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An Investment-based Explanation for the Forward Premium Puzzle

Ehab Al-Yamani† Aaron D Smallwood

Jackson State University University of Texas-Arlington

ehab.yamani@jsums.edu smallwood@uta.edu

(817) 673-6883 (817) 272-3062

January 14, 2016

†Corresponding author: Ehab Yamani, Economics, Finance & General Business Department,

Jackson State University, 1400 John R. Lynch St, Jackson, MS 39217, email:

ehab.yamani@jsums.edu

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An Investment-based Explanation for the Forward Premium Puzzle

Abstract

This paper investigates an investment-based explanation for the forward premium puzzle arising

from the excess returns from the carry trade strategy. We propose a theoretical and an empirical

international investment-based asset-pricing model that involves a stochastic discount factor

related to the marginal rate of transformation derived from the firm’s first-order conditions. The

main proposition of our production-based explanation is that the risk of the carry trade

speculation strategy is measured by the covariance of the currency returns with the marginal rate

of transformation, proxied by the investment returns. Thus, the production-based model predicts

that investing in high interest rate currencies is risky because they tend to depreciate when the

marginal rate of transformation is high (“bad times”), while low interest rate currencies

appreciate.

JEL classification: G12 E23

Keywords: Interest rate parity; Carry trade; Q-theory; production-based model.

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1. Introduction

One of the most puzzling anomalies in the international finance literature is the forward

premium puzzle resulting from the failure of uncovered interest rate parity (UIP). The UIP

condition states that exchange rate changes will eliminate any profit opportunities arising from

interest rate differentials between countries. According to UIP, therefore, we should expect a

depreciation of the high interest rate currency against the low interest rate currency by the same

amount as the interest rate differential. However, there is overwhelming empirical evidence

against UIP, suggesting that the high interest rate currency does not depreciate by the same

magnitude as the differential in interest rates. In direct consequence to the failure of UIP, carry

trade strategies (CT), where traders take a net long in high interest rate currencies relative to low

interest rate counterparts, have emerged as an important profitable tool for many speculators in

international finance.

Under covered interest rate parity, where interest differentials are offset by the forward

premium or discount on a currency, the violation of UIP is equivalent to a violation the forward

rate unbiasedness hypothesis (FRUH). The lack of empirical support for the unbiasedness

hypothesis was first forcefully espoused by Fama (1984), who showed empirically that the

forward rate was not only a biased predictor of the future sport rate, it was perverse, predicting

depreciations of currencies trading at forward premium. Over 30 years since Fama (1984), the

literature on the FRUH has yielded various explanations for the forward premium puzzle such as

crash risk (e.g., Brunnermeier, Nagel, and Pedersen, 2009), peso problems (e.g., Farhi and

Gabaix, 2008, and Burnside et al., 2010), liquidity risk (e.g., Brunnermeier et al., 2008, Plantin

and Shin, 2008, Mancini et al., 2013), adverse selection problems (Burnside, Eichenbaum, and

Rebelo, 2009), default risk (e.g., Coudert and Mignon, 2013), macroeconomic news (e.g.,

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Hutchison and Sushko, 2013), and monetary policy (e.g., Backus et al., 2010, Moore and Roche,

2012). By applying an asset pricing approach, some studies examine the risk-based explanation

for the profitability of the carry trade strategy through relating excess foreign exchange returns to

different risk factors such as equity-based factors related to CAPM and the Fama-French three

factor model (e.g., Lustig and Verdelhan, 2007; and Burnside, 2011); consumption based factors

(e.g., Lustig and Verdelhan, 2007, and Du, 2013), and currency based factors (e.g., Lustig,

Roussanov, and Verdelhan, 2011, Rafferty, 2011, and Menkhoff et al., 2012).

In this paper, our objective is to propose a theoretical and an empirical production based

approach to price currency returns as an alternative explanation to the forward premium puzzle.

While there are an increasing number of studies examining the risk explanations for the forward

premium puzzle, to the best of our knowledge, this is the first attempt to explain the forward

premium puzzle in a production-based framework through relating currency returns to marginal

rates of transformation. The main proposition of our production-based model is that the risk of

the carry trade speculation strategy is measured by the covariance of the currency returns with

the marginal rate of transformation, proxied by investment returns. The production-based model

predicts that investing in high interest rate currencies is risky because they tend to depreciate

when the marginal rate of transformation is high (“bad times”), while low interest rate currencies

appreciate.

Our study is motivated by two important observations. First, standard equity-based factor

models and consumption-based approaches have not yet produced a satisfactory resolution to the

puzzle (Burnside, 2011). Second, there has been virtually no literature that has explored a

potential production based risk approach to currency returns, in spite of the significant success of

this modeling approach to other asset classes following the seminal work of Cochrane (1991).

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Important contributions using production-methods have been made in explaining the behavior of

U.S. stock returns (e.g., Cooper, Gulen, and Schill, 2008, Liu, Whited, and Zhang, 2009, and Li

and Zhang, 2010), international stock returns (e.g., Watanabe et al., 2013), the value premium

(e.g., Zhang, 2005), external financing constraints (e.g., Li, Livdan, and Zhang, 2009), equity

premiums (e.g., Cochrane, 1988, and Jermann, 2010), and the term premium (Jermann, 2013).

The remainder of the paper is organized as follows. Section 2 motivates our investigation

with a brief review of the related literature and a presentation of the testable hypothesis. In

section 3, we propose a theoretical production-based model as an alternative explanation to the

forward premium puzzle. Empirical methodology is set forth in section 4. Data and variables are

explained in section 5, and a final section concludes.

2. Literature review

In this section, we briefly review the literature on risk-based explanations for the carry

trade strategy. According to the risk story, high average returns to carry trades are compensations

for bearing risk. From the asset pricing perspective, the risk explanation is based on relating the

returns on the carry trade strategy cross-sectionally to risk factors. Thus, the starting point of any

risk-based explanation of the forward premium puzzle involves identifying the risk factors that

covary with the returns on the carry trade strategy. The literature proposes several candidate risk

factors for pricing returns to carry trades such as equity-based risk factors, consumption-based

factors, and currency-based factors.

The first approach involves relating cross-sectional returns to carry trades to the

traditional equity-based asset pricing variables, typically using either CAPM, which uses the

market excess return as a single factor, or the Fama-French three factor model, where it is

standard to use the market premium, size premium, and value premium as risk factors. Lustig

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and Verdelhan (2007) and Burnside (2011) find that these traditional models fail to explain the

returns on the carry trades.

A second risk-based explanation to the forward premium comes from the consumption-

based asset pricing models that involve a stochastic discount factor related to the marginal utility

of consumption derived from consumer’s first-order conditions. In general, the main proposition

of the consumption-based models is that assets are risky if they deliver low returns when the

investor’s consumption growth is low. In equilibrium, therefore, these assets must offer a

positive excess return as a compensation for their risk. For example, Lustig and Verdelhan

(2007) link exchange rates to aggregate consumption growth in a single consumption-based

factor model. They find that aggregate consumption growth risk explains a large fraction of

variations in exchange rates conditional on interest rates. Burnside (2011) extends the model

developed by Lustig and Verdelhan (2007) uses market returns, the growth rate for the

consumption of durables, and the growth rate of the service flow as factors to study the carry

trade returns. Burnside (2011) provides conflicting evidence, as he does not find any significant

statistical correlation between these consumption-based factors, whether used individually in a

single model or together in a three factor model, and the payoffs the carry trade.1

A third risk-based explanation relates the returns on carry trades to currency-based risk

factors in a cross-sectional setting. Lustig, Roussanov and Verdelhan (2011) construct two

factors: dollar risk factor, measured as the average of currency returns, and high-minus-low

(HML) carry trade risk factor, which is calculated as the return differential between the portfolio

with the largest forward discount and the one with the smallest forward discount. The dollar and

HML risk factors are analogous to the market risk and high-minus-low book-to-market risk

1 Other studies employing consumption-based asset pricing approaches include Bekaert and Hodrick (1992), Backus

et al. (2001), and Du (2013).

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factors, respectively, in the popular Fama and French (1993) three factor model. Menkhoff et al.

(2012) use a dollar risk factor analogous to the one created by Lustig, Roussanov and Verdelhan

(2011), and a factor that measures global currency volatility. Finally, Raffetry (2011), drawing

on the currency crash risk literature (e.g., Brunnermeier, Nagel, and Pedersen, 2009), creates a

global currency skewness risk factor in addition to a dollar risk factor, to explain currency

returns. Burnside (2011) empirically re-examines all of the above three currency-based models

and finds that the currency-based models have some success in explaining currency returns.

While all of the above studies examine risk as an explanation to the forward premium

puzzle, no study thus far has addressed the question of whether the production-based modeling

approach can explain the forward puzzle. This paper fills such a gap in the literature and

hypothesizes a production-based explanation for the forward premium puzzle arising from the

excess returns from the carry trade strategy.

3. Investment-Based Pricing to Currency Returns

Our objective is to explore an investment-based explanation that could explain the risk

premium on excess currency returns. We suggest an investment-based model as a candidate

solution for the forward premium puzzle. Our goal in this section is two-fold. First, we present a

production-based model that relates investment returns in a Q-theory framework (Tobin, 1969),

as a theoretical framework through which we can derive a stochastic discount factors for home

and foreign countries. Next, we show how we use these two discount factors in pricing the

returns on the carry trade strategy.

3.1 Investment-based Real Model

We introduce a two-country model (Home and foreign country). Saving and investment

can differ for an individual country that participates in the world capital market. We assume a

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world with open economies with intertemporal trade so that a country can borrow resources from

the rest of the world or lend them abroad. With the aid of loans from foreigners, an economy

with a temporary income shortfall can avoid sharp contraction in investment. Similarly, a

country with ample savings can lend and participate in productive investment projects overseas.

Uncertainty: Uncertainty comes from a future state variable 𝔰 which occurs with

probability 𝜋(𝔰) and can take one of a finite N values, so that 𝔰 = (𝔰0, 𝔰1, … , 𝔰𝑁). The cumulative

history of shocks up to and including time 𝑡 is given by 𝔰𝑡 ≡ (𝔰0, 𝔰1, … , 𝔰𝑡), with 𝔰𝑡 is the current

period realization. We assume that there is a worldwide market in which firms in both home and

foreign countries can buy or sell noncontingent as well as contingent claims. Firms are allowed

to borrow and lend, that is to sell and buy noncontingent (or riskless) bonds that pay 1 + 𝑟 per

unit on date 𝑡 regardless of the state of nature, where 𝑟 is the riskless real rate of interest. Firms

can trade internationally also in contingent risky assets such as currencies and their derivatives

(such as currency forward contracts). The payoffs of these contingent claims depend on the state

of nature, so that 𝑃(𝔰𝑡) is the time 0 world price to a claim to a unit of a single good delivered at

time t in state 𝔰𝑡. Indeed, the market value of the foreign currency-denominated contracts with

uncertain foreign exchange returns depends in part on its effectiveness as means of insurance.

The representative competitive home firm thus faces uncertainty over the future path of

unexpected output, which is subject also to exogenously varying productivity shocks 𝐴𝑗(𝔰𝑡+1).

Real Model: The model represents the producer’s choice of capital inputs for a given

state price process. We assume that the home country’s output 𝑌𝑡(𝔰𝑡) is produced by a

representative home firm which uses 𝑗 capital stock 𝐾𝑗(𝔰𝑡+1) accumulated during period 𝔰𝑡 in

addition to other costless inputs to produce homogenous output. The firm has access to 𝐽

technologies (𝑗 = 1, 2, … . , 𝐽) with which it can transfer some of the consumption good forward

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through time. We abstract from the labor market, and we assume that producers can sell claims

to their future outputs. The firm thus chooses a production plan using the following production

function for the new output:

𝑌𝑡(𝔰𝑡) =∑𝐴𝑗(𝔰

𝑡+1). 𝐹 (𝐾𝑗(𝔰𝑡+1))

𝐽

𝑗=1

(1)

Given such setup, the firm aims to maximize its contingent claim as follows

𝑉𝑡(𝔰𝑡) ≡ max𝐸𝑡 [𝑀(𝔰𝑡+1|𝔰

𝑡)𝐷𝑗(𝔰𝑡)] ≡ 𝑚𝑎𝑥∑∑𝑃(𝔰𝑡)[𝐷𝑗(𝔰

𝑡)]

𝔰𝑡

∞

𝑡=0

(2)

𝑠. 𝑡. 𝐾𝑗(𝔰𝑡) = 𝐾𝑗(𝔰

𝑡−1)(1 − 𝛿𝑗) + 𝐼𝑗(𝔰𝑡) (3)

Equation (2) is the firm’s discounted future profits where 𝑉𝑡(𝔰𝑡) is the firm’s cum-dividend

market value of equity is so that residents of different countries can exchange fractional shares;

and 𝐷𝑗(𝔰𝑡) is the firm’s dividend payout to the existing domestic and foreign shareholder and it

equals to the operating revenues {Π(𝐾𝑗(𝔰𝑡−1), 𝔰𝑡)} minus the total cost of investment

{∅ (𝐼𝑗(𝔰𝑡), 𝐾𝑗(𝔰

𝑡−1))} 2. Equation (3) is the standard capital accumulation constraint, which says

that output is produced using capital, 𝐾𝑗,𝑡, which in turn, can be accumulated through investment

𝐼𝑗,𝑡. The end of period capital level 𝐾𝑗(𝔰𝑡) equals current investment 𝐼𝑗(𝔰

𝑡) plus beginning of

period capital which depreciates at an exogenous rate of 𝛿𝑗.

2 The firm’s total costs of investment [∅ (𝐼𝑗(𝔰

𝑡), 𝐾𝑗(𝔰𝑡−1))] equals the actual cost of purchasing the new capital

goods (𝐼𝑗(𝔰𝑡)) plus a deadweight installation or adjustment cost which represents the firms’ foregone operating

profit since they have to reduce sales to increase investment. In reality, capital cannot be installed or moved to

alternative uses without incurring frictional costs. Therefore, the total cost of investing in capital is given by

∅(𝐼𝑡 , 𝐾𝑡−1) = 𝐼𝑡 + (𝑎

2(𝐼𝑗(𝔰

𝑡)

𝐾𝑗(𝔰𝑡−1))2

𝐾𝑗(𝔰𝑡−1)), where a > 0 is a constant parameter and captures the curvature of the

adjustment cost (Li, Livdan and Zhang, 2009; and Liu, Whited and Zhang, 2009).

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Asset Prices and producer’s first order condition: Let 𝑞𝑗(𝔰𝑡) be the Lagrangian

multiplier associated with the capital accumulation constraint. 𝑞𝑗(𝔰𝑡) (or what is called marginal

q) is the firm’s internal shadow price of capital. The first order conditions with respect to capital

𝐾𝑗 for each 𝑗 is

𝑞𝑗(𝔰𝑡) = ∑𝑃

𝔰𝑡+1

(𝔰𝑡+1|𝔰𝑡) {(

𝜕𝛱 (Kj(𝔰t−1))

𝜕𝐾𝑗(𝔰𝑡−1)

) − (𝜕∅(𝐼𝑗(𝔰

𝑡), 𝐾𝑗(𝔰𝑡−1))

𝜕𝐾𝑗(𝔰𝑡−1)

) + ((1 − 𝛿𝑗)𝑞𝑗(𝔰𝑡, 𝔰𝑡+1))} (4)

Equation (4) is the investment Euler equation that equates the marginal costs of investing to the

marginal benefits, as the Q-theory predicts (e.g., Abel and Blanchard, 1986, and Gilchrist and

Himmelberg, 1995). It states that, at an optimum for the firm, the shadow price of an extra unit

of capital is the discounted sum of (1) the capital marginal product next period; (2) the capital

marginal contribution to lower adjustment costs next period; and (3) the shadow price of capital

next period. Dividing both sides of equation (4) by 𝑞𝑗(𝔰𝑡), we obtain

1 = ∑P

st+1

(𝔰t+1|𝔰t) {(∂Π (Kj(𝔰

t−1)) ∂Kj(𝔰t−1)⁄ ) − (∂∅ (Ij(𝔰

t), Kj(𝔰t−1)) ∂Kj(𝔰

t−1)⁄ ) + (1 − δj)qj(𝔰t, 𝔰t+1)

qj(𝔰t)

} (5)

Therefore, we define investment return as the term in the bracket in equation (6), as follows

𝑅𝑗𝐼(𝔰𝑡, 𝔰𝑡+1) ≡ {

(𝜕𝛱 (𝐾𝑗(𝔰𝑡−1)) 𝜕𝐾𝑗(𝔰

𝑡−1)⁄ ) − (𝜕∅ (𝐼𝑗(𝔰𝑡), 𝐾𝑗(𝔰

𝑡−1)) 𝜕𝐾𝑗(𝔰𝑡−1)⁄ ) + (1 − 𝛿𝑗)𝑞𝑗(𝔰

𝑡, 𝔰𝑡+1)

𝑞𝑗(𝔰𝑡)

} (6)

Equation (6) is the standard investment returns derived from the standard production based

models (e.g., Cochrane, 1991 and 1996; Li, Vassalou and Xing, 2006; Gomes, Yaron and Zhang,

2006; and Liu, Whited and Zhang, 2009). The investment returns measures the stochastic rate of

return that results from investing a little more today and then investing a little less tomorrow. A

critical feature of equation (6) is its implication that the desired capital stock is independent of

domestic consumption preferences.

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Our main proposition is that currency riskiness can be measured by its covariance with

investment returns 𝑅𝑗𝐼(𝔰𝑡, 𝔰𝑡+1), proxied by equation (6), as follows:

𝐸𝑡 (𝑚(𝔰𝑡+1|𝔰𝑡) 𝑅𝑗

𝐼(𝔰𝑡, 𝔰𝑡+1)) = 1 (7)

Where 𝐸𝑡 denotes the mathematical expectation operator conditional on information available at

time 𝑡, and 𝑚(𝔰𝑡+1|𝔰𝑡) is the stochastic discount factor for the home country. The first order

condition in equation (7) can be stated in terms of state prices in the home country 𝑃(𝔰𝑡)

∑P

𝔰t+1

(𝔰t+1|𝔰t) 𝑅𝑗

𝐼(𝔰𝑡, 𝔰𝑡+1) = 1 (8)

Equation (8) is the producer’s first order condition which describes a relation between asset

returns and production variables regardless the consumer preferences. The first order condition

just say to operate each technology up to the point where the marginal cost equals the marginal

benefits

Production-based model: The trouble with developing a production-based asset pricing

model is that technologies allow firms to transform goods across time, but not across states of

nature. Production functions are kinked (Leontief) across states of nature, so we cannot read

contingent claim prices from outputs (Cochrane, 2005). One way to put marginal rates of

transformation into asset pricing model is to allow a large number of underlying technologies, as

in Jermann (2010) who pursues the idea of spanning across two states of nature with two

technologies to reproduce the equity premium. It is the key that there are as many capital stocks

as there states of nature next period. Without this property, recovering state prices from the

firm’s production choices would not be possible.

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To recover state prices from investment returns, thus, it is necessary to have ′𝑁′ number

of states of nature to be equal to ′𝐽′ number of types of capital inputs. Thus, the state price vector

in equation (8) can be rewritten in a matrix form as follows

[R1I (𝔰t, 𝔰1) R1

I (𝔰t, 𝔰2) ⋯ R1I (𝔰t, 𝔰N)

⋮ ⋱ ⋮RNI (𝔰t, 𝔰1) RN

I (𝔰t, 𝔰2) ⋯ RNI (𝔰t, 𝔰N)

] [P(𝔰1|𝔰

t)⋮

P(𝔰N|𝔰t)] = 𝟏 (9)

As in Jermann (2010), the stochastic discount factor (SDF) 𝑚(𝔰𝑡+1|𝔰𝑡) now can be introduced by

dividing and multiplying the state prices 𝑃(𝔰𝑡+1|𝔰𝑡) by the probabilities 𝜋(𝔰𝑡+1|𝔰

𝑡)

𝑃(𝔰𝑡+1|𝔰𝑡) = (

𝑃(𝔰𝑡+1|𝔰𝑡)

𝜋(𝔰𝑡+1|𝔰𝑡)) 𝜋(𝔰𝑡+1|𝔰

𝑡)

= 𝑚(𝔰𝑡+1|𝔰𝑡) 𝜋(𝔰𝑡+1|𝔰

𝑡) (10)

Therefore, the home stochastic discount factor 𝑚(𝔰𝑡+1|𝔰𝑡) from time 𝑡 to 𝑡 + 1 equals

𝑚𝑡+1 = 𝑚(𝔰𝑡+1|𝔰𝑡) =

𝑃(𝔰𝑡+1|𝔰𝑡)

𝜋(𝔰𝑡+1|𝔰𝑡) (11)

Equation (11) is the stochastic discount factor that derives the production-based capital asset

pricing models since 𝑃(𝔰𝑡+1|𝔰𝑡) is derived from production data by equation (9). The first order

condition says that the firm should arrange its technology shocks to produce more in high-

contingent claim price states of nature, and produce less in states of nature for which its output is

less valuable. In order to evaluate the asset pricing implications of this investment-based model,

we follow Jermann (2013) and model the investment risk premium, denoted as 𝜆𝐼, as a stochastic

process for the investment growth rates

𝜆𝐼(𝔰𝑡, 𝔰𝑡+1) ≡𝐼(𝔰𝑡, 𝔰𝑡+1)

𝐼(𝔰𝑡) (12)

Overall, our goal is to investigate whether the investment risk premium 𝜆𝐼(𝔰𝑡, 𝔰𝑡+1)

(which works through investment growth rates) can explain currency returns. To test this

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conjecture, we develop two hypotheses to investigate an investment risk-based explanation for

the forward premium puzzle and for the carry trade returns.

3.2. Pricing Currency Returns: Revisiting Fama regressions

3.2.1. Exchange Risk Premium

Carry trade has been a very popular speculative strategy for currency investors for more

than three decades (Gagnon and Chaboud, 2007; Galati, Heath, and McGuire, 2007). Consider an

example of an individual currency carry trade in which domestic interest rate 𝑖𝑡 exceeds the

foreign interest rate 𝑖𝑡∗ (𝑖. 𝑒., 𝑖𝑡 > 𝑖𝑡

∗), or equivalently, the foreign currency is at a forward

premium (𝑖. 𝑒., 𝑓𝑡 > 𝑠𝑡). We use the notations 𝑓𝑡 to denote the logarithm of the nominal forward

exchange rate 𝐹𝑡, and 𝑠𝑡 to denote the logarithm of the nominal spot exchange rate 𝑆𝑡.3 This

carry strategy consists of trading in the forward market, betting that the foreign exchange rate

will not change so as to offset the profits made on the forward premium or discount differential.

If the foreign currency is at forward discount (i.e., 𝑓𝑡 < 𝑠𝑡), currency traders long the foreign

currency (or equivalently short the dollar) in the forward market in period 𝑡, and then short the

foreign currency (or equivalently long the dollar) in the spot market in period 𝑡 + 1. In this case,

we can define the expected excess nominal forward foreign exchange payoff 𝑧𝑡+1 as the log

forward rate 𝑓𝑡 minus the expected spot rate 𝑠𝑡+14

𝑧𝑡+1 = 𝑓𝑡 − 𝑠𝑡+1 (13)

3 The exchange rates are measured as the number of units of the U.S. dollar per one unit of foreign currency. An

increase in the spot rate, therefore, means a depreciation of the home currency (i.e., U.S. dollar).

4 We measure the currency excess returns using forward markets. Alternatively, the excess return to investing in the

carry trade while funded in USD can be measured also as the difference between the interest rate differential and the

exchange rate changes, as follows: 𝑧𝑖,𝑡∗ = (𝑖𝑡

∗ − 𝑖𝑡) − ∆𝑠𝑡. The interest rate differential (it∗ − it) is the interest rate

difference between the foreign country and the U.S, where 𝑖𝑡∗ is the foreign interest rate in units of foreign currency

and 𝑖𝑡 is the nominal interest rate in US currency. As in Lustig, Roussanov, and Verdelhan, 2011 and 2014, the merit

of focusing our attention to investments in forward markets (compared to investment in interest rates) is that forward

contracts are subject to low default risk. In addition, the data on forward exchange rates are easily available.

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Such profitable carry trade strategy exploits the failure of the covered interest rate parity (CIP).

While the CIP predicts that exchange rate changes will eliminate any arbitrage opportunities

arising from forward premium/discount differentials between currencies, there is overwhelming

empirical evidence that reverse holds, namely the low interest rate currency tend to depreciate

while the high interest rate currency tend to appreciate5.

Fama (1984) attributes these excess currency returns to a time-varying risk premium 𝑝𝑡,

which can be estimated from any forecasting model as the conditional expectation of the payoff

as follows

𝑝𝑡 ≡ 𝐸𝑡[𝑧𝑡+1] = 𝑓𝑡 − 𝐸𝑡[𝑠𝑡+1] (14)

Where 𝐸𝑡 denotes the mathematical expectation operator conditional on information available at

time 𝑡. If we add and subtract 𝑠𝑡 from both sides of equation (14), the risk premium can be

rewritten as

𝑝𝑡 ≡ (𝑓𝑡−𝑠𝑡) − (𝐸𝑡[𝑠𝑡+1]−𝑠𝑡) (15)

To the extent that exchange rate is well-approximated by a martingale (𝑖. 𝑒. , 𝐸𝑡[𝑠𝑡+1] = 𝑠𝑡), then

the risk premium to a carry trade is simply equal to the forward premium (𝑖. 𝑒., 𝑝𝑡 = (𝑓𝑡−𝑠𝑡)).

3.2.2. Hypothesis 1: Pricing Currency Excess Returns 𝑓𝑡 − 𝑠𝑡+1

Fama (1984) shows how to deduce some properties of risk premium 𝑝𝑡 using the analysis

of omitted variable bias in the following regression:

𝑓𝑡 − 𝑠𝑡+1 = 𝛼0 + 𝛼𝑓𝑝(𝑓𝑡 − 𝑠𝑡) + 휀1,𝑡+1 (16)

If the CIP holds, the estimation of equation (16) would give 𝛼𝑓𝑝 = 1 and 𝛼0 = 0. However, as

previous literature has shown, 𝛼𝑓𝑝 is often found smaller than 1, or even negative.

5 For a survey on the failure of the UIP, see Froot and Thaler (1990), Engel (1996), Obstfeld and Rogoff (2001).

15

The starting point of any risk-based explanation of the excess currency returns 𝑧𝑡+1 is to

identify a stochastic discount factor that prices payoffs of these returns. The stochastic discount

factors are the basis of modern theories in asset pricing. We propose a new perspective about the

fundamental determinants of the these currency excess return, as we hypothesize that a SDF

derived from production and investment data can be used to price returns to carry trade. In

particular, since the carry trade strategy is a zero net-investment strategy (i.e., it involves no

payments at time 𝑡), we propose that carry return payoffs satisfy

𝐸𝑡(𝑚𝑡+1𝑧𝑡+1) = 𝐸𝑡(𝑚𝑡+1 (𝑓𝑡 − 𝑠𝑡+1)) = 0 (17)

Where 𝑚𝑡+1 is derived from production and investment data by equation (11).

Why should investment returns be factors for carry trade returns? Our answer to that

question builds on the work of Fama and Bliss (1987), Cochrane (1988), and Jermann (2013).

Fama and Bliss (1987) pointed out that forward term premium display a cyclical pattern. In the

1970s, the forward rate moved slightly before business cycles in investment, while in the 1960s

and in 1979, it moved contemporaneously. Fama and Bliss (1987) find evidence that variation in

the forward rate term premium is almost entirely due to variation in a real risk premium and that

the risk premium has a cyclical correlation with production variables.

Cochrane’s (1988) working paper presents a two sector investment model and shows that

production data can be used to calculate multiperiod bond prices as follows. Cochrane (1998)

derives the price of a one period bond that pays one dollar at time 𝑡 + 1, denoted as 𝑃$(1)(𝑠𝑡), as

follows:

𝑃$(1)(𝔰𝑡) = ∑𝑃(𝔰𝑡, 𝔰𝑡+1) (18)

𝑠𝑡+1

16

Similarly, the price of a two-period bond is6

𝑃$(2)(𝔰𝑡) = ∑

𝔰𝑡+1

∑𝑃(𝔰𝑡, 𝔰𝑡+1𝔰𝑡+2)

𝑃(𝔰𝑡) (19)

𝑠𝑡+2

The current year term premium (the ex-post return from holding an X-year bond for one year

minus the return from holding a one year bond) therefore is

𝐶𝑢𝑟𝑟𝑒𝑛𝑡 𝑦𝑒𝑎𝑟 𝑡𝑒𝑟𝑚 𝑝𝑟𝑒𝑚𝑖𝑢𝑚 =𝑃$(𝑋)(𝔰𝑡)

𝑃$(𝑋−1)(𝔰𝑡) (20)

Assets with payoffs specified in currencies can be priced in the same way as any other asset such

as bonds. Consider first a nominal bond denominated in a generic home country’s currency,

which we refer to as “dollars”. One dollar’s worth of currency bonds returns a certain 1 + 𝑖𝑡+1

dollars in period 𝑡 + 1, where 𝑖 is the nominal interest rate on dollars. Since nominal bonds and

currency have identical price-level risk, the nominal interest rate 𝑖 captures the opportunity cost

of holding money rather than nominal bonds. An alternative version of using the carry trade

strategy is to borrow low-interest rate currencies in order to lend high-interest rate currencies, but

without using the forward market to hedge the associated currency risk. Using such logic,

Cochrane (1998) shows that forward rate term premium (forward rate minus spot rate) equals the

current year term premium

𝑓(𝑋)(𝔰𝑡) =

𝑃$(𝑋)(𝔰𝑡)

𝑃$(𝑋−1)(𝔰𝑡) (21)

Where 𝑃(𝔰𝑡+1|𝔰𝑡) is state prices derived from investment data in equation (10). We therefore

state our first hypothesis as follows

6 Jermann (2013) builds on Cochrane’s (1988) work and use a production-based model to price nominal bonds.

Jermann (2013) introduces inflation into the model. If we assume for simplicity that inflation is independent of

investment, as in Jermann (2013), the price of a nominal bond is simply the price of a real bond times the expected

loss due to inflation.

17

H1: There is a significant relation between investment returns

and currency excess returns.

To verify our first hypothesis that the investment return explains the forward bias at least partly,

we introduce the investment return 𝑅𝑡𝐼 proxy into the Fama regression in equation (16). This

“augmented Fama regression” is written as follows:

𝑓𝑡 − 𝑠𝑡+1 = 𝛼0 + 𝛼𝑓𝑝(𝑓𝑡 − 𝑠𝑡) + 𝛼𝐼𝑅𝑡𝐼 + 휀1,𝑡+1 (22)

3.2.3. Hypothesis 2: Pricing Spot Rate Changes 𝑠𝑡+1 − 𝑠𝑡

The forward unbiasedness hypothesis (FUH) states that the forward exchange rate should

be an unbiased predictor of the future spot exchange rate. The forward unbiasedness hypothesis

is generally tested by estimating Fama (1984) regression of the realized exchange rate change

∆𝑠𝑡+1 on the forward premium (𝑓𝑡 − 𝑠𝑡) as follows

∆𝑠𝑡+1 = 𝑠𝑡+1 − 𝑠𝑡 = 𝛽0 + 𝛽𝑓𝑑(𝑓𝑡 − 𝑠𝑡) + 휀2,𝑡+1 (23)

If the FUH held, the estimation of Equation (23) would give 𝛽𝑓𝑑 = 1 and 𝛽0 = 0. Empirical

research however has consistently rejected the FUH. The lack of empirical support for the

unbiasedness hypothesis was first evidenced by Fama (1984), who show empirically that forward

rates are generally biased predictors of future spot exchange rates because they predict

depreciations of currencies trading at forward premium (i.e., there is a negative association

between forward premiums and subsequent exchange rate returns). This stylized fact is

commonly referred to as the ‘forward bias puzzle’.

According to equation (14) (𝑝𝑡 ≡ (𝑓𝑡−𝑠𝑡) − (𝐸𝑡[𝑠𝑡+1]−𝑠𝑡)), the conditional risk

premium on exchange rate risk corresponds to the conditional expectation of the currency payoff.

This implies that the conditional risk premium equals

𝑝𝑡 = (𝑓𝑡 − 𝑠𝑡) − 𝐸𝑡∆𝑆𝑡+1 ≡𝑐𝑜𝑣𝑡(𝑚𝑡+1, ∆𝑆𝑡+1)

𝐸𝑡(𝑀𝑡+1) (24)

18

Equation (24) implies that any risk-based explanation of the carry trade returns relies on

identifying an SDF that correspond to an observable time series and covaries with the rate of the

rate of the appreciation of the foreign currency ∆𝑆𝑡+1 (Burnside, 2011; and Burnside et al.,

2010). We hypothesize that the SDF derived from production data by equation (11) covaries with

the rate of the rate of the appreciation of the foreign currency ∆𝑆𝑡+1.

We now tackle an important question that may have occurred to the reader already: why

producers should care about the exchange rate market? Why should investment returns be factors

for spot exchange rate changes, ∆𝑠𝑡+1? In order to answer these questions, we turn now to two

popular models of exchange rate determination – the balance of payment approach and the

monetary approach. The former focuses on the demand for imports and supply of exports, while

the latter focuses on the demand for and supply of money.

The BOP Approach: The balance of payment approach emphasizes trade flows and

capital movements as exchange rate determinants. The demand for and supply of foreign

currency indicates that there is demand for imports and supply of exports. Whenever trade takes

place, the demand and supply schedules shift up or down. By using a balance of payment 𝐵𝑂𝑃𝑡

equation, we can determine the factors that affect these two schedules:

𝐵𝑂𝑃𝑡 = 𝐶𝐴 (𝑆𝑡𝜋𝑡

∗

𝜋𝑡, 𝑌𝑡 , 𝑌𝑡

∗) + 𝐾𝐴(𝑖𝑡 − 𝑖𝑡∗) (25)

Where CA is the current account, 𝑆𝑡 is the spot exchange rate, 𝜋𝑡 is the domestic price level, 𝑌𝑡 is

the domestic output, 𝜋𝑡∗ is the foreign price level, 𝑌𝑡

∗ is the foreign output, KA is the capital

account, and 𝑖𝑡 − 𝑖𝑡∗ is the interest rate differential. From equation (15), we can solve for the

exchange rate 𝑆𝑡 and express all the variables in natural logarithms, except interest rates, and we

can obtain the fundamental equation for the BOP model as follows:

𝑠𝑡 = 𝛼0 + 𝛼1(𝜋𝑡 − 𝜋𝑡∗) + 𝛼2(𝑦𝑡 − 𝑦𝑡

∗) + 𝛼3(𝑖𝑡 − 𝑖𝑡∗) + 휀𝑡 (26)

19

We turn now to investigate the linkage between investment and exchange rate. To this

end, we explore first how investment affects the current account, and then we show how current

account affects exchange rate.

First, we discuss the linkage between investment and current account. We focus on the

foreign asset accumulation view of the current account rather than net export view. According to

the foreign asset accumulation view of the current account, a country’s current account balance

over period is the change in the value of its net claims on the rest of the world – the change in its

net foreign assets. A country with positive net exports must be acquiring foreign assets of equal

value because it is selling more to foreigners than it is buying from them; and a country with

negative net exports must be borrowing an equal amount to finance its deficit with foreigners.

Thus, every positive item of net exports in the current account is associated with an equal-value

negative item in its capital account. As a pure matter of accounting, the net export surplus and

the capital account surplus sum identically to zero. Historically, one of the main reasons

countries have borrowed abroad is to finance productive investments that would have been hard

to finance out of domestic savings alone7. The current account balance is said to be in surplus if

positive, so that the economy as a whole is lending, and in deficit if negative, so that the

economy is borrowing.

This approach allows the capital investment 𝐼𝑡 to be reflected in the current account of the

balance of payments. In general, a country’s current account is national saving less domestic

investment (𝐶𝐴𝑡 = 𝑆𝑎𝑣𝑖𝑛𝑔𝑠𝑡 − 𝐼𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡𝑡), where national saving can flow into domestic

capital 𝐾𝑡 as well as foreign assets. National saving in excess of domestic capital formation flows

into net foreign asset accumulation. In addition, we assume in our model that home and foreign

7 In the nineteenth century, the railroad companies that helped open up the Americas drew on European capital to

pay laborers and obtain rails, rolling stock and other inputs. More recently, Norway borrowed extensively in world

capital markets to develop its North Sea oil resources in the 1970s after world oil prices shot up.

20

outputs (𝑌𝑡 𝑎𝑛𝑑 𝑌𝑡∗)are produced using capital (𝐾𝑡 𝑎𝑛𝑑 𝐾𝑡

∗), which, in turn can be accumulated

through investment (𝐼𝑡 𝑎𝑛𝑑 𝐼𝑡∗). For notational purposes, we use subscript * to refer to the

corresponding variable in the foreign country. The balance of payment 𝐵𝑂𝑃𝑡 equation, thus can

be rewritten as follows:

𝐵𝑂𝑃𝑡 = 𝐶𝐴 (𝑆𝑡𝜋𝑡

∗

𝜋𝑡, 𝐾𝑡, 𝐾𝑡

∗, 𝐼𝑡 , 𝐼𝑡∗) + 𝐾𝐴(𝑖𝑡 − 𝑖𝑡

∗) (27)

The impact of investment on the balance of payment through current account emerges from the

impact of productivity shifts. In particular, suppose that the stochastic process governing home

productivity shocks𝐴𝑡+1 in equation (1) is given by

𝐴𝑡+1 − 𝐴′ = 𝜌(𝐴𝑡+1 − 𝐴

′) + 휀𝑡+1 (28)

Where 0 ≤ 𝜌 ≤ 1 and 휀𝑡+1 is serially uncorrelated shock with 𝐸𝑡휀𝑡+1 = 0. The shocks’ effects

decay geometrically overtime provided 𝜌 <1 and they are permanent only if 𝜌 = 1. The saving-

investment identity is a vital analytical tool because it shows that current account, saving, and

investment are jointly determined endogenous variables that respond to common exogenous

shocks. An unanticipated productivity increase on date 𝑡 therefore affects the date 𝑡 current

account via two channels – investment and saving. However, the net impact of the change in

current productivity shock on the current account depends on the degree of persistence (i.e., the

magnitude of 𝜌). Since 0 ≤ 𝜌 ≤ 1, let’s differentiate between 3 different cases.

Let’s assume first the extreme case if 𝜌 = 0. In this case, there is no investment response

at all because a surprise date t productivity increase does not imply that productivity is expected

to be any higher at date t+1. Home saving, however, increases at every interest rate. The home

country thus runs a higher current account surplus on date t to spread overtime its temporarily

higher output.

21

Now, suppose that home capital becomes unexpectedly productive (𝐴𝑡+1 is above its

conditional mean 𝐴′) but temporarily (i.e., 𝜌 is above zero but below one). The positive

productivity shock in this case induces investment and therefore domestic residents borrow

abroad to cushion their consumption in the face of unusually high investment needs. They

choose to accumulate interest yielding foreign assets as a way of smoothing consumption over

future periods. Countries wish to avoid sharp temporary drops in consumption by borrowing

foreign savings, rather than financing extraordinarily profitable opportunities entirely out of

domestic savings. The productivity increase affects saving. However, the magnitude of 𝜌

influences whether date 𝑡 saving rises, and if so, by more or less than investment. In general, the

more persistent productivity shocks are, the lower is current account.

Finally, suppose that in period 𝑡 the productivity coefficient in the home production

function rises unexpectedly and permanently (𝜌 = 1) from its previously constant level to a

higher level. In this case, a current account deficit in the home country emerges in period t that

converges to zero only in the long run. These dynamics follow from the gradual adjustment of

the capital stock to its new higher level since capital adjustment costs slow the response of

investment to location-specific shocks. As a result, savings fall because expected future output

rises by more than current output on date t. At the same time, current investment rises but

expected future investment doesn’t change. Saving therefore falls, while investment rises and

current account deficit occurs. To sum up, productivity shocks lead to changes in investment

which, in turn, leads to imbalances in the current account.

Now, we turn to discussing how these current account imbalances are reflected in the

spot exchange rate movements. The foreign asset accumulation view of the current account

allows current account imbalances to affect the exchange rate. The current account imbalance is

22

said to be in surplus if positive, so that the economy as a whole is lending, and in deficit if

negative, so that the economy is borrowing. The current account balance over period 𝑡 is the

change in the value of a country’s net claims on the rest of the world (the change in its net

foreign assets). A current account deficit therefore is a transfer of wealth from domestic residents

to foreign residents (and a transfer of unemployment from the domestic economy to the foreign

one). The decrease in domestic wealth can depreciate the home currency and the spot rate

increases. Equation (16) can be expanded by using other pairs of variables such as investment

differential (𝑙𝑛𝐼𝑡 − 𝑙𝑛𝐼𝑡∗). The above mechanism can be summarized as follows

𝑈𝑛𝑒𝑥𝑝𝑒𝑐𝑡𝑒𝑑 𝑝𝑟𝑜𝑑𝑢𝑐𝑡𝑖𝑣𝑖𝑡𝑦 𝑆ℎ𝑜𝑐𝑘 𝑦𝑖𝑒𝑙𝑑𝑠→ 𝒄𝒉𝒂𝒏𝒈𝒆 𝒊𝒏 𝒊𝒏𝒗𝒆𝒔𝒕𝒎𝒆𝒏𝒕

𝑦𝑖𝑒𝑙𝑑𝑠→ 𝐶𝑢𝑟𝑒𝑛𝑡 𝐴𝑐𝑐𝑜𝑢𝑛𝑡 𝑖𝑚𝑏𝑎𝑙𝑎𝑛𝑐𝑒𝑠

𝑦𝑖𝑒𝑙𝑑𝑠→ 𝐶ℎ𝑛𝑎𝑔𝑒 𝑖𝑛 𝑐𝑢𝑟𝑟𝑒𝑛𝑐𝑦 𝑣𝑎𝑙𝑢𝑒

𝑦𝑖𝑒𝑙𝑑𝑠→ 𝒄𝒉𝒂𝒏𝒈𝒆 𝒊𝒏 𝒔𝒑𝒐𝒕 𝒓𝒂𝒕𝒆

The Monetarist Approach: The monetary approach to exchange rate determination shifts

the responsibility for determining exchange rates to money markets. The fundamental equation

for the monetary model is

𝑠𝑡 = (𝑚𝑡 −𝑚𝑡∗) − 𝛽1(𝑦𝑡 − 𝑦𝑡

∗) + 𝛽2(𝑖𝑡 − 𝑖𝑡∗) + 휀𝑡 (29)

According to the monetary model, therefore, there are three factors affecting exchange rate: the

money differential between home and foreign countries (𝑚𝑡 −𝑚𝑡∗), the income differential (𝑌𝑡 −

𝑌𝑡∗), and interest rate differential (𝑖𝑡 − 𝑖𝑡

∗). One of the key building blocks of the flexible-price

monetary policy is the assumption of the purchasing power parity PPP (𝑝𝑡 = 𝑠𝑡𝑝𝑡∗). This model

assumes instantaneous adjustment in all markets. However, there are restrictions (such as long-

term contracts, imperfect information, high costs of acquiring information) which do not allow

prices to change instantaneously, but adjust gradually. This means that PPP may be a good

approximation in the long run, but it does not hold in the short run. An important modification to

23

the monetary policy was thus set forth by Dornbusch (1976), who assumed that asset markets

adjust instantaneously, whereas prices in goods markets adjust gradually. This sticky price

version is a Keynesian model of the monetary approach. The key assumption of these models is

that good’s prices are sticky while prices of currencies are flexible.

The key feature of such sticky prices approach is that it allows the monetary policy to

have effects on real variables in the system such as production and investment. When a monetary

shock occurs in period 𝑡1, the market will adjust to a new equilibrium which will be between

prices and quantities. Due to price stickiness in the goods market, the short run equilibrium will

be achieved through shifts in financial market prices. As prices of goods increase gradually

toward the new equilibrium in period 𝑡2, the foreign exchange continuous repricing approaches

its long-term equilibrium level. Thus a new long-run equilibrium will be attained in the domestic

money, currency, and goods markets.

Consider for example an unanticipated decrease in the domestic money supply. Such

monetary shock will lower the demand for domestic bonds and thus lowering their prices. When

a tight domestic monetary policy causes the interest differential to rise above its equilibrium

level, the home country can borrow abroad at the world interest rate since the home country will

never wishes to pass up domestic investment opportunities that offer a net rate of return above

the world interest rate. As a result, capital inflow occurs causing the value of the home currency

to rise (spot rate falls) proportionately above its equilibrium level. This gives us a real model of

exchange rate determination, as follows:

𝐻𝑜𝑚𝑒 𝑚𝑜𝑛𝑒𝑦 𝑠𝑢𝑝𝑝𝑙𝑦 𝑑𝑒𝑐𝑟𝑒𝑎𝑠𝑒𝑠 𝑦𝑖𝑒𝑙𝑑𝑠→ 𝑑𝑒𝑚𝑎𝑛𝑑 𝑜𝑛 𝑏𝑜𝑛𝑑𝑠 𝑑𝑒𝑐𝑟𝑒𝑎𝑠𝑒𝑠

𝑦𝑖𝑒𝑙𝑑𝑠→ 𝐵𝑜𝑛𝑑 𝑝𝑟𝑖𝑐𝑒𝑠 𝑑𝑒𝑐𝑟𝑒𝑎𝑠𝑒

𝑦𝑖𝑒𝑙𝑑𝑠→ 𝑯𝒐𝒎𝒆 𝒊𝒏𝒕𝒆𝒓𝒆𝒔𝒕 𝒓𝒂𝒕𝒆 𝒊 𝒊𝒏𝒄𝒓𝒆𝒂𝒔𝒆𝒔

𝒚𝒊𝒆𝒍𝒅𝒔→ 𝑯𝒐𝒎𝒆 𝒊𝒏𝒗𝒆𝒔𝒕𝒎𝒆𝒏𝒕 𝒊𝒏𝒄𝒓𝒆𝒂𝒔𝒆𝒔

𝑦𝑖𝑒𝑙𝑑𝑠→ 𝐶𝑎𝑝𝑖𝑡𝑎𝑙 𝑖𝑛𝑓𝑙𝑜𝑤

𝑦𝑖𝑒𝑙𝑑𝑠→ 𝐻𝑜𝑚𝑒 𝑐𝑢𝑟𝑟𝑒𝑛𝑐𝑦 𝑎𝑝𝑝𝑟𝑒𝑐𝑖𝑎𝑡𝑒𝑠

𝑦𝑖𝑒𝑙𝑑𝑠→ 𝒕𝒉𝒆 𝒔𝒑𝒐𝒕 𝒓𝒂𝒕𝒆 𝒇𝒂𝒍𝒍𝒔

24

Exchange rates are the “relative prices of money”. They have monetary causes. The asset

(foreign money) can be held for its own sake because of its expected appreciation against other

kind of money, or money may be exchanged for other goods (assets) such as credit instruments,

stocks and shares, or for direct investment in firms. In this sense, the exchange rate, as viewed by

asset holders, is perhaps best described as “a relative double asset price”. The price of the asset

‘foreign money’ most likely to be exchanged and conditioned by investment opportunities in

other assets of that currency area. This concept of exchange rate determination is not in

compatible with a basically monetary approach but it gives it another interpretation or predicts

much more variable quantitative relationships.

To sum up, using both the balance of payment and the monetary approaches, it seems that

thee may be a relation between investment and spot exchange rates. We therefore state our

second hypothesis as follows

H2: There is a significant relation between investment returns

and spot exchange rate changes.

To verify our second hypothesis that investment covaries with the rate of the rate of the

appreciation of the foreign currency ∆𝑆𝑡+1, we introduce the investment return 𝑅𝑡𝐼 proxy into the

Fama regression in equation (23). This “augmented Fama regression” is written as follows:

𝑠𝑡+1 − 𝑠𝑡 = 𝛽0 + 𝛽𝑓𝑑(𝑓𝑡 − 𝑠𝑡) + 𝛽𝐼𝑅𝑡𝐼 + 휀2,𝑡+1 (30)

4. Empirical Testing Framework

The essence of our empirical work is to use the information in investment data to price

currency returns. Following Berk et al. (1999) and Zhang (2005), we parameterize the stochastic

discount factor directly without explicitly modeling the consumer's problem. Formally, we

25

parametrize the stochastic discount factor that price currency excess returns as a linear function

of both spot exchange rate changes 𝑅𝑡+1𝐹𝑋 and investment returns 𝑅𝑡+1

𝐼 as follows

𝑚𝑡+1 = 𝜂0 + 𝜂1𝑅𝑡+1𝐹𝑋 + 𝜂2𝑅𝑡+1

𝐼 (31)

Satisfies equation (17):

𝐸𝑡(𝑚𝑡+1𝑧𝑡+1) = 0

Modeling the stochastic discount factor directly as a function of investment returns 𝑅𝑡+1𝐼 is

similar to the empirical implementation of the investment-based models of Cochrane (1996),

Lamont (2000) and Li, Vassalou and Xing (2003). We include foreign exchange returns 𝑅𝑡+1𝐹𝑋 as

well into the stochastic discount factor for two reasons. As equation (5) predicts, Burnside (2011)

shows that any stochastic discount factor suggested to predict currency excess returns should

covary with the rate of the change of the spot exchange rate. In addition, there are several studies

that show empirically that currency returns is a risk factor that predict excess currency returns

(e.g., Lustig, Roussanov, and Verdelhan, 2011; Burnside, 2011; Rafferty, 2011; and Menkhoff et

al., 2012; Verdelhan, 2013).

4.1. Variables Construction

The exchange rate returns 𝑅𝑡+1𝐹𝑋 is proxied by a dollar factor which is the average change

in the dollar versus all the other currencies. In particular, the country-level dollar risk factor,

denoted by 𝐷𝑂𝐿𝑖𝑡, is given by:

𝐷𝑂𝐿𝑖𝑡 =1

𝑁∑∆𝑧𝑖𝑡

𝑁

𝑖=1

(32)

Where N refers to the available number of currencies during quarter t, and ∆𝑠𝑖𝑡 refers to the

quarterly log change in the spot exchange rate. The dollar risk factor, therefore, can be thought of

as an aggregate FX market quarterly return relative to the base currency, which is the US dollar

26

in our paper (Lustig, Roussanov, and Verdelhan, 2011 and 2014; Burnside, 2011; Rafferty, 2011;

Menkhoff et al., 2012; and Verdelhan, 2013). 8

We develop a new risk factor, denoted as 𝐶𝐴𝑃𝐸𝑋𝑡, which measures the global investment

risk,. We calculate the quarterly investment growth rate for each country in our sample, and then

average all investment growth rates over all countries available on any given quarter.

Mathematically, our proxy for global investment returns is given by

𝐶𝐴𝑃𝐸𝑋𝑖𝑡 =1

𝑁∑∆𝐶𝐴𝑃𝐸𝑋𝑐𝑜𝑢𝑛𝑡𝑟𝑦,𝑡

𝑁

𝑐=1

(33)

Where ∆𝐶𝐴𝑃𝐸𝑋𝑐𝑜𝑢𝑛𝑡𝑟𝑦,𝑡 refers to the quarterly change in the individual’s country’s investment

measured by private capital expenditure. Several studies use investment growth rates as a proxy

for investment returns without any misrepresentation of the model (Cochrane, 1996; Lamont,

2000; Li, Vassalou and Xing, 2003; and Li, Vassalou, and Xing, 2006). To the best of our

knowledge, however, this is the first attempt aiming directly at explaining the variations of

currency returns using an investment-based risk factor.

In order to empirically test the two hypotheses developed from the investment-risk based

model of the return to the carry trade in section three, we estimate the parameters of the model in

equation (14) using three different approaches. First, we measure trades conducted on a currency

by currency basis against the U.S. dollar. Second, we run a panel regression model. Finally, we

examine portfolio-based strategies. For notational purposes, we use 𝑡 as an index for time in

general, 𝑖 as an indication for country/currency-level variables, and 𝑝 as an indication for

portfolio-level variables.

8 For each currency put on the left-hand side of a regression, that currency is excluded from any portfolio that

appears on the right-hand side.

27

4.2. Country-level Analysis

We use both DOL and CAPEX factors to empirically test our two hypotheses. We

empirically study the currency excess returns by relating them to these two risk factors: foreign

exchange risk factor, denoted as DOL, and investment risk factor, denoted as CAPEX, using the

following two equations:

∆𝑠𝑖𝑡+1 = 𝛼 + 𝛽𝑓𝑑(𝑓𝑡 − 𝑠𝑡) + 𝛽𝐷𝑂𝐿𝐷𝑂𝐿𝑡 + 𝛽𝐶𝐴𝑃𝐸𝑋𝐶𝐴𝑃𝐸𝑋𝑡 + 휀𝑖𝑡+1 (34)

𝑧𝑖𝑡+1 = 𝛼 + 𝛽𝐷𝑂𝐿𝐷𝑂𝐿𝑖𝑡+1 + 𝛽𝐶𝐴𝑃𝐸𝑋𝐶𝐴𝑃𝐸𝑋𝑖𝑡+1 + 휀𝑖𝑡+1 (35)

The quarterly currency excess returns (𝑧𝑖𝑡+1) to buying a foreign currency in the forward market

and then selling it in the spot market after three months, is defined in equation (2) (𝑧𝑖𝑡+1 = 𝑓𝑖𝑡 −

𝑠𝑖𝑡+1). The exchange rates are measured as the number of units of the foreign currency per one

U.S. dollar.9

4.3. Panel Risk Factor Analysis – Predictive Tests

To further check our findings from the country-by-country analysis, we run our

estimations also using panel data (i.e., cross-sectional combined with time-series data) using both

pooled OLS regression and fixed effect models. To this end, we classify our countries into three

groups: the complete panel includes all the 37 currencies in the sample, and two subsample

panels that include both developed and developing countries.

First, we run pooled OLS regressions for excess returns 𝑧𝑖𝑡,+1 for individual currencies on

both DOL and CAPEX factors. There are several studies that found that forecasts of exchange

rates built from pooled regression models estimated on panel data outperform those of time-

series regression forecasts (Groen, 2005; Cerra and Saxena, 2010; and Ince, 2014). So far we

have focused on the predictive power of CAPEX and DOL factors, but the IRP suggests that the

9 Note that returns are dated by the time they are known. Thus, the change in exchange rates between 𝑡 and 𝑡 + 1 is

dated 𝑡 + 1.

28

log spot rates ∆𝑠𝑖𝑡+1 are unpredictable and consequently the currency excess returns 𝑧𝑖𝑡+1 are

equal to the forward discounts (i.e., interest rate differentials). We check this conjecture by

reexamining the predictive power of CAPEX factor while controlling for the currency-specific

forward discount (𝐹𝐷𝑖𝑡 = 𝑓𝑖𝑡 − 𝑠𝑖𝑡), as follows

𝑧𝑖𝑡,+1 = 𝛽𝐷𝑂𝐿𝐷𝑂𝐿𝑖𝑡 + 𝛽𝐶𝐴𝑃𝐸𝑋𝐶𝐴𝑃𝐸𝑋𝑖𝑡 + 𝛽𝐹𝐷𝐹𝐷𝑖𝑡 + 휀𝑖𝑡+1 (36)

We run a similar regression for the sport rate changes

∆𝑠𝑖𝑡,+1 = 𝛽𝐷𝑂𝐿𝐷𝑂𝐿𝑖𝑡 + 𝛽𝐶𝐴𝑃𝐸𝑋𝐶𝐴𝑃𝐸𝑋𝑖𝑡 + 𝛽𝐹𝐷𝐹𝐷𝑖𝑡 + 휀𝑖𝑡+1 (37)

Where ∆𝑆𝑖𝑡,+1 is the spot rate changes measured as log returns (i. e., ∆sit+1 = log(Sit+1) −

log(Sit)), and 𝑆𝑖𝑡 is the spot exchange rate of the foreign currency against the USD. We estimate

the above two equations for each group of countries (developed, emerging, and all).

Next, we run fixed effect panel regression model. The data tell us that there is significant

heterogeneity across countries. This means that if we ignore the currency-specific effects, the

pools OLS estimated will be biased and inconsistent. One way to control for the country-specific

effects is via the fixed effect model. The attractive feature of fixed effect models is that they

control for all stable characteristics of the currencies, whether measured or not. This is

accomplished by using only within-currency variation to estimate the regression coefficients. We

focus on estimating the cross-sectional fixed effect model where the heterogeneity comes from

the cross-sectional effects. Our basic model for the cross-sectional fixed effect is

𝑧𝑖𝑡,+1 = 𝛽𝐷𝑂𝐿𝐷𝑂𝐿𝑖𝑡 + 𝛽𝐶𝐴𝑃𝐸𝑋𝐶𝐴𝑃𝐸𝑋𝑖𝑡 + 𝛽𝐹𝐷𝐹𝐷𝑖𝑡 + 𝑢𝑖𝑡+1 (38)

Where 𝑢𝑖𝑡+1 = 𝛾𝑖 + 휀𝑖𝑡+1 and 𝛾𝑖 are the nonrandom predictor variables that are constant over

time, while 휀𝑖𝑡+1 represents purely random variations at each point in time. For each country 𝑖

and for each time-varying variable - both response (𝑧𝑖𝑡+1) and predictor variables (𝐷𝑂𝐿𝑖𝑡+1) and

(𝐶𝐴𝑃𝐸𝑋𝑖𝑡+1) – we convert the observed values of each variable to deviations from the currency-

29

specific means10 and then regress the transformed response variable on the transformed

predictors

𝑧𝑖𝑡+1∗ = 𝛽𝐷𝑂𝐿

∗ 𝐷𝑂𝐿𝑖𝑡∗ + 𝛽𝐼𝑁𝑉

∗ 𝐶𝐴𝑃𝐸𝑋𝑖𝑡∗ + 𝛽𝐹𝐷

∗ 𝐹𝐷𝑖𝑡∗ + 휀𝑖𝑡+1

∗ (39)

Where the asterisks indicate difference scores and time-invariant variables 𝛾𝑖 have been

differenced out of the equation. We run a similar regression for the spot exchange rate changes

differenced variable (∆𝑠𝑖𝑡+1∗ )

∆𝑠𝑖𝑡+1∗ = 𝛽𝐷𝑂𝐿

∗ 𝐷𝑂𝐿𝑖𝑡∗ + 𝛽𝐼𝑁𝑉

∗ 𝐶𝐴𝑃𝐸𝑋𝑖𝑡∗ + 𝛽𝐹𝐷

∗ 𝐹𝐷𝑖𝑡∗ + 휀𝑖𝑡+1

∗ (40)

4.4. Portfolio Analysis

Our last test focuses on the portfolio construction used by several studies (e.g., Lustig and

Verdelhan, 2007; Lustig, Roussanov, and Verdelhan, 2011; Burnside, 2011; Rafferty, 2011;

Menkhoff et al., 2012; Verdelhan, 2013). The merit of using a portfolio-based approach

compared to using individual currencies is that we can eliminate to a large extent the currency

specific idiosyncratic characteristics and, therefore, focus our attention on the non-currency

specific characteristics. We employ two groups of sorting: single sorts by CAPEX growth and

double sorts by CAPEX growth and forward discount.

The first groups of our sorted portfolios are single-sorted portfolio where our sample

countries are sorted on CAPEX growth. At the end of each quarter 𝑡 we sort all the currencies in

our sample into five portfolios on the basis of individual country’s CAPEX growth, and then

rank them from low to high CAPEX growth. These are labelled CAPEX portfolios. The 20% of

countries with lowest CAPEX growth are allocated to portfolio C1, the next 20% to C2 and so on

10 We compute the means over time for that country, as follows: 𝑟𝑥𝑖̅̅ ̅̅ =

1

𝑛𝑖∑ 𝑟𝑥𝑖𝑡𝑡 , 𝐷𝑂𝐿𝑖̅̅ ̅̅ ̅̅ ̅ =

1

𝑛𝑖∑ 𝐷𝑂𝐿𝑖𝑡𝑡 , 𝐶𝐴𝑃𝐸𝑋𝑖̅̅ ̅̅ ̅̅ ̅̅ ̅̅ =

1

𝑛𝑖∑ 𝐶𝐴𝑃𝐸𝑋𝑖𝑡𝑡 , and 𝐹𝐷𝑖̅̅ ̅̅ ̅ =

1

𝑛𝑖∑ 𝐹𝐷𝑖𝑡𝑡 where 𝑛𝑖 is the number of measurements for each country 𝑖. Next, we obtain

the cross-sectional effects by converting the observed values of each variable to deviations from the currency-

specific means from: 𝑟𝑥𝑖𝑡∗ = 𝑟𝑥𝑖𝑡 − 𝑟𝑥𝑖̅̅ ̅̅ ; 𝐷𝑂𝐿𝑖𝑡

∗ = 𝐷𝑂𝐿𝑖𝑡 − 𝐷𝑂𝐿𝑖̅̅ ̅̅ ̅̅ ̅; 𝐶𝐴𝑃𝐸𝑋𝑖𝑡∗ = 𝐶𝐴𝑃𝐸𝑋𝑖𝑡 − 𝐶𝐴𝑃𝐸𝑋𝑖̅̅ ̅̅ ̅̅ ̅̅ ̅̅ , and 𝐹𝐷𝑖𝑡

∗ =𝐹𝐷𝑖𝑡 − 𝐹𝐷𝑖̅̅ ̅̅ ̅.

30

to portfolio C5 which contains the 20% of countries with the highest CAPEX growth. Panel A in

tables 6 and 7 show the means and standard deviations for the excess currency returns and sport

exchange rate changes, respectively, of portfolios sorted on individual country’s CAPEX growth.

The second groups of our sorted portfolios are double-sorted portfolio where countries

are sorted on both CAPEX growth and forward discount. In order to control for the currency-

specific forward discount (𝐹𝐷𝑖𝑡 = 𝑓𝑖𝑡 − 𝑠𝑖𝑡), we sort all the sample currencies at the end of each

quarter into five portfolios on the basis of their forward discount (𝑓𝑡 − 𝑠𝑡) against the USD, and

then rank them from small to large forward discounts. This procedure produces five currency

portfolios, denoted as P1, P2, P3, P4, and P5 and we label them CURRENCY portfolios.

Portfolio 1 is the one with the smallest forward discount (or equivalently the one with the lowest

interest rate currencies), and portfolio 5 is the one with the largest forward discount (or the one

with the highest interest rate currencies).

The double sorting is performed as follows. At the end of every quarter, all sample

countries are allocated to the 5 CAPEX portfolios based on their CAPEX growth, and then they

are allocated in an independent sort to 5 CURRENCY portfolios based on their forward discount.

The final portfolios are the 25 (5 × 5) intersections of the five CAPEX and the five

CURRENCY portfolios. Panel B of tables 6 and 7 shows the currency average excess returns and

spot exchange rate changes, respectively for the 25 CAPEX-CURRENCY portfolios.

Following Lustig, Roussanov, and Verdelhan (2011), Rafferty (2011), and Menkhoff et

al. (2012), we construct a portfolio-level dollar factor, denoted by 𝐷𝑂𝐿𝑝,𝑡, corresponds to the

average change in exchange rate across all five portfolios at each point in time:

𝐷𝑂𝐿𝑝,𝑡 =1

5∑∆𝑠𝑝,𝑡

5

𝑝=1

(41)

31

Similarly, we create a portfolio-level global investment risk factor denoted as 𝐶𝐴𝑃𝐸𝑋𝑝,𝑡 given

by:

𝐶𝐴𝑃𝐸𝑋𝑝,𝑡 =1

5∑∆𝐶𝐴𝑃𝐸𝑋𝑝,𝑡

5

𝑝=1

(42)

5. Data Description

In this section, we describe our data sources for exchange rates and investment data. Our

data span the period from January 1995 to June 2014 although the sample period varies by

currency. The empirical analysis is carried out at the quarterly frequency. We build three baskets

of currencies – developed, emerging, and all currencies. Our developed basket includes 15

developed countries – Australia, Belgium, Canada, Denmark, France, Germany, Italy, Japan, the

Netherlands, New Zealand, Norway, Sweden, Switzerland, the United Kingdom and the United

States. Our second basket includes 23 emerging countries – Argentina, Brazil, Chile, Mexico

(from Latin America); Hong Kong, India, Indonesia, Malaysia, Philippines, Russia, Saudi

Arabia, Singapore, South Korea, Taiwan, Thailand, United Arab Emirates (from Asia); Czech

Republic, Hungary, Poland, Portugal, Turkey (from Emerging Europe); Egypt and South Africa

(from Africa). Our last basket includes both developed and emerging countries in our sample.

Our raw currency dataset consist of quarterly observations for spot exchange rates, and

three month forward exchange rates. We denote spot and forward rates in logs as 𝑠𝑡 and 𝑓𝑡,

respectively. As we consider the point of view of a risk-averse US resident, the exchange rate of

a foreign country is denominated in units of US dollars per foreign currency unit (USD/FCU).

All spot and forward exchange rates are obtained from Datastream, with Reuters as the

underlying source.

32

In order to construct the investment factor, we use quarterly data on aggregate private

capital expenditures on plants and equipment (i.e., non-residential investment) in each of our

sample countries. All the real aggregate investment data are taken from the World Economic

Situation (WES)11 and it is available at DATASTREAM.

Figure (1)

Table (1)

6. Empirical Results

6.1. Results of Testing H1

Table (2)

Table (3)

Table (4)

Table (5)

Table (6)

6.2. Results of Testing H2

Table (7)

Table (8)

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36

Table (1): Descriptive Statistics

This table presents descriptive statistics for quarterly country-level currency and investment data. The

sample consists of three baskets of currencies – developed (panel A), emerging (Panel B), and all

currencies (Panel C) – over the period from Q1 1985 until Q2 2014. The table shows statistics for 5

variables – FX rate changes ∆st+1, currency excess return 𝑧𝑖𝑡, ∆𝐶𝐴𝑃𝐸𝑋𝑐𝑜𝑢𝑛𝑡𝑟𝑦, CAPEX factor, and DOL

factor. Sub-Panels 1 report the means and standard deviations, and sub-panel 2 shows the Pearson

correlation coefficients with the probability> |r| under null hypothesis Rho = 0.

The spot rate changes, ∆st+1, are the spot exchange rate changes measured as log returns (i. e., ∆st+1 =

log(St+1) − log(St)), where 𝑆𝑡 is the spot exchange rate of the foreign currency against the USD,

measured as the number of units of the foreign currency per one U.S. dollar. The excess return, 𝑧𝑖𝑡+1, is

measured as the log forward rate (𝑓𝑡) minus the log 3-month expected spot rate (𝑖. 𝑒. , 𝑧𝑖𝑡+1 = 𝑓𝑡 − 𝑠𝑡+1).

The CAPEX_country is the country’s quarterly investment growth measured as the quarterly change in

aggregate private capital expenditures on plants and equipment (i.e., non-residential investment) in each

of our sample countries. The CAPEX factor is our measure of global investment risk factor, and it is

measured as the average of all countries’ investment returns (∆𝐶𝐴𝑃𝐸𝑋𝑐𝑜𝑢𝑛𝑡𝑟𝑦) over all currencies

available on any given quarter. The CAPEX factor is calculated for each of the three baskets of currencies

(𝐶𝐴𝑃𝐸𝑋𝑑𝑒𝑣𝑒𝑙𝑜𝑝𝑒𝑑, 𝐶𝐴𝑃𝐸𝑋𝑑𝑒𝑣𝑒𝑙𝑜𝑝𝑖𝑛𝑔, and 𝐶𝐴𝑃𝐸𝑋𝐴𝑙𝑙). The DOL factor is the average of all countries’

changes in the spot exchange rate of the foreign currency against the USD dollar versus all the other

currencies. The DOL factor is calculated for each of the three baskets of currencies

𝐷𝑂𝐿𝑑𝑒𝑣𝑒𝑙𝑜𝑝𝑒𝑑, 𝐷𝑂𝐿𝑑𝑒𝑣𝑒𝑙𝑜𝑝𝑖𝑛𝑔, and 𝐷𝑂𝐿𝐴𝑙𝑙).

Panel A: Developed Countries (Number of Observations = 1046)

A.1 Descriptive Statistics

Spot Rate

Changes

Excess

Returns ∆𝐶𝐴𝑃𝐸𝑋𝑐𝑜𝑢𝑛𝑡𝑟𝑦 𝐶𝐴𝑃𝐸𝑋𝑑𝑒𝑣𝑒𝑙𝑜𝑝𝑒𝑑 𝐷𝑂𝐿𝑑𝑒𝑣𝑒𝑙𝑜𝑝𝑒𝑑

Mean -0.00218 -0.03574 0.00731 0.00156 -0.00206

St. Dev 0.05206 0.43296 0.95723 0.48093 0.04134

A.2 Covariance Matrix

Spot Rate

Changes

Excess

Returns ∆𝐶𝐴𝑃𝐸𝑋𝑐𝑜𝑢𝑛𝑡𝑟𝑦 𝐶𝐴𝑃𝐸𝑋𝑑𝑒𝑣𝑒𝑙𝑜𝑝𝑒𝑑 𝐷𝑂𝐿𝑑𝑒𝑣𝑒𝑙𝑜𝑝𝑒𝑑

Spot Rate Changes 1.0000 -0.08361

0.0066

-0.16683

<0.0001

-0.18581

<0.0001

0.75004

<0.0001

Excess Returns -0.08361

0.0066 1.0000

0.02008

0.5149

0.03710

0.2288

-0.07502

0.0148

∆𝐶𝐴𝑃𝐸𝑋𝑐𝑜𝑢𝑛𝑡𝑟𝑦 -0.16683

<0.0001

0.02008

0.5149 1.0000

0.38896

<0.0001

-0.12726

<0.0001

𝐶𝐴𝑃𝐸𝑋𝑑𝑒𝑣𝑒𝑙𝑜𝑝𝑒𝑑 -0.18581

<0.0001

0.03710

0.2288

0.38896

<0.0001 1.0000

-0.24443

<0.0001

𝐷𝑂𝐿𝑑𝑒𝑣𝑒𝑙𝑜𝑝𝑒𝑑 0.75004

<0.0001

-0.07502

0.0148

-0.12726

<0.0001

-0.24443

<0.0001 1.0000

37

Panel B: Developing Countries (Number of Observations = 1373)

B.1 Descriptive Statistics

Spot Rate

Changes

Excess

Returns ∆𝐶𝐴𝑃𝐸𝑋𝑐𝑜𝑢𝑛𝑡𝑟𝑦 𝐶𝐴𝑃𝐸𝑋𝑑𝑒𝑣𝑒𝑙𝑜𝑝𝑖𝑛𝑔

DOL_

Developing

Mean 0.00484 0.00580 0.00029 -0.00646 0.00615

St. Dev 0.06231 0.06962 1.13602 0.40756 0.03224

B.2 Covariance Matrix

Spot Rate

Changes

Excess

Returns ∆𝐶𝐴𝑃𝐸𝑋𝑐𝑜𝑢𝑛𝑡𝑟𝑦 𝐶𝐴𝑃𝐸𝑋𝑑𝑒𝑣𝑒𝑙𝑜𝑝𝑖𝑛𝑔 𝐷𝑂𝐿𝑑𝑒𝑣𝑒𝑙𝑜𝑝𝑖𝑛𝑔

Spot Rate Changes 1.0000 -0.84509

<0.0001

-0.15490

<0.0001

-0.20972

<0.0001

0.45616

<0.0001

Excess Returns -0.84509

<0.0001 1.0000

0.13859

<0.0001

0.19698

<0.0001

-0.39157

<0.0001

∆𝐶𝐴𝑃𝐸𝑋𝑐𝑜𝑢𝑛𝑡𝑟𝑦 -0.15490

<0.0001

0.13859

<0.0001 1.0000

0.24026

<0.0001

-0.12204

<0.0001

𝐶𝐴𝑃𝐸𝑋𝑑𝑒𝑣𝑒𝑙𝑜𝑝𝑖𝑛𝑔 -0.20972

<0.0001

0.19698

<0.0001

0.24026

<0.0001 1.0000

-0.42020

<0.0001

𝐷𝑂𝐿𝑑𝑒𝑣𝑒𝑙𝑜𝑝𝑖𝑛𝑔 0.45616

<0.0001

-0.39157

<0.0001

-0.12204

<0.0001

-0.42020

<0.0001 1.0000

Panel C: All Countries (Number of Observations = 2416)

C.1 Descriptive Statistics

Spot Rate

Changes

Excess

Returns ∆𝐶𝐴𝑃𝐸𝑋𝑐𝑜𝑢𝑛𝑡𝑟𝑦 𝐶𝐴𝑃𝐸𝑋𝐴𝑙𝑙 𝐷𝑂𝐿𝐴𝑙𝑙

Mean 0.00176 -0.01224 0.00318 -0.00286 0.00356

St. Dev 0.05820 0.29092 1.06232 0.38498 0.03312

C.2 Covariance matrix

Spot Rate

Changes

Excess

Returns ∆𝐶𝐴𝑃𝐸𝑋𝑐𝑜𝑢𝑛𝑡𝑟𝑦 𝐶𝐴𝑃𝐸𝑋𝐴𝑙𝑙 𝐷𝑂𝐿𝐴𝑙𝑙

Spot Rate Changes 1.0000 -0.16668

<0.0001

-0.15931

<0.0001

-0.21368

<0.0001

0.55503

<0.0001

Excess Returns -0.16668

<0.0001 1.0000

0.03158

0.1201

0.05136

0.0114

-0.11306

<0.0001

∆𝐶𝐴𝑃𝐸𝑋𝑐𝑜𝑢𝑛𝑡𝑟𝑦 -0.15931

<0.0001

0.03158

0.1201 1.0000

0.29824

<0.0001

-0.13372

<0.0001

𝐶𝐴𝑃𝐸𝑋𝐴𝑙𝑙 -0.21368

<0.0001

0.05136

0.0114

0.29824

<0.0001 1.0000

-0.39532

<0.0001

𝐷𝑂𝐿𝐴𝑙𝑙 0.55503

<0.0001

-0.11306

<0.0001

-0.13372

<0.0001

-0.39532

<0.0001 1.0000

38

Table (2): Country-Level Analysis for H1 – Developed Countries

This table report results of country-level regression for excess returns for individual currencies on both

the dollar and capex risk factors for two groups of countries - developed (Panel A) and all countries

(Panel B). The table shows the constant 𝛼, the slope coefficients 𝛽, the 𝑅2 of the regression, and the

standard errors in parentheses.

In particular, Panel A reports country-level results for developed countries from the following regression:

𝑧𝑖𝑡+1 = 𝛼 + 𝛽𝐷𝑂𝐿𝐷𝑒𝑣𝑒𝑙𝑜𝑝𝑒𝑑

𝐷𝑂𝐿𝑖𝑡+1𝐷𝑒𝑣𝑒𝑙𝑜𝑝𝑒𝑑

+ 𝛽𝐶𝐴𝑃𝐸𝑋𝐷𝑒𝑣𝑒𝑙𝑜𝑝𝑒𝑑

𝐶𝐴𝑃𝐸𝑋𝑖𝑡+1𝐷𝑒𝑣𝑒𝑙𝑜𝑝𝑒𝑑

+ 휀𝑖𝑡+1,

The 𝑧𝑖𝑡+1 is the excess return measured as the log forward rate minus the log 3-month expected spot rate.

The 𝐷𝑂𝐿𝑖𝑡𝐷𝑒𝑣𝑒𝑙𝑜𝑝𝑒𝑑

is the quarterly average of all spot exchange rate changes, using data from our

developed countries sample. The 𝐶𝐴𝑃𝐸𝑋𝑖𝑡+1𝐷𝑒𝑣𝑒𝑙𝑜𝑝𝑒𝑑

is the quarterly average of investment growth over our

basket of developed countries.

Panel B reports country-level results from the following regression:

𝑧𝑖𝑡+1 = 𝛼 + 𝛽𝐷𝑂𝐿𝐴𝑙𝑙 𝐷𝑂𝐿𝑖𝑡+1

𝐴𝑙𝑙 + 𝛽𝐶𝐴𝑃𝐸𝑋𝐴𝑙𝑙 𝐶𝐴𝑃𝐸𝑋𝑖𝑡+1

𝐴𝑙𝑙 + 휀𝑖𝑡+1,

The 𝐷𝑂𝐿𝑖𝑡𝐴𝑙𝑙 is the quarterly average of all spot exchange rate changes, using data from our all countries

sample The 𝐶𝐴𝑃𝐸𝑋𝑖𝑡𝐴𝑙𝑙 is the quarterly average of all countries’ investment growth over our entire sample

of developed and emerging currencies available on any given quarter.

Panel A: Developed Countries Panel B: All Countries

Country 𝛽𝐷𝑂𝐿𝐷𝑒𝑣𝑒𝑙𝑜𝑝𝑒𝑑

𝛽𝐶𝐴𝑃𝐸𝑋𝐷𝑒𝑣𝑒𝑙𝑜𝑝𝑒𝑑

𝑅2 𝛽𝐷𝑂𝐿𝐴𝑙𝑙 𝛽𝐶𝐴𝑃𝐸𝑋

𝐴𝑙𝑙 𝑅2

Australia 0.71371

1.12991

0.14980

0.09453 0.0330

-0.58313

1.54644

0.10105

0.13074 0.0144

Belgium -1.18355***

0.04883

-0.01459***

0.00423 0.8986

-1.31715***

0.11979

-0.02904***

0.01037 0.6479

Canada -0.41059***

0.09625

0.02032**

0.00870 0.2861

-0.68703***

0.11312

0.02968***

0.00989 0.4762

Denmark -1.21672***

0.04847

-0.01466***

0.00412 0.8937

-1.33491***

0.12071

-0.02815***

0.01035 0.6214

France -1.18329***

0.05130

-0.01424***

0.00434 0.8979

-1.40679***

0.12311

-0.02979***

0.01016 0.6835

Germany -1.17495***

0.05004

-0.01464***

0.00439 0.8962

-1.28388***

0.12143

-0.02648**

0.01063 0.6394

Italy -1.17278***

0.04908

-0.01449***

0.00426 0.8958

-1.29897***

0.11997

-0.02881***

0.01045 0.6404

Japan -0.44438***

0.16384

-0.01273

0.01451 0.0886

-0.59087***

0.22319

-0.02431

0.01948 0.0852

Netherlands -1.17978***

0.04885

-0.01387***

0.00424 0.8984

-1.30786***

0.11945

-0.02751***

0.01039 0.6468

New Zealand 0.48765

1.13264

0.15399*

0.09353 0.0345

-0.82158

1.53831

0.11749

0.13046 0.0216

Norway -1.07909***

0.08557

0.00830

0.00714 0.7003

-1.25921***

0.13593

0.00282

0.01160 0.5718

Sweden -1.14064***

0.07317

0.01387**

0.00634 0.7828

-1.34422***

0.12399

0.00500

0.01066 0.6468

Switzerland -1.05592***

0.08994

-0.01197

0.00772 0.6479

-1.13594***

0.15334

-0.03015**

0.01346 0.4210

UK -0.35243

0.48505

0.00232

0.04144 0.0076

-1.05964

0.64561

0.00456

0.05568 0.0409

*Significant at 10% level, **Significant at 5% level, ***Significant at 1% level.

39

Table (3): Country-Level Analysis for H1 - Developing Countries

Panel A: Developing Countries Panel B: All Countries

Country 𝛽𝐷𝑂𝐿_𝐷𝑒𝑣𝑒𝑙𝑜𝑝𝑖𝑛𝑔 𝛽𝐶𝑎𝑝𝑒𝑥_𝐷𝑒𝑣𝑒𝑙𝑜𝑝𝑖𝑛𝑔 𝑅2 𝛽𝐷𝑂𝐿_𝐴𝑙𝑙 𝛽𝐶𝑎𝑝𝑒𝑥_𝐴𝑙𝑙 𝑅2

Argentina -0.20594

0.15694

-0.00065154

0.01202 0.0536

-0.19222

0.14719

-0.00159

0.01272 0.0503

Brazil -1.71974***

0.31216

0.00946

0.02348 0.5246

-1.42677***

0.28923

0.02838

0.02462 0.5077

Chile -1.03006***

0.31079 0.00566 0.02381

0.2869 -0.93290***

0.28628 0.01117 0.02469

0.2924

Czech -1.31071***

0.22931 -0.02478

0.01831 0.3355

-1.71773

0.16784

-0.03020**

0.01421 0.6179

Egypt -0.37068**

0.14165

-0.01879*

0.01086 0.1569

-0.35725***

0.13226

-0.01521

0.01139 0.1611

Hong Kong 0.00509

0.01091

-0.00163*

0.00092607 0.0560

-0.00215

0.01085

-0.00176*

0.0009631 0.0449

Hungary -1.85738***

0.24260

-0.02211

0.01701 0.4968

-1.98584***

0.18236

-0.02641*

0.01442 0.6679

India -0.65876***

0.12460

0.01730*

0.00943 0.4170

-0.58525***

0.12198

0.01493

0.01014 0.3668

Indonesia -1.43677**

0.56763

0.05759

0.04429 0.1525

-1.50605***

0.55014

0.02647

0.04628 0.1335

Malaysia -0.58840***

0.10387

0.00540

0.00774 0.6264

-0.52290***

0.10243

0.00905

0.00854 0.5962

Mexico -0.41137**

0.19595

0.03107*

0.01620 0.1656

-0.21447

0.19395

0.03779**

0.01702 0.1213

Philippine -0.29479*

0.16183

0.02119*

0.01256 0.3013

-0.27296*

0.15747

0.02062

0.01341 0.2697

Poland -2.27030***

0.21365

-0.00145

0.01521 0.7572

-2.01364***

0.17742

0.00708

0.01493 0.7876

Portugal -0.88045***

0.17335

-0.01602

0.01394 0.2853

-1.30532***

0.11906

-0.02699***

0.01013 0.6471

Russia -1.41329***

0.17160

0.00989

0.01257 0.7186

-1.23706***

0.16321

0.01729

0.01378 0.6965

Saudi 0.00732

0.00569

0.00097772**

0.00049455 0.0517

0.00516

0.00551

0.00111**

0.00048790 0.0633

Singapore -0.80166***

0.06993

-0.01620***

0.00600 0.6443

-0.76259***

0.06551

-0.00757

0.00584 0.6604

S Africa -1.03464***

0.28695

0.02768

0.02271 0.2189

-1.07950***

0.26478

0.03973*

0.02250 0.2765

S Korea -1.08092***

0.19598

0.00845

0.01469 0.4904

-0.93955***

0.16232

0.02676*

0.01398 0.5700

Taiwan -0.56928***

0.10130

0.00272

0.00854 0.3713

-0.53277***

0.10014

0.00367

0.00888 0.3440

Thailand -1.01833

0.22633

-0.02493

0.01774 0.2154

-0.83527***

0.22768

-0.01621

0.01956 0.1569

Turkey -0.78724

0.64840

0.06689

0.05106 0.0731

-0.68361

0.59568

0.11867**

0.05073 0.1313

UAE 0.00890

0.00540

0.00096079**

0.00045190 0.0669

0.01026**

0.00516

0.00134***

0.00045465 0.1158

*Significant at 10% level, **Significant at 5% level, ***Significant at 1% level.

40

Table (4): Panel Regression Analysis for H1

This table report results of panel regression for excess returns, 𝑧𝑡+1, for individual currencies on DOL

factor, CAPEX factor, and forward discount (FD) (lines 1 through 4), for each group of countries -

developed (panel A), emerging (Panel B), and all (Panel C),

𝑧𝑡+1 = 𝛼 + 𝛽𝐷𝑂𝐿𝐷𝑒𝑣𝑒𝑙𝑜𝑝𝑒𝑑

𝐷𝑂𝐿𝑡+1𝐷𝑒𝑣𝑒𝑙𝑜𝑝𝑒𝑑

+ 𝛽𝐶𝐴𝑃𝐸𝑋𝐷𝑒𝑣𝑒𝑙𝑜𝑝𝑒𝑑

𝐶𝐴𝑃𝐸𝑋𝑡+1𝐷𝑒𝑣𝑒𝑙𝑜𝑝𝑒𝑑

+ 𝛽𝐹𝐷(𝑓𝑡 − 𝑠𝑡) + 휀𝑡+1 (𝑃𝑎𝑛𝑒𝑙 𝐴),

𝑧𝑡+1 = 𝛼 + 𝛽𝐷𝑂𝐿𝐷𝑒𝑣𝑒𝑙𝑜𝑝𝑖𝑛𝑔

𝐷𝑂𝐿𝑡+1𝐷𝑒𝑣𝑒𝑙𝑜𝑝𝑖𝑛𝑔

+ 𝛽𝐶𝐴𝑃𝐸𝑋𝐷𝑒𝑣𝑒𝑙𝑜𝑝𝑖𝑛𝑔

𝐶𝐴𝑃𝐸𝑋𝑡+1𝐷𝑒𝑣𝑒𝑙𝑜𝑝𝑖𝑛𝑔

+ 𝛽𝐹𝐷(𝑓𝑡 − 𝑠𝑡)

+ 휀𝑡+1 (𝑃𝑎𝑛𝑒𝑙 𝐵),

𝑧𝑡+1 = 𝛼 + 𝛽𝐷𝑂𝐿𝐴𝑙𝑙 𝐷𝑂𝐿𝑡+1

𝐴𝑙𝑙 + 𝛽𝐶𝐴𝑃𝐸𝑋𝐴𝑙𝑙 𝐶𝐴𝑃𝐸𝑋𝑡+1

𝐴𝑙𝑙 + 𝛽𝐹𝐷(𝑓𝑡 − 𝑠𝑡) + 휀𝑡+1 (𝑃𝑎𝑛𝑒𝑙 𝐶),

We report also the coefficients after replacing the CAPEX risk factor with individual country’s

investment growth (𝐶𝐴𝑃𝐸𝑋𝑡+1𝐶𝑜𝑢𝑛𝑡𝑟𝑦

) in the above three regressions (lines 5 through 8)

For each group of countries we report the slope coefficients 𝛽 using both cross-sectional fixed effect and

pooled OLS estimation. In the cross-sectional fixed Effect model, the underlying assumption is that the

heterogeneity comes from country’s cross sectional effects. Therefore, the raw data is converted to

deviations from a cross section’s mean. In pooled OLS model, the underlying assumption is that there are

no fixed effects or random effects present in the data. The standard errors are in parentheses.

Panel A: Developed Countries

A.1 Fixed Effect Coefficients A.2 Pooled OLS Coefficients

𝛽𝐷𝑜𝑙𝐷𝑒𝑣𝑒𝑙𝑜𝑝𝑒𝑑

𝛽𝐶𝑎𝑝𝑒𝑥𝐷𝑒𝑣𝑒𝑙𝑜𝑝𝑒𝑑

𝛽𝐶𝑎𝑝𝑒𝑥𝐶𝑜𝑢𝑛𝑡𝑟𝑦

𝛽𝐹𝐷 𝛽𝐷𝑜𝑙𝐷𝑒𝑣𝑒𝑙𝑜𝑝𝑒𝑑

𝛽𝐶𝑎𝑝𝑒𝑥𝐷𝑒𝑣𝑒𝑙𝑜𝑝𝑒𝑑

𝛽𝐶𝑎𝑝𝑒𝑥𝐶𝑜𝑢𝑛𝑡𝑟𝑦

𝛽𝐹𝐷

1 0.0373***

0.0108

0.0364

0.0277

2 -0.1649

0.1291

0.0339***

0.0111

-0.1861

0.3328

0.0325

0.0286

3 0.0117***

0.0042

0.9174***

0.0120

0.009509**

0.00428

0.9953***

0.0047

4 -0.0486

0.0504

0.0107**

0.0043

0.9170***

0.0120

-0.0391

0.0513

0.0087**

0.0044

0.9952***

0.0047

5 0.0043

0.0054

0.0068

0.0139

6 -0.2527**

0.1267

0.0029

0.0055

-0.2627

0.3255

0.0054

0.0141

7 0.0023

0.0021

0.9199***

0.0120

0.0022

0.0022

0.9955***

0.0048

8 -0.0729

0.0495

0.0019

0.0021

0.9191***

0.0120

-0.0582

0.0503

0.001841

0.00217

0.9954***

0.0048

41

Panel B: Developing Countries

B.1 Fixed Effect Coefficients B.2 Pooled OLS Coefficients

𝛽𝐷𝑜𝑙𝐷𝑒𝑣𝑒𝑙𝑜𝑝𝑖𝑛𝑔

𝛽𝐶𝑎𝑝𝑒𝑥𝐷𝑒𝑣𝑒𝑙𝑜𝑝𝑖𝑛𝑔

𝛽𝐶𝑎𝑝𝑒𝑥𝐶𝑜𝑢𝑛𝑡𝑟𝑦

𝛽𝐹𝐷 𝛽𝐷𝑜𝑙𝐷𝑒𝑣𝑒𝑙𝑜𝑝𝑖𝑛𝑔

𝛽𝐶𝑎𝑝𝑒𝑥𝐷𝑒𝑣𝑒𝑙𝑜𝑝𝑖𝑛𝑔

𝛽𝐶𝑎𝑝𝑒𝑥𝐶𝑜𝑢𝑛𝑡𝑟𝑦

𝛽𝐹𝐷

1 0.0220***

0.0046

0.0219

0.0045

2 0.06406

0.0643

0.0242***

0.0051

0.0446

0.0638

0.0234***

0.0050

3 0.0232***

0.0041

0.93337***

0.0476

0.0232***

0.0041

0.8527***

0.0446

4 -0.0085

0.0569

0.0229***

0.0045

0.93383***

0.0477

-0.0077

0.0567

0.0229***

0.0044

0.8530***

0.0447

5 0.0035**

0.0016

0.0035**

0.0016

6 -0.0511

0.0591

0.0033**

0.0017

-0.0661

0.0587

0.0033**

0.0017

7 0.0039***

0.0015

0.9310***

0.0481

0.0037**

0.0015

0.8497***

0.0450

8 -0.1166**

0.0523

0.0034**

0.0015

0.9379***

0.0481

-0.1154**

0.0523

0.0033**

0.0015

0.8546***

0.0450

Panel C: All Countries

C.1 Fixed Effect Estimates C.2 Pooled OLS Estimates

𝛽𝐷𝑜𝑙𝐴𝑙𝑙 𝛽𝐶𝑎𝑝𝑒𝑥

𝐴𝑙𝑙 𝛽𝐶𝑎𝑝𝑒𝑥𝐶𝑜𝑢𝑛𝑡𝑟𝑦

𝛽𝐹𝐷 𝛽𝐷𝑜𝑙𝐴𝑙𝑙 𝛽𝐶𝑎𝑝𝑒𝑥

𝐴𝑙𝑙 𝛽𝐶𝑎𝑝𝑒𝑥𝐶𝑜𝑢𝑛𝑡𝑟𝑦

𝛽𝐹𝐷

1 0.0320***

0.0065

0.0321**

0.0153

2 -0.1968**

0.0819

0.0253***

0.0070

-0.23793

0.1938

0.024051

0.0167

3 0.0197***

0.0035

0.8865***

0.0116

0.0182***

0.0036

0.9868***

0.0048

4 -0.0637

0.0443

0.0175***

0.0038

0.8858***

0.0116

-0.0455

0.0452

0.0168***

0.0039

0.9867***

0.0048

5 0.0038

0.0024

0.0046

0.0056

6 -0.3029***

0.0761

0.0025

0.0024

-0.33465*

0.1797

0.00321

0.00561

7 0.0031**

0.0013

0.8893***

0.0117

0.0030**

0.0013

0.9871***

0.0048

8 -0.1332**

0.0412

0.0025**

0.0013

0.8872***

0.0117

-0.1119***

0.0421

0.0024*

0.00131

0.9868***

0.005

*Significant at 10% level, **Significant at 5% level, ***Significant at 1% level.

42

Table (5): Portfolio Analysis for H1 – Descriptive Statistics

Panel A shows the means for the excess currency returns of portfolios sorted on individual country’s

forward discount. The countries are sorted into 5 portfolios. The 20% of countries with lowest forward

discount are allocated to portfolio P1, the next 20% to P2 and so on to portfolio P5 which contains the

20% of countries with the highest forward discount. Panel B reports the means for the excess currency

returns of portfolios sorted on both individual country’s CAPEX growth and forward discount. The

countries are sorted into 5 portfolios. The 20% of countries with lowest CAPEX growth are allocated to

portfolio C1, the next 20% to C2 and so on to portfolio C5 which contains the 20% of countries with the

highest CAPEX growth.

Panel A: Single Sorting

Developed Sample Developing Sample All Countries Sample

Portfolio 𝑧𝑖𝑡 CAPEX 𝑧𝑖𝑡 Portfolio 𝑧𝑖𝑡 CAPEX

P1 -0.56598 -0.01627 -0.01096 P1 -0.56598 -0.01627

P2 -0.01187 0.16986 0.00420 P2 -0.01187 0.16986

P3 -0.00190 -0.05571 0.00750 P3 -0.00190 -0.05571

P4 0.00984 0.04737 0.00721 P4 0.00984 0.04737

P5 0.38970 -0.11388 0.02103 P5 0.38970 -0.11388

Panel B: Double Sorting

B.1 Developed Countries

Portfolio C1 C2 C3 C4 C5 C5-C1

P1 -0.6693 -0.5406 -0.5218 -0.4464 -0.6374 0.0319

P2 -0.0165 -0.0099 -0.0086 -0.0173 -0.0097 0.0068

P3 -0.0267 -0.0037 0.0081 0.0043 0.0092 0.0359

P4 -0.0090 0.0113 0.0159 0.0130 0.0162 0.0252

P5 0.2719 0.3241 0.5131 0.4841 0.3943 0.1224

B2. Developing Countries

Portfolio C1 C2 C3 C4 C5 C5-C1

P1 -0.0298 -0.0016 -0.0058 -0.0209 -0.0003 0.0295

P2 0.0001 -0.0064 0.00060 0.0171 0.0045 0.0044

P3 -0.0084 -0.0029 0.0127 0.0186 0.0213 0.0297

P4 -0.0205 -0.0041 0.0239 0.0175 0.0201 0.0406

P5 -0.0312 0.0251 0.0421 0.0317 0.0471 0.0783

B3. All Countries

Portfolio C1 C2 C3 C4 C5 C5-C1

P1 -0.3663 -0.2691 -0.1736 -0.2191 -0.2543 0.112

P2 -0.0156 -0.0032 0.0063 -0.0024 0.0043 0.0199

P3 -0.0069 0.0036 0.0063 0.0178 0.0110 0.0179

P4 -0.0080 0.0035 0.0224 0.0157 0.0241 0.0321

P5 0.1175 0.1715 0.1674 0.2106 0.2217 0.1042

43

Table (6): Portfolio Analysis for H1 – Factor Betas

Panel A: One Factor Model

Developed Countries Developing Countries All Countries

Portfolio Intercept 𝛽𝐶𝑎𝑝𝑒𝑥𝐷𝑒𝑣𝑒𝑙𝑜𝑝𝑒𝑑

Intercept 𝛽𝐶𝑎𝑝𝑒𝑥𝐷𝑒𝑣𝑒𝑙𝑜𝑝𝑖𝑛𝑔

Intercept 𝛽𝐶𝑎𝑝𝑒𝑥𝐴𝑙𝑙

P1 -0.60556***

(0.03794)

0.07474

(0.09133)

-0.01167

(0.00480)

0.02771**

(0.01162)

-0.34951***

(0.02826)

0.02730

(0.07039)

P2 -0.00325

(0.00462)

0.00866

(0.01113)

0.00253

(0.00220)

0.00861

(0.00533)

-0.00228

(0.00360)

0.01895**

(0.00897)

P3 -0.00295

(0.00427)

0.02714***

(0.01028)

0.00469

(0.00469)

0.01817

(0.01136)

0.00326

(0.00376)

0.01832**

(0.00936)

P4 0.00309

(0.00475)

0.02048*

(0.01144)

0.00880**

(0.00443)

0.02267**

(0.01072)

0.00792*

(0.00459)

0.02641**

(0.01145)

P5 0.63798***

(0.04535)

0.15206

(0.10916)

0.02140***

(0.00704)

0.05247***

(0.01703)

0.22319***

(0.01491)

0.09390**

(0.03716)

Panel B: Two Factor Model

Developed Countries Developing Countries All Countries

Portfolio 𝛽𝐷𝑂𝐿𝐷𝑒𝑣𝑒𝑙𝑜𝑝𝑒𝑑

𝛽𝐶𝑎𝑝𝑒𝑥𝐷𝑒𝑣𝑒𝑙𝑜𝑝𝑒𝑑

𝛽𝐷𝑂𝐿𝐷𝑒𝑣𝑒𝑙𝑜𝑝𝑖𝑛𝑔

𝛽𝐶𝑎𝑝𝑒𝑥𝐷𝑒𝑣𝑒𝑙𝑜𝑝𝑖𝑛𝑔

𝛽𝐷𝑂𝐿𝐴𝑙𝑙 𝛽𝐶𝑎𝑝𝑒𝑥

𝐴𝑙𝑙

P1 2.16344***

(0.19505)

-0.04774

(0.05787)

0.87376***

(0.13317)

0.00506

(0.00996)

3.20926***

(0.23978)

-0.09136**

(0.03967)

P2 0.00910

(0.03844)

0.00814

(0.01140)

0.46428***

(0.05476)

-0.00343

(0.00410)

0.14692***

(0.05336)

0.01352

(0.00883)

P3 0.05340

(0.03500)

0.02411**

(0.01039)

1.04463***

(0.11039)

-0.00891

(0.00826)

0.13128**

(0.05644)

0.01347

(0.00934)

P4 0.00426

(0.03953)

0.02024*

(0.01173)

0.96027***

(0.10734)

-0.00222

(0.00803)

0.15140**

(0.06929)

0.02081*

(0.01146)

P5 2.76980***

(0.20348)

-0.00475

(0.06037)

1.65707***

(0.15340)

0.00950

(0.01148)

1.36114***

(0.17146)

0.04357

(0.02837)

44

Table (7): Panel Regression Analysis for H2

This table report results of panel regression for spot rate changes, ∆𝑠𝑡+1, for individual currencies on

DOL factor, CAPEX factor, and forward discount (FD) (lines 1 through 4), for each group of countries -

developed (panel A), emerging (Panel B), and all (Panel C),

∆𝑠𝑡+1 = 𝛼 + 𝛽𝐹𝐷(𝑓𝑡 − 𝑠𝑡) + 𝛽𝐷𝑂𝐿𝐷𝑒𝑣𝑒𝑙𝑜𝑝𝑒𝑑

𝐷𝑂𝐿𝑡𝐷𝑒𝑣𝑒𝑙𝑜𝑝𝑒𝑑

+ 𝛽𝐶𝐴𝑃𝐸𝑋𝐷𝑒𝑣𝑒𝑙𝑜𝑝𝑒𝑑

𝐶𝐴𝑃𝐸𝑋𝑡𝐷𝑒𝑣𝑒𝑙𝑜𝑝𝑒𝑑

+ 휀𝑡+1 ,

We report also the coefficients from replacing the CAPEX risk factor with country’s individual

investment growth (𝐶𝐴𝑃𝐸𝑋𝑡𝐶𝑜𝑢𝑛𝑡𝑟𝑦

) in the above regressions (lines 5 through 8).

For each group of countries we report the slope coefficients 𝛽 using both cross-sectional fixed effect and

pooled OLS estimation. In the cross-sectional fixed Effect model, the underlying assumption is that the

heterogeneity comes from country’s cross sectional effects. Therefore, the raw data is converted to

deviations from a cross section’s mean. In pooled OLS model, the underlying assumption is that there are

no fixed effects or random effects present in the data. The standard errors are in parentheses.

Panel A: Developed Countries

Fixed Effect Estimates Pooled OLS Estimates

𝛽𝐹𝐷 𝛽𝐷𝑜𝑙𝐷𝑒𝑣𝑒𝑙𝑜𝑝𝑒𝑑

𝛽𝐶𝑎𝑝𝑒𝑥𝐷𝑒𝑣𝑒𝑙𝑜𝑝𝑒𝑑

𝛽𝐶𝑎𝑝𝑒𝑥𝐶𝑜𝑢𝑛𝑡𝑟𝑦

𝛽𝐹𝐷 𝛽𝐷𝑜𝑙𝐷𝑒𝑣𝑒𝑙𝑜𝑝𝑒𝑑

𝛽𝐶𝑎𝑝𝑒𝑥𝐷𝑒𝑣𝑒𝑙𝑜𝑝𝑒𝑑

𝛽𝐶𝑎𝑝𝑒𝑥𝐶𝑜𝑢𝑛𝑡𝑟𝑦

1

-

0.0092***

0.0034

-

0.0092***

0.0033

2 0.0406

0.0401

-0.0083**

0.0035

0.0408

0.0399

-0.0083**

0.0034

3 0.0184*

0.0096

-

0.0097***

0.0034

0.0043***

0.0037

-

0.0093***

0.0033

4 0.0187*

0.0096

0.0421

0.0403

-0.0088**

0.0035

0.0043***

0.0037

0.0406

0.0401

-0.0084**

0.0035

5 -0.0027

0.0017

-0.0027

0.0017

6 0.0572

0.0393

-0.0024

0.0017

0.0574

0.0391

-0.0024

0.0017

7 0.0163*

0.0096

-0.0028

0.0017

0.0040

0.0038

-0.0027

0.0017

8 0.0171*

0.0096

0.0595

0.0395

-0.0024

0.0017

0.0041***

0.0038

0.0572

0.0393

-0.0024

0.0017

45

Table (7): Continued

Panel B: Developing Countries

Fixed Effect Estimates Pooled OLS Estimates

𝛽𝐹𝐷 𝛽𝐷𝑜𝑙𝐷𝑒𝑣𝑒𝑙𝑜𝑝𝑖𝑛𝑔

𝛽𝐶𝑎𝑝𝑒𝑥𝐷𝑒𝑣𝑒𝑙𝑜𝑝𝑖𝑛𝑔

𝛽𝐶𝑎𝑝𝑒𝑥𝐶𝑜𝑢𝑛𝑡𝑟𝑦

𝛽𝐹𝐷 𝛽𝐷𝑜𝑙𝐷𝑒𝑣𝑒𝑙𝑜𝑝𝑖𝑛𝑔

𝛽𝐶𝑎𝑝𝑒𝑥𝐷𝑒𝑣𝑒𝑙𝑜𝑝𝑖𝑛𝑔

𝛽𝐶𝑎𝑝𝑒𝑥𝐶𝑜𝑢𝑛𝑡𝑟𝑦

1 -0.0232***

0.0040

-0.0234***

0.0041

2 0.0128

0.0567

-0.0228***

0.0045

0.0164

0.0569

-0.0228***

0.0045

3 0.0566

0.0475

-0.0232***

0.0040

0.1412***

0.0446

-0.0232***

0.0041

4 0.0561

0.0477

0.0084

0.0568

-0.0229***

0.0045

0.1409***

0.0447

0.0078

0.0568

-0.0229***

0.0045

5 -0.0036**

0.0015

-0.0034**

0.00148

6 0.1213**

0.0522

-0.0032**

0.0015

0.1247**

0.0524

-0.0030**

0.0015

7 0.0590

0.0480

-0.0036**

0.0015

0.1442***

0.0450

-0.0034**

0.0015

8 0.0521

0.0480

0.1177**

0.0523

-0.0032**

0.0015

0.1392***

0.0450

0.1167**

0.0523

-0.003**

0.0015

Panel C: All Countries

Fixed Effect Estimates Pooled OLS Estimates

𝛽𝐹𝐷 𝛽𝐷𝑜𝑙𝐴𝑙𝑙 𝛽𝐶𝑎𝑝𝑒𝑥

𝐴𝑙𝑙 𝛽𝐶𝑎𝑝𝑒𝑥𝐶𝑜𝑢𝑛𝑡𝑟𝑦

𝛽𝐹𝐷 𝛽𝐷𝑜𝑙𝐴𝑙𝑙 𝛽𝐶𝑎𝑝𝑒𝑥

𝐴𝑙𝑙 𝛽𝐶𝑎𝑝𝑒𝑥𝐶𝑜𝑢𝑛𝑡𝑟𝑦

1

-0.0185***

0.0030

-0.0185***

0.0031

2 0.0433

0.0384

-0.0170***

0.0033

0.0421

0.0385

-0.0171***

0.0033

3

-0.0188***

0.0030

-0.0186***

0.0031

4 0.0462

0.0385

-0.0172***

0.0033

0.0432

0.0386

-0.0172***

0.0033

5

-0.0033***

0.0011

-0.0032**

0.0011

6

0.1097**

*

0.0358

-0.0028**

0.0011

0.1090***

0.0359

-0.0027**

0.0011

7

-0.0033***

0.0011

-

0.0032***

0.0011

8

0.1130**

*

0.0359

-0.0028**

0.0011

0.1101***

0.0360

-0.0027**

0.0011

*Significant at 10% level, **Significant at 5% level, ***Significant at 1% level.

46

Table (8): Portfolio Analysis for H2

The table reports the means for the spot exchange rate changes, ∆𝑠𝑖𝑡, for portfolios sorted on both

individual country’s CAPEX growth and forward discount. The countries are sorted first into 5 portfolios

according to the forward discount: The 20% of countries with lowest forward discount are allocated to

portfolio P1, the next 20% to P2 and so on to portfolio P5 which contains the 20% of countries with the

highest forward discount. These portfolios are then sorted into 5 portfolios according to the CAPEX

growth, so that the 20% of countries with lowest CAPEX growth are allocated to portfolio C1, the next

20% to C2 and so on to portfolio C5 which contains the 20% of countries with the highest CAPEX

growth. Each panel reports statistics for portfolios based on the developed, developing, and the full

sample.

Panel A. Developed Countries

Portfolio C1 C2 C3 C4 C5 C5-C1

P1 0.03318 0.00415 -0.02300 -0.00845 -0.01149

P2 0.01261 0.00521 0.00361 0.01241 0.00619

P3 0.02522 0.00256 -0.00981 -0.00474 -0.01077

P4 0.01002 -0.00990 -0.01518 -0.01172 -0.01599

P5 0.00196 -0.01326 -0.01167 -0.00734 -0.02421

Panel B. Developing Countries

Portfolio C1 C2 C3 C4 C5 C5-C1

P1 0.01918 -0.000251 -0.00052 0.00531 -0.00376

P2 0.0000733 0.00724 -0.00589 -0.01471 -0.00376

P3 0.01571 0.00800 -0.00814 -0.01360 -0.01808

P4 0.03298 0.01620 -0.00866 -0.00485 -0.00685

P5 0.06992 0.00434 0.01118 0.01428 0.00602

Panel C. All Countries

Portfolio C1 C2 C3 C4 C5 C5-C1

P1 0.03126 0.00377 -0.00606 0.00127 -0.00270

P2 0.01301 0.00252 -0.00781 0.00216 -0.00598

P3 0.00909 -0.00241 -0.00531 -0.01714 -0.01076

P4 0.01477 0.00294 -0.01517 -0.00896 -0.01671

P5 0.05359 0.00726 0.00788 0.00419 -0.00180

47

Figure (1): Average Values of Spot rate changes, excess returns, DOL and CAPEX factors

This figure displays average quarterly values of four variables - Spot rate changes, excess

returns, dollar and CAPEX factors for our full sample of countries. The spot rate changes, ∆st+1,

are the spot exchange rate changes measured as log returns, where 𝑆𝑡 is the spot exchange rate of

the foreign currency against the USD, measured as the number of units of the foreign currency

per one U.S. dollar. The excess return is measured as the log forward rate minus the log 3-month

expected spot rate. The CAPEX factor is measured as the average of all countries’ investment

returns (CAPEX_country) over all currencies available on any given quarter. The DOL factor is

the average of all countries’ changes in the spot exchange rate of the foreign currency against the

USD dollar versus all the other currencies. The sample period is from Q1 1985 until Q2 2014.

1. CAPEX_ALL 2. DOL_ALL

3. Excess Returns 4. Spot Rate Changes