A Risk-Oriented Model for Factor Rotation Decisions

7/30/2019 A Risk-Oriented Model for Factor Rotation Decisions

1/38Electronic copy available at: http://ssrn.com/abstract=2159301

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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


c Vice President, Global Quantitative Research, Citigroup


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.


2/38Electronic copy available at: http://ssrn.com/abstract=2159301

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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 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.


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.


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.


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.


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.


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.


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.



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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

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A Risk-Oriented Model for Factor Rotation Decisions

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