the case for style investing - aqr capital management investing with style: the case for style...

AQR Capital Management, LLC

Two Greenwich Plaza

Greenwich, CT 06830

p: +1.203.742.3600

f: +1.203.742.3100

w: aqr.com

* Antti Ilmanen can be reached by email: [email protected]

We would like to thank Cliff Asness, April Frieda, Georgi Georgiev, Sarah

Jiang, David Kabiller, Johnny Kang, John Liew, Thomas Maloney, and

Mark Stein for helpful comments and suggestions, and Jennifer Buck for

design and layout.

Investing with Style

The Case for Style Investing

Antti Ilmanen, Ph.D.*

Principal

Ronen Israel

Principal

Tobias J. Moskowitz, Ph.D.

Fama Family Professor of Finance

Booth School of Business, University of Chicago

Research Associate

National Bureau of Economic Research

December 2012

Investors are bombarded by a variety of investment

strategies and alternatives from an ever-growing

and increasingly complex financial industry, each

claiming to improve returns and reduce risk. Amid

the clamor, academic and practitioner research has

sifted through the vast landscape and found four

intuitive investment strategies that, when applied

effectively, have delivered positive long-term

returns with low correlation across a multitude of

asset classes, markets, and time periods using very

liquid securities. These four investment “styles” are

Value, Momentum, Carry, and Defensive, which

form the core foundation in explaining the cross-

section of returns of most asset classes.

Investing with Style: The Case for Style Investing 1

In this paper, we will describe “style investing,”

discuss the intuition and evidence for the four

pervasive styles, and detail how to implement a

strategy that can access these premia to improve

the risk and return characteristics of traditional

portfolios. Despite a wealth of academic evidence

on style premia, an accessible investment vehicle

that delivers a very broad yet consistent set of

style returns (at reasonable terms) has not

existed. We seek to change that by offering a new

fund that provides investors with an intuitive,

transparent, and cost-effective approach to gain

exposure to these pervasive investment styles.

Introduction

Most existing portfolios, even seemingly

diversified ones like the traditional 60%

stocks/40% bonds, have excessive dependence on

equity risk. This proved especially painful during

the 2008 global financial crisis. Further, most

investors currently recognize that traditional

sources of returns, such as stocks and bonds, may

not do as well as they have in the past.

Consequently, investors have turned their

attention to alternative sources of return,

specifically those uncorrelated with traditional

assets. One way to achieve these returns is to seek

“alpha.” Alpha is a loaded word in Finance. In

theory, true alpha is the extra return achieved

beyond any known risks or systematic strategies

and is unrelated to any of those strategies. It is

therefore often taken as a measure of unique

managerial skill.

Unfortunately, alpha is at best elusive and, more

often than not, illusive. First, the definition of

alpha is confusing and often misused. Academics

and practitioners struggle to define true alpha

and debate its very existence. Second, even if we

can agree on a definition, alpha is often cloaked

inside a broader portfolio that contains simple

market exposures (e.g., betas). Since a single fee

is charged for the portfolio, investors willing to

pay high fees for alpha end up paying exorbitant

fees for beta.1 In addition, even when alpha is

identifiable and attainable, it is usually packaged

in illiquid vehicles with little transparency and

very high fees. For example, hedge fund investors

have often paid too much and accepted

unfriendly terms for strategies that are common

and well-known.2

While the definition and pursuit of alpha is

elusive and the generation of alpha is opaque,

expensive, and not easily scalable, there are other

ways to seek returns that can significantly

improve investor portfolios. Putting semantics

aside, all an investor should care about is

receiving positive returns that are uncorrelated

with what she currently owns. Regardless of

what you call them, these returns will look like

alpha to the investor. In this article, we focus on

a proven set of strategies that can produce such

returns, which we call “styles.” Style investing

delivers long-term positive returns with little

correlation to traditional asset classes. And, it

achieves this in a more intuitive and cost-

effective manner using liquid securities that allow

for more scalability.3 In essence, investing can be

made much simpler and more effective by

focusing on the core foundations of returns—

building blocks we call styles. Practically

speaking, if an investor is not already exposed to

style premia, it is alpha! But, it is identifiable

alpha, not concealed amongst traditional betas,

and offered at significantly better terms.

Think of a style as a disciplined and systematic

method of investing that produces unique long-

term positive returns across markets and asset

1 Asness, Krail, and Liew (2001) and Asness (2004). 2 Berger, Crowell, Israel, and Kabiller (2012). Also see AQR Alternative

Thinking (July 2012) which discusses other ways to label and classify

long-short strategies than style premia: alternative beta premia, exotic

betas, smart betas, and hedge fund risk premia. 3 While there are other sources of returns that can be achieved through

illiquidity, providing insurance, and arbitrage trades, these are separate

topics and strategies not considered here.

2 Investing with Style: The Case for Style Investing

classes, backed by scientific data. For years,

academics and practitioners have been studying

markets, trying to identify persistent, systematic

sources of return. Many attempts to identify

additional return premia have turned out to lack

robustness, possibly the result of data mining (for

example, research claiming to find stock return

predictability from sun spots, seasonal affective

disorder, and moon phases—no kidding!).

However, sifting through the research and data

has resulted in the identification of a set of classic

long-short styles that deliver consistent long-term

performance backed by sound economic

reasoning across many unrelated asset classes, in

different markets, and in out-of-sample tests.

They are value, momentum, carry, and

defensive.4

Style investing has been most widely studied in

equity markets, with a classic example being the

influential work of Eugene Fama and Kenneth

French (1992, 1993), who describe the cross-

section of U.S. stock returns through two main

styles, in addition to the market equity-risk

premium: value and size. Subsequent research

into stocks added two additional styles, namely

momentum5 and low-beta or low-risk.6 Research

on value, momentum, and low-beta has been

extended to international stocks as well as to

other asset classes that include bonds, currencies,

commodities, derivatives, and real estate, with

similarly strong results.7 Size, on the other hand,

has not proven as robust,8 can’t be easily applied

across other asset classes such as currencies or

commodities, and entails betting on illiquid

securities, which is a feature we aim to avoid in

constructing a liquid strategy. The last style,

carry, was first applied in currencies and bonds

4 Ilmanen (2011) provides an overview. 5 Jegadeesh and Titman (1993) and Asness (1994).

6 Black (1972) and Frazzini and Pedersen (2011a). 7 Asness, Moskowitz, and Pedersen (2012), Asness-Liew-Stevens

(1997), and Frazzini and Pedersen (2011a,b). 8 Israel and Moskowitz (2012).

(and later, commodities) as a powerful

investment tool and more recently has been

studied in equity indices, individual stocks, and

options.9

Identifying robust return sources is the first

ingredient of successful style premia investing,

and finding consistent evidence in many markets

and asset classes achieves this aim. The second

key ingredient is diversifying across as many

styles and asset classes as possible, especially

since the styles are uncorrelated, and sometimes

negatively correlated, to each other. Finally,

proper long-short implementation of these styles

provides for hedged returns that have low

correlations with traditional equity risk premia.

Historically, investors may have been exposed to

individual styles indirectly and, as we will argue,

inadequately through portfolios that simply add a

style tilt onto predominantly long equity-market

risk exposure, but often disguised and priced as

alpha. Our approach is to provide pure,

diversified exposure to all four styles

simultaneously in a transparent vehicle, designed

to have low correlation to traditional risks and at

a fair price. Our unique approach provides direct

exposure to all four styles, not one at a time, and

not commingled with traditional sources of risk.

A skeptic might say “there must be a catch.” There

is, of course, but it is a small one that can (and

must) be managed. In order to achieve proper risk

balance and attain the high returns and low

correlation properties investors seek, style

investing requires the “three dirty words in

finance”—leverage, short-selling, and derivatives.

This is a consequence of three desires: market

neutrality (or removing traditional betas), risk

(not dollar) diversification, and decently sized

expected returns. Leverage, shorting, and

derivatives are necessary to achieve these

9 Koijen, Moskowitz, Pedersen, and Vrugt (2012).


important objectives efficiently. Hence, putting

together a portfolio of style premia requires

careful portfolio design decisions, proper

portfolio construction, effective implementation

and cost control, as well as sound risk

management. We discuss these below.

In Part I, we describe the style premia in greater

detail, followed by empirical evidence in Part II.

In Part III we discuss how best to put the four

styles together into one cohesive portfolio.

Finally, in Part IV we address the benefits of

adding style premia to a traditional portfolio.

Part I: What are Style Premia?

We focus on the four classic styles: Value,

Momentum, Carry, and Defensive. We first

discuss the basis for each of these styles,

including the underlying economic intuition

behind them. Then, we present empirical

evidence showing their long-term return, risks,

and correlations.

Value investing is probably the best-known style,

especially in equities. The idea of buying

undervalued assets (and selling overvalued ones)

dates back to at least Benjamin Graham. For

almost 30 years, value investing in stocks has

been studied extensively in academia, most

prominently by Fama and French.10 The

10

Fama and French (1992), Fama and French (1993), Fama and French

implementation of the value style can be

straightforward. Take a set of stocks and sort

them by some measure of fundamental value to

price. Go long or overweight the stocks that have

high fundamental value to price and short or

underweight the ones that have low fundamental

value to price. By being explicitly long and short,

the resulting portfolio has very little correlation

with the overall equity market, and when applied

across many assets, can capture the aggregate

return to value investing while diversifying away

idiosyncratic security risk. The traditional choice

of value measure is the ratio of the book value of a

company relative to its price (B/P), but other

measures can be used and applied

simultaneously to form a more robust and reliable

view of a stock’s value. For example, investors

can look at a variety of fundamentals beyond

book value, including earnings, cash flows, and

sales, relative to price. It is our view (and

experience) that more measures provide for more

robust portfolios.11

Value can be applied beyond the original context

of stock selection to equity indices and other asset

classes. In equity indices, an aggregate measure

of B/P for the entire market can be used to

implement value investing. Extending the value

concept to bonds, currencies, and commodities

requires using measures not derived from

accounting statements, but still retains the notion

of fundamentals to price.12 For bonds, a measure

of real bond yields, defined as the yield of a 10-

year government bond index minus forecasted

inflation for the next 12 months, is used. In the

case of currencies and commodities, a measure of

(1996), Fama and French (2004), Fama and French (2008), Fama and

French (2012). 11 Israel and Moskowitz (2012). 12

Asness, Moskowitz, and Pedersen (2012).

Value means buying assets that are “cheap” relative to their fundamental value and selling “expensive” assets.

Momentum involves buying assets that recently outperformed their peers and selling those that recently underperformed.

Carry implies buying high-yielding assets and selling low-yielding assets.

Defensive consists of buying low-risk, high-quality assets and selling high-risk, low-quality assets.


the 5-year reversal in price, reflecting mean

reversion, is related to value.13 In all cases, a

systematic process that first sorts assets by these

measures, going long the cheap (relative to

fundamentals) assets and short the expensive

ones, is applied.

Academics still debate why the value premium

exists. For example, there are explanations rooted

in investor behavioral biases, such as excessive

extrapolation of growth trends, as well as risk-

based explanations like value assets having

greater default risk. Both sets of theories are

grounded in economic intuition with ample

theoretical foundation. Given the economic

motivation and strong empirical evidence, value

investing is clearly a persistent source of excess

returns.

Momentum investing is an almost equally well-

known style, supported by evidence that is as

robust and pervasive as the evidence behind

value investing. Momentum is the tendency of

assets, in every market and asset class, to exhibit

persistence in their relative performance for some

period of time. Since being documented in

academia in the early 1990s among U.S. equities,

momentum has been studied extensively in a

variety of contexts. The typical approach is to

look at the past 12 months of returns for a

universe of assets, going long the ones that have

outperformed their peers and short the

underperformers. By being long and short, the

resulting portfolio has little correlation to

traditional markets, and when applied across

many assets, captures the aggregate return to

momentum while diversifying away idiosyncratic

security risk.

Similar to value investing, momentum investing

does not need to be confined to a single measure,

13 DeBondt and Thaler (1985, 1987), Fama and French (1996), and

Asness, Moskowitz, and Pedersen (2012).

in this case price momentum. It has been shown

that measures of fundamental momentum, such

as earnings momentum, changes in profit

margins, and changes in analysts’ forecasts for

stocks, are also useful in forming profitable

portfolios. For both price and fundamentally

based momentum strategies, the evidence of

strong risk-adjusted returns is pervasive across

time and markets.

Similar to the debate about why value investing

works, there is an active academic discussion

about why momentum is related to average

returns. This debate again rests on two possible

explanations: risk-based and behavioral theories.

Risk-based stories posit that high-momentum

stocks are riskier and therefore command a

higher discount rate. An example is high-

momentum stocks containing more growth

options in earnings that make them more

sensitive to aggregate shocks. In addition, strong

correlations among momentum stocks suggest

the presence of a common source of risk.

Behavioral theories, on the other hand, argue that

under-reaction to new information due to

anchoring or inattention, and/or overreaction to

price moves due to feedback trading (becoming

more confident in one’s positions and beliefs

when they are supported) and investor herding

may be prominent sources of momentum. In

addition, the disposition effect, which is the

tendency for investors to sell winners too soon

and hold on to losers too long, may be a

significant contributor to momentum.

Carry is a well-known style particularly among

macro-economists and practitioners in currency

markets. At its core, carry is based on investing

(lending) in higher yielding markets or assets and

financing the position by shorting (borrowing) in

lower yielding markets or assets. A simplified

description of carry is the return an investor


would receive (net of financing) if market

conditions (e.g., prices) remain the same. A

classic application is often found in currency

markets, where sorting countries by their short

term (say, 3-month) lending rate, and going long

the countries with the highest rates and short the

markets with the lowest is a profitable strategy

over several decades. Likewise, carry strategies in

fixed income and commodity futures, where

backwardation or contango are exploited across

various commodities, have also been profitable

over time. For stocks, the carry earned is the

expected dividend yield. Thus, in the case of

equities, carry is closely related to value, but the

two measures are not identical. Moreover, carry is

quite different than value in other asset classes.

The economic intuition behind carry is balancing

out supply and demand for capital across

markets. High interest rates can signal an excess

demand for capital not met by local savings; low

interest rates suggest an excess supply of capital.

Traditional economic theory would argue, in the

case of currencies, for example, that the rate

differentials would be offset by currency

appreciation or depreciation, such that the return

an investor would experience would be the same

across currency markets. The evidence is that a

currency carry strategy not only can collect the

yield differential, but has often captured some

capital gains from currency appreciation as well.

This is perhaps caused by the presence of non-

profit-seeking market participants, such as

central banks, who introduce inefficiencies to

currency markets and interest rates, due to other

more political motives.

The strategy is certainly not without risk, as there

can be sharp periodic unwinds when capital flees

for low-yielding “safe havens.” The positive

performance over the long term could be

compensation for investing in a strategy with

negative skewness and larger left tails,

specifically in bad economic environments.

However, and importantly, those risks tend to be

asset-class specific and are largely diversified

away in a portfolio where carry is applied across

many asset classes.14 Hence, strong positive carry

returns can be captured while mitigating (though

not avoiding) much of the occasional carry

crashes that occur in a particular asset class like

currencies. The concept of carry, applied more

broadly across other asset classes besides

traditional currency trades, is a clear example of

how style investing, when applied universally,

can generate more attractive risk and return

characteristics.

Defensive, or low beta/low risk, strategies have

experienced a resurgence in recent years. The

initial motivation for defensive strategies dates

back to Fischer Black, who in 1972 saw that the

security market line (the line linking beta to

average returns) was too flat, relative to what

theory (the Capital Asset Pricing Model, or

CAPM) would predict. In other words, high-risk

assets didn’t offer high-enough returns relative to

low-risk assets. Subsequent research has shown

that this phenomenon can be extended to many

different markets and asset classes beyond

stocks.15 In the case of stocks, we sort by

forecasted betas and go long the stocks with the

lowest betas and short the ones with the highest

betas. By applying some leverage to the lower-

beta stocks to equalize the long portfolio’s beta

with the short side, a portfolio retains its market

neutrality, while capturing the fact that the lower-

beta stocks offer a better risk-adjusted return than

the higher-beta stocks. By being diversified across

many assets, we capture the defensive return

premium while diversifying away idiosyncratic

security risk. Extending the low- vs. high-risk

14 Koijen, Moskowitz, Pedersen, and Vrugt (2012), and Ilmanen (2011,

chapters 13 and 22). 15

Black (1972) and Frazzini and Pedersen (2011a,b).


concept more broadly, we also can go beyond

beta to include more fundamental measures of

risk—or conversely “quality”—by seeking high

profitability,16 low leverage, and stable earnings

among stocks, or by favoring short-duration

assets in fixed income.

There are a number of competing theories for

why lower-risk assets may offer higher risk-

adjusted returns. We believe the most compelling

reason resides in the fact that leverage needs to

be applied to lower-risk assets to raise the overall

risk and return expectations. Since most investors

are leverage-averse or leverage-constrained, they

typically choose to hold the higher-risk assets,

thereby lowering the prospective returns for those

assets.17 As a result, an investor who is willing to

take the other side of that trade and hold the

levered, lower-risk asset may be well-rewarded in

the long run.18

Part II: Empirical Evidence of Style Premia

To provide empirical evidence of the style

premia, we create composites of the four styles by

applying long-short strategies across seven

different asset classes (or contexts): individual

stocks globally, industries,19 country equity

indices, government bond indices, interest rate

futures, currencies, and commodities. In each

case we develop a set of measures that robustly

define the style in a straightforward manner. For

example, in the case of stocks, we use five well-

known measures of value: book-to-price,

earnings-to-price, forecasted earnings-to-price,

cash flow-to-price, and sales-to-enterprise value

(an adjusted measure of price). In other asset

16 Novy-Marx (2012). 17 Asness, Frazzini, and Pedersen (2012). 18 Frazzini, Kabiller, and Pedersen (2012) show that Warren Buffett is one

extraordinarily successful example of such an investor. 19 We deploy strategies in stocks and industries separately because of a

wealth of evidence showing distinct predictability among industries

separate from individual stocks (Asness, Porter, and Stevens (2000),

Moskowitz and Grinblatt (1999)).

classes and for other styles we similarly use

several intuitive measures for robustness.

We create a large universe of securities to

maximize diversification benefits. In the case of

stocks and industries, we use approximately 1,500

stocks across the major developed equity markets,

weighting each market by its relative liquidity

and breadth as follows: U.S. 50%, Japan 20%,

Europe ex-U.K. 20%, and U.K. 10%. We also

apply the four styles to 21 equity index futures, six

bond futures, five interest rate futures, 19

currencies, and eight commodity futures. For

capacity and cost reasons, we focus exclusively on

liquid assets, leaving out illiquid segments of

traditional assets (e.g., small-cap stocks, non-

government bonds and other illiquid fixed

income, and emerging-market equities and

commodities beyond the most liquid six to eight

markets in each group).

Equity country allocation and currency allocation

are separately conducted in developed markets

(75%) and emerging markets (25%), motivated by

their relative liquidity/capacity. Similarly, we

weight long-dated government bonds three times

more than short-dated interest-rate futures to

avoid using excess leverage. Overall, 60% of total

risk is equity-related20 (stocks, industries, and

equity indexes) and 40% of risk is in other asset

classes (fixed income, currencies, and

commodities) based on the risk decomposition

that follows:

Stocks (32%) and industries (8%)

Country equity index futures (20%)

Country bond futures (11%) and interest-rate

futures (4%)

20

Note: equity-related risk does not mean long equity market exposure. In

this case 60% of the risk is in long-short styles that use some form of

equities, either from individual stocks, industries, or equity index futures,

but the exposure is equity-neutral (non-directional) in the sense that

equity risk is taken equally on the long and short sides.


Currencies (15%)

Commodity futures (10%)

where balanced long-short strategies are deployed

within each category. These choices are based on

careful portfolio analysis that balances the

correlations among the assets and styles along

with capacity and liquidity considerations, all

designed to achieve the highest and most reliable

return-to-risk ratio while helping diversify

traditional portfolios. The factors or

characteristics we select to identify each style in

each asset class range from very simple single

factors like momentum that uses the past 12-

month return (for stocks, skipping the most

recent month’s return), to more complicated

composites of multiple factors that vary across

assets (e.g., value, which uses a composite of

several accounting ratios to price in equities, real

bond yields for fixed income, and mean reversion

estimates for currencies and commodities). The

measures used are always intuitive and attempt

to achieve what we believe are the purest and

strongest signals of each style, while maintaining

transparency and clarity. In general, our design

choices favor simplicity.

Exhibit 1 presents the performance results of

simulations of the diversified style premia

portfolios, highlighting the positive risk-adjusted

returns (Sharpe ratios ranging from 0.9 to 1.4)

and ability to diversify away from equity-

directional risk (correlations to global equities

ranging from approximately -0.1 to 0.2). (Here

and throughout the paper we use monthly returns

from January 1990 to June 2012.) All strategies

are scaled to 10% annual volatility for ease of

comparison. Each style is a composite measure of

various indicators of that style, applied across the

seven asset classes or contexts we consider.

Exhibit 1: Style Premia Simulations

1990 – 2012 VALUE MOMENTUM CARRY DEFENSIVE

Annual Excess Return 9.0% 11.5% 13.7% 9.3%

Volatility 10.0% 10.0% 10.0% 10.0%

Sharpe Ratio 0.90 1.15 1.37 0.93

Correlation to Equities 0.03 -0.03 0.22 -0.13

Correlation to 60% Equities/

40% Bonds 0.03 -0.01 0.22 -0.11

Equity Tail Return 6.5% 9.7% -2.8% 11.2%

Skew -0.37 0.02 -0.33 -0.29

Kurtosis 0.43 0.57 0.69 0.10

Auto-correlation 0.20 0.13 0.14 0.04

Source: AQR. Correlations are measured against the MSCI World equity

index and the Barclays Global Aggregate bond index. Equity tail return is

the style’s annualized average return in the worst 10% of months for

global equities. Please see the Appendix for important disclosures.

Exhibit 2 presents the Sharpe ratios of the styles

broken out by asset class.21 The Sharpe ratios

largely range from 0.3 to 0.9, with only one being

slightly negative (value for commodities). As the

table shows, there is pervasive evidence across

many asset classes of the efficacy of these four

styles.

Exhibit 2: Style Premia Sharpe Ratios

by Asset Class

1990 – 2012 VALUE MOMENTUM CARRY DEFENSIVE

Stock Selection 0.82 0.97 0.95

Industry Selection 0.07 0.92 0.40

Equity Country Selection 0.61 0.48 0.33

Bonds Country Selection 0.40 0.02 0.90 0.09

Interest Rate Futures 0.69 0.89 0.65

Currencies 0.34 0.63 0.79

Commodities -0.09 0.81 0.82

Composite 0.90 1.15 1.37 0.93

Source: AQR.

Exhibit 3 plots the cumulative gains of each style

composite over time. We plot the time series from

21 The six empty cells in the matrix are due to either extreme overlap with

other strategies or difficulty in applying the style concept to some securities. For example, the empty cells for carry strategies in equities

could be filled with dividend yield strategies, but because these strategies

are so similar to equity value strategies, we decided to exclude them. The

lack of defensive strategies for interest rate futures, currencies, and

commodities is because it is difficult to apply the low-beta or quality

concepts in these markets. However, we are pursuing further research

into both topics.


1990 to 2012, but evidence on the efficacy of these

styles in many markets goes back much further

(e.g., 1926 in U.S. stocks, 1970 in commodities).

Exhibit 3: Style Premia Growth

of $1 in Log Terms

1990 – 2012

Source: AQR.

Exhibit 4 presents the correlations of the various

style premia to each other. Note, that the styles

provide a tremendous amount of diversification

with each other in addition to a portfolio of

traditional assets as presented in Exhibit 1. In

particular, the correlation between value and

momentum is -0.6, indicating the two styles are

powerful diversifiers of each other while still both

having long-term positive risk-adjusted returns.

The other correlations are very close to zero, with

the most positive correlation between momentum

and carry of only 0.21.

Exhibit 4: Style Premia Correlations

1990 – 2012

VALUE MOMENTUM CARRY DEFENSIVE

VALUE 1.00

MOMENTUM -0.60 1.00

CARRY -0.08 0.21 1.00

DEFENSIVE 0.02 0.12 -0.03 1.00

Source: AQR.

Finally, Exhibit 5 analyzes the risk-reward

relationship of different style premia to equity

markets using a concept of “tail return,” defined

as the style’s annualized average performance in

the worst 10% of months for global equities. This

risk measure captures an investment’s correlation

with extremely bad times, when investors may

care about performance the most, and therefore

drives risk premia according to financial theory.

Exhibit 5, which sorts asset class styles by the tail

risk measure, shows that the currency carry

premium is particularly risky. However, the tail

returns of the other styles and asset classes

oscillate above and below zero, which suggests

that a broad composite of style premia diversify

away the “tail returns” of each style in each asset

class and provide for long-term market neutrality.

Exhibit 5: “Tail Return” of Style Premia

by Asset Class

1990 – 2012

Source: AQR.

Part III: Keys to Building a Style Premia Portfolio

Although the notion of style premia is

straightforward, there is a tremendous amount of

judgment and experience required to properly

implement a style premia portfolio in order to

efficiently harvest returns and manage risk.

Diversification is one of the key elements in style

premia portfolio design. While each of the styles

employed is strong by itself, they also naturally

diversify each other (Exhibit 4) to provide even

stronger performance. Furthermore, a robust

portfolio of all style-asset pairs leads to more

Value Momentum Carry Defensive

-20%

-15%

-10%

-5%

0%

5%

10%

15%

Tail Return Avg Return


consistent returns over time. While some style-

asset pairs appear stronger than others over our

sample period, we believe that the long-term

efficacy of each pair is sufficiently similar to (or

statistically indistinguishable from) others that

our aim is to build a well-balanced, diversified

portfolio and not to over- or under-weight certain

styles. Even within styles, as discussed above, we

also try to diversify our definitions to avoid over-

reliance on any one particular measure. We are

conservative in specifying predictors, trying to

avoid complexity and overfitting, while trying to

capture as much of the style premia as possible.

Beyond diversification, skillful portfolio

construction is required, as is cost-effective

execution. When putting the building blocks

together, we employ many portfolio design

features that help achieve this aim, including:

Well-balanced risk. Balanced contributions

are maintained with the help of dynamic

position sizing to more accurately target

volatility/risk. In practice, we cannot achieve

exactly equal risk allocation across styles, but

we get close.

Volatility targeting. Overall, we target 10% to

12% portfolio volatility in the long run, but

allow short-term deviations from this target

when “agreement” across style factors is

abnormally high or low (as explained next).

Factor “agreement.” This reflects the amount

by which the various styles lead to similar

positions. For example, if the value signal

favors European stocks but the momentum

signal favors U.S. stocks, the net position of

such offsetting signals will be modest. We do

not want to scale up such weak views to

achieve some long-run target risk. In contrast,

when all style signals are in agreement, the

overall portfolio risk could become quite high.

In that situation, we might cap it above the

long-run risk target, so as to minimize tail

risk.

Risk overlays. One aspect of diversification is

making sure risk isn’t too heavily

concentrated in any particular industry or

country. Even after these efforts, there may

be some unintentional directional bets that

we then also try to mitigate by overlaying a

final strategy beta hedge.22

Drawdown control. Beyond ex-ante

diversification, risk targeting, and exposure

controls, we also apply disciplined drawdown

control if ex-post returns disappoint. At pre-

specified drawdown levels, we scale position

sizes mechanically down based on realized

losses and short term tail risk estimates. The

drawdown control is only applied at the total

portfolio level (no strategy-specific stop-loss

limits).

Efficient implementation. We seek to control

costs by avoiding excessive turnover and

trading using algorithms that systematically

seek to provide rather than demand

liquidity.23 Each style is traded at a frequency

that allows efficient style capture without

excessive trading costs. When portfolios are

built, they are optimized by taking into

account the various styles and forecasted

trading costs, and are traded in an efficient

and patient manner that seeks to minimize

transactions costs while maintaining low

tracking error to each style.

To illustrate the potential benefits of

diversification and skillful portfolio construction,

we simulate a composite portfolio that is roughly

equally weighted (in risk terms) across the four

22 The style premia portfolio emphasizes a market-neutral approach also

by focusing on cross-sectional long-short strategies and by avoiding

directional styles (market timing). The emphasis is on strategic harvesting

of consistent return sources rather than tactical positioning. 23 Frazzini, Israel, and Moskowitz (2012) discuss trading costs in value,

momentum, and other equity strategies.


styles, following the weighting scheme above for

asset classes. Exhibit 6 presents summary

statistics for the composite portfolio, showing the

attractive risk-adjusted, uncorrelated returns that

are obtained by combining all four style premia

into one portfolio.

Exhibit 6: Style Premia Composite Simulations

1990 – 2012

COMPOSITE

Annual Excess Return 25.2%

Volatility 10.0%

Sharpe Ratio 2.52

Correlation to Equities 0.02

Correlation to 60% Equities/40% Bonds 0.05

Equity Tail Return 16.7%

Skew 0.22

Kurtosis 0.51

Auto-correlation 0.15

Source: AQR. Please see the Appendix for important disclosures.

A Sharpe ratio in excess of 2 is almost certainly not

achievable, even when it is for a highly diversified

portfolio (as it is here). As is common in academic

and industry writings, this Sharpe ratio is based on

simple, simulated gross returns of long-short

portfolios without subtracting trading costs or fees

and without any discounting for the possibility of

overfitting or 'the world has changed' arguments.24

As a result, Exhibit 7 presents the results of a

realistic portfolio that starts with the composite

portfolio presented above, overlays real-world

value added portfolio design and implementation

considerations, and then applies conservative,

estimated transactions costs and a level of

discounting (as high as 50%25) to adjust for any

24

Even if every researcher individually is meticulously careful about not

overfitting, or data mining, the general field of study may still contain

overfitted results due to the literature and practice focusing on those studies that yielded significant results and discarding or ignoring those

that did not, where it is likely some of those results could have been

generated by chance. Apart from overfitting concerns, it may be argued

that when factors become well known, or the costs of accessing them fall,

their prospective returns decline. 25 The actual discounting schedule varies through time, whereby there is

a greater amount of discounting in the early part of the sample and less

upward biases that might be present in the

simulated results. We think this more realistic

portfolio maintains the characteristics of the four

style premia and the composite, providing strong

risk-adjusted returns (Sharpe ratio close to 1) with

little correlation to traditional assets.

Exhibit 7: Style Premia Portfolio Simulations

1990 – 2012

PORTFOLIO

Annual Excess Return 9.8%

Volatility 10.0%

Sharpe Ratio 0.98

Correlation to Equities 0.01

Correlation to 60% Equities/40% Bonds 0.02

Equity Tail Return 3.0%

Skew 0.05

Kurtosis 0.33

Auto-correlation 0.16


Exhibit 8 shows the cumulative excess returns

(log scale) of the strategy and graphically depicts

the impact of each of the main adjustments to the

simple, simulated gross returns. Overlaying

trading costs reduces the long-run Sharpe ratio

from 2.5 to 1.9, while discounting simulated

returns reduces it further to just below 1.0. The

further impact of risk exposure and drawdown

controls and that of management fees is more

limited once these other adjustments are

incorporated.26

discounting in the more recent periods. The discounting methodology

simply subtracts off the average return over the period multiplied by the

discount factor for that period from each month’s simulated returns,

without affecting the realized volatility of each series. 26 Note that some of the benefits of aggressive risk diversification,

dynamic volatility targeting and industry neutralization (in stock selection)

were already included in the gross returns.


Exhibit 8: Moving from Theoretical Gross

Returns to More Realistic Expectations

Source: AQR.

Part IV: Style Premia as a Portfolio Diversifier

The broad style portfolio itself is highly

diversified, but it is more important to many

investors that it serves as an effective diversifier

for their own portfolios. We examine the

correlation of our style premia portfolio to

traditional portfolios as well as to alternatives

such as hedge funds. Since many institutional

portfolios hold 60% in equities and 40% in bonds,

it is appealing that the correlation between the

style premia portfolio and the global 60/40

portfolio in stocks and bonds is 0.06 on average—

essentially zero.27 The correlation between the

style premia portfolio and the hedge fund

composite index from DJCS is a little bit higher,

but still only 0.20 on average. Hence, style premia

provide extremely low correlations to traditional

portfolios and alternative investments, making

them a very attractive diversifier to most existing

portfolios.

27 We present style premia as long-short strategy returns. More constrained investors may apply style tilts to their long-only portfolios

and get a meaningful portion of the return improvements but limited

diversification benefits. Ilmanen and Kizer (2012) show that style

diversification is more effective than asset class diversification mainly

when short-selling is allowed. Long-only style-tilted portfolios have higher

correlations with each other, with equity markets, and with other

traditional portfolios.

Exhibit 9 plots the time-series of correlations

between the style premia portfolio and the global

60/40 strategy as well as the DJCS hedge fund

index. Correlations are estimated using rolling 36-

month windows. There is significant time-

variation in the correlations through time. The

dark blue line in the graph shows that the

correlation of the style premia portfolio with the

60/40 traditional global portfolio ranges from -0.4

and +0.4, averaging zero over the long run. Even

at the most extreme correlation of +0.4, there are

still significant diversification benefits from

investing in style premia, and over time those

benefits are larger. The same is true for the

correlation between style premia and the hedge

fund index, indicated by the light blue line. The

correlations range from -0.4 to +0.5, which means

there are tremendous diversification benefits

even at the most extreme end. Finally, the orange

line on the graph plots the correlation between

the traditional global 60/40 portfolio and the

DJCS hedge fund index. Here, the correlations

are much higher, averaging 0.6 over time and

ranging from +0.3 to +0.9. Thus, the

diversification benefits of combining a traditional

portfolio with traditional, hedge fund alternatives

are much smaller than they are from using style

premia. Perhaps even more disturbing is the

upward trend in correlations between the

traditional 60/40 strategy and hedge funds, which

has been creeping up over time and currently

hovers around 0.9. The style premia portfolio

does not exhibit these trends and offers much

lower correlation.

80

800

8000

Cu

mu

lati

ve

ex

ce

ss

re

turn

,

log

sc

ale

Theoretical Composite Apply t-costs

Apply discounting Apply risk overlays

Apply fees

fees

discounting

t-costs SR2.52

SR1.91

SR0.98

SR0.85


Exhibit 9: Rolling 36-month Correlation of Style

Premia Portfolio to Global 60/40 Portfolio and

Hedge Fund Index

1990 – 2012

Source: AQR. The global 60/40 portfolio is a combination of the MSCI

World equity index and the Barclays Global Aggregate bond index. The

DJCS hedge fund index uses data from the Hedge Fund Research hedge

fund index before 1994.

To illustrate the potential benefits of style

investing as a diversifier for traditional portfolios,

Exhibit 10 shows the impact of allocating pro-

rata away from the 60/40 portfolio into the style

composite (net of trading costs and discounting)

at three levels of investment: 10%, 20%, and 30%

devoted to the style premia portfolio. As the

exhibit shows, the Sharpe ratio of the resulting

combinations improves by a wide margin,

indicating that adding a broad style composite

may improve performance and should reduce risk

exposure significantly.

Exhibit 10: Impact of Adding 10/20/30%

of Style Premia Portfolio to Global 60/40

1990 – 2012

60/40 + 10%

STYLES + 20%

STYLES + 30%

STYLES

Annual Return 6.8% 7.7% 8.7% 9.6%

Volatility 9.6% 8.8% 8.2% 7.8%

Sharpe Ratio 0.30 0.44 0.59 0.74

Correlation to Equities 0.99 0.98 0.94 0.86


Conclusion

Although the equity premium is thought to be the

most reliable source of long-run returns, most

investors over-rely on it and overweight it. We

believe excessive dependence on any single

source of risk is inefficient diversification, even

(or perhaps especially) if everyone does it. In a

world with multiple risk factors, in our opinion

there are better ways to construct portfolios. We

believe the most reliable way to sustained

investment success involves cost-effectively

harvesting multiple return sources such as long-

only market premia, style premia, and other

forms of alternative risk premia. In this article we

focused on the return and diversification benefits

of style premia and on how to construct an

efficient style strategy in a transparent and cost-

effective way to enhance any investment

portfolio.

So, why haven’t more investors embraced simple

style premia? One answer might be lack of

knowledge. Although the evidence in favor of

these styles has existed in the literature for some

time, it is somewhat scattered and not previously

linked together fully. As a result, investors often

view each style premium separately and often

chase returns across styles as their performance

varies, failing to appreciate the diversification

benefits of combining different styles.28

A second answer is the continual pursuit of

alpha. Too many investors think they can

identify alpha and find alpha producers. The

reality is that the pursuit of alpha is very difficult

and expensive. Moreover, this pursuit has led to

an overinvestment in high-fee hedge funds whose

largest exposure is traditional equity risk, since

alpha (including style premia) is often buried

28 Indeed, one advantage of a multi-strategy style product is that it may

discourage investors from chasing recently winning strategies, which not

only provides better diversification, but also perhaps trading cost savings.

-1

-0.5

0

0.5

1

Co

rre

lati

on

Style Premia Composite vs. Global 60/40

Style Premia Composite vs. DJCS HF Index

DJCS HF Index vs. Global 60/40


within simple equity exposure. Investors

increasingly recognizing this problem have

sought alternatives. Self-servingly we note that, to

date, investors have not had access to a well-

managed broad set of long-short style factors at

reasonable fees and at risk levels that impact

their portfolios enough. Such a multi-strategy,

multi-asset-class product was simply not

available until now.

A third answer is the prevalent aversion to

leverage, shorting, and/or derivatives. An

efficient style premia strategy uses these tools.

Indeed, one of the main style premia—

defensive—is itself the result of taking advantage

of other investors’ leverage aversion. For the

investor who can take a little LSD (leverage,

shorting, and derivatives, that is!), there is the

potential for huge rewards in terms of better and

more stable returns. Not everyone has the ability

to manage these risky tools, but we think they can

be managed successfully to produce large and

needed diversification benefits to most investors

today.

Finally, there is also the risk of deviating from the

herd. In almost every endeavor, it is famously

dangerous to lose unconventionally—far more

dangerous than losing conventionally. But

history also teaches us that great rewards await

pioneers, especially when the evidence is so

clearly in favor of a new path. A diversified, well-

constructed style premia portfolio may offer an

investor substantial long-term, risk-adjusted

returns that are uncorrelated with traditional

assets. We believe the improvement on the

efficiency of most existing portfolios is too great

to pass up.


Related Studies

AQR Capital Management (2012), “AQR Alternative Thinking – July 2012.” AQR quarterly.

Asness, C. (2004), "An Alternative Future. An Exploration of the Role of Hedge Funds." Journal of

Portfolio Management, 30th Anniversary Issue.

Asness, C. (1994), “Variables That Explain Stock Returns: Simulated And Empirical Evidence.” Ph.D.

Dissertation, University of Chicago.

Asness, C., A. Frazzini, and L. Pedersen (2011), “Leverage Aversion and Risk Parity.” Financial

Analysts Journal, Vol. 68, No. 1, 47-59.

Asness, C., R. Krail and J. Liew (2001), "Do Hedge Funds Hedge?" Journal of Portfolio Management,

Vol. 28, Fall, 6-19.

Asness, C., J. Liew, and R. Stevens (1997), ‘‘Parallels Between Cross-Sectional Predictability of Stock

and Country Returns.’’ Journal of Portfolio Management, Vol. 23, Spring, 79-87.

Asness, C., T. Moskowitz, and L. Pedersen (2012), ‘‘Value and Momentum Everywhere.’’ Journal of

Finance, forthcoming.

Asness, C., B. Porter and R. Stevens (2000), "Predicting Stock Returns Using Industry-Relative Firm

Characteristics." On review with the Journal of Finance.

Berger, A., B. Crowell., R. Israel, and D. Kabiller (2008), “Is Alpha Just Beta Waiting To Be

Discovered?” AQR Whitepaper.

Black, F. (1972), “Capital Market Equilibrium with Restricted Borrowing.” Journal of Business, Vol. 45,

No. 3, 444-455.

DeBondt W., and R.Thaler (1985), “Does the Stock Market Overreact?” Journal of Finance, Vol. 40, No.

3, 793-805.

-- (1987), “Further Evidence on Investor Overreaction and Stock Market Seasonality.” The Journal of

Finance, Vol. 42, No. 3, 557-581.

Fama, E., and K. French (1992), “The Cross-section of Expected Stock Returns.” Journal of Finance,

Vol. 2, No. 47, 427-465.

-- (1993), “Common Risk Factors in the Returns on Stocks and Bonds.” Journal of Financial Economics,

33, 3-56.

-- (1996), “Multifactor Explanations of Asset Pricing Anomalies.” Journal of Finance, Vol. 51, No 1, 55-

84.

-- (1998), “Value versus growth: The international evidence,” Journal of Finance, Vol. 53, 1975-1999.

-- (2006), "The Value Premium and the CAPM,” Journal of Finance, Vol., 61, 2163-2185.

-- (2008), "Dissecting Anomalies,” Journal of Finance, Vol. 63, 1653-1678.


-- (2012), “Size, value, and momentum in international stock returns,” Journal of Financial Economics,

forthcoming.

Frazzini, A., R. Israel, and T. Moskowitz (2012), “Trading Costs of Asset Pricing Anomalies.” working

paper, AQR Capital Management.

Frazzini, A., D. Kabiller, and L. Pedersen (2012), “Buffett’s Alpha.” working paper, AQR Capital

Management.

Frazzini, A., and L. Pedersen (2011a), “Betting Against Beta.” working paper, AQR Capital

Management, New York University and NBER (WP 16601).

Frazzini, A., and L. Pedersen (2011b), “Embedded Leverage.” working paper, AQR Capital

Management, New York University.

Grinblatt, M., and T. Moskowitz (1999), “Do Industries Explain Momentum?” The Journal of Finance,

Vol. 54, No. 4, 1249-1290.

Ilmanen, A. (2011), Expected Returns, Wiley.

Ilmanen, A., and J. Kizer (2012), “The Death of Diversification Has Been Greatly Exaggerated.” The

Journal of Portfolio Management, Vol. 38, No. 3, 15-27.

Israel, R., and T. Moskowitz (2012), “The Role of Shorting, Firm Size, and Time on Market Anomalies.”

Journal of Financial Economics, forthcoming.

Jagadeesh, N., and S. Titman (1993), “Returns to Buying Winners and Selling Losers: Implications for

Stock Market Efficiency.” Journal of Finance, Vol. 48, No. 1, 65-91.

Koijen, R., T. Moskowitz, L. Pedersen, and E. Vrugt (2012), “Carry.” working paper, University of

Chicago Booth School of Business, New York University, University of Amsterdam.

Moskowitz, T. and M. Grinblatt (1999), "Do Industries Explain Momentum?" Journal of Finance, Vol.

54, No. 1, 1249-90.

Novy-Marx, Robert (2012), “The Other Side of Value: The Gross Profitability Premium” Journal of

Financial Economics, forthcoming.


Biographies

Antti Ilmanen, Ph.D., AQR Principal

Antti manages AQR’s Portfolio Solutions Group, which advises institutional investors and sovereign

wealth funds, and develops the firm’s broad investment ideas. Before AQR, Antti spent seven years as a

senior portfolio manager at Brevan Howard, a macro hedge fund, and a decade in a variety of roles at

Salomon Brothers/Citigroup. He began his career as a central bank portfolio manager in Finland. Antti

earned M.Sc. degrees in economics and law from the University of Helsinki and a Ph.D. in finance

from the University of Chicago. Over the years, he has advised many institutional investors, including

Norway’s Government Pension Fund Global and the Government of Singapore Investment

Corporation. Antti has published extensively in finance and investment journals and has received a

Graham and Dodd award and Bernstein Fabozzi/Jacobs Levy awards for his articles. His book

Expected Returns (Wiley, 2011) is a broad synthesis of the central issue in investing. Antti recently

scored a rare double in winning the best-paper and runner-up award for best articles published in 2012

in The Journal of Portfolio Management (co-authored articles “The Death of Diversification Has Been

Greatly Exaggerated” and “The Norway Model”).

Ronen Israel, AQR Principal

Ronen’s primary focus is on portfolio management and research. He was instrumental in helping to

build AQR’s Global Stock Selection group and its initial algorithmic trading capabilities, and he now

also runs the Global Alternative Premia group, which employs various investing styles across asset

classes. He has published in The Journal of Financial Economics and elsewhere, and sits on the executive

board of the University of Pennsylvania’s Jerome Fisher Program in Management and Technology. He

has been a guest speaker at Harvard University, Columbia University and New York University, and is

a frequent conference speaker. Prior to AQR, Ronen was a senior analyst at Quantitative Financial

Strategies Inc. He earned a B.S. in economics from the Wharton School at Penn, a B.A.S. in biomedical

science from Penn’s School of Engineering and Applied Science, and an M.A. in mathematics,

specializing in mathematical finance, from Columbia..

Tobias J. Moskowitz, Ph.D., Fama Family Professor of Finance, Booth School of Business

A prominent figure in economics, who won the 2007 Fischer Black Prize, which honors the top finance

scholar in the world under the age of forty, Tobias Moskowitz is one of today’s highly sought-after

economic thought leaders. He has been praised for his "ingenious and careful use of newly available

data to address fundamental questions in finance,” and he brings his innovative thinking to financial

audiences around the world. Moskowitz is the Fama Family Professor of Finance at the University of

Chicago Booth School of Business and is a member of the National Bureau of Economic Research,

whose work has been cited in numerous publications and the media including CNBC, The New York

Times, Financial Times, Wall Street Journal, and a 2005 speech by then Federal Reserve Chairman Alan

Greenspan.

We would like to thank Cliff Asness, April Frieda, Georgi Georgiev, Sarah Jiang, David Kabiller, Johnny Kang, John Liew, Thomas Maloney, and Mark Stein

for helpful comments and suggestions, and Jennifer Buck for design and layout.


Disclosures

The information set forth herein has been obtained or derived from sources believed by the author and AQR Capital

Management, LLC (“AQR”) to be reliable. However, the author and AQR do not make any representation or warranty, express

or implied, as to the information’s accuracy or completeness, nor does AQR recommend that the attached information serve as

the basis of any investment decision. This document has been provided to you for information purposes and does not

constitute an offer or solicitation of an offer, or any advice or recommendation, to purchase any securities or other financial

instruments, and may not be construed as such. This document is intended exclusively for the use of the person to whom it has

been delivered by AQR and it is not to be reproduced or redistributed to any other person. AQR hereby disclaims any duty to

provide any updates or changes to the analyses contained in this presentation.

Hypothetical performance results (e.g., quantitative backtests) have many inherent limitations, some of which, but not all, are

described herein. No representation is being made that any fund or account will or is likely to achieve profits or losses similar

to those shown herein. In fact, there are frequently sharp differences between hypothetical performance results and the

actual results subsequently realized by any particular trading program. One of the limitations of hypothetical performance

results is that they are generally prepared with the benefit of hindsight. In addition, hypothetical trading does not involve

financial risk, and no hypothetical trading record can completely account for the impact of financial risk in actual trading. For

example, the ability to withstand losses or adhere to a particular trading program in spite of trading losses are material points

which can adversely affect actual trading results. The hypothetical performance results contained herein represent the

application of the quantitative models as currently in effect on the date first written above and there can be no assurance that

the models will remain the same in the future or that an application of the current models in the future will produce similar

results because the relevant market and economic conditions that prevailed during the hypothetical performance period will

not necessarily recur. There are numerous other factors related to the markets in general or to the implementation of any

specific trading program which cannot be fully accounted for in the preparation of hypothetical performance results, all of

which can adversely affect actual trading results. Discounting factors may be applied to reduce suspected anomalies. This

backtest’s return, for this period, may vary depending on the date it is run.

Diversification does not eliminate the risk of experiencing investment losses.

Past performance is not an indication of future performance.

There is a risk of substantial loss associated with trading commodities, futures, options, derivatives and other financial

instruments. Before trading, investors should carefully consider their financial position and risk tolerance to determine if the

proposed trading style is appropriate. Investors should realize that when trading futures, commodities, options, derivatives

and other financial instruments one could lose the full balance of their account. It is also possible to lose more than the initial

deposit when trading derivatives or using leverage. All funds committed to such a trading strategy should be purely risk

capital.

The Drawdown Control System described herein will not always be successful at controlling a fund’s risk or limiting portfolio

losses. This process may be subject to revision.

AQR Capital Management, LLC

Two Greenwich Plaza, Greenwich, CT 06830 p: +1.203.742.3600 I f: +1.203.742.3100 I w: aqr.com

the case for style investing - aqr capital management investing with style: the case for style...

Documents