The large drawdowns and extreme

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1 KHALID (KAL) GHAYUR is a managing partner and CIO at Westpeak Global Advisors, LLC, in Lafayette, CO. kg@westpeak.com RONAN HEANEY is a partner and director of research at Westpeak Global Advisors, LLC, in Lafayette, CO. rgh@westpeak.com STEPHEN PLATT is a partner and director of portfolio management, at Westpeak Global Advisors, LLC, in Lafayette, CO. scp@westpeak.com Low-Volatility Investing: Balancing Total Risk and Active Risk Considerations KHALID (KAL) GHAYUR, RONAN HEANEY, AND STEPHEN PLATT The large drawdowns and extreme volatility of the recent equity market environment has led to a heightened interest in risk-based or low-volatility investing. Low-volatility strategies have been shown to have lower total risk and drawdown than the market, while offering the potential to outperform the market in the long run. They are sometimes included in a strategy classification referred to as alternative betas. 1 Index providers have launched a variety of risk-based indices over the last few years that offer investors passive vehicles to implement low-volatility investing. These include the S&P Low Volatility indices, MSCI Minimum Volatility indices, and Russell-Axioma Low Beta and Low Volatility indices, among others. Despite the appeal of low-volatility investing, investors have not adopted riskbased indices on a widespread basis. One reason might be that most investors approach low-volatility investing from an active beta perspective, as opposed to an alternative beta perspective. From an active beta viewpoint, investors remain sensitive to strategies relative performance versus a capitalization-weighted policy benchmark. Low-volatility strategies involve an inherent trade-off between total risk (standard deviation of returns) and active risk (tracking error relative to the policy benchmark). Currently available, passive alternatives emphasize total risk reduction at the expense of high and uncontrolled active risk, making it difficult for investors to implement low-volatility investing within the constraints of their active risk budgets. To address these challenges, we discuss a new approach for implementing low-volatility investing from an active beta perspective. We introduce a rules-based methodology for building long-only, active risk-targeted volatility portfolios that achieve a better trade-off between total risk and active risk by reducing idiosyncratic risk. We construct low-volatility portfolios (henceforth referred to as volatility portfolios) for U.S. and global developed and emerging equity markets, and show that these portfolios have lower active risk for a given level of total risk, compared to other commonly used passive alternatives. LITERATURE REVIEW Risk-based pricing anomalies are well documented in the academic literature. For example, Black et al. [1972] reported that between 1931 and 1965, the performance of low-beta stocks in the United States was higher than that predicted by the capital asset pricing model (CAPM), while the performance of high-beta stocks was lower. Fama and French [1992] extended the analysis through 1990 and confirmed the pattern of abnormally IT IS ILLEGAL TO REPRODUCE THIS ARTICLE IN ANY FORMAT FALL 2013 THE JOURNAL OF PORTFOLIO MANAGEMENT 49 Copyright 2013

2 high returns for low-beta stocks and abnormally low returns for high-beta stocks. More recently, Ang et al. [2006] showed that U.S. stocks with low idiosyncratic risk outperformed stocks with high idiosyn cratic risk. In a subsequent study, Ang et al. [2009] extended the analysis to global markets and found that the low-volatility anomaly was present across 23 developed markets. Haugen and Baker [1991] and Clarke et al. [2006] analyzed the performance of minimum-variance portfolios for U.S. stocks. These studies found that the minimum-variance portfolio realizes approximately 25% lower risk than the market, without sacrificing returns. Blitz and Vliet [2007] studied the performance of equal-weighted decile portfolios formed on historical volatility and found that the lowest-volatility decile has lower total risk and a higher Sharpe ratio than the minimum-variance portfolio that Clarke et al. [2006] documented. They argued that their approach represents a simple alternative to the minimum-variance portfolio for implementing low-volatility investing with better risk and return characteristics. Other studies also demonstrate that various riskbased strategies are largely driven by the low-volatility, low-beta anomaly. For example, Scherer [2010] provided analytical proof that the minimum-variance portfolio invests in low residual risk and low-beta stocks. Clarke et al. [2011] showed that low-beta stocks dominate longonly, minimum-variance portfolios. They report that at the end of 2009, 85% of the MSCI World Minimum Volatility Index was in the lowest two beta quintiles. Leote de Carvalho et al. [2011] also found that the longonly, minimum-variance portfolio invests in a small number of mostly low-beta stocks. They further documented that minimum variance and maximum diversification (Choueifaty and Coignard [2008]) are similar strategies that produce largely overlapping portfolios and are insensitive to the specific risk model used. As Scherer [2010] pointed out, these findings suggest that minimum variance is not a forecast-free strategy. Rather, its performance relies on the persistence of the low-volatility pricing anomaly. Although there is no clear consensus on what drives the volatility anomaly, possible explanations include borrowing restrictions (e.g., Black [1972]), behavioral biases of investors (e.g., Shefrin and Statman [2000]), and benchmarks as limits to arbitrage (e.g., Baker et al. [2011]). This article makes several contributions to the existing literature on low-volatility investing. First, Blitz and Vliet [2007] documented the volatility effect over the period from December 1985 to January We conduct a similar analysis of volatility-ranked deciles for U.S. stocks and confirm the results of Blitz and Vliet [2007] over a longer and more recent time period (January 1979 through September 2012), and for a broader universe (Russell 1000 Index versus FTSE USA). Second, although low-volatility strategies total risk and efficiency (Sharpe ratio) improvements have been extensively documented and discussed, much less attention has been given to their active risk and relative efficiency (information ratio) attributes. We discuss these relative risk attributes, which highlight the trade-off between total risk and active risk inherent in low-volatility investing. Specifically, we show that existing passive alternatives incur high active risk in their pursuit of total risk reduction. Third, we propose a new rules-based methodology that achieves a better trade-off between total risk and active risk. This methodology also allows for portfolios to be constructed at targeted levels of active risk, thus making low-volatility investing more accessible to active beta investors with limited active risk budgets. In this article, the next section analyzes the performance characteristics of volatility-ranked deciles for U.S. stocks and highlights their relative risk attributes. We also document and compare the risk and efficiency characteristics of other quantile portfolios. We then describe the construction methodology for the proposed volatility portfolios. Finally, we compare the performance of various active risk-targeted volatility portfolios with other commonly used passive alternatives. PERFORMANCE ANALYSIS OF VOLATILITY DECILES We begin by analyzing the historical performance of volatility deciles derived from the Russell 1000 universe. Each month, we rank stocks on trailing 12-month daily volatility and form deciles containing approximately 100 stocks each, assigning the lowest-volatility stocks to decile 1(D1). 2 We calculate one-month forward returns for each decile and report annualized risk and return statistics. Exhibit 1 presents performance statistics for the equal-weighted (panel A) and capitalization-weighted (panel B) deciles from January 1, 1979, through September 30, Exhibit 2 graphs the equal-weighted deciles key performance attributes. 50 LOW-VOLATILITY INVESTING: BALANCING TOTAL RISK AND ACTIVE RISK CONSIDERATIONS FALL 2013

3 E XHIBIT 1 Volatility Deciles Historical Performance Statistics for Russell 1000 Universe (January 1979 September 2012) FALL 2013 THE JOURNAL OF PORTFOLIO MANAGEMENT 51

4 Exhibit 1, panel A, demonstrates a clear relationship between ex ante volatility and realized volatility. The total risk of D1 (11.08%) is 30% lower than the market and less than one-third the total risk of D10 (36.17%). The maximum drawdown statistics also reflect the significantly lower downside risk of D1 ( 33.01%) versus both the market ( 51.01%) and D10 ( 94.34%). The magnitude of D10 is particularly alarming, given that the drawdown occurs over a period of less than three years. Total returns vary modestly from D1 through D9, and fall sharply for D10. Despite smaller differences in return across most of the deciles, significant total risk differences result in a monotonic decline in realized total efficiency (Sharpe ratio). D1 stocks have a much higher Sharpe ratio than the market (0.45); this difference is significant at the 5% level. The Sharpe ratio of D1 (0.76) is also dramatically higher than D10 (0.12); the difference is statistically significant at the 1% level. 3 E XHIBIT 2 Equal-Weighted Volatility Deciles Russell 1000 Universe (January 1979 September 2012) 52 LOW-VOLATILITY INVESTING: BALANCING TOTAL RISK AND ACTIVE RISK CONSIDERATIONS FALL 2013

5 The data reported in panel A also show the strongly positive relationship between historical volatility and realized CAPM beta. 4 The beta of D1 is 0.49, compared to 1.85 for D10. Low-beta stocks are associated with higher returns and Sharpe ratios than are high-beta stocks, a fact that is an obvious contradiction of the CAPM and points toward a negative relationship between risk and return over the analysis period. Our findings corroborate the general results of Blitz and Vliet [2007]. Similar to Blitz and Vliet [2007], we find an approximately 30% reduction in total risk for D1 versus the market. However, we find a much larger improvement in Sharpe ratio (68% versus 28% over the market). We extend the analysis to capitalizationweighted deciles and find similar results, presented in panel B. Like the equal-weighted deciles, the Sharpe ratios exhibit a monotonic relationship, albeit at smaller magnitudes. The lower Sharpe ratios stem primarily from large-capitalization stocks underperformance over the period. 5 In comparing their U.S. results to those of Clarke et al. [2006], Blitz and Vliet [2007] concluded that the reduction in total risk and improvement in Sharpe ratio of D1 is stronger than that provided by the minimumvariance portfolios in Clarke et al. [2006]. While that may be true, it is important to note that both the universes (U.S. top 1000 versus FTSE USA) and analysis periods ( versus ) are substantially different. Nonetheless, the lower risk and higher Sharpe ratios led Blitz and Vliet [2007] to conclude that their approach is a simple alternative to the minimumvariance portfolio. The unique benefits lower total risk and higher Sharpe ratio that low-volatility investing offers come at the cost of high active risk and market underperformance risk. Panel A reports the realized active risk of volatility deciles against the Russell 1000 Index. Total risk deviations from the benchmark result in proportionately higher active risk and are most evident in the extreme deciles. For instance, the low total risk achieved by D1 (11.08%) is associated with remarkably high active risk (11.31%). Relative risk differences across deciles are also evident in the worst annual underperformance and maximum three-year annualized underperformance. Due to their low betas, low-volatility stocks are expected to outperform in falling markets and underperform in rising markets. 6 For example, D1 (0.49 beta) realizes a worst annual underperformance of 31% in 1999, when the technology/internet boom caused the Russell 1000 Index to rise sharply. The realized information ratio (IR) of D1 is a modest 0.20, highlighting why lowvolatility strategies are generally less attractive from an active management perspective. The high active risk of D1 motivates us to explore portfolio construction alternatives that gain similar exposure to low-volatility stocks at lower levels of active risk. One alternative is to simply hold more stocks in the lowest-volatility portfolio. Applying the same methodology used to construct deciles, we form capitalizationweighted portfolios of the lowest 20% (quintile), lowest 33% (tercile), and lowest 50% (half) of stocks, based on historical volatility. Exhibit 3 reports the performance of various quantile portfolios derived from the Russell 1000 universe. The higher-coverage, more-diversified quantile portfolios result in lower active risk levels and are generally more attractive alternatives to the low-decile portfolios. For example, the lowest-quintile portfolio (Q1) has similar total risk to D1 but substantially lower active risk (8.32% versus 11.69%) and higher efficiency (Sharpe ratio and IR). 7 T1 has similar active risk to D3 but lower total risk and a higher Sharpe ratio. H1 has lower total risk and a higher Sharpe ratio than all but two of the deciles, while incurring the lowest active risk. Decomposing total risk into systematic risk (beta) and idiosyncratic risk components helps explain why Q1 has total risk similar to that of D1, but with much lower active risk. The Q1 beta is substantially higher than that of D1 (0.63 versus 0.48), which implies a 2.3% (0.15 * 15.6%) higher total risk, all else being equal. However, the reduction in idiosyncratic risk of Q1 is enough to offset the higher systematic risk, resulting in very similar total risk. The combination of lower active systematic risk (i.e., a CAPM beta closer to 1) and lower idiosyncratic risk results in lower active risk for Q1. Capitalization weighting potentially introduces large security active weights (overweights or underweights, relative to the market), which may contribute to a high level of idiosyncratic risk. The active weights of securities in capitalization-weighted quantile portfolios are a function of the securities relative size and the proportion of the benchmark s capitalization that the quantile portfolio covers. For example, if a quintile portfolio FALL 2013 THE JOURNAL OF PORTFOLIO MANAGEMENT 53

6 E XHIBIT 3 Risk and Efficiency Characteristics of Capitalization-Weighted Quantile Portfolios (January 1979 September 2012) Idiosyncratic risk can be calculated using the following formula: 2 2 δ = σ β σ β 2 p p p m where δ p = idiosyncratic risk of portfolio p σ p = total risk of portfolio p β p = CAPM beta of portfolio p σ m = total risk of market portfolio covers 20% of the parent index market capitalization, a stock with a 2% weight in the parent index will have a total weight of 10% and an active weight of 8% in the quintile portfolio. Exhibit 3 s last two columns show the average maximum underweights and overweights for each quantile. Although the quantile portfolios achieve lower total risk than the market by overweighting the lowestrisk stocks, the maximum active weights suggest that they may incur unnecessary idiosyncratic risk. This provides the motivation for developing an alternative construction methodology, which constrains active weights in order to reduce idiosyncratic risk. VOLATILITY FACTOR PORTFOLIO CONSTRUCTION METHODOLOGY Our portfolio construction methodology seeks to gain similar exposure to low-volatility stocks as the quantile portfolios, but with lower idiosyncratic risk and active risk. We achieve this by making the stock active weights proportional to inverse volatility, rather than to capitalization, and limiting the magnitude of active positions. 8 We define stock volatility as the standard deviation of past 12-month daily total returns and take the log of these values to mitigate the volatility distribution s positive skew. 9 We invert the log values and calculate standardized z-scores, then winsorize the z-scores at 3 and +3 to mitigate the outliers influence. We then proportionally convert the z-scores into active positions, subject to the long-only constraint. Since a stock underweight s magnitude in a long-only portfolio cannot be greater than its benchmark weight, we determine underweights first, then overweights. Two parameters, a cutoff z-score and a maximum stock underweight position, regulate the number and magnitude of individual underweight positions. The cutoff z-score controls the number of underweight positions by assigning underweights only to stocks below the cutoff z-score. Target underweight positions increase linearly with volatility z-scores from zero to the maximum stock underweight position, although the target underweight is not always achieved, due to the long-only constraint. Increasing the cutoff z-score and maximum stock underweight position increases the underweights number and magnitude, leading to higher active risk. The individual stock underweights are calculated using this formula: zi zc TgtUWi = MaxUW, for zi < zc Max( z z ) (1) i c UW i = min(tgtuw i, BW i ) (2) 54 LOW-VOLATILITY INVESTING: BALANCING TOTAL RISK AND ACTIVE RISK CONSIDERATIONS FALL 2013

7 where TgtUW i = target underweight for stock i UW i = underweight achieved for stock i z i = volatility z-score for score i z c = cutoff z-score MaxUW = maximum stock underweight position BW i = benchmark weight of stock i We sum the underweights achieved in individual stocks to calculate the total underweight position, which is then allocated to all stocks with z-scores greater than the cutoff z-score. Each stock s overweight is linearly proportional to its z-score. The individual stock overweights are calculated using this formula: TotUW = Σ(UW i ) for z i < z c (3) zi zc OWi = TotUW for zi > zc (4) Sum( z z ) i c where TotUW = total underweight position OW i = overweight for stock i Exhibit 4 plots the stock z-scores versus active weights for the Russell 1000 universe using a cutoff z-score of zero and a maximum stock underweight position of 0.50%. The scattered active weights on the left side of the chart illustrate the impact of the long-only constraint on the underweights. Because the lowerranked, more volatile stocks tend to have smaller capitalizations (and benchmark weights), only a few stocks reach their targeted underweight positions. PERFORMANCE OF VOLATILITY FACTOR PORTFOLIOS Applying the construction methodology to the Russell 1000 universe, with a cutoff z-score of zero and a maximum constituent underweight position of 0.50% E XHIBIT 4 Active Weights of a Volatility Portfolio (Long-Only) Russell 1000 Universe FALL 2013 THE JOURNAL OF PORTFOLIO MANAGEMENT 55

8 produces volatility portfolio 4 (4% target active risk) that matches the total risk of the capitalization-weighted, lowest-half quantile portfolio. By increasing the cutoff z-score to 0.30, 0.60, and 1.50, while keeping the maximum stock underweight position at 0.50%, we derive volatility portfolio 5, volatility portfolio 6, and volatility portfolio 7. These portfolios roughly match the total risk levels of the capitalization-weighted lowesttercile, lowest-quintile, and lowest-decile portfolios, respectively. We also construct volatility portfolio 10 by increasing the cutoff z-score to 1.80 and the maximum constituent underweight position to 1.50%. Exhibit 5 reports these volatility portfolios historical performance. As observed in the quantile analysis, active risk increases as total risk drops, and a strong monotonic relationship exists between total risk and Sharpe ratio. Volatility portfolio 10 has the lowest total risk and highest Sharpe ratio (10.20% and 0.77, respectively), while incurring the highest level of active risk (10.50%). However, volatility portfolio 4 shows that it is still possible to take advantage of the low-volatility anomaly at low levels of active risk, as a meaningful increase in Sharpe ratio and reduction in total risk over the market can be achieved. Exhibit 6 compares the risk and efficiency characteristics of the capitalization-weighted quantile portfolios and the volatility portfolios. The volatility portfolios have lower active risk for similar total risk versus their corresponding quantile portfolios. The reduction in active risk ranges from 21% to 37%. Exhibit 7 illustrates the reduction in active risk and also highlights the trade-off between active and total risk. In all cases, the reduction in active risk comes from lower idiosyncratic risk and lower active systematic risk (higher CAPM beta). For example, volatility portfolio 7 in Exhibit 6 achieves the same level of total risk as D1, albeit with a notably higher beta. The higher beta produces lower active systematic risk, which when combined with lower idiosyncratic risk, results in a meaningful reduction in active risk. The average reduction in idiosyncratic risk of the volatility portfolios, versus their corresponding quantile portfolios, is an impressive 37%. Smaller active positions are the primary source of the lower idiosyncratic risk, as reflected in the average maximum underweight and overweight columns. For example, the average maximum overweight for volatility portfolio 7 is one-fifth the size of D1 (13.1% versus 2.8%). E XHIBIT 5 Historical Performance of Volatility Portfolios Russell 1000 Universe (January 1979 September 2012) 56 LOW-VOLATILITY INVESTING: BALANCING TOTAL RISK AND ACTIVE RISK CONSIDERATIONS FALL 2013

9 E XHIBIT 7 Active vs. Total Risk Russell 1000 Universe (January 1979 September 2012) E XHIBIT 6 Risk and Efficiency Characteristics of Quantile and Volatility Portfolios (January 1979 September 2012) When comparing portfolios with similar active risk, volatility portfolios realize lower total risk due to both lower systematic and idiosyncratic risk (e.g., volatility portfolio 6 and T1). Similarly, for a given level of systematic risk, volatility portfolios realize lower total and active risk due to lower idiosyncratic risk (e.g., volatility portfolio 7 and Q1). Exhibit 8 compares volatility portfolios performance with that of various publicly available indices: Russell-Axioma Low Volatility and Low Beta indices, MSCI Minimum Volatility indices, and the S&P 500 Low Volatility Index. The Russell-Axioma indices are derived from the Russell 1000 universe and use the Axioma risk model and optimizer to maximize exposures to the volatility and beta factors, while limiting the exposure to other risk factors. The MSCI indices are minimum-variance strategies constructed using the Barra risk models and optimizer. The S&P 500 Low Volatility Index weights the 100 least-volatile stocks in the S&P 500 Index by inverse volatility. We construct the volatility portfolios using the same parent universe as each public index. Panel A provides a comparison in which the volatility portfolios are constructed to roughly match the FALL 2013 THE JOURNAL OF PORTFOLIO MANAGEMENT 57

10 E XHIBIT 8 Volatility Portfolios Compared (periods ending September 2012) E XHIBIT 9 Volatility Portfolio Compared to MSCI USA Minimum Volatility Index, Relative to MSCI USA Index (January 1999 September 2012) 58 LOW-VOLATILITY INVESTING: BALANCING TOTAL RISK AND ACTIVE RISK CONSIDERATIONS FALL 2013

11 total risk of the public indices. Panel B matches on active risk. The available history of the public index dictates the start date for each comparison. As in the quantile comparisons, the volatility portfolios matched on total risk (panel A) achieve lower idiosyncratic risk and active systematic risk (higher beta). For example, volatility portfolio 6 has total risk that is similar to the MSCI World Minimum Volatility Index, but a 21% lower active risk (5.55% versus 7.00%). Volatility portfolios matched on active risk (panel B) have lower total risk than the comparable public index does. For example, volatility portfolio 7 has similar active risk, but a lower total risk than the MSCI World Minimum Volatility Index (10.25% versus 11.00%). The similarity of risk characteristics between volatility portfolio 10 and the S&P 500 Low Volatility Index is particularly notable. Despite very different construction methodologies, the inverse volatility-weighted S&P index and volatility portfolio 10 realize very similar total and active risk characteristics, due to similar active weight profiles. Although the diverse construction methodologies affect the trade-off between total risk and active risk, they result in similar active returns. The pair-wise active return correlations between the volatility portfolios and public indices shown in Exhibit 8, panel B, range from 88% to 97%. This reflects the fact that the low-volatility effect drives the various risk-based strategies. As an illustration of similar return patterns, Exhibit 9 plots the cumulative active returns over time for the volatility portfolio 7 versus the MSCI USA Minimum Volatility Index. CONCLUSION Low-volatility investing may offer considerable benefits to alternative-beta investors who seek to maximize the Sharpe ratio. By considering low-volatility stocks in the strategic asset allocation process, these investors can potentially create more efficient overall policy portfolios. However, many investors adopt a benchmarkrelative, active-beta perspective in seeking to implement low-volatility investing. Our proposed approach provides an additional passive alternative for both alternative-beta and active-beta investors. On the one hand, alternative-beta investors with a high tolerance for active risk can realize lower total risk and higher Sharpe ratios, compared to other passive alternatives. On the other hand, active-beta investors can implement lowvolatility investing within the constraints of their active and market-underperformance risk budgets. ENDNOTES The authors gratefully acknowledge insightful comments and contributions from an anonymous referee at JPM, as well as helpful comments from Kevin Bong at GIC, Ray Venner at CalPERS, and Patrick Chrysler at RogersCasey. 1 The notion of beta typically refers to regression loading on the excess return of the market. However, practitioners often use the term alternative beta to refer to indices that use a weighting scheme other than capitalization weighting to construct a more efficient alternative to the capitalization-weighted market index. Examples of alternatively weighted indices include minimum-variance indices and fundamentally weighted indices. 2 Using a longer estimation window, such as the last three years, to calculate the volatility signal does not result in meaningful performance differences. 3 Following Blitz and Vliet [2007], we use the Jobson and Korkie [1981] significance test with the Memmel [2003] correction. 4 The strong positive relationship derives from the fact that a security s beta is equal to its correlation with the market multiplied by the ratio of the security s volatility to the market volatility. 5 As an illustration, over the analysis period, an equalweighted Russell 1000 Index outperformed the capitalizationweighted Russell 1000 Index by 1.90% per annum. 6 D1 stocks outperformed 84% of the time in falling markets and 34% in rising markets over the analysis period. Falling and rising markets refer to months in which the market registers a negative or positive return, respectively. 7 The high Sharpe ratio of Q1 is achieved due to its inclusion of D2, which has the highest Sharpe ratio among the capitalization-weighted deciles, as well as the diversification benefits of holding more stocks. 8 The portfolio construction methodology discussed in this section is the patented intellectual property of Westpeak Global Advisors, LLC. 9 Clarke et al. [2010] documented that whether the volatility factor is specified in terms of idiosyncratic risk or total security risk makes little practical difference. We prefer the use of total return volatility, rather than beta or residual risk, as it is a simple and direct measure of risk. FALL 2013 THE JOURNAL OF PORTFOLIO MANAGEMENT 59

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