Smart Beta Is Not Monkey Business
Transcription
Smart Beta Is Not Monkey Business
Smart Beta Is Not Monkey Business The Journal of Index Investing 2016.6.4:12-29. Downloaded from www.iijournals.com by Taras Zlupko on 03/09/16. It is illegal to make unauthorized copies of this article, forward to an unauthorized user or to post electronically without Publisher permission. Noël Amenc, Felix Goltz, and Ashish Lodh Noël A menc is a professor of finance at EDHEC Risk Institute and the CEO of ERI Scientific Beta in Singapore. [email protected] Felix Goltz is the head of applied research at EDHEC Risk Institute and the research director at ERI Scientific Beta in Nice, France. [email protected] Ashish L odh is the deputy research director at ERI Scientific Beta in Nice, France. [email protected] I n the marketing of smart beta strategies, index providers focus primarily on the ability of these strategies to deliver outperformance over the cap-weighted (CW) benchmark. The issue of the risk exposure of these indexes and performance attribution to well-defined risk factors is rarely addressed by index providers. The existence of so many smart beta strategies coupled with so little information on their sources of performance poses a risk of confusion and overgeneralizations. Arnott et al. [2013, p. 91] claimed that smart beta “necessarily results in value and size tilts, regardless of the weighting method chosen” and concluded that “the investment beliefs upon which many investment strategies are ostensibly based play little or no role in their outperformance.” Likewise, Hsu, Kalesnik, and Li [2012, p. 12] wrote that “outwardly different smart betas produce nearly similar premiums for similar reasons.” The argument that all smart beta strategies lead to all but identical performance and risk factor exposures is further supported by two claims put forward by Brightman [2013, p. 5]. First, Brightman argued that “strategies premised on seemingly sensible investment beliefs […] add the same or more value when inverted.” Second, the author argued that smart beta strategies “add value […] like Malkiel’s monkey” because their performance is similar to randomly generated 12 Smart Beta Is Not Monkey Business portfolios, also termed monkey portfolios. Since the idea that smart beta strategies are as good as random deviations from cap-weighting is at the heart of all the preceding claims, we collectively refer to these as the monkey portfolio argument. In this article, we report the results of a series of straightforward tests of these claims. To test the various claims, we distinguish the three main claims made by monkey portfolio proponents: 1. All smart beta strategies lead to similar performance. 2.All smart beta strategies have unavoidable value and small cap tilts resulting in performance that is similar across strategies. 3.Smart beta strategies are as good as inverse or upside-down strategies. Our results are not supportive of the monkey portfolio argument. We find that various smart beta strategies display pronounced differences in performance characteristics and factor exposures. We also obtain a reassuring finding that inverting a portfolio strategy does not, in general, lead to the same performance as the original. Our f indings imply that analyzing smart beta performance and risks is not monkey business. For a better understanding of smart beta strategies, it is crucial to analyze Spring 2016 their construction principles, performance characteristics, and risk factor exposures—including not only value and small-cap factors but also a variety of other welldocumented risk factors, such as momentum, profitability, investment, low risk, and possibly others. The Journal of Index Investing 2016.6.4:12-29. Downloaded from www.iijournals.com by Taras Zlupko on 03/09/16. It is illegal to make unauthorized copies of this article, forward to an unauthorized user or to post electronically without Publisher permission. OUR SET OF SMART BETA STRATEGIES Obviously, whether or not the previously mentioned arguments hold may depend heavily on which class of strategies one includes. Although their empirical tests are limited to selected strategies, the authors putting forward the monkey portfolio arguments claim that these results apply to smart beta strategies in general, meaning that an analysis of any choice of smart beta strategies should fulfill their claims. Our selection of strategies focuses mainly on explicit factor-tilted smart beta strategies, which correspond to indexes that providers have launched relatively recently. In fact, the first generation of smart beta indexes usually changed the weighting scheme from market cap weighting, while paying no attention to explicitly controlling the exposures to systematic risk factors. Such strategies provided implicit tilts to systematic factors. More recently, many providers have launched factortilted indexes to extract factor premiums (explicit factor tilts). For a discussion of this development, we refer readers to Amenc and Goltz [2013] and Amenc, Goltz, and Lodh [2012]. The increasing interest in factor-tilted smart beta indexes is also due to the success of factor investing, especially since the Norwegian Oil Fund report by Ang, Goetzmann, and Schaefer [2009], which showed that the returns relative to a cap-weighted benchmark of the fund’s actively managed portfolio can be explained by exposure to a set of well-documented alternative risk factors. Among possible strategies, we included a broad set of smart beta strategies in our tests. First, we included the popular fundamental-weighted portfolio strategy and the equal-weighted strategy based on a broad universe. Given that many monkey portfolio proponents (e.g., Hsu, Kalesnik, and Li [2012]; Arnott et al. [2013]) are also promoters of fundamental-weighted indexes, it is interesting to first check whether their general claims apply to the type of smart beta strategy they promote. Second, we included a variety of strategies that seek explicit exposure to a given risk factor by selecting stocks Spring 2016 with desired factor exposures. Such smart beta strategies are being offered as so-called factor indexes by most major index providers. We incorporated two approaches in our tests: First, we included indexes that select stocks by factor score and apply a diversification-based weighting scheme (diversified factor indexes); and second, we included indexes that, in addition to selecting stocks with the highest factor exposure, also use a weighting that favors stocks with desired characteristics (concentrated factor indexes). It should be noted that our set of strategies deliberately differs from the strategies tested by Arnott et al. [2013], who did not include explicit factor-tilted strategies in their set of test portfolios. Our research can thus be understood as a test of whether the claims of monkey portfolio proponents apply only to the specifications of smart beta the authors have selected for their empirical tests or whether they apply more generally, to a broader set of commonly used smart beta strategies. In particular, given the recent interest in explicit factor-tilted strategies, it appears to be relevant to test the degree to which the strong claims of monkey portfolio proponents carry over to such strategies. In fact, our article differs from Arnott et al. [2013] in the three following ways. First, it considers additional factor exposures of smart beta strategies (like low beta, profitability, and investment). Second, it employs different portfolio construction techniques. Third, it provides a more detailed performance analysis including factor risk contributions and dependencies of performance on market regimes. If such changes in tests lead to differences in results with respect to those obtained by Arnott et al. [2013], we would conclude that their findings do not hold in general, but are specific to the particular test setup and strategies that they tested. Exhibit 1 provides an overview of the smart beta strategies we have constructed for our tests. In addition to the broad fundamental-weighted strategy1 and simple quarterly rebalanced equal-weighted strategy, we constructed several factor-tilted smart beta strategies that select half the stocks in the universe to obtain the desired factor tilt. For example, to obtain a value tilt, our test portfolios select 50% of the stocks with the highest book-to-market ratio. In the same way, we constructed portfolios that select stocks so as to tilt to momentum, size, low volatility, profitability and investment. We applied two different types of weighting schemes to these stock selections. The Journal of Index Investing 13 Exhibit 1 The Journal of Index Investing 2016.6.4:12-29. Downloaded from www.iijournals.com by Taras Zlupko on 03/09/16. It is illegal to make unauthorized copies of this article, forward to an unauthorized user or to post electronically without Publisher permission. Distinctions among Various Smart Beta Strategies Categorized by the Kind of Factor Exposure (implicit vs. explicit) and Weighting Scheme One method of designing factor-tilted portfolios is to use a weighting scheme that aims at improved diversification. Many such weighting schemes exist, including simple equal weighting, equal risk weighting, and optimization-based weighting schemes such as minimum volatility. We followed an approach introduced by Amenc et al. [2014] that applies five commonly used alternative weighting schemes to portfolios that select 50% of stocks in the investment universe by desired factor exposure, and then combine these different 14 Smart Beta Is Not Monkey Business weighting schemes with equal weights. We used this weighting scheme, which is known as diversified multistrategy, for our first set of factor-tilted test portfolios.2 Our second set of factor-tilted smart beta strategies is based on the same stock selections by factor exposure, but uses the factor scores to determine constituent weights3 among selected stocks. For example, in the case of the value score–weighted portfolio, we selected the top 50% value stocks from the stock universe and then weighted them by adjusting their market cap weight by Spring 2016 The Journal of Index Investing 2016.6.4:12-29. Downloaded from www.iijournals.com by Taras Zlupko on 03/09/16. It is illegal to make unauthorized copies of this article, forward to an unauthorized user or to post electronically without Publisher permission. their value scores. Such score-weighting is employed by factor indexes from a variety of major providers.4 The factor tilts we consider here relate to the most widely used and documented factor tilts, namely low volatility, momentum, size, value, high profitability, and low investment.5 Additionally, for both diversified multi-strategy and score-weighting, we constructed multi-factor portfolios by combining the six factor-tilted portfolios in equal proportion on a quarterly basis. All factor-tilted portfolios are rebalanced quarterly. All strategies are applied to the U.S. large-cap stock universe (500 stocks) over a period of 40 years (December 31, 1973, to December 31, 2013). To avoid any hindsight bias, all parameters used in selecting and weighting the stocks are based on data observed prior to each respective rebalancing date. All stock price data were obtained from the Center for Research in Security Prices (CRSP) database, and fundamental data were obtained from WorldScope. HOW SIMILAR IS SMART BETA PERFORMANCE ACROSS STRATEGIES? A key argument of monkey portfolio proponents is that all smart beta strategies are similar. They have argued that “outwardly different smart betas produce nearly similar premiums for similar reasons” (Hsu, Kalesnik, and Li [2012, p. 12]) and “any one of these strategies can be mimicked by combinations of the others” (Chow et al. [2011, p. 37]). A simple way of assessing such claims is to compare returns across the different strategies. However, it is necessary to look beyond a simple comparison of long-term average returns because concluding that all smart beta strategies are similar to each other simply because the long-term excess returns look similar is not justified. In this section, we provide an overview of descriptive performance statistics including not only unconditional performance, but also performance in different market conditions. We also look directly at the similarity of strategies by assessing the correlation of relative returns across different strategies. Exhibit 2 shows basic descriptive statistics for the different test portfolios. Concerning their long-term average returns, the strategies are similar in the sense that they all outperform cap-weighted indexes, which may lead at first glance to the monkey portfolio conclusion that all strategies are similar. However, it also appears Spring 2016 that some performance differences exist over the long term, especially among smart beta strategies that tilt toward different risk factors. For example, the size-tilted (i.e., mid cap) portfolios have much higher returns and Sharpe ratios compared to their low volatility counterparts. In the diversified multi-strategy category, the outperformance ranges from an annualized average of 4.72% for mid cap tilt to 2.95% for the low volatility tilt. Similarly, in the score weighting category, the mid cap tilt results in 4.45% outperformance compared to a mere 0.54% for the low volatility tilt. The fundamentalweighted strategy, during the same period, returns 1.56% of excess return over the broad cap-weighted index, and the equal-weighted index returns 2.87% over the capweighted index. More striking than differences across long-term returns and Sharpe ratios are differences in conditional returns. In particular, the results in Exhibit 2 reveal that the performance differs across various smart beta strategies in bull and bear market conditions depending on the risk exposure of the strategy. From a relative returns perspective, the fundamental-weighted strategy is more favored in bear markets, whereas the equalweighted strategy performs better in bull markets. Differences are even more pronounced for strategies that provide explicit factor tilts. For example, the low volatility–tilted score-weighted strategy generates outperformance mainly in bear markets, whereas the corresponding size-tilted strategy generates outperformance mainly in bull markets. To be more specific, the low volatility score–weighted strategy returns almost 9% relative return during bear markets but underperforms by more than 5% during bull markets. In contrast, the corresponding size tilt (mid cap score–weighted) displays outperformance of almost 7% in bull markets but only adds about 1% of returns during bear markets. This observation is quite intuitive because risk factors carry time varying risk premiums (Asness [1992]; Cohen, Polk, and Vuolteenaho [2003]), and therefore all risk factors must not be expected to outperform in the same periods or by the same magnitude. Overall, although long-term performance may be similar across many strategies, conditional performance is quite different across different factor-tilted smart beta indexes. A simpler and more intuitive way to understand the difference across the set of smart beta strategies is to examine the correlation matrix of excess returns over the cap-weighted benchmark. Exhibit 3 shows the The Journal of Index Investing 15 Exhibit 2 The Journal of Index Investing 2016.6.4:12-29. Downloaded from www.iijournals.com by Taras Zlupko on 03/09/16. It is illegal to make unauthorized copies of this article, forward to an unauthorized user or to post electronically without Publisher permission. Absolute, Relative, and Conditional Performance Notes: All statistics are annualized, and daily total returns from December 31, 1973 to December 31, 2013 are used for the analysis. The CRSP S&P 500 index is used as the cap-weighted benchmark. Yield on Secondary U.S. Treasury bills (3M) is used as a proxy for the risk-free rate. Calendar quarters with positive cap-weighted index returns comprise bull markets, and the rest constitute bear markets. Effective number of stocks, a measure of portfolio concentration, is the inverse of Herfindahl Index, which in turn is defined as the sum of square of portfolio weights. We show the average effective number over all quarterly rebalancing dates. Pearson correlation coefficients of the relative returns of our test strategies over the cap-weighted reference index. The results in Exhibit 3 suggest that the correlations across different smart beta strategies are far less than one (i.e., the strategies are far from identical in terms of their relative returns over time). Low correlations of relative returns are even observed across strategies that do not provide explicit factor tilts and thus correspond to strategies that were included in the monkey portfolio proponents’ original tests. In particular, the fundamental-weighted strategy’s and the equal-weighted portfolio’s correlation of excess returns is a mere 0.51 (i.e., the two strategies are far from similar). Likewise, when it comes to strategies with explicit factor tilts, the levels of correlation are far below one. Some pairwise correlations of relative returns across factor-tilted strategies are even negative. These findings show that although all of these strategies outperform cap-weighted indexes, they do so with very different behavior over time. 16 Smart Beta Is Not Monkey Business Overall, although monkey portfolio proponents claim that “the investment beliefs upon which many investment strategies are ostensibly based play little or no role in their outperformance” (Arnott et al. [2013, p. 91]), it is evident from simple descriptive statistics that different strategies based on different investment beliefs do lead to different returns. This is true in particular for different factor tilts, which translate different investment beliefs and lead to indexes that have different conditional performance and far from perfect correlation of relative returns. DO ALL SMART BETA STRATEGIES OUTPERFORM SOLELY DUE TO SIZE AND VALUE LOADINGS? Monkey portfolio proponents have argued that, once we deviate from selecting and weighting stocks by their market cap, as is done in cap-weighted market indexes, we necessarily introduce a positive value and Spring 2016 Exhibit 3 The Journal of Index Investing 2016.6.4:12-29. Downloaded from www.iijournals.com by Taras Zlupko on 03/09/16. It is illegal to make unauthorized copies of this article, forward to an unauthorized user or to post electronically without Publisher permission. Correlation of Excess Returns of Smart Betas Notes: All statistics are annualized, and daily total returns from December 31, 1973 to December 31, 2013 are used for the analysis. The CRSP S&P 500 index is used as the cap-weighted benchmark. a positive size factor exposure (Chow et al. [2011]). These proponents have also argued that the same effect would occur with randomly generated portfolios, also referred to as monkey portfolios—see also Clare, Motson, and Thomas [2013]. Similarly, Arnott et al. [2013, p. 91] stated that any smart beta strategy “necessarily results in value and size tilts, regardless of the weighting method chosen,” and Chow et al. [2011, p. 41] claimed that smart beta strategies “outperform because of the positive value and size loadings” given that “none of these strategies are different from naive equal weighting.” Such claims seem at least surprising, given the well-documented findings on relevant risk factors in portfolio performance. For example, it has been shown that risk-based strategies (e.g., minimum variance and Spring 2016 equal risk contribution) take on exposures to low beta and low idiosyncratic risk factors (Leote de Carvalho, Lu, and Moulin [2012]; Clarke, de Silva, and Thorley [2013]). Moreover, there is ample evidence that stock portfolios seeking exposures to momentum, quality, or low beta factors generate returns that cannot be explained by the value and small cap factors (Asness, Frazzini, and Pedersen [2013]; Asness, Moskowitz, and Pedersen [2013]; Frazzini and Pedersen [2014]). To assess the role of such additional factors in commonly used smart beta strategies relative to the value and size factor, we performed regressions using a multi-factor model including a wide range of consensual equity factors. In particular, we used a seven-factor model that uses the betting-against-beta (BAB) factor from Frazzini and Pedersen [2014] 6 and the high profitability factor and The Journal of Index Investing 17 The Journal of Index Investing 2016.6.4:12-29. Downloaded from www.iijournals.com by Taras Zlupko on 03/09/16. It is illegal to make unauthorized copies of this article, forward to an unauthorized user or to post electronically without Publisher permission. low investment factor from Fama and French [2015] in addition to the four factors of Carhart [1997], namely the market, value, size, and momentum factors.7 The resulting regression coefficients are reported in Exhibit 4. If the monkey portfolio claims hold for our test portfolios, regression coefficients for size and value factors should be significantly positive for all strategies. Moreover, regression coefficients for all factors but size and value should be insignificant. Finally, in comparison with equal-weighting, none of the strategies should provide a different direction of factor tilt. However, inspection of the results in Exhibit 4 shows that none of these conditions is satisfied by the results. Exhibit 4 shows that, even though most strategies have positive exposure to size and value, some strategies do have negative exposure, sometimes to both of these factors. This is notably the case for the low volatility and high profitability score–weighted strategies. Despite deviating from the cap-weighted index, these strategies do not lead to a value and small cap tilt, but rather to a growth and large cap tilt. Therefore, it is not valid to claim that all smart beta strategies have positive value and size loadings, even though many strategies do. Moreover, given the negative exposure of some strategies to value and small cap, it would not make sense to claim that the outperformance of these portfolios is fully explained by their size and value exposure. The results also show that most strategies have significant exposures to factors other than value and small cap, in particular to the BAB factor, the momentum factor, the profitability factor, and the investment factor. This is not surprising given the ample evidence on the importance of these factors and the fact that some indexes in our set of strategies explicitly seek exposure to such factors. For example, the high profitability strategies (diversified multi-strategy and score weighted) lead to profitability factor loadings of 0.08 and 0.19, respectively; the low-investment strategies (diversified multi-strategy Exhibit 4 Seven-Factor Regression Notes: The market factor is the excess returns of the CRSP S&P 500 index over the risk-free rate. The yield on secondary U.S. Treasury bills (3M) is used as a proxy for the risk-free rate. The size, value, momentum, high profitability, and low investment factors were obtained from the Kenneth French data library. The BAB factor was obtained from the Andrea Frazzini data library. The Newey–West (Newey and West [1987]) estimator is used to correct for autocorrelation. Daily total returns from December 31, 1973 to December 31, 2013 are used for the analysis. Regression coefficients that have P-values less than 5% are highlighted in bold. Alphas are annualized. 18 Smart Beta Is Not Monkey Business Spring 2016 The Journal of Index Investing 2016.6.4:12-29. Downloaded from www.iijournals.com by Taras Zlupko on 03/09/16. It is illegal to make unauthorized copies of this article, forward to an unauthorized user or to post electronically without Publisher permission. and score weighted) lead to investment factor loadings of 0.32 and 0.52; and the low volatility strategies (diversified multi-strategy and score weighted) lead to BAB factor loadings of 0.10 and 0.09, respectively. The momentum diversified multi-strategy portfolio has a momentum beta of 0.17, whereas the momentum score–weighted strategy has an even higher momentum beta of 0.40. Even when these strategies also tilt to value and size, the other factor exposures of these strategies are important in magnitude relative to the size and value exposures. However unsurprising they may be, these results invalidate the monkey portfolio proponents’ claim that smart beta does nothing but tilt to small cap and value. It is also interesting to assess whether all strategies really behave like equal-weighting in terms of factor exposure. In fact, the results in Exhibit 4 confirm the monkey portfolio proponents’ findings that equal-weighting leads to positive size and value exposure. Unfortunately, though, monkey portfolio proponents have not provided any discussion of other factor tilts implicit in equal-weighted indexes. Exhibit 4 shows that the broad equal-weighted index also has negative momentum exposure. It is interesting to compare this to the momentum exposures of the other strategies. Although the fundamentalweighted portfolio also has negative momentum exposure, seven of the twelve single factor–tilted strategies have significantly positive momentum exposure. Our results thus provide evidence that most of these strategies are opposed to equal-weighting in terms of momentum exposure. Moreover, the equal-weighted strategy does not have significant exposures to the BAB factor and the profitability factor. On the contrary, many of the factor-tilted strategies have significant exposure the BAB and high profitability factor. In this sense, the factor-tilted indexes offer investment opportunities that cannot be captured by an equal-weighted index. Such factor-tilted indexes allow investors to express investment beliefs (concerning factors) that cannot be captured through the equal-weighted index. The factor exposures in Exhibit 4 directly invalidate monkey portfolio proponents’ claim that no smart beta strategy is any different from equal weighting. To provide more intuition on the role of different factors in the performance and risk of different smart beta strategies, we complement our analysis of regression coefficients with attributions of the relative return and tracking error of these strategies to their factor exposures. The reason for this additional analysis is that factor coefficients may not be easy to interpret because Spring 2016 the contributions that a factor makes to the risk and return of a strategy of course depend not only on the factor loading of the strategy, but also on the risk and return properties of the factor. Exhibit 5 shows the breakdown of the excess returns and tracking error of these smart beta strategies into the components derived from factors and the unexplained part. The performance of a portfolio over risk-free rate can be attributed to the given factors using the following Equations: 7 R P,t − R rfr,t = α + ∑ βFi R Fi ,t + ε i =1 (1) 7 R P − R rfr = Unexplained (alpha) + ∑ βFi R Fi i =1 (2) Another set of regressions described in Equation (3) was run, and then Equation (4) was used to break down the square of tracking error (TE) into three parts: the unexplained (or idiosyncratic) part, the TE attributable to each factor, and the TE attributable to the interaction of factors: 7 R + + ∑ β R P,t − RCWT ,t = α ε Fi Fi ,t i =1 (3) 7 2 Var( R ) TE 2 = ∑ β Fi F,t i =1 7 2 2 2 (4) + 2 ∑ β Fi β F j Cov(R Fi ,t , R F j ,t ) + σ ε i , j =1 ( i ≠ j ) R P,t represents portfolio return series, RCWT,t represents cap-weighted benchmark return series, R rfr,t represents risk-free rate time series, and R Fi,t represents the time series of returns of the seven factors listed in Exhibit 4. R P , R rfr , and R Fi represent annualized average returns. The second term in Equation (4), involving the covariance across the factors, is labeled as an “Interaction” component; and the last term in Equation (4), representing the unexplained TE, is labeled as an “Idiosyncratic” component of TE in Exhibit 5. Since Equation (4) is quadratic, both sides of the equation are divided by TE to remove the square term. This is an approximation that allows us to represent the division of TE across factors in a simple way without affecting their relative contribution to TE. The Journal of Index Investing 19 Exhibit 5 The Journal of Index Investing 2016.6.4:12-29. Downloaded from www.iijournals.com by Taras Zlupko on 03/09/16. It is illegal to make unauthorized copies of this article, forward to an unauthorized user or to post electronically without Publisher permission. Seven-Factor Performance and Tracking Error Attribution Notes: The market factor is the excess returns of the CRSP S&P 500 index over risk-free rate. The yield on secondary U.S. Treasury bills (3M) is used as a proxy for the risk-free rate. The size, value, momentum, high profitability, and low investment factors were obtained from the Kenneth French data library. The BAB factor was obtained from the Andrea Frazzini data library. The Newey–West (Newey and West [1987]) estimator is used to correct for autocorrelation. Daily total returns from December 31, 1973 to December 31, 2013 are used for the analysis. 20 Smart Beta Is Not Monkey Business Spring 2016 The Journal of Index Investing 2016.6.4:12-29. Downloaded from www.iijournals.com by Taras Zlupko on 03/09/16. It is illegal to make unauthorized copies of this article, forward to an unauthorized user or to post electronically without Publisher permission. As seen in Exhibit 5, factors other than value and size play a major role in the returns and the risk of many strategies. In particular, the low volatility– and momentum-tilted portfolios, irrespective of the weighting scheme, derive a large portion of their performance from their exposure to BAB and momentum factors, respectively. The contributions of factors other than value and size to portfolio risk and return again invalidate the claim that these strategies are not different from equal-weighting. Although many of the strategies tested go beyond value and small cap exposure and offer pronounced exposure to additional factors, the presence of a considerable portion of unexplained performance suggests that the portfolio construction of these indexes captures effects that cannot be explained fully by the relevant factors. One possible explanation for this unexplained part of performance is that the improved diversification scheme allows value to be added beyond the explicit factor tilts. Another explanation is that other additional factors, which are omitted from the factor model, are at work. Our results unmistakably show that smart beta strategies can have exposure to factors other than small size and value. As mentioned previously, this finding may not be surprising and is fully consistent with the academic literature, which has documented the importance of various equity risk factors beyond value and small cap (Leote De Carvalho, Lu, and Moulin [2012]; Asness, Frazzini, and Pedersen [2013]; Asness, Moskowitz, and Pedersen [2013]; Clarke, de Silva, and Thorley [2013]). However, although our findings are in line with this literature, they are in stark contradiction to the claims of monkey portfolio proponents who have argued that there is nothing beyond value and small-cap exposure in smart beta strategies. Instead, our results suggest that different smart beta strategies derive performance from different exposures to several factors that may go beyond size and value. Importantly, our results also show that differences in product design of course lead to differences in factor exposures, and the investment philosophy on which smart beta strategies are based is therefore nowhere near irrelevant for performance. Our differences in results with those documented by monkey portfolio proponents suggest that monkey portfolio arguments do not apply generally. Our findings directly invalidate the monkey portfolio proponents’ claims that smart beta is simply about small cap and value exposure. Although we do not claim to provide an Spring 2016 exhaustive set of smart beta strategies used in practice, we include some of the commonly used strategies and come to opposite conclusions from the monkey portfolio argument. This suggests that the monkey portfolio claims may apply only to a specific selection chosen by the proponents, without taking into account the full range of smart beta strategies used in practice. One should thus be careful to refrain from overgeneralizing these results. DO SMART BETA STRATEGIES ADD THE SAME OR MORE VALUE WHEN INVERTED? Another key claim of monkey portfolio proponents is that smart beta strategies “add the same or more value when inverted,” as suggested by Brightman [2013, p. 5]. An even stronger version of this claim was put forward by Arnott et al. [2013, p. 98], who stated that “popular strategy indexes, when inverted, produce even better outperformance.” Clearly, if one were to confirm such results for inverted strategies, this would be strong evidence suggesting that “the investment beliefs upon which many investment strategies are ostensibly based play little or no role in their outperformance” (Arnott et al. [2013, p. 91]). In this subsection, we empirically assess the validity of such claims with respect to our set of test portfolios. In the preceding section, we already visited the problem of selecting particular strategies to test claims relating to their performance and then overgeneralizing the findings to all of smart beta. This problem, of course, also applies to selecting strategies for the creation of inverse portfolios. Whether a strategy behaves differently from its inverse will depend heavily on the type of strategy that one tests. Let us take the example of an equal-weighted (also known as 1/N) strategy, which is the simplest form of smart beta strategies. If one inverts its weights using the methodology of Arnott et al. [2013], one would arrive at the original portfolio (i.e., the inverse of the 1/N portfolio is the portfolio itself ). Therefore, this smart beta strategy and its inverse are identical, and both outperform the cap-weighted benchmark identically. Similarly, by using portfolios that are constrained to correspond to some optimization objective while keeping a close distance to equal-weighted portfolios, one would bias the results in favor of the claim that inverse strategies have as much merit as the original strategies. This problem may be exacerbated by the fact that The Journal of Index Investing 21 The Journal of Index Investing 2016.6.4:12-29. Downloaded from www.iijournals.com by Taras Zlupko on 03/09/16. It is illegal to make unauthorized copies of this article, forward to an unauthorized user or to post electronically without Publisher permission. monkey portfolio arguments have been derived using simulated strategies that do not correspond to the actual index rules used in practice, as mentioned in the disclaimers in Arnott et al. [2013] and Chow et al. [2011]. We used the fundamental-weighted strategy and single factor-tilted portfolios to assess the claim that the performance of smart beta strategies remains the same or increases if their weights are inverted. The equalweighted strategy is excluded because, as argued earlier, the equal-weighted portfolio is its own inverse portfolio. To analyze this effect, we constructed the inverse or upside-down portfolios for each smart beta strategy in a manner similar to that of Arnott et al. [2013].8 In particular, we applied two methods of turning strategy weights upside-down, which we refer to as type-1 and type-2 upside-down strategies. It should, however, be noted that our test portfolios include a stock selection step for the explicit factor-tilted portfolios. Therefore, in addition to inverting the portfolio weights, we also invert the direction of the stock selection. In the upside-down strategy for value, for example, we selected the stocks with the lowest value score (i.e., the highest inverse value score) and then tilted the weights by the inverse of their value score. In fact, a key contribution of our article relative to Arnott et al. [2013] is that we include a more general class of smart beta strategies that do not only use alternative weighting schemes to reweight a given stock universe, but also select stocks based on factor characteristics. Contrary to our approach, Arnott et al. [2013] only tested broad smart beta strategies that reweight stocks from a broad universe and often resemble equal-weighted strategies by construction. Of course, one would expect that such strategies, when inverted, remain quite similar to the original strategies. When inverting strategies that include a stock selection, it is clear that by selecting stocks with the opposite characteristics, the upside-down version of such strategies is expected to display more pronounced differences. It is important to note that by omitting strategies with a stock selection step, Arnott et al. [2013] have omitted a practically important class of smart beta strategies. Our article fills this gap by considering additional types of smart beta strategies, which are widely used in practice. To illustrate how the creation of upside-down strategies works, we provide a simple example. Exhibit 6 shows the weights of the risk-weighting scheme and its upside-down type-2 version, with and without low volatility stock selection, applied to the top 10 stocks by total market cap as of December 2013. This is an illustrative example, which aims to show the differences that arise when one does or does not Exhibit 6 Illustrative Examples of Portfolio Weights of Risk-Weighted, Equal-Weighted, and Their Upside-Down Type-2 Versions Notes: The portfolios are constructed using a sample universe consisting of the 10 largest U.S. stocks by total market capitalization as of December 20, 2013. Risk weighting strategy weights the stocks in the proportion of the reciprocal of their past two-year volatilities. The low volatility selection picks five stocks with the lowest past two-year volatilities. 22 Smart Beta Is Not Monkey Business Spring 2016 The Journal of Index Investing 2016.6.4:12-29. Downloaded from www.iijournals.com by Taras Zlupko on 03/09/16. It is illegal to make unauthorized copies of this article, forward to an unauthorized user or to post electronically without Publisher permission. use stock selection in designing a smart beta strategy and its inverse. We can see that inverting not only the weights but also the stock selection naturally leads to more pronounced differences in weight between the strategy and its inverse. The illustration also shows that even when using a weighting scheme that targets equal weights, inverting the stock selection step would lead to pronounced differences between the upside-down strategy and the original. The stock selection stage plays an important role in the methodologies of commonly used smart beta strategies (see Amenc, Goltz, and Lodh [2012]). Therefore, inverting not only the weighting scheme but also the stock selection methodology is necessary for a relevant analysis of upside-down strategies. Having clarified the methodology used to create upside-down strategies, we now turn to the results obtained when inverting a broad range of smart beta strategies. Exhibit 7 shows performance and risk statistics for our test strategies as well as for the corresponding upside-down strategies. The results in Exhibit 7 are very homogeneous across the different strategies. Overall, the results suggest that most upside-down strategies have lower returns than the originals, as well as lower Sharpe and information ratios. Indeed, many of the original smart beta portfolios outperform their upside-down counterparts, and they mostly do so by large margins. For example, the mid cap and value diversified multi-strategy portfolios outperform their upside-down portfolios by more than 3%, and this figure for the momentum diversified multistrategy is about 1.5%. Intuitively, this result can be expected to arise if the inverse of a factor-tilted portfolio tilts negatively toward the rewarded factor and hence does not benefit from risk premiums. To test this explanation of the results of upside-down strategies, we will assess their factor exposures. In addition to looking at the explicit factor tilt strategies, it is also interesting to see if the upside-down version of the fundamental-weighted portfolio provides similar performance to the original. The monkey portfolio proponents’ claim is only partly valid concerning this strategy, as the upside-down type-1 strategy of the fundamentally weighted portfolio indeed has similar returns to the original strategy, but the type-2 upsidedown strategy underperforms the original. When looking at risk-adjusted returns in the form of Sharpe ratios, the results in Exhibit 7 show that all explicit factor-tilted strategies in our set of test portfolios Spring 2016 have Sharpe ratios superior to those of the inverted strategies. The information ratio and probability of outperformance of the original smart beta strategies is also consistently higher than that of the respective inverted portfolios. Our findings, while perfectly in line with common sense, contradict the claims made by monkey portfolio proponents. To better understand the effect inverting a smart beta strategy has on its risk profile, we employed the multi-factor model from earlier and then looked at how factor loadings are affected by the inversion of the strategy. Exhibit 8 shows the seven-factor exposures of original and inverted smart beta strategies to explain this performance difference. Overall, the results in Exhibit 8 suggest that the upside-down strategies result in less rewarding factor exposures, which is consistent with their lower performance compared to the original strategies. The value exposure of the value diversified multistrategy is 0.40, whereas its inverse portfolios have negative value exposure. Similarly, the low volatility diversified multi-strategy has an exposure of 0.10 to the BAB factor and 0.88 to the market factor, whereas its inverse portfolios have negative BAB betas and market betas greater than one. In fact, for each factor tilt, it is shown that inverting a factor-tilted smart beta portfolio will result in a portfolio with reduced exposure to the concerned factor. The previous f indings are similar for scoreweighted portfolios. When compared to its upsidedown type-1 portfolio, the momentum (low volatility) score–weighted portfolio has a higher exposure to the momentum (BAB) factor. The fact that the momentum (low volatility) score–weighted portfolio outperforms its type-1 inverse by 4.81% (2.43%) per annum suggests that the momentum (BAB) factor is the main driver of its performance. Since this process of “artificially” inverting the portfolios does not rely on a stock’s characteristics, such as its SMB (small minus big) or HML (high minus low) score, it is possible that inverting a factor-tilted portfolio increases its SMB or HML exposure. That said, it does not mean that the inverted portfolio will exhibit superior performance compared to the original smart beta strategy. The case of the low investment diversified multi-strategy and high profitability diversified multi-strategy portfolios in Exhibit 8 provides an excellent example to this effect. The Journal of Index Investing 23 Exhibit 7 The Journal of Index Investing 2016.6.4:12-29. Downloaded from www.iijournals.com by Taras Zlupko on 03/09/16. It is illegal to make unauthorized copies of this article, forward to an unauthorized user or to post electronically without Publisher permission. Performance and Risk Analysis of Upside-Down Strategies Notes: The probability of outperformance is the probability of obtaining positive excess returns from investing in the strategy for a period of three years at any point during the history of the strategy. All statistics are annualized, and daily total returns from December 31, 1973, to December 31, 2013 are used for the analysis. The CRSP S&P 500 index is used as the cap-weighted benchmark. Yield on secondary U.S. Treasury bills (3M) is used as a proxy for the risk-free rate. 24 Smart Beta Is Not Monkey Business Spring 2016 Exhibit 8 The Journal of Index Investing 2016.6.4:12-29. Downloaded from www.iijournals.com by Taras Zlupko on 03/09/16. It is illegal to make unauthorized copies of this article, forward to an unauthorized user or to post electronically without Publisher permission. Regression Analysis of Upside-Down Strategies Notes: The market factor is the excess returns of the CRSP S&P 500 index over risk-free rate. The yield on secondary U.S. Treasury bills (3M) is used as a proxy for the risk-free rate. The size, value, momentum, high profitability, and low investment factors were obtained from the Kenneth French data library. The BAB factor was obtained from the Andrea Frazzini data library. The Newey–West (Newey and West [1987]) estimator is used to correct for autocorrelation. Daily total returns from December 31, 1973 to December 31, 2013 are used for the analysis. Regression coefficients that have P-values less than 5% are highlighted indicated in bold font. The regression coefficient that corresponds to the variable used in stock selection is indicated by a shaded background. Alphas are annualized. Spring 2016 The Journal of Index Investing 25 The Journal of Index Investing 2016.6.4:12-29. Downloaded from www.iijournals.com by Taras Zlupko on 03/09/16. It is illegal to make unauthorized copies of this article, forward to an unauthorized user or to post electronically without Publisher permission. We notice that inverting these two smart beta strategies increases the portfolio’s exposure to SMB and HML factors. However, it does not improve the performance. Upon close inspection of the results, it is apparent that the process of inversion also deteriorates momentum, investment, and profitability betas. In the case of these two strategies, the overall performance drag resulting from these decreasing betas outweighs the performance gain that stems from SMB and HML factors, which explains the overall performance of these smart betas and their upside-down portfolios. It is therefore important to examine the effect of factors in addition to small size and value. The factor loadings are also able to provide perspective on the behavior of the fundamentally weighted portfolio’s inverse. We saw earlier that the fundamentally weighted upside-down strategy (at least for type-1) shows risk and returns characteristics similar to the original strategy. In fact, this is consistent with the fact that inversion of this portfolio reduces the value beta on the one hand and increases the small size beta on the other. A similar observation can be made when inspecting the results of Arnott et al. [2013]. Our results in Exhibits 7 and 8 suggest that investment beliefs in the form of explicit factor tilts do indeed play an important role in determining the performance of an investment strategy. Inverting the strategy not only turns the weights upside-down but also changes the results, both in terms of performance and factor exposures. This finding contradicts the monkey portfolio claim, at least for the explicit factor-tilted strategies tested here. CONCLUSION: ASSESSING SMART BETA STRATEGIES IS NOT MONKEY BUSINESS The main arguments of monkey portfolio proponents are that all smart beta strategies generate positive value and small-cap exposure similar to that generated by any random portfolio strategy, and the inverses of such strategies perform similarly or better. Although we have not attempted to conduct an exhaustive assessment of these claims across all possible strategies, our analysis of some commonly employed smart beta strategies suggests that these statements do not hold in general. Our results show that, although some strategies such as fundamental equity indexation may perhaps be mostly driven by a value tilt and may generate similar 26 Smart Beta Is Not Monkey Business performance to their upside-down counterpart, many smart beta strategies display exposure to additional factors, as well as pronounced differences in factor exposures across different strategies. Moreover, and perhaps reassuringly, the inverses of these strategies generate lower performance. The differences with the original results underlying the monkey portfolio arguments can be explained by the fact that we considered strategies that explicitly tilt toward a variety of risk factors, whereas the evidence in favor of monkey portfolio claims omitted such strategies and instead focused on a particular selection of strategies that may better correspond to such claims. In particular, if one selects strategies that stay relatively close to equal-weighting, it may not be entirely surprising that the performance of such strategies is extensively driven by value and small cap exposure, as has been documented for equal-weighted strategies. Moreover, it may not be surprising that strategies that are close to equal-weighting can be inverted while maintaining comparable performance benefits. An important insight from our tests is that one should be careful to not overgeneralize results that have been derived from testing particular strategies. Although the monkey portfolio arguments may apply to particular strategies, they have been invalidated for the explicit factor strategies we chose as our main test portfolios here, and therefore these claims cannot be applied to smart beta strategies in general. Our findings of significant differences across various smart beta strategies imply that care must be taken not to fall into the trap of oversimplification and overgeneralization. The differences in factor exposures across smart beta strategies imply that using a particular set of indexes corresponds to particular factor selection and factor allocation decisions. Moreover, the different factor tilts play an important role in shaping the risk–return profile of smart beta strategies. Factor-tilted smart beta strategies perform due to large positive exposure to their respective factors, whereas their inverted counterparts underperform the originals due to less pronounced or negative exposure to the same factors. When considering the adoption of smart beta strategies, investors should carefully consider which set of factor exposures is best aligned with their investment beliefs and objectives. Making a selection from among smart beta strategies is not monkey business after all. Spring 2016 A P P E N DIX The Journal of Index Investing 2016.6.4:12-29. Downloaded from www.iijournals.com by Taras Zlupko on 03/09/16. It is illegal to make unauthorized copies of this article, forward to an unauthorized user or to post electronically without Publisher permission. DESCRIPTION OF DIVERSIFICATION-BASED WEIGHTING SCHEMES The maximum deconcentration weighting scheme is a naive diversification strategy that aims at maximizing the effective number of stocks of an equity portfolio. The strategy owes its popularity mainly to its robustness, and it has been shown to deliver attractive performance despite highly unrealistic conditions of optimality, even when compared to sophisticated portfolio optimization strategies (DeMiguel, Garlappi, and Uppal [2009]). The diversified risk–weighted strategy aims to achieve equal risk contribution from all stocks under the assumption of identical pairwise correlation across stocks, and it is the same as inverse volatility weighting. It aims to balance risk exposures across portfolio constituents and can thus be seen as a response to issues with risk concentration, which may arise in cap-weighted equity indexes (Maillard, Roncalli, and Teiletche [2010]). The maximum decorrelation weighting scheme aims at minimizing portfolio volatility under the assumption that stock volatilities are identical, thus only exploiting the correlation structure. In line with the idea that correlation effects are the main driver of diversification, this approach is an application of the diversification measure suggested by Christoffersen et al. [2010] for equity portfolio construction. Exhibit A1 Closed Form Solutions and Required Parameters for Five Weighting Schemes The efficient minimum volatility weighting scheme attempts to minimize the portfolio volatility using the information on stock volatilities and pairwise correlations. Theoretically, it is the portfolio on the efficient frontier with the lowest level of volatility and is the only one that does not require estimates of expected returns (Markowitz [1952]). The efficient maximum Sharpe ratio weighting scheme aims to maximize the Sharpe ratio—the risk-adjusted performance. Theoretically, it is the portfolio on the efficient frontier with the highest reward per unit of risk and is the only portfolio of risky assets that should be of interest to a rational investor (Tobin [1958]). The diversified multi-strategy weighting scheme combines these five weighting schemes in equal proportions to reduce the unrewarded or specific risks of each strategy. ENDNOTES 1 The weight of a stock in the fundamental-weighted portfolio is calculated using its composite fundamental score. The composite fundamental score is the average of four scores, each based on current book value, trailing five-year cash f low, trailing five-year dividend, and trailing five-year sales, respectively. When the score of certain fundamental variables is not available for a particular stock, its composite fundamental score is the average score across remaining variables. For example, for the companies that did not distribute dividends (i.e., their dividend score is missing), we omitted the dividend variable score and instead used the average across the other three fundamental variable scores. The fundamental-weighted portfolio is rebalanced yearly on the third Friday in March. 2 Amenc et al. [2014] introduced diversified multistrategy weighting as an equal-weighted combination of the following five weighting schemes: maximum deconcentration, diversified risk weighted, maximum decorrelation, efficient minimum volatility, and efficient maximum Sharpe ratio. For a detailed description, refer to the Appendix. 3 For a given factor, each stock is assigned a factor Z-score. The cumulative distribution function (CDF) of a normal distribution with zero mean and unit standard deviation is used to convert Z-scores to standardized S-scores. The S-scores range from 0 to 1. Z Si = Notes: The exhibit lists the closed form solutions and the required parameters for the five weighting schemes. N is the number of stocks, µ is the (N × 1) vector of expected return, 1 is the (N × 1) vector of ones, σ is the (N × 1) vector of volatilities, Ω is the (N × N) correlation matrix, and Σ is the (N × N) covariance matrix. Spring 2016 2 1 i − 2x ∫ e dx 2 π −∞ Score weighting is done by weighting the stocks in proportion to their market-cap times the S-score of the respective factor. The Journal of Index Investing 27 Wi = S × MC i Σ Sk × MC k i N k =1 The upside-down type-1 (UD1) portfolio weights are given by the following expression: The Journal of Index Investing 2016.6.4:12-29. Downloaded from www.iijournals.com by Taras Zlupko on 03/09/16. It is illegal to make unauthorized copies of this article, forward to an unauthorized user or to post electronically without Publisher permission. 4 We also tested the same strategies using simple scoreweighting rather than score-adjusted market cap weighting. The results with these portfolios do not lead to different conclusions on the validity of the monkey portfolio arguments from our analysis of diversified tilted portfolios and score-adjusted market cap weighted portfolios. Because of this, and because of the fact that indexes used in practice do not commonly employ direct score weighting, we do not report these results here. 5 The following selection rules are applied to select stocks for each tilt. Mid cap: bottom 50% free f loat-adjusted market cap stocks are selected. Value: top 50% stocks are selected by book-to-market (B/M) ratio, defined as the ratio of the available book value of shareholders’ equity to company market cap. High momentum: top 50% stocks are selected by returns over the past 52 weeks, minus the last four weeks. Low volatility: bottom 50% stocks are selected by their standard deviation of weekly stock returns over the past 104 weeks. Low investment: bottom 50% stocks with two-year total asset growth rate. High profitability: top 50% stocks with highest gross profit/total asset ratio. The score-based selection is done twice a year ( June and December) for momentum and once a year ( June) for the remaining five factors. 6 Rank-weighted portfolios that are long the 50% low market beta stocks and short the 50% high market beta stocks were constructed. Betas were estimated using the shrinkage method of Vasicek [1973] for long and short legs separately. Both long and short portfolios were rescaled to have a beta of one at portfolio formation. 7 The size, value, momentum, high profitability, and low investment factors were obtained from Kenneth French’s data library (http://mba.tuck.dartmouth.edu/pages/faculty/ ken.french/data_library.html). The BAB factor was obtained from Andrea Frazzini’s data library (http://www.econ.yale .edu/~af227/data_library.htm). 8 The idea of turning a strategy upside-down is to make counter bets (i.e., to overweight stocks that are underweighted in the smart beta strategy and vice versa). Therefore, to turn a factor-tilted strategy upside-down would require the remaining half of the stock universe to be selected and then the weights in smart beta portfolios to be inverted in this subuniverse. For example, the upside-down version of the mid cap diversified multi-strategy portfolio is the portfolio obtained by inverting the large cap diversified multi-strategy portfolio. Let the weight vector of a smart beta strategy be given by W: W = (w1 , w 2 , …, w n ) w max = max(w1 , w 2 , …, w n ) 28 Smart Beta Is Not Monkey Business w − w1 , w max − w 2 , , w max − w n WUD1 = max n. w max − 1 n. w max − 1 n. w max − 1 and the second inverted, or upside-down type-2 (UD2), portfolio weights are given by the following expression: WUD2 1 1 1 wn w1 , w2 , , = n n n 1 ∑ 1w ∑ 1w ∑ wk k =1 k =1 k =1 k k Similarly, the UD1 and UD2 versions of the mid cap score–weighted portfolio is the portfolio obtained by inverting the size scores of large cap stocks such that larger stocks have higher S-scores: SiUD1 = max(S1 , S2 , …, Sn ) − Si 1 SiUD2 = Si These scores are then used to tilt the market capweighted portfolio of large cap stocks as follows: Wi UD1 = ∑ SiUD1 .MC i n k =1 S UD1 k .MC k , Wi UD2 = ∑ SiUD2 .MC i n k =1 S UD2 k .MC k REFERENCES Amenc, N., and F. Goltz. “Smart Beta 2.0.” The Journal of Index Investing, Vol. 4, No. 3 (2013), pp. 15-23. Amenc, N., F. 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