Style Rotation

Quantitative Strategy North America United States

18 April 2012

Portfolios Under Construction Reseach Summary Uncertainty and episodic shifts in risk appetite can rotate style factors towards unwanted and even dangerous risk profiles. We investigate the drivers and dynamics behind these stealth rotations and show how to monitor, control and even profit from them.

Uncertainty and Style Dynamics

Uncertainty, style dynamics and factor rotation strategies

Deutsche Bank Securities Inc.

Note to U.S. investors: US regulators have not approved most foreign listed stock index futures and options for US investors. Eligible investors may be able to get exposure through over-the-counter products. Deutsche Bank does and seeks to do business with companies covered in its research reports. Thus, investors should be aware that the firm may have a conflict of interest that could affect the objectivity of this report. Investors should consider this report as only a single factor in making their investment decision. DISCLOSURES AND ANALYST CERTIFICATIONS ARE LOCATED IN APPENDIX 1.MICA(P) 146/04/2011.

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Team Contacts Miguel-A Alvarez Strategist (+1) 212 250-8983 [email protected] Yin Luo, CFA Strategist (+1) 212 250-8983 [email protected] Rochester Cahan, CFA Strategist (+1) 212 250-8983 [email protected] Javed Jussa Strategist (+1) 212 250-4117 [email protected] Zongye Chen Strategist (+1) 212 250-2293 [email protected] Sheng Wang Strategist ( +1) 212 250-8983 [email protected]

Risk appetite changes and involuntary style rotation We perform a forensic analysis of recent factor behavior to show how sharp and rapid shifts in risk appetite can rotate factors away from their steady state compositions. Indeed, as we show in the case of Momentum these rotations can unexpectedly position factors towards stocks that have been overbought and away from stocks that have been severely oversold.

Vigilant monitoring and understanding factor dynamics We propose a simple and effective way to monitor factor dynamics in the face of uncertainty and strong changes in risk aversion. We also investigate style dynamics in the past to analyze factor shifts in past episodes of market uncertainty.

VRP to the rescue We use the variance risk premium (VRP) to take a proactive stance in the face of continuing macroeconomic uncertainty and recurring style shifts. We devise two simple factor-timing strategies based on the VRP. We find these strategies to be highly effective at switching; especially during episodes of shifting risk appetite (risk-on/risk-off).

18 April 2012 Portfolios Under Construction

Page 2 Deutsche Bank Securities Inc.

Table of Contents

Letter to our readers ......................................................................... 3 Uncertainty continues… ............................................................................................................ 3

Risk appetite and style dynamics – a recent synopsis ................... 4 Risk-on, risk-off and recent style dynamics ............................................................................... 4 Recent factor performance ....................................................................................................... 6 The Beta connection ................................................................................................................. 8 Factor Dynamics and Regimes ............................................................................................... 15

VRP and style rotation .................................................................... 16 Variance risk premium and risk appetite changes ................................................................... 16 Implementing the VRP strategy .............................................................................................. 18 VRP for style rotation .............................................................................................................. 19

References ........................................................................................ 23


Deutsche Bank Securities Inc. Page 3

Letter to our readers Uncertainty continues…

Last year saw a series of events that caused havoc for some investors, while others found themselves well-positioned and outperformed. General consensus has it that 2011 saw a reversal from past years, in that, quantitative investors generally outperformed while fundamental managers struggled1.

Indeed, our own long/short equity QCD Model Portfolio 2 had an IR of 2.1 while the performance of many conventional quantitative factors ended in positive territory in 2011. The large cap universe was somewhat of a different story and while our factors did show overall positive performance over 2011, the numbers were not nearly as robust as those across the full spectrum of US stocks.

What actually happened in 2011? Why where quantitative factors working so robustly again and what happened to quants in January 2012 when many saw significant drawdowns in performance?

In this report, we aim to address these questions and much more. We will link much of the outperformance of conventional quantitative factors over 2011, especially that corresponding to the de-risking episode in the summer, to the outperformance of low Beta stocks and significant underperformance of high Beta stocks during this period.

This low-risk outperformance during the summer and fall was driven by the de-risking episode caused by a worsening of the European sovereign debt crisis. The crisis induced fears of recession sending investors overwhelmingly towards safety and out of risk in which they piled into quality and other low-risk stocks; while at the same time dumping riskier stocks.

We look at the effect of these de-risking and subsequent re-risking episodes not only in the context of factor performance, but also on the dynamics underlying factor rotation. We will see that aside from driving significant levels of performance, these episodes can reposition factors and may sometimes make different factors across different style more correlated, or driving some factors to take very concentrated risk exposures.

Lastly, we use the variance risk premium (VRP) together with the analysis on style factor dynamics under changes in risk-appetite to devise two simple factor rotation schemes that is adept at picking factors that will outperform during these episodes.

Thanks,

Yin, Rocky, Miguel, Javed, John & Sheng.

1 Our conversations with clients lead us to believe that performance across large cap quantitative funds was more mixed than overall good. 2 See Luo et al, 2012 “QCD Model: DB Quant Handbook” for a detailed model methodology.



Risk appetite and style dynamics – a recent synopsis Risk-on, risk-off and recent style dynamics

One of the determining drivers of investor risk appetite is economic sentiment. Therefore, the enduring global macroeconomic instability and the uncertainty it propagates to financial markets has been a major catalyst for the abrupt and sharp reversals experienced in risk appetite since the financial crises. Indeed, “risk-on/risk-off” along with “re-risking/de-risking” will be the defining labels for market behavior over this tumultuous period.

Measuring changes in risk-appetite Risk appetite can be interpreted, loosely, as the demand for risky assets. Increases in risk appetite corresponds to greater demand for risk causing prices of riskier assets to increase relative to those of lower risk. Conversely, decreases in risk appetite generate greater demand for lower risk assets and will cause their prices to increase relative to those of higher risk. A simplistic yet effective means to quantify the demand for higher/lower risk is via the return to a portfolio that is long high-risk stocks and short low-risk stocks. When risk appetite increases, the return to this kind of portfolio should be positive, while periods of decreasing risk appetite would generate negative portfolio returns.3 Stock risk can be measured in many different ways, but a conventional means is to use stock Beta4.

Figure 1 shows the monthly and cumulative return to a portfolio that is long the top decile of stocks ranked by Beta and short the bottom decile for our DBQS universe5 since January 2011. The figure also shows the return to the market capitalization portfolio which correlated strongly with risk appetite especially during strong episodes of changing risk appetite.

Figure 1: US Monthly & Cumulative return to high minus low Beta Portfolio (Decile 10

minus Decile 1) and Market Portfolio (capitalization weighted), US DBQS universe.

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Source: Axioma, Russell, S&P, Deutsche Bank Quantitative Strategy

3 We are aware that this definition and characterization of the demand for risk is oversimplified. However, as we will see, this characterization is sufficient to gauge risk preferences within the aggregate equity universe. 4 Unless otherwise noted, we will use stock Predicted Beta from the Axioma medium horizon risk model. 5 Our DBQS universe is covers a similar universe to the Russell 3000.



The negative returns to Beta and the market during August and September of 2011 correspond to sharp declines in risk appetite (aka de-risking) brought along in most part by the worsening European risk landscape as Italian sovereign yields increased to dangerous levels. The subsequent re-risking episodes in October and more recently in January correspond to what many are calling a resolution to “tail risk” in Europe. While we are unsure of the full resolution of Europe’s economic troubles, we do agree that the likelihood of a US recession has decreased since the summer.

Last, we note from Figure 1 that positive returns to the market portfolio do not always coincide with larger returns to higher Beta stocks, i.e., positive market return does not necessarily translate to increases in risk appetite. Two good examples are April 2011 and March 2012. A risk explanation for this phenomenon would lie in the generally accepted notion that Beta is not the sole driver of systematic return. Fundamentally, it is the result of the Market having a much larger Size bias than the Beta portfolio. Therefore, these episodes can be interpreted as investors shifting towards Size in a stronger way than they are shifting away from higher Beta.

Risk appetite in other markets Outside the US, we find that risk appetite in the rest of the world had similar behavior during 2011 and beginning of 2012 (Figure 2).

Figure 2: Global ex-US Monthly & Cumulative return to high minus low Beta Portfolio

(D10 – D1) and Market Portfolio (cap weighted), S&P BMI Global ex-US universe.

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Other measures of risk appetite Another measure that is commonly used to look at risk appetite in general is the TED spread. Many investors take the spread to be a “fear index”. It is simply the spread between Libor and the three-month US Treasury Bill6. Higher levels of the TED spread are associated with higher risk aversion (lower risk appetite) and vice versa. Therefore, we expect that changes in the TED spread should be inversely related to the returns to the Beta portfolio. Figure 3 and Figure 4 show that indeed the TED spread and the return to global Beta have a strong inverse relationship.

6 http://www.wikinvest.com/rate/TED_Spread



Figure 3: TED spread versus cumulative return to Global

Beta factor portfolio (D10-D1)

Figure 4: Changes in TED spread versus monthly return

to Global Beta factor portfolio (D10-D1)

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Source: Axioma, Russell, S&P, Bloomberg LLP, Deutsche Bank Quantitative Strategy Source: Axioma, Russell, S&P, Bloomberg LLP, Deutsche Bank Quantitative Strategy

Recent factor performance

What effect did the strong decrease in risk appetite during the summer 2011 have on style factors? As uncertainty increases, investors will eventually trade off riskier stocks that may not sustain their expected cash flows in a recession for more defensive stocks that are more resistant to economic contractions. Sectors and industry matter, but we can also characterize defensive stocks via style factors such as ROE, Dividend Yield and Earnings dispersion. For practical purposes, we will analyze a subset of factors from our factor library which are conventionally used to represent investment styles. The goal is not to analyze every factor, but rather to analyze factor shifts arising from changes in risk-regime changes. Figure 5 lists the styles and factors we will use in this analysis. In addition, unless otherwise noted, we will work with decile spread portfolios.

Figure 5: Factors and styles Style Factor Direction

Value

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FY1 Earnings Yield

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Two factor categories during 2011 Based on the evolution of cumulative factor performance over 2011 and the beginning of 2012, a naïve categorization detects two groups of factors. A first set (Figure 6) which outperformed during the summer/fall de-risking episode, while underperforming during the re-risking in October 2011 and subsequent to December 2011. The second set (Figure 7) underperformed or were flat during the summer de-risking and slightly outperformed (or were flat) during the subsequent re-risking episode. Other factors were mixed, which we detail below.



Figure 6: Cumulative return outperforming factors

during the de-risking in summer 2011. Russell 1000

Figure 7: Cumulative return for under-performing

factors that during summer 2011. Russell 1000.

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Source: Axioma, Russell, S&P, Deutsche Bank Quantitative Strategy Source: Axioma, Russell, S&P, Deutsche Bank Quantitative Strategy

A closer look at factor performance in Figure 6 shows that the de-risking episode starting in August generated significant gains for each of the factors with exception to 12-month Momentum. Similarly, the factors depicted in Figure 6 underperformed during the re-risking in October and subsequently in January and February of 2012.

Conversely, the factors depicted in Figure 7 showed to underperform during the de-risking episodes, while outperforming (albeit slightly in the case of Earnings Revision) during the episodes of re-risking. Figure 8 shows the performance to the other factors in our study. The returns refer to the decile portfolio spreads.

Figure 8: Factor decile spread portfolio statistics over Jan 2011 – Mar 2012 Factor Average Return Volatility Sharpe Ratio

ROE 9.61% 5.90% 1.63

EPS Growth (5yr) 11.97% 10.11% 1.18

FY1 EPS Dispersion 13.85% 13.29% 1.04

Market 11.81% 15.79% 0.75

YoY EPS Growth 5.27% 8.46% 0.62

Momentum 12-month 5.01% 10.68% 0.47

FY1 Dividend Yield 5.73% 12.62% 0.45

Price-to-Sales 1.66% 11.35% 0.15

FY1 EPS Revisions 0.41% 4.68% 0.09

FY1 Earnings Yield 0.61% 7.75% 0.08

Momentum 6-month -1.87% 20.38% -0.09

Beta (D10-D1) -13.73% 33.65% -0.41

Price-to-Book -6.59% 7.26% -0.91Source: Axioma, Russell, S&P, Deutsche Bank Quantitative Strategy

Is risk appetite driving factor performance? In the last section, we saw how factor performance was strongly influenced by recent episodes of re-risking and de-risking. To get a better sense of the link between factor performance and recent changes in risk appetite, Figure 9 and Figure 10 compare the monthly returns of a subset of factors to our risk-appetite factor, Beta. The negative (Figure 9) and positive (Figure 10) correlation between the factors and Beta is evident; especially across periods when risk appetite experiences strong changes (i.e. when the magnitude of the return to Beta is large).



Figure 9: FY1 Dividend Yield and FY1 EPS Dispersion vs.

Beta return decile spreads, Russell 1000

Figure 10: FY1 Earnings Yield & YoY EPS Growth versus

Beta return decile spreads. Russell 1000

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Figure 9 and Figure 10 show that during the summer of 2011 to early 2012, the comovement between Beta and style factors was very strong. However, not all factors were linked in the same way, i.e. the relationship between Beta and different factors seem to vary widely even between factors representing the same styles. For example, Dividend Yield and Earnings Yield are both considered to be Value factors, but their performance and their relationship with Beta was very different during this period7. In the next section, we discuss how to measure the relationship between a factor and Beta in an accurate and timely manner. This will prove useful to determine ex-ante how certain style factors will perform during an episode of de-risking or re-risking.

The Beta connection

In previous research, we have documented the link between Beta and style factors8. In those studies, we found that style factors could possess an inherent exposure to Beta and pick up significant exposure to Beta during certain market regimes or which could have adverse effects on performance. Moreover, we found that this exposure was dynamic and could, at times, have large and rapid shifts.

One of the more important findings in that research underlined the need to include cross-sectional information when computing exposures and correlations across factors. This is because the cross-sectional analysis provides a snapshot of the current factor composition and does not depend solely on past data that could be stale depending on factor dynamics.

In the following analysis, we will use two cross-sectional measures to characterize the link of a factor to Beta:

Portfolio Beta

Expected Correlation between the factor portfolio and the Beta portfolio

The first is simply the Beta of the factor portfolio and is computed in the typical manner, i.e. the portfolio weighted average stock Beta. In general, the Beta of a portfolio lends insight in that it will provide a sense of the direction of the comovement (positive Beta implies positive comovement and vice versa). However, it is of little use for quantifying an accurate measure of the co-dependency between two factors.

7 In fact, many investors regard Dividend Yield more representative of Quality than Value. 8 See Alvarez et al, 2010, “Portfolios Under Construction: Volatility=1/N”.



The second metric is a forward estimate of the correlation between the factor portfolio and the Beta portfolio9. This measure is somewhat more involved and requires a stock covariance matrix, but is essential if accuracy is the primary objective. The expected correlation measure is quite powerful in that it yields timely and accurate forecasts of factor co-dependency. More importantly, it is a useful tool for monitoring and understanding factor dynamics as well as for applications in risk and portfolio construction.

In the following sections, we analyze the exposures and correlation of each of the style factors to Beta. We will show how Beta affects the performance of the factors, but more importantly how episodes of de-risking/re-risking dynamically rotate their risk exposures profiles.

In addition, we will use the changes in factor correlations to Beta gain insight into the interactions and dynamic relationships between the factors.

9 This can be generalized to factor scores in general (not just decile spread portfolios) as we showed in Alvarez et al, 2011 “Reviving Momentum: Mission Impossible?”



Value Value factors did not exhibit similar cumulative performance during 2011-2012 (Figure 6 and Figure 7). In this section, we shed more light on the role that Beta plays in driving the divergence and convergence across Value style factor performance.

We begin with a simple synopsis covering the more recent period. The top graph in Figure 11 shows the expected correlation to Beta for different value factors during 2011-2012. The first half of 2011 saw varying levels of correlation across the different Value factors. In addition, the chart shows that FY1 Earnings Yield and Price-to-Book have significant shifts in their correlation to Beta. With exception to FY1 Dividend Yield, the de-risking/re-risking episodes during the summer and fall of 2011 cause a series of shifts in Beta correlations culminating in convergence. These numbers suggests that the homogeneity between different value factors can be quite dynamic over time and across varying market conditions.

But is Beta driving performance? The graph at the bottom of Figure 11 shows that Beta will overwhelm factor performance when both the correlation to Beta and the magnitude of the return of the Beta portfolio is significant. For example, note that during the first half of 2011 when Beta return magnitude was relatively low, there was not much consistency between the correlations to Beta and factor performance. However, during the de-risking/re-risking episodes in the second half of the year, Beta plays a more significant role in driving factor performance. Also note the mixed performance during November and December 2011, which saw relatively low magnitudes to the Beta portfolio returns.

Figure 11: Expected correlation with Beta (top chart) and performance (bottom

chart) between Value factors during 2011-2012. Russell 1000




If we analyze the past (Figure 12 through Figure 15), we find that the dynamic relationship with Beta is a common theme across value factors. In addition, the exposures and correlations to Beta can vary widely across value factors over different market regimes. Also note that in contrast to the behavior in Figure 11, the Dividend Yield factor can actually experience shifts in Beta exposure and correlation over time. For example, note that leading into the Financial Crisis of 2008, the Dividend Yield factor became more correlated with higher Beta stocks. This is due to the fact that the sell-off of risky stocks during this period was so robust that it even penetrated dividend paying stocks – mainly financial stocks that had by that time become the riskier (higher Beta) of that group.

Figure 12: Portfolio Beta: FY1 Earnings Yield, FY1

Dividend Yield, Russell 1000

Figure 13: Expected Correlation with Beta: FY1 Earnings

Yield, FY1 Dividend Yield, Russell 1000

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Last, it is worthwhile to note that Figure 14 and Figure 15 lend insight into the relationship between Price-to-Book and Price-to-Sales factors. The exposures and correlations show that the two factors exhibit a similar Beta profile over time with exception to the period after the technology bubble circa 2000 – 2003. –

Figure 14: Portfolio Beta: Price-to-Book, Price-to-Sales.

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Figure 15: Expected Correlation with Beta: Price-to-

Book. Price-to-Sales, Russell 1000

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Momentum and Earnings Revisions In past research, we documented how this behavior could cause these strategies to accumulate overwhelming levels of exposure to Beta causing them to be vulnerable to strong and rapid shifts in risk appetite10. In addition, the dynamic nature of these strategies do not make them well suited to be analyzed from a time-series perspective and so cross-sectional measures are paramount to understanding their exposure to risk-appetite over time.

A good illustration of their sensitivity to Beta can be seen during 2011-2012 depicted in Figure 16. First, we note that the correlation to Beta dropped off a cliff during the de-risking episodes in August and September for both 12-month Momentum and EPS Revisions. This rapid and strong rotation set up the factors to severely underperform during the re-risking episode in January 2012 as investors increased risk appetite buying oversold risky (high Beta) stocks and selling off overbought safe (low Beta) stocks.

Figure 16: Expected correlation with Beta (top chart) and performance (bottom chart)

of Momentum/Sentiment factors (Decile Spread Portfolios). Russell 1000


Note that correlations were significant leading into the de-risking, both factors held up rather well. This indicates that their non-Beta component (e.g. stock-specific component) had positive performance over this period. Indeed, the correlation levels between 25-50% indicate that Beta will account for only a quarter to half of the variability of returns. The historical correlation to Beta of both factors (Figure 18) shows that both the 12-month

10 See Alvarez et al 2011, “Reviving Momentum, Mission Impossible?” and Alvarez et al 2010, “Neutralization and Beyond”.



Momentum and FY1 EPS Revision factors had picked up on lower Beta stocks during the de-risking in the summer of 2010. This helps explain the outperformance of these factors during the slow de-risking in the beginning of 2011 as well as the flat performance during the stronger de-risking in August and September of 2011.

Last we note that a historical analysis of Beta exposure and correlation of both factors (Figure 17 and Figure 18) show that both factors exhibit very similar profiles to Beta over time. Indeed, this suggests that in aggregate, analyst revisions are strongly tied to past stock return momentum.

Figure 17: Portfolio Beta: Momentum (12M) and FY1

EPS Revisions factors, Russell 1000

Figure 18: Expected Correlation with Beta: Momentum

(12M) and FY1 EPS Revisions factors, Russell 1000

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Quality Typical factors used to characterize firm quality such as Return on Equity (ROE) and Earnings Dispersion also varied to some extent over 2011 and early 2012, albeit factor performance for this style was more heterogeneous than that found for Value.

Quality factors typically load up on safer assets with lower Beta and overall risk profiles. This is evident when looking at the exposure and correlation to Beta of these factors over time (Figure 19 and Figure 20).

Figure 19: Portfolio Beta: ROE, FY1 Earnings Dispersion

(3M Avg). Russell 1000

Figure 20: Expected Correlation with Beta: ROE, FY1

Earnings Dispersion (3M Avg). Russell 1000

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However, the historical analysis reveals that these factors can also exhibit different and varying Beta sensitivity over time. Indeed, the more recent period saw the correlation between ROE and Beta to increase to relatively high levels.



Growth Two factors commonly used to describe firm Growth are year-over-year EPS growth (YoY EPS Growth) and five year EPS growth (EPS Growth 5yr.). Fundamentally, the two are similar except that they try to capture different cycles. However, the Beta exposure and correlation analysis shown in Figure 21 and Figure 22 show that the two can exhibit significantly different risk profiles as measured by their exposure and correlation to Beta.

Figure 21: Portfolio Beta: YoY EPS Growth and 5yr EPS

Growth. Russell 1000

Figure 22: Expected Correlation with Beta: YoY EPS

Growth and 5yr EPS Growth. Russell 1000

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Factor Dynamics and Regimes

We can also use the expected correlation to Beta measure to analyze factor dynamics by comparing the Beta alignment across factors related by similar fundamental measures. For example, the FY1 Earnings Yield factor analyzed in Figure 11 is a function of price and analyst FY1 EPS estimates. Therefore, the factor’s increase in correlation during the beginning of 2011 may be due to either high Beta stocks becoming cheaper relative to lower Beta stocks or to analyst increasing their estimates to higher Beta stocks. In addition, we can use the Beta correlation to the trailing earnings yield factor (FY0 Earnings Yield) as an auxiliary comparison metric.

We can infer from Figure 23 that the increase Beta alignment of the FY1 Earnings Yield factor is mainly due to an increase in EPS revisions for higher Beta stocks as suggested by the increasing correlation of the FY1 EPS Revision factor. Note that the moderately negative returns to Beta may have also had a slight impact on the rise in the FY1 correlation is suggested by the slight increase in the Beta correlation to the FY0 Earnings Yield factor11. Yet another likely scenario is that higher Beta stocks did indeed increase their EPS relative to lower Beta stocks.

Figure 23: Expected correlation between FY1 Earnings Yield, FY0 Earnings Yield and

FY1 EPS Revisions and performance of the Beta portfolio. Russell 1000


One last interesting bit of insight we can get from Figure 23 is to observe the Beta correlations during the periods of strong de-risking and re-risking. Note that during August de-risking episode; analyst began their downward revisions of higher Beta stocks so much that it offset an increase the correlation that would happen naturally by strong de-risking episodes in which higher Beta stocks experience stronger decreases in price and consequently making them “cheaper” relative to their past (see Figure 13).

11 One last scenario is that Beta d



VRP and style rotation Variance risk premium and risk appetite changes

A topical and recurring theme in our research is what academics have dubbed the variance risk premium (VRP). Simply, the measure can be thought as the difference between market implied variance and expected realized variance. As the name implies, the measure is considered to be a premium for the risk embedded in asset markets and it has been shown to have predicted power of equity market returns.

Indeed in our prior research12 on VRP, we have found that it has predictive power for equity market timing, country rotation and for asset allocation. In this section, we explore its efficacy for capturing strong and persistent changes in risk-appetite and show how to implement it for market or Beta timing.

In addition, we will investigate its efficacy for timing style factors and propose two simple strategies that use VRP to predict and select a set of style factors that outperform an equal weighted factor benchmark.

Did VRP forecast changes in risk-appetite during 2011 and early 2012? The strong and persistent changes in risk appetite experienced in the summer and fall of 2011 and early 2012 provide a good test environment in which to analyze the link between VRP and risk appetite as well as its efficacy for market and Beta timing. Figure 24 overlays the VRP estimate from the prior month over the monthly returns to the market and Beta portfolios. The graph shows that VRP was able to forecast the Beta and Market portfolio quite effectively over this period. In fact, there was only one month in 2011 when VRP got the forecast completely wrong (August 2011).

Figure 24: VRP(t-1) versus Market and Beta (D10-D1) monthly return (DBQS universe)


A rolling correlation analysis over time (Figure 25) shows that the predictive power observed in Figure 24 is consistent over time, albeit recent predictive power is much stronger than the historical norm.

12 See Luo et al, 2012, “Quantitative Tactical Asset Allocation” and Luo et al. 2012 “New Insights in Country Rotation”.



Figure 25: Rolling 60-month correlation with one-month lagged VRP: Market and Beta

Portfolios (Decile 10 minus Decile 1). US DBQS universe.

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VRP as a proxy for macroeconomic risk One strand of the literature on VRP suggests that it is a risk premium for the macroeconomic uncertainty embedded in asset markets (see Londono, [2011] or Bansal and Yaron [2004]). The predictive power for Market and Beta timing shown in Figure 25 lends credit to this hypothesis in that VRP shows to be a good predictor of changes in risk appetite as measured by the Beta and Market portfolios.

Another way we can verify the link between VRP and macroeconomic uncertainty is to link it to stock return correlation and the systematic component of the cross sectional dispersion of stock returns (aka the opportunity set). In a prior paper13, we showed how stock return correlation was linked to systematic component of cross-sectional return dispersion as well as macroeconomic uncertainty. Figure 26 and Figure 27 show both of these measures against the volatility of VRP and suggest that VRP volatility is strongly related to other measures we have shown are affected by macroeconomic uncertainty. Note that high VRP volatility indicates high levels of uncertainty about market direction.

Figure 26: Volatility of VRP versus Relative Macro-

related Opportunity Set. Russell 1000.

Figure 27: Volatility of VRP versus pairwise stock return

correlation within sectors (Russell 1000)

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13 See Alvarez et al, 2012, “Correlation and Consequences”.



Implementing the VRP strategy

The results in the last sections suggest that VRP can be used for Beta and market timing purposes. However, exactly how to use it in a strategy is not so clear. One question that comes up is how much market or Beta exposure should one take given the level of VRP? In the following we propose a scheme to use it in a market or Beta-timing context.

VRP is given in variance units so it is not directly a return forecast (alpha). Therefore, the trick is to convert the VRP today to a forecast of return for the next period. Specifically, the goal is to obtain the best forecast of forward return conditional on the current value of VRP. A simple way to get this estimate is to use linear regression14. The dependent variable will be the market return over t-1 to t and the independent variable is the value of VRP at time t-1 as follows:

ttVRPMRtM VRPR εβα ++= −1,, ( )1

In this equation tMR , is the return to the market over t-1 to t; VRPMR ,β is the beta of the forward market return to the current value of VRP; the intercept, α , captures the mean effect of both variables; and tε is a random error term.

To estimate the VRPMR ,β and α parameters in equation (1), we can simply use OLS15. Once these parameters are estimated, then the forecast of the next period market return is:

tVRPMRtM VRPR ,,ˆˆˆ βα +=+1 ( )2

In practice, we will update our estimates VRPMR ,β̂ and α̂ every month so a realistic backtest will follow the same practice. Now we have a realistic forecast of market return for each month that can be used for market timing and asset allocation among other uses.

Scaling the forecast For market timing purposes, it is desired that higher forecasts imply higher market allocation and vice-versa. An intuitive strategy is to allocate to the market portfolio in proportion to the forecasts so that our market weight tW takes on the following form:

1+= tMt RkW ,ˆ .

where k is a constant that we will use to target a specific volatility or tracking error. Then to rescale the forecasts we estimate the volatility of the strategy for 1=k . We can do this analytically through the model or empirically using a history of returns for the strategy for

1=k . To keep things simple, we use the latter and call it 1=kσ̂ . Now we choose a volatility target (or tracking error target) for the timing strategy Targetσ , and set k to:

1==

kk

σσ

ˆTarget

So the weight set to the market portfolio for the timing strategy at time t is:

11

+=

= tMk

t RW ,ˆ

ˆ Target

σσ

In the next example, we set a volatility target of 2.5% annualized and run the timing strategy on its own and then add it to the market portfolio.

14 Under certain assumptions, the regression estimate is optimal in the sense of being the linear unbiased estimator with the minimum amount of estimation error. 15 The error does not satisfy all the properties for OLS optimal estimates, but we leave a more sophisticated model for a future study. The idea is to see how implement the VRP timing strategy in practice.



Figure 28 shows the monthly returns to our VRP market timing strategy with a 2.5% annualized volatility target, while Figure 29 shows the cumulative return of mixing the market portfolio with the same strategy.16

Figure 28: VRP Market-timing strategy monthly return

(2.5% target annual volatility)

Figure 29: Market + VRP Market-timing strategy

cumulative return (VRP strategy run at 2.5% annual vol)

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Source: Russell, S&P, Bloomberg L.L.P., Deutsche Bank Quantitative Strategy Source: Russell, S&P, Bloomberg L.L.P., Deutsche Bank Quantitative Strategy

Last we note that adding the VRP timing strategy to the market in a more optimal manner requires the estimation of the covariance matrix between the timing strategy and the market portfolio, which can be done analytically or empirically. Then a rigorous signal weighting technique could be used to obtain an optimal mean-variance portfolio17

VRP for style rotation

As we saw in the last section, raw style factors may possess significant exposure to changes in risk-appetite, which we argued can be proxied by the return to a portfolio that is long high Beta and short low Beta stocks (i.e. Decile 10 minus Decile 1).

We also saw that the variance risk premium (VRP) is quite adept at forecasting significant changes and reversals in investor risk appetite, especially during the past three years of unprecedented economic uncertainty.

The latter two points suggest that VRP can be used for style-timing or style-rotation. If so, the following question is whether it can only predict the Beta component implicit in style factors or whether it can predict more. We leave the second question for a future report.

In this section we analyze VRP’s potential for style-timing and develop a simple scheme using our correlation analysis from the prior section. This scheme will be used to turn-on and turn-off factors. An upcoming report will develop a more rigorous style rotation algorithm using VRP as well as other macroeconomic and capital market variables18.

Beta-Correlation and VRP for timing style factors The results in the prior sections of this report suggest a simple scheme to time style factors using their exposure and correlation to Beta. The basic idea is that style factors exhibiting a positive expected correlation to Beta will have a tilt towards increasing risk appetite, while factors with negative correlation to Beta will have a tilt towards decreasing risk appetite. Then we simply use the VRP forecast to turn-on or turn-off the factors.

16 The estimates for the parameters in the model were computed using an expanding window. 17 See Luo et al, 2011 “Robust Factor Models” or Alvarez et al, 2011, “Driving in the fast lane”. 18 This will be an extension of our previous style rotation research and model (see Luo et al, 2010 “Style Rotation”).



The methodology for the style-timing scheme is outlined in the following 5 steps:

Step 1: Set each factor to the same risk level using the factor portfolio historical volatility or a forecast from a risk model.

Step 2: Identify the expected correlation of each style factor to Beta.

Step 3: Divide style factors into two groups:

A “bullish” group, which consists of those having positive expected correlation

A “bearish” group consisting of those having negative expected correlation

Step 4: Use the VRP forecast to select the bullish or bearish group of factors. To do this we center VRP by subtracting its mean over the last 12-months19. Then for positive values of this centered VRP we select the bullish group of factors; conversely for negative VRP we select the bearish set.

Step 5: Build two models for the weights to the selected group.

VRP-EW: equal weighted: equal weight all the factors in the group chosen in Step 3

VRP-CW: correlation weighted: weight factors selected in Step 3 in proportion to the absolute value of their correlations

Note that the risk scaling in Step 1 ensures that a factor with very high volatility does not dominate the model. We can also consider this to be a naïve version of risk adjustment in the absence of an optimizer.

The correlation weighted model will overweigh factors with higher correlation to Beta, which is an implicit reference to those factors having greater implied alpha as referred to in our last section.

Our benchmark will be the equally weighted factor combination of the all the factors, EQWGT, which as we have documented in past research is not an easy benchmark to beat20.

The results of the three models over different periods are shown in Figure 30. The Sharpe ratios show that over the full period the VRP-EW performs the best in risk-adjusted space. The VRP-CW model shows similar performance to the benchmark (EQWGT) over the full history, but significantly outperforms in subsequent periods, especially post 2009. In fact, the performance subsequent to 2010 is significantly better for the correlation weighted model, suggesting that level (not just the sign) of the correlation between factors is a strong predictor of factor outperformance.

Last, we note that the volatility of the VRP-CW strategy is significantly larger than both other strategies. This is because the VRP-CW model tends to load up heavily on factors with higher/lower correlation to Beta given that we are targeting the Beat component of each of the style factors.

19 The results are quite robust for different window lengths. Specifically, we tried an expanding window, 60, 48, 36 and 24 month windows and all showed similar results. We chose a 12-month window to capture faster dynamics at the cost of higher turnover and possibly more error. 20 See Luo et al, 2010, “Portfolios Under Construction: Robust Factor Models”.



Figure 30: Style rotation results for three style rotation models Period Mean

(Annual) Std. Dev.

(Annual) Sharpe

Ratios

EQWGT VRP-EW VRP-CW EQWGT VRP-EW VRP-CW EQWGT VRP-EW VRP-CW

Jan 1992 – Mar 2012 11% 11% 21% 21% 18% 42% 0.53 0.61 0.50

Jan 2000 – Mar 2012 13% 16% 30% 24% 21% 47% 0.58 0.78 0.63

Jan 2007 – Mar 2012 5% 16% 49% 18% 13% 44% 0.28 1.21 1.12

Jan 2009 – Mar 2012 -6% 13% 56% 18% 12% 44% -0.33 1.04 1.29

Jan 2010 – Mar 2012 5% 13% 45% 14% 12% 26% 0.40 1.14 1.70Source: Axioma, Russell, S&P, Deutsche Bank Quantitative Strategy

Figure 31 and Figure 32 show the return series to both VRP factor timing strategies. Note that in risk adjusted terms, the VRP-EW factor timing strategy outperformed the VRP-CW strategy. However, the more recent period shows that VRP-CW strategy significantly outperformed the VRP-EW strategy. This implies that the level of Beta mattered more during the more recent period. Indeed, this is consistent with both high correlations and higher systematic cross-sectional dispersion (Figure 26 and Figure 27).

Figure 31: VRP-CW style rotation model Figure 32: VRP-EW style rotation model

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The weights to the factors given by the VRP-CW strategy since January 2009 are shown in Figure 33. Note that the cells in blue indicate that the factor is turned off. The factors that are turned on, range from yellow to red, depending on the intensity of the absolute value of the correlation to Beta. Also note that the VRP-EW strategy has the same active factors shown in the figure. The difference is that the VRP-EW strategy equally weights the active factors in the model.

It is also worthwhile to note that Momentum has turned off during the more recent period. More importantly, was turned off during the re-risking that hurt the factor in January 2012. Similarly the models had turned off Momentum during the risk-rally in the spring of 2009; and interestingly enough has only appeared episodically since January 2009. In contrast, Price-to-Book and Price-to-Sales were turned on throughout most of 2009. These factors were ripe for the re-risking that took place throughout that year since they had rotated towards higher Beta stocks that were made cheap during the 2008 de-risking.

Finally Figure 34 shows the VRP-CW factor weights along with factor expected correlations to Beta. If we compare with the last few months in Figure 33, we find that VRP has switched more bearish sentiment as is illustrated above in Figure 24. It has switched its allocation towards the more defensively positioned factors and styles such as Momentum and Quality.



Figure 33: Factor loadings for the VRP-CW model January 2009 – March 2012 Jan-09 Feb-09 Mar-09 Apr-09 May-09 Jun-09 Jul-09 Aug-09 Sep-09 Oct-09 Nov-09 Dec-09

FY1 Dividend Yield (RHS) 17% 20% 23% 22% 4% 0% 0% 0% 0% 0% 0% 11%FY1 Earnings Yield 15% 21% 13% 0% 0% 0% 0% 0% 0% 0% 0% 20%Price-to-Book 35% 31% 33% 41% 52% 53% 41% 37% 31% 28% 36% 0%Price-to-Sales 28% 27% 31% 36% 44% 47% 38% 35% 29% 28% 31% 0%Momentum (12M) 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0%Momentum (6M) 0% 0% 0% 0% 0% 0% 22% 27% 40% 44% 33% 0%ROE 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 21%FY1 EPS Dispersion 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 20%YoY EPS Growth 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 18%EPS GROWTH (5Yr) 6% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 8%FY1 EPS Revision 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 2%

Jan-10 Feb-10 Mar-10 Apr-10 May-10 Jun-10 Jul-10 Aug-10 Sep-10 Oct-10 Nov-10 Dec-10FY1 Dividend Yield (RHS) 10% 12% 13% 15% 17% 16% 0% 17% 0% 0% 20% 0%FY1 Earnings Yield 20% 22% 19% 16% 18% 20% 0% 19% 0% 0% 12% 0%Price-to-Book 0% 0% 0% 0% 0% 0% 25% 0% 23% 17% 0% 28%Price-to-Sales 0% 0% 0% 0% 0% 0% 27% 0% 23% 26% 0% 38%Momentum (12M) 0% 0% 0% 0% 0% 0% 27% 0% 1% 0% 0% 4%Momentum (6M) 0% 0% 0% 6% 0% 0% 0% 7% 0% 0% 17% 0%ROE 21% 23% 22% 20% 22% 22% 0% 20% 0% 0% 18% 0%FY1 EPS Dispersion 20% 22% 22% 21% 23% 23% 0% 22% 0% 0% 20% 0%YoY EPS Growth 17% 17% 16% 16% 12% 6% 1% 0% 29% 35% 0% 29%EPS GROWTH (5Yr) 8% 5% 9% 6% 8% 13% 0% 15% 0% 0% 13% 0%FY1 EPS Revision 4% 0% 0% 0% 0% 0% 20% 0% 23% 23% 0% 0%

Jan-11 Feb-11 Mar-11 Apr-11 May-11 Jun-11 Jul-11 Aug-11 Sep-11 Oct-11 Nov-11 Dec-11 Jan-12 Feb-12 Mar-12FY1 Dividend Yield (RHS) 0.192028 0 0.236637 0.311962 0.331006 0.36996 0.400082 0 0.285303 0 0 0.14783 0 0 0FY1 Earnings Yield 0.178586 0 0.148297 0.019851 0 0 0 0.165365 0 0.279379 0.212653 0 0.217863 0.220262 0.222494Price-to-Book 0 0.163218 0 0.03068 0.088089 0.135135 0.239542 0 0 0.166944 0.155782 0 0.242979 0.229495 0.294093Price-to-Sales 0 0.202718 0 0 0 0 0.032063 0.095594 0 0.286247 0.274596 0 0.264078 0.276759 0.357995Momentum (12M) 0 0.111048 0 0 0 0 0 0.229961 0 0 0 0.150566 0 0 0Momentum (6M) 0 0.294686 0 0 0 0 0 0 0.202833 0 0 0.163803 0 0 0ROE 0.184169 0 0.177604 0.1555 0.134873 0.084403 0.013361 0 0.162924 0 0 0.118958 0 0 0FY1 EPS Dispersion 0.200319 0 0.246433 0.312195 0.315973 0.340666 0.314953 0 0.271174 0 0 0.156504 0 0 0YoY EPS Growth 0 0.22833 0 0 0 0 0 0.243417 0 0.267429 0.356969 0 0.27508 0.273484 0.125418EPS GROWTH (5Yr) 0.170959 0 0.191029 0.169812 0.130059 0.069836 0 0.00668 0.077767 0 0 0.12725 0 0 0FY1 EPS Revision 0.073938 0 0 0 0 0 0 0.258983 0 0 0 0.135089 0 0 0


Factors and correlations for April 2012 The VRP-CW implied factors weights and the expected factor correlations with Beta are shown in Figure 34 for April 2012. The weights suggest that the 12-month centered VRP factor has taken on a slight “bearish” sentiment (see Figure 24).

Figure 34: VRP-CW factor weights and expected Beta correlations for April 2012

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Source: Axioma, Russell, S&P, Bloomberg LLP, Deutsche Bank Quantitative Strategy



References

Alvarez, M., Luo, Y., Cahan, R., Jussa, J., Chen, J., [2010], “Portfolios Under Construction: Volatility=1/N”, Deutsche Bank Quantitative Strategy, June 16, 2010.

Alvarez, M., Kassam, A., Mesomeris, S. [2010], “Factor Neutralization and Beyond”, Deutsche Bank Quantitative Strategy, September 21, 2010.

Alvarez, M., Luo, Y., Cahan, R., Jussa, J., Chen, J., [2010], “Portfolios Under Construction: Driving in the fast lane”, Deutsche Bank Quantitative Strategy, April 26, 2011.

Alvarez, M., Luo, Y., Cahan, R., Jussa, J., Chen, J., [2011], “Signal Processing: Reviving Momentum: Mission Impossible?”, July 6, 2011.

Alvarez, M., Luo, Y., Cahan, R., Jussa, J., Chen, J., [2011], “Portfolios Under Construction: Correlation and Consequences”, January 24, 2012.

Bansal, R., Khatchatrian, V., and Yaron, A., 2005, “Interpretable Asset Markets?”, European Economic Review, Vol. 49.

Luo et al, 2010, “QCD Model: DB Quant Handbook”, Deutsche Bank Quantitative Strategy, 22 July 2010.

Luo, Y., Cahan, R., Jussa, J. Alvarez, M., [2010], “Signal Processing: Style Rotation”, Deutsche Bank Quantitative Strategy, September 7, 2010.

Luo, Y., Cahan, R., Jussa, J. Alvarez, M., [2011], “Portfolios Under Construction: Robust Factor Modeling”, Deutsche Bank Quantitative Strategy, January 21, 2011.

Luo, Y., Cahan, R., Jussa, J. Alvarez, M., Chen, J., [2011], “Signal Processing: Quant Tactical Asset Allocation (QTAA)”, Deutsche Bank Quantitative Strategy, September 19, 2011.

Luo, Y., Cahan, R., Jussa, J. Alvarez, M., Chen, J., Sheng, W., [2012], “Signal Processing: New Insights in Country Rotation”, Deutsche Bank Quantitative Strategy, September 2012.

Londono, J.M., (2011), “The Variance Risk Premium Around the World”, FRB International Finance Discussion Paper No. 1035, available at SSRN: http://ssrn.com/abstract=2009065



Appendix 1 Important Disclosures

Additional information available upon request

For disclosures pertaining to recommendations or estimates made on a security mentioned in this report, please see the most recently published company report or visit our global disclosure look-up page on our website at http://gm.db.com/ger/disclosure/DisclosureDirectory.eqsr.

Analyst Certification

The views expressed in this report accurately reflect the personal views of the undersigned lead analyst(s). In addition, the undersigned lead analyst(s) has not and will not receive any compensation for providing a specific recommendation or view in this report. Miguel-A Alvarez/Yin Luo/Rochester Cahan/Javed Jussa/Zongye Chen/Sheng Wang

Hypothetical Disclaimer Backtested, hypothetical or simulated performance results have inherent limitations. Unlike an actual performance record based on trading actual client portfolios, simulated results are achieved by means of the retroactive application of a backtested model itself designed with the benefit of hindsight. Taking into account historical events the backtesting of performance also differs from actual account performance because an actual investment strategy may be adjusted any time, for any reason, including a response to material, economic or market factors. The backtested performance includes hypothetical results that do not reflect the reinvestment of dividends and other earnings or the deduction of advisory fees, brokerage or other commissions, and any other expenses that a client would have paid or actually paid. No representation is made that any trading strategy or account will or is likely to achieve profits or losses similar to those shown. Alternative modeling techniques or assumptions might produce significantly different results and prove to be more appropriate. Past hypothetical backtest results are neither an indicator nor guarantee of future returns. Actual results will vary, perhaps materially, from the analysis.



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Aside from within this report, important conflict disclosures can also be found at https://gm.db.com/equities under the “Disclosures Lookup” and “Legal” tabs. Investors are strongly encouraged to review this information before investing.

2. Short-Term Trade Ideas

Deutsche Bank equity research analysts sometimes have shorter-term trade ideas (known as SOLAR ideas) that are consistent or inconsistent with Deutsche Bank’s existing longer term ratings. These trade ideas can be found at the SOLAR link at http://gm.db.com.

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The information and opinions in this report were prepared by Deutsche Bank AG or one of its affiliates (collectively “Deutsche Bank”). The information herein is believed to be reliable and has been obtained from public sources believed to be reliable. Deutsche Bank makes no representation as to the accuracy or completeness of such information. Deutsche Bank may engage in securities transactions, on a proprietary basis or otherwise, in a manner inconsistent with the view taken in this research report. In addition, others within Deutsche Bank, including strategists and sales staff, may take a view that is inconsistent with that taken in this research report. Deutsche Bank may be an issuer, advisor, manager, distributor or administrator of, or provide other services to, an ETF included in this report, for which it receives compensation. Opinions, estimates and projections in this report constitute the current judgement of the author as of the date of this report. 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Each of these analysts may use differing methodologies to value the security; as a result, the recommendations may differ and the price targets and estimates of each may vary widely. In August 2009, Deutsche Bank instituted a new policy whereby analysts may choose not to set or maintain a target price of certain issuers under coverage with a Hold rating. In particular, this will typically occur for “Hold” rated stocks having a market cap smaller than most other companies in its sector or region. We believe that such policy will allow us to make best use of our resources. Please visit our website at http://gm.db.com to determine the target price of any stock. The financial instruments discussed in this report may not be suitable for all investors and investors must make their own informed investment decisions. Stock transactions can lead to losses as a result of price fluctuations and other factors. 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