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A Risk-Oriented Model for Factor Rotation Decisions
Keith L. Miller
a,
, Hong Li
b,
, PhD, Tiffany G. Zhou
c,
, and Daniel Giamouridis
d,
, PhDa Managing Director, Head, Global Quantitative Research, Citigroup
388 Greenwich Street
New York, NY 10013Fax: +1 (212) 816 3144
Tel: +1 (212) 816 2285E-mail: [email protected]
c Managing Director, Global Quantitative Research, Citigroup
Tel: +1 (212) 816 1844E-mail: [email protected]
c Vice President, Global Quantitative Research, Citigroup
Tel: +1 (212) 816 4659E-mail: [email protected]
Assistant Professor, Department of Accounting and Finance, Athens University of Economics andBusiness, Athens, Greece
Athens University of Economics and BusinessDepartment of Accounting and Finance76 Patission Street10434 Athens, Greece
Tel: +30 210 8203925Fax: +30 210 8203936
E-mail: [email protected]
Please indicate affiliation as: Daniel Giamouridis is an assistant professor in the Department of
Accounting and Finance at Athens University of Economics and Business in Athens, Greece; asenior visiting fellow in the Faculty of Finance at Cass Business School, City University in London,UK; and a research associate at EDHEC-Risk Institute in Nice, France.
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Abstract
We develop a factor rotation model that is suitably tailored to accommodate severe market
conditions and largely to-date neglected phenomena, like factor crowdness, macroeconomic risks
(concentration), and sudden factor reversals. Our model uses classification tree analysis on a
number of fundamental factor characteristics as well as novel measures we develop through
detailed risk attribution analysis of the factor. The model we propose provides significant value
when applied in a single-factor setting. The outperformance of our model is even more
pronounced when it is used in a dynamic multi-factor setting, where the risk/reward more than
triples and the hit ratio improves by about 15% relative to the equally weighted model.
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Introduction
One principal decision in equity portfolio management is the determination of portfolio factor
tilts. That is, given equity markets are segmented segments comprise stocks with common
characteristics such as beta, size, value, growth, quality, momentum, among others and stocks
from different segments realize different average risk-adjusted returns for extended periods, it is
critical for an equity portfolio manager to be able to time a segment of the market. This facet of
the investment decision process is typically referred to as style rotation or factor timing.
Factor timing has for long attracted the interest of academics and practitioners. As a concept it is
a variant of market timing between cash and equities which was first studied by Sharpe (1975).
Kester (1990) expanded the scope of market timing strategies by including small firms, while
subsequent works by Case and Cusimano (1995) and Sorensen and Lazzara (1995) among others
study tactical allocations to value and growth stocks. Ahmed, Lockwood, and Nanda (2002),
Arshanapalli, Switzer, and Panju (2007), Bauer, Derwall, and Molenaar (2004), Desrosiers, et al.
(2006), Kao and Shumaker (1999), L'Her, Mouakhar, and Roberge (2007), Levis and Liodakis
(1999), and Miller et al. (2012) are indicative studies that have more recently documented
significant added value from over-weighted positions in the outperforming segment during the
appropriate periods.
Quantitative approaches for factor allocation decisions are broadly speaking based on two
building blocks. One building block is the set of variables that are assumed to explain the time
variation of style returns. The second block is the model used to facilitate the relationship
between the explanatory variables and the style return. The models (and variables) that have thus
far been proposed can be classified in four broad categories: a) models based on return
momentum (see, e.g. Clare, Sapuric, and Todorovic, 2010, Chen and De Bondt, 2004), b)
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multivariate regressions based on economic fundamentals, business cycle variables, or predictors
to the stock market or aggregate fundamentals (see, e.g. Copeland and Copeland, 1999, Lucas,
van Dijk, and Kloek, 2002), c) logit multivariate models using similar variables as the
multivariate linear models (see, e.g. Bauer, Derwall, and Molenaar, 2004, Levis and Liodakis,
1999), and d) non-parametric techniques such as the Classification and Regression Decision Tree
(see, e.g. L'Her, Mouakhar, and Roberge, 2007). Miller et al. (2012) develop a hybrid model that
relies on the Classification and Regression Decision Tree approach but also on multivariate
predictive regressions.
Recent episodes in financial markets however suggest that these approaches, even the most
sophisticated ones, might not be perfectly suited to tackle these, undoubtedly, unprecedented
events.1 Our investigation of the events reaches three main conclusions that are particularly
important for factor rotation decisions. Our first conclusion suggests that there can be instances
when the number of similarly constructed portfolios increases dramatically, i.e. factor portfolios
become highly correlated and crowded, and this in turn induces significant systemic risk. Our
second conclusion, which is our main motivation, is that there may be periods when
macroeconomic factors become the most important drivers of style portfolio returns. Given the
global reach of these factors, this represents risky periods. Further we observe that most stock
selection factors have experienced very high volatility and frequent reversals in performance over
the last few years. Factor/style rotations have been compressed into shorter periods of time. We
conclude that understanding the systematic risk of factors is important for predicting their future
performance.
1 Lo (2012) provides a comprehensive review of books written about the recent crisis while an earlier paper byKhandani and Lo (2011) provides a more focused analysis for quantitative equity investors.
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We argue that modern style rotation decision models should provide the best possible account for
these conclusions. The model we develop in this article integrates measures that are suitably
tailored to capture events of risk concentration on macroeconomic (or other) factors. We apply
our model with shorter time rebalancing to capture potential short-term factor reversals and
overall conclude that the framework we propose adds significant value. Although independently
developed, our framework encompasses the premises identified as critical for contemporary
active quantitative portfolio management in a recent thought provoking work by Li and Sullivan
(2011). Before we proceed with the detailed presentation of our approach, in the next Section we
present the empirical analysis that led us to the conclusions we refer to earlier and, ultimately, to
the development of our dynamic factor rotation model.
What have we learned from recent market episodes?
The recent history of quantitative equity investing has experienced a series of unfortunate events.
Like other investment processes and styles, quantitative strategies regularly experience periods of
underperformance. What makes the recent past unique and particularly painful is the extended
period of underperformance. Over the last few years, the underlying causes of underperformance
have, to some degree, varied. In this Section we explore the nature of the recent events to further
our understanding on the fundamental causes of these episodes and build our priors as to what
directions should be pursued for improving factor rotation decision models.
We conduct our investigation with four common quantitative equity factors, namely Momentum,
Earnings Revision, Book Yield, and Earnings Yield. These factors represent long/short portfolios
of stocks. They are constructed based on quintile ranks of the S&P 500 stocks on the respective
factor, and equal weighting. The Momentum factor is a portfolio that holds the top quintile of
S&P 500 stocks ranked with respect to their past 12 months (excluding last month) performance
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and sells short the bottom quintile. The Earnings Revision factor comprises stocks quintiled with
respect to their 4-week change in FY1 estimates. Book Yield and Earnings Yield are portfolios
constructed on the basis of the firms Book-to-Price and Earnings-to-Price ratios respectively.
Khandani and Lo (2011) use similar quantitative equity factors in their analysis (i.e. Book-to-
Market, Earnings-to-Price, Cashflow-to-Market, Price Momentum and Earnings Momentum).
The 2007 Liquidity Crisis. The long-term success of many quantitative strategies brought about
their widespread adoption by many investors including hedge funds. The sustained low volatility
and low return environment resulted in greater use of leverage. Leverage combined with the
commonality of many quant strategies made this a crowded trade (see also Li and Sullivan,
2011). Losses in other strategies in other asset classes induced liquidation of equity-market-
related strategies. This in turn resulted in the simultaneous failure of what are normally
uncorrelated stock selection factors. Brunnermeier (2009) and Brunnermeier and Pedersen (2012)
formalize this interpretation with the concepts of the loss spiral and the margin/haircut spiral.
We thus hypothesise that measures of crowdness should be associated with the failure of stock
selection factors and hence have a negative impact on factor returns.
To validate this hypothesis we conduct a factor short-interest analysis. We consider short interest
as a proxy for measuring factor crowdness. We expect that the extent to which similar
quantitative equity market portfolios are constructed in the market, will be reflected on the
amount of stocks shorted given the nature (i.e. long/short) of these strategies. Hwang and Liu
(2012) adopt a similar approach to infer investors involvement in certain anomalies. For
economy of space we present in Figure 1 results only for the Momentum factor (results for all
other factors are available upon request). Figure 1 indicates the rank correlation between short
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interest ratios, defined as short interest outstanding divided by shares outstanding, and price
momentum rankings from 1995.
[Figure 1 about here]
An increasingly negative correlation indicates that there is growing short interest in lower
momentum stocks and shrinking short interest in higher momentum stocks. This could signal a
strong and perhaps overly bullish view on the prospects for high momentum stocks and hence
suggest the strategy is becoming crowded. The evidence in Figure 1 suggests that this correlation
measure has been constantly trending downwards in 2007 and has reached its full period
historical low in late 2007. We reach similar conclusions when we examine rank correlations for
Earnings Revisions and Book Yield (in 2008 in particular). This pattern is less pronounced for
Earnings Yield. The overall evidence suggests that the 2007 episode was likely a manifestation of
systemic risk due to extensive investment in similar quantitative equity portfolios. Khandani and
Lo (2011) also document that the Quant Meltdown of August 2007 was the combined effects of
portfolio deleveraging and a temporary withdrawal of market-making risk capital using
transaction data analysis.
2008: Simultaneous Failure of Factors in the Face of a Worsening Credit Crisis. With much
of the deleveraging having already occurred in 2007, quantitative strategies continued to struggle,
especially globally in 2008. Over the course of 2008, the simultaneous failure of value and
momentum factors occurred on multiple occasions. During these moments, the credit sensitivity
of value factors was exposed while concerns around global economic growth negatively impacted
momentum factors. During this period, both fundamental and quantitative investors struggled.
Therefore we argue that the macroeconomic regime can under certain market conditions be a
significant determinant of factor return. This is evident in our investigation. We conduct risk
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analysis of the factors and measure the degree of total factor return variation that is explained by
distinct broad risks, i.e. macroeconomic, market/sector, style/size, and idiosyncratic. In this
Section we focus on the results of this investigation. We provide details of our risk analysis
approach later in the text.
[Figure 2 about here]
Figure 2 illustrates select results of this analysis. The top graph illustrates the risk decomposition
of the factor. In the bottom two graphs, the bars represent the net betas to each risk factor and the
line represents the underlying risk factor. Panel A of Figure 2 shows that the portion of
Momentum risk attributable to macroeconomic risk factors almost doubled during 2008 and
2009. Towards the end of the first half of 2008, Momentum presents with increasingly positive
oil exposure (during a period when oil prices rose from $75 to above $140). These positive oil
exposures resulted in a significant performance drag as oil prices collapsed afterwards.
Fortunately, the negative impact of falling oil prices was somewhat offset by a defensive credit
exposure, which benefited from widening credit spreads as the global financial crisis intensified.
Panel B of Figure 2 suggests that at times over the last few years of the sample, macroeconomic
risks have become a substantial part of the total risk of Earnings Revision. It also illustrates the
variation in the factor exposure to oil prices and credit spread over time. The evidence we gather
from this analysis overall suggest that macro risk and risk concentration is an important
determinant of factor performance.
The Risk Rally of 2009 and the better-than-expected performance of 2010-2011. Since
March 2009, previously beaten down stocks have rallied strongly with the improving economic
outlook. Specifically, low price-to-book, low price-to-sales, high CAPM beta stocks have posted
very strong performance while earnings revisions and long-term price momentum, and
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profitability strategies have significantly underperformed. Table 1illustrates the performance of
the four factors we consider in our analysis. Similar patterns are observed in unreported analysis
for the rest of the factors we examined. Rank correlations between factors have been largely
dynamic. Quantitative strategies were not well positioned for this low quality risk rally. Common
risk exposures to oil in 2008 as well as common risk exposures to credit in 2009 are the main
reasons why the factors failed simultaneously. While quantitative investors had de-risked over the
previous two years, many still underperformed due to the negative correlation between value and
momentum, which led to an underweighting of the highest beta stocks. In 2010-2011 we saw a
marked improvement in performance compared to the performance in the 2007-2009. That said,
2010-2011 also saw several significant reversals in factor performance, as is evident in Table 1 ,
which left most investors with near-benchmark results.This evidence overall suggests that factors
have been very dynamic and may exhibit strong reversals in certain market regimes.
[Table 1 about here]
In 2012 we observe significant increase in the macroeconomic risk portion of total risk. For
example, for momentum, the macro portion of risk has risen above 70%, which represents a 13-
year high.
In summary our investigation reaches three main conclusions that are important for making
educated style rotation decisions. First, that there can be instances when the number of similarly
constructed portfolios increases dramatically, i.e. factor portfolios become highly correlated and
crowded, and this in turn induces significant systemic risk. Second, that there may be periods
when macroeconomic factors become largely important drivers of style returns. Given the global
reach of these factors this represents risky periods. Third, that factor/style rotations have been
compressed into shorter periods of time. Understanding the systematic risk of factors is extremely
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important for predicting their future performance. We therefore propose integrating these ideas in
the context of style rotation for the first time in the literature.
A risk-oriented factor rotation model
We structure the presentation of the proposed model as follows. First we discuss the variables
that we consider as relevant for predicting factor returns. Next, we discuss the statistical
technique that we use to associate the hypothesized relevant variables with subsequent factor
returns.
The predictive variables
The set of independent variables we propose comprises two groups of variables. The first group
consists of variables that measure the fundamental characteristics of factors. The second group
comprises macroeconomic and market exposures of factors. These are all combined in a
predictive model which we discuss in the subsequent sub-section. Hence our approach is able to
capture characteristics as well as betas which have both been found in numerous studies to
explain the cross-sectional variation in expected stock returns (see, e.g. Chordia, Goyal, and
Shanken, 2012).
We measure the fundamental characteristics of the factors through aggregate, i.e. bottom-up,
measures of mainly valuation, growth, momentum, and risk. Our variable is then the relative
distance of the bottom-up measure of the factor top portfolio vs. the factor bottom portfolio. To
give an example, one of our variables is the factor relative book-to-price. This is simply the
equally-weighted book-to-price of every stock in the top portfolio of the factor, e.g. the S&P 500
stocks in the top quintile of the price momentum factor, divided by the equally-weighted book-to-
price of every stock in the bottom portfolio of the factor, i.e. S&P 500 stocks with the lowest 20%
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of price momentum. The full set of fundamental characteristics includes the earnings yield,
earnings growth rate, return on equity, dividend yield, historical volatility, momentum, earnings
revisions, forward earnings yield, and market beta.
Macroeconomic and market exposures of style returns are obtained from Citis US Risk Attribute
Model (USRAM hereafter). The USRAM is a highly regarded risk analysis model that was first
introduced in 1989 and has since been widely used by equity portfolio professionals. It is a
macroeconomic time series factor model, which can be represented by the following equation for
an individual stocki:
ME ME EM EM S S
it i ij jt ij jt i t it
j j
r a b F b F b F e= + + + + (1)
where:
itr = the total return of the stock during period t,
ia = the expected total return of the stock when all of the factors equal zero; a constant
component of the stock return that is independent of both the factors and the
period,
ME
jtF = the realization of the macroeconomic factorj during period t,
ME
ijb = the sensitivity of the stock to macroeconomic factorj,
EM
jtF = the realization of the equity market factorj during period t,
EMijb = the sensitivity of the stock to equity market factorj,
=S
tF the sector (the stock belongs) factor during period t,
=S
ib the sensitivity of the stock to its sector factor,
ite = the unsystematic (idiosyncratic) component of the styles total return that is
independent of the factors during period t.
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The macroeconomic factors of the model include: Inflation shock, measured as the actual vs.
consensus expectation of monthly change in CPI, long-term interest rates, which are proxied by
the 10-year US Treasury note yields, short-term interest rates, measured as the 3-month US
Treasury bill yields, credit spread, which is the yield spread between Citi High Yield index and
US 10-year note, oil price, that is the price of WTI benchmark crude oil, and dollar exchange
rate, which is measured as the Bank of England trade-weighted effective rate US dollar index.
The market-based risk factors comprise: market, the S&P 500 Index returns,small cap premium,
the return spread of Russell 2000 index vs. S&P 500 Index, growth/value premium, the return
spread of S&P 500 Growth Index vs. Value Index, andsector, the S&P 500 GICS sector returns.
Intuitively the USRAM model can be viewed as a Fama and French (1993) three-factor model
augmented with macroeconomics risk factors. It nests many of the variables proposed by Li and
Sullivan (2011) as those that quantify big-picture issues. All market-based risk factors are
orthogonilized with respect to the macroeconomic factors.Our factor return explanatory variables
are estimates of the betas from equation (1) when it is applied to equity style (as opposed to
single stock) returns. We also use as explanatory variables the variance of certain groups of
factors as a fraction of the total return variance of the style. We provide more details on USRAM
in the Appendix where we also show evidence that macroeconomic risk has recently become
extremely important and in particular has accounted for more than 50% of the total explained risk
in 2010-2012.
The model
The model we develop uses classification tree analysis to determine a forecast. Classification
decision tree analysis (DT hereafter) is a multivariate statistical technique that explores
conditional relationships between a dependent variable and a set of explanatory variables.
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Sorensen, Miller, and Ooi (2000) provide a very detailed discussion of the DT methodology.
Miller et al. (2012) find that the DT approach - as an element of a multiple predictive regression
model - is largely successful in the context of size rotation. The DT statistical technique examines
the historical values of a set of variables and determines the subset that has the greatest power to
explain the one period ahead Information Coefficient2 (IC hereafter) of a factor. Using data for
the period we examine we find that in many instances macroeconomic variables as well as
variables related to the percentage of total factor return variation explained by a group of factors
had the greatest explanatory power in the classification tree model.
The DT analysis also determines the optimalsequence for screening with these variables, as well
as the optimal screening criteria. Figure 3 depicts a complete decision tree estimated for
Momentum (Panel A) and Earnings Revisions (Panel B). Our model found that (see Panel A of
Figure 3) if the fraction of the total return variance of the Momentum factor that is explained by
the Size risk factor was above the eightieth percentile of its historical values (where the first
percentile contains the lowesthistorical values) at the end of a month, then firms in the bottom
quintile of past 12 months (excluding last month) performance were more likely to outperform
their top quintile counterparts during the next month (Reversal). However, if this condition held
but the Momentum style (Growth/Value) slope was below the 34th
percentile of its historical
values, then the bottom quintile of past 12 months (excluding last month) performance were more
likely to underperform their top quintile counterparts in the next month (Momentum). Similarly
we found that (see Panel B of Figure 3) the Earnings Revision factor performance depends on the
fraction of the total return variance of the factor that is explained by the Style risk factor. It is
further conditional on the total return variance of the factor that is explained by macroeconomic
2 The Information Coefficient measures the cross-sectional correlation between the security retun forecasts comingfrom a factor and the subsequent actual returns for securities.
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risk factors. Proceeding in this manner, the model estimates a complete decision tree whose path
is determined by applying a specific if-then rule at each branch. Thus, the DT analysis allows
us to explore nonlinear relationships, measure the interactions among variables, and capture the
conditional relationships between factor performance and the explanatory variables.
[Figure 3 about here]
Advantages of the model
The models most important novel element is the integration of systemic risk variables in the set
of independent variables. Recent evidence suggests that systemic risk measures are important for
market timing purposes (Kritzman et al., 2011) as well as for identifying instances of increasing
likelihood of market crashes (Berger and Pukthuanthong, 2012). Moreover, Khandani and Lo
(2011) argue that the Quant Meltdown of August 2007 was largely a consequence of systemic
risks posed by the hedge-fund industry.
Our model tackles two different facets of systemic risk.3 First, the perspective of a likely crowded
trade; and second the perspective of macroeconomic risk concentration. To best measure the
former we would ideally have liked to use direct measures4
or even short interest data.
Unfortunately, these data do not currently present with sufficient history for our analysis. We
believe that particularly our variables that measure the fraction of total return variation of a factor
explained by a (group of) factor(s) provide an indication of a crowded traded. It is in the spirit of
Pojarliev and Levich (2011) who provide a measure of crowdness that is based on the
sensitivities of a large cross-section of individual manager returns on common forex related
factors. We measure macroeconomic risk concentration through the fraction of total return
3 Bisias et al. (2012) in their comprehensive survey of systemic risk analytics argue that systemic risk is complex andadaptive and hence more than one measure is needed to capture it.4 A direct measure could involve transaction data in light of the insights of Khandani and Lo (2011).
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variation of a factor explained by macroeconomic variables. Our variables provide stronger
economic justification relative to Kritzman et al. (2011) and Berger and Pukthuanthong (2012)
who rely on Principal Component Analysis, and are more suitably tailored for factor rotation
decisions. We are not aware of any other study that is concerned with the impact of increased
systemic risk in the context of factor rotation although as we discuss earlier it is extremely
important.
Another critical aspect of the model we propose is the actual statistical technique that we use to
facilitate the relationship between the predictive variables and the Information Coefficient of the
factor. L'Her, Mouakhar, and Roberge (2007) highlight that parametric approaches, i.e. predictive
regressions or logit models, are attractive for the reasons that they are not hard to
implement/estimate, identify a specific correlation structure between the predictive and the
predicted variables, and in most instances use parsimonious models. However they suggest that
parametric models have inherent limitations due to the restrictive distributional assumptions, the
linear functional forms which are also not a priori known, and the sensitivity to outliers. Kao
and Shumaker (1999) also stress that regression analysis is based on stringent assumptions. The
DT approach on the other hand lets the data determine the structure of the variable association, is
not subject to strict assumptions of linearity and normality, and is robust in handling outliers.
This is an important improvement also over measures such as the Absorption Ratio (Kritzman et
al., 2011) or the Fragility Index (Berger and Pukthuanthong, 2012) which, although effective in
measuring systemic risk, maintain a fixed structure and rely on some ad-hoc assumptions.5
L'Her,
Mouakhar, and Roberge (2007) however stress that the DT approach bears significant risk of
5 Kritzman et al. (2011) for example fix the number of eigenvectors at approximately 1/5 th the number of assets intheir sample.
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over-fitting, and may in some cases yield relations that are contrary to theory or intuition, and are
generally very data-consuming.
Empirical analysis
Our empirical analysis is applied with stocks from the S&P 500. We use monthly data from
December 1978 to December 1998 to fit our model. The model was recalibrated on a monthly
basis using an expanding window. Our out-of-sample analysis covers the period January 1999 to
August 2012. To tackle the dynamic behaviour of factors we rebalance the factor portfolio
monthly. We apply three trading schemes. Our baseline model (Baseline) is a portfolio strategy
that holds stocks in the top quintile of the factor and shorts stocks in the bottom quintile of the
factor, i.e. a constant bet on the factor. In terms of our rotation models, we test two versions. One
that buys the top quintile and sells the bottom quintile if the DT forecast is positive, and 0 if the
DT forecast is negative (Active). And a second, that buys the top quintile and shorts the bottom
quintile if the DT forecast is positive, and buys the bottom quintile and shorts top quintile if the
DT forecast is negative (Aggressive). Contrasting these three trading approaches helps us
determine the incremental value of our model to predict future factor returns.
Single factor evidence
In Table 2 we present a number of performance metrics that will help us conclude whether the
model we propose adds value. We present the results relating to the analysis of the Momentum
factor in Panel A, Panel B depicts the performance metrics for the Earnings Revision factor, and
Panel C and Panel D tabulate the results for Book Yield and Earnings Yield respectively.
We overall conclude that the proposed methodology adds significant value for single factor
rotation. For all the factors we examine the Active and Aggressive models that rely on
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predictions of the proposed model largely outperform the Baseline model across literally all
metrics. In particular, the Baseline strategy produces average annualized returns that are not
significant for any of the four factors examined. In sharp contrast the respective average
annualized returns produced through the Active trading scheme are highly significant for Book
Yield (p-value=0.01) and also for Earnings Yield (p-value=0.06). The returns of the Aggressive
strategy are largely significant for Earnings Revisions (p-value=0.04), Book Yield (p-value=0.01)
and Earnings Yield (p-value=0.03) and at the margin for Momentum (p-value=0.14). The Active
and Aggressive model compare favourably in terms of risk/reward, hit ratio, average return when
the prediction is correct (as well as when it is not correct) relative to the Baseline model. The
bottom two rows of Table 2 suggest that the DT model (which is the basis of both the Active and
the Aggressive schemes) passes the Henrikson and Merton (1981) non-parametric (a p-stat higher
than 1 indicates that the model has genuine predictive ability) and parametric tests for market
timing. Moreover, a possible criticism for the DT model, that it requires more frequent switches,
which in the context of portfolio management translate into higher transaction costs, does not
seem to be a concern given the relatively small number of switches we report. Statistical
significance for the mean is tested with a t-test. The statistical significance of the return per unit
of risk ratio is tested on the basis of 10,000 bootstrapped samples from the strategies original
return sample.
[Table 2 about here]
Dynamic factor weighting model
In this subsection we illustrate how the proposed model can be used in a setting that is more
relevant for equity portfolio managers. From that perspective, what is critical is a process that
combines multiple stock level signals in the portfolio construction process. We propose a scheme
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that is based on the insights we provide earlier. Our active decisions in the multi-factor setting are
based on dynamic weighting that depend on the predicted ICs. In particular we term Active
Dynamic a strategy that assigns double weights to positive IC factors relative to the negative IC
factors. We also term Aggressive Dynamic a strategy that uses equal-weighting of positive IC
factors only, and zero if all four factors have negative ICs. We benchmark these strategies against
a Baseline Multi-Factor approach that uses equal-weighting across the four factors.
[Figure 4 about here]
In Figure 4, we show the historical monthly performance of the models from January 1999
through to August 2012. We plot the cumulative total return index level of the portfolios obtained
through the Baseline Multi-Factor, the Active Dynamic, and the Aggressive Dynamic
approaches. We assigned a value of 100 to each index at the end of December 1998. The results
suggest that the Aggressive Dynamic approach with terminal index of 344 outperforms both the
Active Dynamic and the Baseline Multi-Factor, which present with terminal values of 200 and
123 respectively. The increase in terminal wealth of the Active Dynamic and the Aggressive
Dynamic models over the Baseline Multi-Factor is of the magnitude of 72% and 180%
respectively.
[Table 3 about here]
In Table 3 we present several performance metrics that overall provides strong support for the
dynamic factor rotation model we propose. The Active Dynamic model outperforms the Baseline
Multi-Factor in terms of average arithmetic annualized return by almost 4% per year. The
outperformance of the Aggressive Dynamic model over the Baseline Multi-Factor is about 8%
per year. Comparing the Aggressive Dynamic model with the Baseline Multi-Factor provides
favourable assessments for the former for almost all metrics we report. The risk / reward of the
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Aggressive Dynamic model more than triples relative to the Baseline Multi-Factor, from 0.18 to
0.58. The hit ratio improves by about an absolute 10%, from 55.49% to 64.02%, which is more
than 15% in relative terms. This improvement does not seem to come at a significant
implementation cost as we can infer from the turnover statics we present in the bottom row of
Table 3.
[Figure 4 about here]
To rule out the possibility that the results of our analysis are concentrated in certain periods that
make up for poor performance in other periods, we carry out a sub-period analysis. We split the
sample in two almost equal sub-samples, i.e. from January 1999 to December 2005 and from
January 2006 to August 2012, and repeat the analysis. We report the results in Table 4. These
results should be interpreted cautiously given the relative short time series they represent. The
results indicate that the conclusions reached in the previous section for the whole period hold true
in the sub-periods. We observe that all models perform better in the first sub-sample; however the
relative ranking of the models remains intact in the second sub-period. In fact, in the second sub-
period we observe that the economic benefits of the Aggressive Dynamic model are more
pronounced; in fact it is the only model that produces positive average returns.
[Table 4 about here]
In additional analysis (available on request) we used a binomial distribution (and assumptions
about its normality) to assess the statistical significance of the incremental value of the
Aggressive Dynamic model over the Active Dynamic model, as well as over the Baseline Multi-
Factor model with respect to their hit rates. In the full sample, we concluded that the Aggressive
Dynamic models incremental value over the Active Dynamic was marginally statistically
significant at the 5% significance level (t-statistic=1.96). We also found that the Aggressive
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Dynamic models incremental value over the Baseline Multi-Factor was highly statistically
significant (t-statistic=4.43). In the sub-samples the respective statistics are 1.00 and 3.66 for the
first sub-period and 1.79 and 2.68 for the second sub-period. We also tested similar hypotheses
with respect to the mean returns of the three strategies and obtained qualitatively similar results.
Given the relatively small number of observations in the sample and the impact of this on the
calculated statistics, we suggest interpreting the statistics with caution.
Conclusion
This article investigates recent episodes in financial markets and their impact on factor rotation
decisions. Our investigation of the events reaches three main conclusions that are particularly
important for factor rotation decisions. First, that factor portfolios can at times become crowded
and this poses significant systemic risk. Second macroeconomic factors can become largely
important drivers of factor portfolio returns which we characterize as another form of systemic
risk given the global reach of these factors. Third, that factor/style rotations have been
compressed into shorter periods of time.
We integrate these observations in a new factor rotation model that is suitably tailored to
accommodate episodes of this kind. Our model uses novel predictive variables that we are able to
obtain through risk attribution analysis and a non-parametric statistical technique that is well
behaved in modeling highly dynamic systems. The model we propose provides significant value
when appliead in a single-factor setting. We demonstrate that the outperformance of the model is
even more pronounced when it is used in a dynamice multi-factor setting. The results we produce
are robust in the sub-periods we examined and in relative terms are better in the second half of
our sample that inludes the Global Financial Crisis as well as other severe episodes in the
financial markets.
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Appendix
The U.S. Equity Risk Attribute Model (RAM) is a macroeconomic time series type of risk model.
It estimates volatility and tracking error of a portfolio relative to its benchmark. The model
decomposes both individual security and portfolio risk into a systematic component common to
all stocks as well as an unsystematic or stock-specific (idiosyncratic) component. The systematic
component of risk is then further broken down into components attributable to each of the
factors. The U.S. RAM Model uses eight macroeconomic factors and four equity market factors.
The factor sensitivities, or betas, of an individual stock are estimated by regressing ten years of
monthly stock total returns on the monthly values of the 12 factors.
This RAM risk model can help investors estimate the risk of their portfolio, and identify where
the risk is coming from. By doing so, investors can better understand the performance of the
portfolio as how it varies with changes in the market and economy; such as wider credit spreads,
falling interest rates, rising oil prices, a weak dollar and small-cap underperformance.
Below, we provide definitions of the risk factors used in U.S. RAM Version 4.0:
Macroeconomic Factors
Economic growth shock. The economic growth factor is the difference of actual vs. consensus
expectation of monthly change in industrial production, surprise in monthly industrial production.
A positive beta to this factor implies that the portfolio is likely to benefit from positive surprise in
economic growth reflected in industrial production.
Inflation shock. The inflation shock factor is the difference of actual vs. consensus expectation
of monthly change in CPI. A positive portfolio beta to this factor implies that the portfolio is
likely to benefit from an increase in unexpected inflation.
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Long-term interest rates. The long-term interest rate factor is the monthly change of 10-year US
treasury bond yields. A positive portfolio beta to this factor implies that the portfolio is likely to
benefit from rising long-term interest rates.
Short-term interest rates. The short-term interest rate factor is the monthly change of 3-month
US treasury bill yields. A positive portfolio beta to this factor implies that the portfolio is likely
to benefit from rising short-term interest rates.
Credit spread. The credit factor is the monthly change of yield spreads between Citi High Yield
index and 10-year U.S. government bond. A positive portfolio beta to this factor implies that the
portfolio is likely to benefit from widening credit spread.
Oil. The oil factor is the monthly percentage change of prices of WTI benchmark crude oil. A
positive portfolio beta to this factor implies that the portfolio is likely to benefit from rising oil
prices.
Trade-weighted dollar. The U.S. dollar factor is the monthly percentage change of the Bank of
England trade-weighted effective rate US dollar index. A positive portfolio beta to this factor
implies that the portfolio is likely to benefit from stronger U.S. dollar.
Illiquidity. The illiquidity factor is the monthly change of the equal-weighted average of
illiquidity measure of Russell 1000 stocks, defined as the absolute value of return over dollar
trading volume. A positive portfolio beta to this factor implies that the portfolio is likely to be
more defensive against less liquidity in the equity market.
Equity Market Factors
Equity market performance is impacted by macroeconomic factors and the correlations between
different segments of the market. Therefore, the U.S. RAM measures the U.S. market, small-cap
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premium, growth/value style premium, and sector factors after adjusting for the correlations with
other factors. These adjusted factors are refered to as residualized factors.
Market. The market factor is the monthly S&P 500 Index returns, residualized against all the
macroeconomic factors listed above. A positive portfolio beta to this factor means that the
portfolio is likely to benefit from rising U.S. equity market.
Small-Cap Premium. The small-cap size factor is the monthly return spread of Russell 2000
index vs. S&P 500 Index, residualized against all the macroeconomic factors and the market
factor listed above. A positive portfolio beta to this factor implies that the portfolio is likely to
benefit from small-cap outperformance over large caps.
Growth/Value Premium. The style premium factor is the monthly return spread of S&P 500
Large Cap Growth Index vs. Value Index, residualized against all the macroeconomic factors and
the market, size premium factors listed above. A positive portfolio beta to this factor implies that
the portfolio is likely to benefit from growth stock outperformance over value stocks.
Sector. The sector factor is the monthly S&P 500 GICS sector index returns, residualized against
all the macroeconomic factors and the market, size and style premium factors listed above. A
positive portfolio beta to this factor implies that the portfolio is likely to benefit from rising sector
performance.
Figure 5 shows the capitalization-weighted R-squared for the period 2006 to 2012 (August) for
the stocks in the S&P 1500. For every stock in the universe, we measured the variance of the
returns explained by all 12 factors and only with eight macroeconomic factors as a percentage of
the total variance of the returns. While the R-squared of all factors has been relatively stable, the
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R-squared of the eight macro factors continues to increase, from 18% in 2006 to 33% in the
middle of 2012, contributing a higher percentage of RAMs explanatory power.
[Figure 5 about here]
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Tables and Figures
Figure 1 Cross-sectional Correlation between Price Momentum and Short Interest Ratio
July 2007 January 2008
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Figure 2 Style total return risk decomposition and Macro loadings
Panel A: Momentum
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Figure 2 (continued)
Panel A: Earnings Revisions
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Figure 3 Decision Tree for Determining the Direction of the Information Coefficient
Momentum
Panel A: Momentum
Panel B: Earnings Revisions
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Figure 4 Historical Performance of Dynamic Factor Rotation Strategies
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Figure 5 U.S. RAM Explanatory Power (S&P 1500 Universe)
R-Squares by Factor Groups
0%
10%
20%
30%
40%
50%
60%
70%
2006 2007 2008 2009 2010 2011 2012
Market Factors
Macro Factors
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Table 1 Performance of quant factors, March 2009 to August 2012
March
toDecember
2009
January
toApril
2010
May
toAugust
2010
September
toDecember
2012
January
toSeptember
2011
October
2011
November
toDecember
2011
January
toFebruary
2012
March
toJune
2012
August
2012
Momentum -61.29 6.87 -3.43 -2.69 -2.18 -2.55 3.75 -11.81 18.49 -2.55Earnings Revision -39.18 -1.47 -1.40 -3.42 3.40 -3.83 1.55 -5.03 4.41 0.07Book Yield 59.80 7.54 -4.01 1.79 -15.53 5.57 -2.40 3.96 -5.64 2.73Earnings Yield -13.50 -9.49 6.85 -4.10 3.91 -0.14 0.23 1.05 -2.82 1.56
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Table 2 Descriptive statistics of Single Factor Timing Strategies
Baseline Active Aggressive Baseline Active Aggressive
Panel A: Momentum Panel B: Earnings Revision
Geometric Mean Return (annualized) -4.47 0.20 3.94 -3.34 1.80 6.25Arithmetic Mean Return (annualized) -0.08 4.05 8.17 -2.13 2.63 7.39p-value (H0: Arithmetic Mean0) 0.50 0.29 0.14 0.70 0.22 0.04Standard Deviation (annualized) 28.12 26.44 28.02 15.25 12.75 15.11Return / risk (annualized) 0.00 0.15 0.29 -0.14 0.21 0.49p-value (H0: Mean Return /risk0) 0.00 0.00 0.00 1.00 0.00 0.00Hit ratio 57.93 59.15 59.15 54.88 61.59 61.59Average return when correct 2.73 2.67 3.08 1.35 1.21 1.75Average return when wrong -2.74 -2.33 -2.39 -1.53 -0.99 -1.13Predicted switches NaN 16.00 16.00 NaN 44.00 44.00H-M non-parametric test p-stat NaN 1.05 1.05 NaN 1.18 1.18H-M parametric test t-stat NaN 2.62 2.62 NaN 3.72 3.72
Panel C: Book Yield Panel D: Earnings Yield
Geometric Mean Return (annualized) 2.52 7.39 10.41 2.54 5.09 7.07Arithmetic Mean Return (annualized) 4.24 8.16 12.07 3.88 6.11 8.34p-value (H0: Arithmetic Mean0) 0.20 0.01 0.01 0.19 0.06 0.03Standard Deviation (annualized) 18.75 12.71 18.46 16.22 14.28 16.08Return / risk (annualized) 0.23 0.64 0.66 0.24 0.43 0.52p-value (H0: Mean Return /risk0) 0.00 0.00 0.00 0.00 0.00 0.00Hit ratio 55.49 64.02 64.02 56.71 58.54 58.54Average return when correct 1.94 1.15 2.27 1.71 1.55 1.90Average return when wrong -1.59 -0.47 -1.26 -1.39 -1.04 -1.20Predicted switches NaN 25.00 25.00 NaN 12.00 12.00H-M non-parametric test p-stat NaN 1.27 1.27 NaN 1.08 1.08
H-M parametric test t-stat NaN 4.75 4.75 NaN 5.06 5.06
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Table 3 Descriptive statistics of Multi-Factor Timing Strategies
Baseline
Multi-Factor
Active
Dynamic
Aggressive
Dynamic
Geometric Mean Return (annualized) 1.49 5.08 9.06Arithmetic Mean Return (annualized) 3.03 6.81 10.89p-value (H0: Arithmetic Mean0) 0.26 0.08 0.02Standard Deviation (annualized) 17.26 18.26 18.89Return / risk (annualized) 0.18 0.37 0.58p-value (H0: Return / risk0) 0.00 0.00 0.00Hit ratio 55.49 60.37 64.02Average return when correct 3.23 3.50 3.79Average return when wrong -3.46 -3.90 -4.21Turnover 448.18 474.14 524.74
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Table 4 Multi-Factor Timing Strategies in Sub-Periods
Baseline
Multi-Factor
Active
Dynamic
Aggressive
Dynamic
Baseline
Multi-Factor
Active
Dynamic
Aggressive
Dynamic
JAN 1999 DEC 2005 JAN 2006 AUG 2012
Geometric Mean Return (annualized) 8.41 13.04 15.19 -5.72 -3.21 2.66Arithmetic Mean Return (annualized) 10.29 15.16 17.66 -4.60 -1.96 3.79p-value (H0: Arithmetic Mean0) 0.08 0.03 0.02 0.79 0.63 0.26Standard Deviation (annualized) 19.39 20.34 21.87 14.50 15.51 15.03Return / risk (annualized) 0.53 0.75 0.81 -0.32 -0.13 0.25p-value (H0: Return / risk0) 0.00 0.00 0.00 1.00 1.00 0.00Hit ratio 60.71 67.86 70.24 50.00 52.50 57.50Average return when correct 4.07 4.15 4.42 2.17 2.61 2.97Average return when wrong -4.11 -4.83 -5.49 -2.93 -3.23 -3.27Turnover 440.08 456.05 508.97 456.58 492.90 541.09