Blitz and van Vliet [2007] document

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1 DVID BITZ is the head of Quantitative Equity esearch at obeco sset Management in otterdam, the Netherlands. The Value of ow Volatility DVID BITZ Blitz and van Vliet [2007] document the existence of a strong low-volatility effect in the U.S., European, and Japanese equity markets over the period from 1986 to 2006: portfolios consisting of stocks with the lowest historical 3-year volatility exhibit statistically significantly higher risk-adjusted returns than the market. In a follow-up paper, Blitz, Pang, and van Vliet [2013] find a similar low-volatility effect in emerging equity markets. The lowvolatility effect appears to be stronger than the closely related low-beta effect. Studies such as Black, Jensen, and Scholes [1972], Fama and MacBeth [1973], and Haugen and Heins [1975] already observed that the relation between beta and return is flatter than predicted by the apital sset Pricing Model (PM). Fama and French [1992] even conclude that beta is completely unpriced in the cross section of stock returns when controlling for size effects. The low-volatility effect is also closely related to studies that report superior riskadjusted returns for minimum-variance portfolios such as Haugen and Baker [1991] and larke, de Silva, and Thorley [2010], and the work of ng et al. [2006, 2009], who document a similar anomaly for very short-term idiosyncratic volatility. More recent studies that confirm the low-volatility and/or lowbeta effects include those of Baker, Bradley and Wurgler [2011], Baker and Haugen [2012], and Frazzini and Pedersen [2014]. One might wonder if the low-volatility effect is merely a manifestation of another well-known effect the value effect, in particular. t certain moments there indeed appears to be a strong overlap between low-volatility and value investment strategies. During the tech bubble, for instance, low-volatility and value strategies both avoided risky, expensive tech stocks. If the low-volatility effect can be explained by the value effect, this might explain why Fama and French [1993] augmented the PM with size and value factors, yet maintained the linear positive relation between PM beta and expected stock returns predicted by the PM even though their own [1992] study shows that PM beta is not priced in the cross section after controlling for size. Most of the existing low-volatility literature concludes that the effect is a distinct phenomenon that cannot be explained by the value effect. For example, Blitz and van Vliet [2007] and Blitz, Pang and van Vliet [2013] control for value parametrically and non-parametrically and find that this does not explain the alpha of low-volatility portfolios in global and emerging equity markets. nother example is Frazzini and Pedersen [2014], who report a highly significant 3-factor alpha for U.S. long short beta-sorted portfolios over the full enter for esearch in Security Prices (SP) sample period. In addition to these empirical results, there also seems to be a IT IEG TO EPODUE TH TIE IN NY FOMT 94 THE VUE OF OW VOTIITY SPING 2016

2 completely different economic rationale behind the two effects. For instance, Fama and French [1992] suggest that the value effect is a reward for the risk of financial distress that is, value stocks earn higher returns because they are particularly risky. ow-volatility portfolios, on the other hand, exhibit lower risk than market portfolios regardless of which risk measure is used. Some of the more popular explanations proposed for the low-volatility effect include agency issues and leverage constraints (see Blitz, Falkenstein, and van Vliet [2014] for an extensive overview), which are quite different from the various risk-based and behavioral explanations that have been proposed for the value effect. One troubling piece of evidence, however, is that value does seem to explain the alpha of low-volatility when the most commonly used performance evaluation test is applied (the Fama French 3-factor model) to the biggest market (the U.S.) over the sample period typically used in academic research (the post-1963 period). For instance, how et al. [2011] and Shah [2011] report economically small and statistically insignificant alphas for minimum-variance strategies after controlling for the high-minus-low (HM) value factor of Fama French. Goldberg, eshem, and Geddes [2014] also observe that the outperformance of U.S. minimum-variance strategies is largely attributable to implicit value tilts. Baker, Bradley, and Wurgler [2011] consider only 1-factor alphas in their analysis of U.S. low-volatility strategies over the period, so it remains unclear whether their results are robust to controlling for the Fama French factors. In this article, I examine the apparently insignificant 3-factor alpha of U.S. low-volatility strategies over the post-1963 period in more detail. I show that the insignificant 3-factor alpha is present only for large-capitalization, low-volatility strategies, and concentrated in the relatively short July 1963 December 1984 subperiod. The Fama French value factor fails to explain the alpha of large-cap low-volatility strategies pre-1963 as well as post-1984, when the Fama French value factor itself ceased to be effective in the large-cap segment of the market. It also fails to explain the performance of small-cap low-volatility strategies in any sample period. In other words, the value factor is able to explain only the performance of lowvolatility strategies applied specifically to the E XHIBIT 1 HM Performance large-cap segment of the market during a specific period in the middle of the SP sample which makes up less than a quarter of the entire SP sample. In addition to these time-series tests, I conduct Fama MacBeth regressions to estimate the extent to which a unit of PM beta exposure is rewarded in the cross section of stock returns. PM beta turns out to be unpriced in the cross section in all subsamples which implies that even in the most difficult period for lowvolatility strategies, the evidence is, in fact, still mixed. ombining my findings with those of other studies discussed above, I conclude that the low-volatility effect is a distinct phenomenon that cannot simply be dismissed as another manifestation of the value effect. omparing the results for the two effects, we can infer that the combined evidence for the low-volatility effect is at least as strong as that for the value effect, or perhaps even stronger. HM PEFOMNE I begin by reviewing the performance of the HM value factor of Fama and French [1993]. They define HM as the return difference between stocks with a high book-to-market ratio and stocks with a low book-to-market ratio 50/50 based on the large- and small-cap segments of the market (using the NYSE median market capitalization as the breakpoint between large and small). Exhibit 1 reports mean monthly returns IT IEG TO EPODUE TH TIE IN NY FOMT Note: ***, **, and * represent the 1%, 5%, and 10% significance levels, respectively. SPING 2016 THE JOUN OF POTFOIO MNGEMENT 95

3 and 1-factor alphas for standard HM and its separate large- and small-cap components, over the entire sample period and various subperiods. The last column of Exhibit 1 shows that HM is effectively zero in the large-cap segment of the market over the subperiod. In other words, over the last 30 years the Fama French value factor has been completely ineffective among large-cap stocks. This observation is consistent with the findings of Hsu [2014], who examines the performance of widely used value indexes. In light of this result, I consider not only the period in this article, but also the separate and subperiods. nother notable result in the table is that even though HM and its large- and small-cap components exhibit strong raw returns during the pre-1963 period, the associated 1-factor alphas are, in fact, statistically insignificant, because of large positive PM beta exposures. In other words, the market risk that is implicitly present in HM during the early part of the sample explains so much of its return that the remaining part is small and insignificant. In short, the HM value factor has some robustness issues. OW-VOTIITY PEFOMNE I constructed U.S. low-volatility strategies using the SP database, defining volatility as the standard deviation of the total returns of a stock over the preceding 36 months. Following the methodology used by Fama and French [1993] to construct the HM value factor, I distinguished between large-cap and small-cap low-volatility strategies using, at each point in time, the NYSE median market capitalization as the breakpoint between large and small stocks. lso following their approach, I took the top 30% stocks with the lowest volatility in each of these market segments and considered portfolios on a value-weighted (VW) as well as on an equally weighted (EW) basis. Focusing on long-only low-volatility portfolios is a conservative choice, because studies such as Blitz and van Vliet [2007], ng et al. [2006], and Garcia-Feijóo et al. [2015] find that the negative alpha of highvolatility stocks is considerably larger than the positive alpha of low-volatility stocks. eturns for the Fama French factors were obtained from the online data library of Professor Kenneth French. ll returns were taken in excess of the risk-free return. Because three years of data are needed to construct the lowvolatility portfolios, the first low-volatility portfolio is constructed at the end of The sample periods ends in December Exhibit 2 reports mean excess returns, standard deviations, and Sharpe ratios on a monthly basis over the full sample period and the various subperiods. Note that in this table and throughout the remainder of this article, we use arithmetic averaging for calculating mean returns, which is again a conservative choice because the added value of low-volatility strategies is known to be significantly larger when geometric averaging is used instead. The table shows that the average returns of the large-cap low-volatility strategies are similar to or slightly higher than the market over the entire sample period and also during each subperiod. t the same time, the volatility of the large-cap low-volatility strategies is about 20% below that of the market. s a result, the Sharpe ratios of these strategies are consistently higher than those of the market, which confirms the existence of a low-volatility effect. E XHIBIT 2 ow-volatility eturn Statistics IT IEG TO EPODUE TH TIE IN NY FOMT 96 THE VUE OF OW VOTIITY SPING 2016

4 EXHIBIT 3 N Y FO M T lphas for Various ow-volatility Strategies IN The small-cap low-volatility strategies also exhibit consistently higher Sharpe ratios in fact, even more so than their large-cap counterparts but mainly because of their high mean return. The volatility of the small-cap lowvolatility strategies shows a mixed picture higher than the market in some instances and lower than the market in others. We can also see that equally weighted, low-volatility portfolio returns are consistently a bit higher than valueweighted, low-volatility portfolio returns for each sample period, and in the large-cap space as well as in the small-cap space. E DOES HM EXPIN OW VOTIITY? IT I EG TO EP O D U E TH TI Exhibit 3 presents alphas for the various low-volatility strategies. The table reports 1and 3-factor alphas for large- and small-cap low-volatility portfolios on both a valueweighted and equally weighted basis over the full sample period, as well as during subperiods. The first column of the table shows that the 1- and 3-factor alphas for the various lowvolatility strategies are all significant at the 1% level over the full sample period, January 1929 December The large-cap lowvolatility strategies exhibit small full-sample loadings on the HM value factor ( ), as a result of which their 3-factor alphas are close to their 1-factor alphas. The small-cap low-volatility strategies exhibit considerably higher HM loadings and, obviously, significant loadings on the small-minus-big (SMB) size factor, but their alpha remains significant after controlling for both these exposures. The second column of the table contains results for Note: ***, **, and * represent the 1%, 5%, and 10% significance levels, respectively. the January 1929 June 1963 subperiod. The HM loadings turn out to be lower over this the loading of the low-volatility strategies on the HM period, even to the extent that they are negative for the value factor turns out to be much larger over the postlarge-cap low-volatility strategies. ll 1- and 3-factor 1963 period than over the pre-1963 period. This suggests alphas remain strong, both economically and statistithat the HM loading of low-volatility varies significally, over this period. In short, there is a distinct lowcantly over time, and therefore the full-sample 3-factor volatility effect that is not explained by the value effect alpha estimate may be unreliable. Over the post-1963 over the full sample period or the first subperiod. period, the large-cap low-volatility strategies still show The third column of Exhibit 3 shows results for decent 1-factor alphas. However, because of their large the July 1963 December 2014 subperiod. Interestingly, loadings on the HM factor, their 3-factor alphas are SPING 2016 THE JOUN OF POTFOIO M NGEMENT 97 JPM-BITZ.indd 97 4/13/16 11:39:26 M

5 economically small, at less than 0.1% per month, and statistically weak, with t-statistics between 1 and 2. This seems to suggest that for at least the last half century, the low-volatility effect can simply be explained by the value effect. In the remainder of this section, however, I will argue that this conclusion is premature. first argument is that the small-cap low-volatility strategies remain strong over the post-1963 period. Their 1-factor alphas are very strong, with t-statistics around 5. lthough their 3-factors are lower because of loadings on the Fama French size and value factors, these remain highly significant as well, with t-statistics between 3 and 4. In other words, the value effect cannot explain the performance of small-cap low-volatility strategies. The second argument comes from splitting the post-1963 period into the same two subperiods used before, shown in the last two columns of Exhibit 3. This analysis shows that the weak performance of the large-cap low-volatility strategy is concentrated in the July 1963 December 1984 period. Over the most recent 30-year subperiod, during which the large-cap HM strategy ceased to be effective, the large-cap low-volatility strategy did deliver. The t-statistics of the 1- and 3-factor alphas range between 1.81 and 3.19, with the equally weighted portfolios showing the best results. The small-cap low-volatility strategies show strong 1- and 3-factor alphas in both these subperiods, with t-statistics varying between 2.13 and ooking at the combined evidence, we conclude that the value effect explains the performance of low-volatility strategies only when specifically considering the large-cap low-volatility strategy over a specific period of about 20 years in the middle of the 86-year-long SP sample period. In all other instances, low-volatility strategies show a strong performance that cannot be explained by implicit exposure to the HM value factor. DOES THE PM ETION EVE HOD? If there is no low-volatility effect for certain samples over certain time periods, one would expect PM beta to show up clearly as a priced risk factor in the cross section of stock returns. In order to test for this, I conducted Fama and MacBeth [1973] regressions, closely following the methodology of Blitz [2014]. I focused on the large-cap segment of the market because the problem seems to be concentrated in that subsample. Specifically, every month I conduct a cross-sectional regression of the returns of all stocks with a market capitalization above the NYSE median in that month on a constant, their PM beta, size, and value characteristics at that point in time. Each such regression empirically estimates the rewards to units of beta, size, and value exposure in a particular month. I next calculated the average returns for units of beta, size, and value exposure over all months and tested whether these average returns were statistically significantly different from zero. Based on the PM and the 3-factor model, one would expect the average constant to be equal to the risk-free return, and the average reward per unit of market beta exposure to be equal to the equity risk premium. I calculated the size of a stock as the natural logarithm of its price times the number of shares outstanding at the end of the previous month. Value is defined as the natural logarithm of the book-to-market ratio. Book values of equity were obtained from the ompustat database and the Moody s Industrial Manuals. I calculated the bookto-market ratio by dividing the book value of common equity at the previous calendar year s fiscal year-end by the market value of equity at the end of the previous calendar year, updated at the end of June each year. ll explanatory variables are winsorized at the 1% and 99% levels in order to avoid a large potential influence from outliers, and cross-sectional z-score normalizations are applied to the size and value variables. s a result, the intercept of the regression can be interpreted as the expected excess return on a stock with average size and value characteristics, adjusted for the part of the return that can be empirically attributed to its PM beta. I conducted Fama MacBeth regressions using only PM beta and using PM beta, size, and value as explanatory variables. Exhibit 4 summarizes the results. The key takeaway from this table is that PM beta is unpriced in the large-cap segment of the market across all subsamples, including, notably, the July 1963 December 1984 period. The various t-statistics range from 0.41 to 1.02, implying that the reward for a unit of beta exposure in the cross section is not even close to being statistically significantly different from zero. The constant in the regressions, however, is highly significant in all cases, implying that the relation between risk and return is essentially flat. This result holds regardless of whether size and value are included as additional control variables. Interestingly, the value factor has the correct sign but is insignificant for the large-cap sample in each subperiod not just in the period as one might expect based on the previous IT IEG TO EPODUE TH TIE IN NY FOMT 98 THE VUE OF OW VOTIITY SPING 2016

6 EXHIBIT 4 IT I EG TO EP O D U E TH TI E IN N Y FO M T fact, is still mixed, because Fama MacBeth regressions still support the exisfama MacBeth egressions arge-ap Universe tence of a low-volatility effect. Other studies have shown that the low-volatility effect cannot be explained by the value effect in the European, Japanese, and emerging equity markets. ast but not least, the economic rationale behind the two effects seems to be entirely different. ltogether, these results imply that the low-volatility effect is a distinct phenomenon that cannot be explained by the value effect. The findings in this article also have practical implications. One implinote: ***, **, and * represent the 1%, 5%, and 10% significance levels, respectively. cation is that in order to unlock the full potential of the low-volatility effect, investors should not create a value-weighted, large-cap results. In sum, the Fama MacBeth regressions provide low-volatility portfolio, but they should consider equal much stronger evidence for PM beta being unpriced in weighting within the large-cap segment of the market. the cross section than for value being priced. These results dditionally, they should seek exposure to low-volatility support the notion that there is a distinct low-volatility effect stocks in the small-cap segment. second implication is that cannot be explained by the value effect. that instead of choosing between harvesting either the value premium or the low-volatility premium, investors SUMMY should simply benefit from both. The two factors are distinct phenomena and the results in this article suggest The 3-factor alpha of a simple U.S. low-volatility that during prolonged periods of time when one factor strategy appears to be insignificant over the post-1963 fails to deliver, the other factor can provide relief. period because of highly significant loading on the HM More recently, the low-volatility effect has come value factor. In this article, I look at this result in more under attack from another angle. Novy-Marx [2014] detail. I find that the value effect fails to explain the perargues that it can be explained by his gross profitability formance of large-cap low-volatility strategies pre-1963 factor, and Fama and French [2015] argue that it can be as well as post-1984, when the Fama French value factor explained by their recently introduced 5-factor model, itself ceased to be effective in the large-cap segment of which is the classic 3-factor model augmented with profthe market. Moreover, the value effect cannot explain the performance of small-cap low-volatility strategies during any period. In other words, the value factor is able to EXHIBIT 5 explain only the performance of large-cap low-volatility Summary strategies during a period roughly in the middle of the SP sample which makes up less than a quarter of the entire SP sample. Exhibit 5 summarizes and compares the performance of low-volatility and value strategies, based on all the results in this article. This overview implies that the evidence for the low-volatility effect is at least as strong as the evidence for the value effect. Even for the one sample for which the value effect Note: ++ indicates strong evidence for positive added value; + indicates seems to explain the performance of low-volatility stratevidence for positive added value; 0 indicates no evidence for added value egies (i.e., large-cap low-volatility strategies over the (neither positive nor negative); indicates evidence for negative added July 1963 December 1984 subperiod), the evidence, in value. SPING 2016 THE JOUN OF POTFOIO M NGEMENT 99 JPM-BITZ.indd 99 4/13/16 11:39:27 M

7 itability and investment factors. n interesting direction for future research would be to examine whether these conclusions stand up to scrutiny. ENDNOTE The author thanks Milan Vidojevic for programming assistance and Pim van Vliet for his valuable comments. EFEENES ng,.,. Hodrick, Y. Xing, and X. Zhang. The ross- Section of Volatility and Expected eturns. Journal of Finance, 61 (2006), pp High Idiosyncratic Volatility and ow eturns: International and Further U.S. Evidence. Journal of Financial Economics, 91 (2009), pp Baker, M., B. Bradley, and J. Wurgler. Benchmarks as imits to rbitrage: Understanding the ow-volatility nomaly. Financial nalysts Journal, 67 (2011), pp Baker, N., and. Haugen. ow isk Stocks Outperform within ll Observable Markets of the World. Working paper, 2012, SSN Black, F., M. Jensen, and M. Scholes. The apital sset Pricing Model: Some Empirical Tests. In Studies in the Theory of apital Markets, edited by M.. Jensen. New York, NY: Praeger Publishing, Blitz, D. gency-based sset Pricing and the Beta nomaly. European Financial Management, 20 (2014), pp Blitz, D., E. Falkenstein, and P. van Vliet. Explanations for the Volatility Effect: n Overview Based on the PM ssumptions. The Journal of Portfolio Management, 40 (2014), pp Blitz, D., J. Pang, and P. van Vliet. The Volatility Effect in Emerging Markets. Emerging Markets eview, 16 (2013), pp Blitz, D., and P. van Vliet. The Volatility Effect: ower isk Without ower eturn. The Journal of Portfolio Management, 34 (2007), pp how, T., J. Hsu, V. Kalesnik, and B. ittle. Survey of lternative Equity Index Strategies. Financial nalysts Journal, 67 (2011), pp larke,., H. de Silva, and S. Thorley. Know Your VMS Exposure. The Journal of Portfolio Management, 36 (2010), pp Fama, E., and K. French. The ross-section of Expected Stock eturns. Journal of Finance, 47 (1992), pp ommon isk Factors in the eturns on Stocks and Bonds. Journal of Financial Economics, 33 (1993), pp Dissecting nomalies with a Five-Factor Model. Working paper, 2015, SSN Fama, E., and J. MacBeth. isk, eturn and Equilibrium: Empirical Tests. Journal of Political Economy, 81 (1973), pp Frazzini,., and. Pedersen. Betting gainst Beta. Journal of Financial Economics, 111 (2014), pp Garcia-Feijóo,.,. Kochard,. Sullivan, and P. Wang. ow-volatility ycles: The Influence of Valuation and Momentum on ow-volatility Portfolios. Financial nalysts Journal, 71 (2015), pp Goldberg,.,. eshem, and P. Geddes. estoring Value to Minimum Variance. Journal of Investment Management, 12 (2014), pp Haugen,., and N. Baker. The Efficient Market Inefficiency of apitalization-weighted Stock Portfolios. The Journal of Portfolio Management, 17 (1991), pp Haugen,.., and.j. Heins. isk and the ate of eturn on Financial ssets: Some Old Wine in New Bottles. Journal of Financial and Quantitative nalysis, 10 (1975), pp Hsu, J. Value Investing: Smart Beta versus Style Indices. The Journal of Index Investing, 5 (2014), pp Novy-Marx,. Understanding Defensive Equity. Working paper, 2014, SSN Shah,. Understanding Minimum Variance Strategies. White paper, Dimension Fund dvisors, IT IEG TO EPODUE TH TIE IN NY FOMT To order reprints of this article, please contact Dewey Palmieri at dpalmieri@iijournals.com or THE VUE OF OW VOTIITY SPING 2016