Outperforming Cap-Weighted Indices with Limited Risk of Underperformance
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JPM_Cover.qxp:Cover 4/17/12 9:02 AM Page 1 THE JOURNAL OF PORTFOLIO MANAGEMENT VOLUME 38 NUMBER 3 www.iijpm.com SPRING 2012 Diversifying the Diversifiers and Tracking the Tracking Error: Outperforming Cap-Weighted Indices with Limited Risk of Underperformance OËL MENC ELIX OLTZ SHISH ODH SPRING 2012 VOLUME 38, NUMBER 3 N A , F G , A L , AND LIONEL MARTELLINI NOËL AMENC odern portfolio theory states Following such early criticism of cap- is a professor of finance that investors should allocate weighted equity portfolios, more recent papers at EDHEC Business their wealth between a tan- have documented that cap-weighted portfo- School and a director of EDHEC-Risk Institute gency portfolio, or maximum lios suffer from numerous shortcomings, and in London, UK. MSharpe ratio (MSR) portfolio, and a riskless various alternative weighting schemes have [email protected] asset. In practice, when trying to follow this been proposed to improve on cap weighting; advice, one obviously has to come up with see Amenc et al. [2011], Arnott, Hsu, and FELIX GOLTZ proxies because neither the true tangency Moore [2005], Choueifaty and Coignard is head of applied research portfolio nor a perfectly risk-free asset can be [2008], and Maillard, Roncalli, and Teiletche at the EDHEC-Risk Insti- tute at EDHEC Business exactly implemented in practice. Traditionally, [2008], to name but a few. School in Nice, France. equity investing has, however, heavily drawn Although it is now commonly accepted [email protected] on the idea of the Tobin separation theorem, that movingThe awayVoi cesfrom of cap Influence weighting | tends iijournals.com and cap-weighted equity indices have long to enhance diversification and increase risk- ASHISH LODH been perceived by many practitioners as rea- adjusted performance over long horizons, it is a quantitative analyst with the EDHEC-Risk sonable proxies for the tangency portfolio. But has to be recognized that each alternative Institute89138_cover.indd at EDHEC 1 a consensus is slowly emerging that market- weighting scheme will expose an investor to 5/11/12 1:18 PM Business School in cap-weighted indices tend to be poorly diver- two related types of risk, namely, model selec- Nice, France. sified portfolios that are not good proxies for tion risk and relative performance risk. [email protected] the tangency portfolio. This result is hardly a Considering model selection risk, it is new finding, because early attempts to provide clear that choosing a weighting scheme corre- LIONEL MARTELLINI is a professor of finance at evidence that cap-weighted portfolios are not sponds to choosing a model of optimal port- EDHEC Business School well-diversified portfolios and thus lead to an folio construction. This is the case, in fact, and scientific director of inefficient risk–return trade-off can be traced even if a weighting scheme does not explic- EDHEC-Risk Institute as far back as Haugen and Baker [1991] or itly refer to portfolio optimization. In fact, in Nice, France. Grinold [1992]. Intuitively, the fact that cap- any weighting scheme can be understood as [email protected] weighted indices are inefficient and poorly reflecting a set of assumptions under which the diversified is perhaps not surprising because resulting portfolio would lead to an optimal they concentrate heavily in the largest mar- portfolio in the sense of modern portfolio ket-cap stocks as a result of their one-dimen- theory; see Martellini [forthcoming] or Melas sional construction mechanism that only takes and Kang [2010]. From a pragmatic perspec- into account a stock’s market cap and thus tive, it seems reasonable to assume that dif- does not allow for any mechanism that can ferent market conditions may favor different enforce proper diversification. assumptions, and thus alternative weighting 72 DIVERSIFYING THE DIVERSIFIERS AND TRACKING THE TRACKING ERROR SPRING 2012 JPM-AMENC.indd 72 4/14/12 11:23:48 AM Diversifying the Diversifiers and Tracking the Tracking Error: Outperforming Cap-Weighted Indices with Limited Risk of Underperformance NOËL AMENC, FELIX GOLTZ, ASHISH LODH, AND LIONEL MARTELLINI NOËL AMENC odern portfolio theory states Following such early criticism of cap- is a professor of finance that investors should allocate weighted equity portfolios, more recent papers at EDHEC Business their wealth between a tan- have documented that cap-weighted portfo- School and a director of EDHEC-Risk Institute gency portfolio, or maximum lios suffer from numerous shortcomings, and in London, UK. MSharpe ratio (MSR) portfolio, and a riskless various alternative weighting schemes have [email protected] asset. In practice, when trying to follow this been proposed to improve on cap weighting; advice, one obviously has to come up with see Amenc et al. [2011], Arnott, Hsu, and FELIX GOLTZ proxies because neither the true tangency Moore [2005], Choueifaty and Coignard is head of applied research portfolio nor a perfectly risk-free asset can be [2008], and Maillard, Roncalli, and Teiletche at the EDHEC-Risk Insti- tute at EDHEC Business exactly implemented in practice. Traditionally, [2008], to name but a few. School in Nice, France. equity investing has, however, heavily drawn Although it is now commonly accepted [email protected] on the idea of the Tobin separation theorem, that moving away from cap weighting tends and cap-weighted equity indices have long to enhance diversification and increase risk- ASHISH LODH been perceived by many practitioners as rea- adjusted performance over long horizons, it is a quantitative analyst with the EDHEC-Risk sonable proxies for the tangency portfolio. But has to be recognized that each alternative Institute at EDHEC a consensus is slowly emerging that market- weighting scheme will expose an investor to Business School in cap-weighted indices tend to be poorly diver- two related types of risk, namely, model selec- Nice, France. sified portfolios that are not good proxies for tion risk and relative performance risk. [email protected] the tangency portfolio. This result is hardly a Considering model selection risk, it is new finding, because early attempts to provide clear that choosing a weighting scheme corre- LIONEL MARTELLINI is a professor of finance at evidence that cap-weighted portfolios are not sponds to choosing a model of optimal port- EDHEC Business School well-diversified portfolios and thus lead to an folio construction. This is the case, in fact, and scientific director of inefficient risk–return trade-off can be traced even if a weighting scheme does not explic- EDHEC-Risk Institute as far back as Haugen and Baker [1991] or itly refer to portfolio optimization. In fact, in Nice, France. Grinold [1992]. Intuitively, the fact that cap- any weighting scheme can be understood as [email protected] weighted indices are inefficient and poorly reflecting a set of assumptions under which the diversified is perhaps not surprising because resulting portfolio would lead to an optimal they concentrate heavily in the largest mar- portfolio in the sense of modern portfolio ket-cap stocks as a result of their one-dimen- theory; see Martellini [forthcoming] or Melas sional construction mechanism that only takes and Kang [2010]. From a pragmatic perspec- into account a stock’s market cap and thus tive, it seems reasonable to assume that dif- does not allow for any mechanism that can ferent market conditions may favor different enforce proper diversification. assumptions, and thus alternative weighting DIVERSIFYING THE DIVERSIFIERS AND TRACKING THE TRACKING ERROR SPRING 2012 JPM-AMENC.indd 72 4/14/12 11:23:48 AM schemes may display different performance depending to overperforming the same index by 11.17%, while on market conditions. In fact, when analyzing the per- the minimum-volatility strategy followed the opposite formance of alternative weighting schemes, it is indeed trend. This kind of behavior points to the fact that each the case that performance differences can be pronounced, model behaves well only in a certain kind of market as evidenced by the results shown in Exhibit 1, which condition. Another noteworthy result is that the differ- uses data for four popular non-cap-weighted indices in ence between returns of the best- and worst-performing the U.S. universe over a relatively short time horizon for strategies is substantial and can be as large as 15%. This which data for all of these indices are available. means that no model can pretend to be uniquely supe- It appears that even in a relatively short span of rior. Rather, different models are apparently favored by nine years no single strategy consistently outperforms all different market conditions, and there is always a risk other strategies, even though all four strategies show out- that the chosen model may not yield attractive perfor- performance with respect to cap-weighted indices more mance in a given period. often than they show underperformance. Considering For investors who are agnostic about either their half-year returns, depending on the market conditions, capacity to identify the model with superior assumptions each of the four strategies has ex post been the best-per- or their capacity to take the risk of choosing a particular forming strategy for some subperiod. Also, the worst- model in the wrong market conditions, it may be rea- per forming strategy in one subperiod can be the best sonable to assess whether anything can be gained from performer in the subsequent subperiod, and vice versa. combining models and thus diversifying model selection For example, across two half-year periods from July 2008 risk; see, for example, Kan and Zhou [2007] for a related to June 2009, the equal-weighted strategy went from discussion about combining portfolio strategies. We underperforming the cap-weighted index by –4.53% explore this question in some detail in the next section.