 1.89t-FM 2.89 2.80 2.84 2.02 8.11 8.12t-Shanken 2.52 2.27 2.13 1.49 1.95 1.62Lev.Inn 0.22 -0.02 0.61t-FM 1.81 -0.03 4.33t-Shanken 1.42 -0.02 0.91
PANEL B: Cross-Sectional R2s and Specification TestsMAPE 0.01 0.01 0.01 0.01 0.03 0.03MAX 0.03 0.02 0.04 0.04 0.09 0.07TOTAL 0.12 0.13 0.14 0.14 0.15 0.13Adj.R2 0.71 0.81 0.75 0.74 0.53 0.61C.I.Adj.R2 [ 0.64 , 0.92 ] [ 0.93 , 1 ] [ 0.7 , 0.93 ] [ 0.79 , 1 ] [ 0.43 , 0.86 ] [ 0.53 , 1 ]χ2N−K 6.83 4.52 1.88 -0.10 7.33 11.48
p-value 1.00 1.00 1.00 1.00 1.00 0.95PANEL C: Test Against Random Factor
Adj.R2 0.01 0.00 0.01 0.01 0.12 0.07MAPE 0.02 0.00 0.01 0.01 0.17 0.08Adj.R2, α 0.01 0.00 0.01 0.01 0.12 0.07
73
Table 16: Cross-Sectional Asset Pricing Tests (Portfolios of International Assets). The tableshows the price of risk (λ) and asset pricing tests estimated for international portfolios (Currencies,Size and Book-to-Market, and Size and Momentum) using the cross-sectional regression E [Re] = λ0 +β′λ.U.S. Adjusted Leverage is equal to the residuals of an AR(1) regression of financial leverage, adjusted forcredit levels, computed using only U.S. data. Adjusted Leverage (EX-US) is equal to the residuals of an OLSregression of Global Adjusted Leverage on the U.S. Adjusted Leverage measure. Panel A summarizes theprices of risk along with their Shanken (1992) and Fama and MacBeth (1973) t-statistics. Panel B shows theresults of a number of additional tests including mean absolute pricing errors (MAPE), adjusted R2 valueswith confidence intervals (Lewellen et al. (2010)), χ2 statistic tests of jointly zero pricing errors. Panel Creports the percentage of times that randomly generated factors produce adjusted R2 values and alphas (α)higher and lower respectively compared to the models considered in the analysis. The data are quarterly andspan a period from 2001-Q1 until 2014-Q1. All returns and risk premia are annualized.
PANEL A: Estimates and t-Statistics of Risk PremiaCUR SBM SMOM
Intercept 0.13 0.11 0.12t-FM 5.88 2.38 1.66t-Shanken 1.46 1.97 1.22LEV.Adj(EX-US) 1.60 0.28 0.38t-FM 8.19 2.34 2.95t-Shanken 2.11 2.01 2.25LEV.Adj(US) -0.07 0.01 0.03t-FM -0.70 0.05 0.16t-Shanken -0.19 0.04 0.12PANEL B: Cross-Sectional R2s and Specification TestsMAPE 0.03 0.01 0.01MAX 0.08 0.03 0.04TOTAL 0.16 0.12 0.14Adj.R2 0.52 0.70 0.74C.I.Adj.R2 [ 0.42 , 1 ] [ 0.69 , 1 ] [ 0.76 , 1 ]χ2N−K 13.23 13.18
p-value 0.90 0.93PANEL C: Test Against Random Factor
Adj.R2 0.13 0.02 0.01MAPE 0.17 0.02 0.01Adj.R2, α 0.13 0.01 0.01
74