VOLUME 39 NUMBER 4 www.iijpm.com SUMMER 2013 The Surprising Alpha From Malkiel’s Monkey and Upside-Down Strategies ROBERT D. ARNOTT, JASON HSU, VITALI KALESNIK, AND PHIL TINDALL The Voices of Influence | iijournals.com JPM-COVER.inddCov103286.indd 11 16/07/138/5/13 10:471:16 PM AM The Surprising Alpha From Malkiel’s Monkey and Upside-Down Strategies RobeRt D. ARnott, JAson Hsu, VitAli KAlesniK, AnD PHil tindall RobeRt D. ARnott nvestment practitioners and many aca- intuitively, when we invert these strategies, the is the chairman and CEO demics are understandably preoccupied resulting portfolios continue to display value of Research Affiliates, LLC with identifying stock characteristics and and small cap bias. We demonstrate this para- in Newport Beach, CA. [email protected] strategies that offer the prospect of high doxical effect mathematically in Appendix A. Irisk-adjusted returns. Many sensible invest- The results we present are puzzling JAson Hsu ment beliefs, when translated into portfolio until one grasps the derivations in the litera- is the CIO at Research weights, result in historical outperformance ture, starting with Berk [1997]. Berk [1997] Affiliates, LLC in Newport relative to the cap-weighted benchmark. and Arnott et al. [2011] argue that low prices Beach, CA, and adjunct The naive expectation is that, when we create size and value effects. Berk ascribes this professor of finance at Anderson School of invert the weighting algorithms of these sen- to hidden risk factors; Arnott et al. [2011] Management at UCLA. sible investment heuristics, effectively turning ascribe this to mean-reverting errors in price. [email protected] them upside down, these inverted strategies Either way, falling prices lead to low book- should underperform by roughly as much as to-market ratios and low market capitaliza- VitAli KAlesniK the original algorithm outperformed. Instead, tion; whenever prices mean-revert, value is a senior vice president and head of equity research we find that these upside-down strategies also and small stocks outperform. Hsu [2006] at Research Affiliates, LLC beat the cap-weighted benchmark, often by and Arnott and Hsu [2008] offer a concep- in Newport Beach, CA. more than the upright originals. Indeed, even tual framework where non-price-weighted [email protected] a portfolio generated by Malkiel’s blindfolded portfolios, which contra-trade against price monkey1 throwing darts outperforms the changes at each rebalancing, necessarily result PHil tindall market.2 in value and size tilts, regardless of the weighting is a senior investment con- sultant at Towers Watson How can it be that a monkey—who method chosen. Limited in Westminster, may have great skill with darts, but presum- In summary, value and small-cap expo- London, UK. ably has no skill in evaluating investments— sures are naturally occurring portfolio char- [email protected] adds value? Our findings suggest that the acteristics, unless an investor constructs a investment beliefs upon which many invest- portfolio to have a positive relationship between ment strategies are ostensibly based play little price and portfolio weights. In this article, we or no role in their outperformance.3 illustrate these theoretical results with simple, This does not mean that these strategies’ easily replicable portfolio back-tests. We do not outperformance is suspect. Rather, as it turns attempt to comment on the interesting debate out, these investment beliefs work because regarding the nature of value and small-cap they introduce, often unintentionally, value premiums. and small cap tilts into the portfolio. Counter- Summer 2013 The Journal of PorTfolio ManageMenT RESEARCH DESIGN We rebalance all portfolios annually, on the last trading day of the year. We back-test the portfolio This research is motivated by the proliferation of schemes using as much historical data as are available in quasi-passive equity index strategies and their note- the CRSP/CompuStat merged database for the United worthy long-term outperformance against traditional States, and the Worldscope and Datastream databases for cap-weighted benchmarks in back-tests, despite some- other developed countries. When necessary for portfolio times diametrically opposed investment beliefs. This construction, we estimate the risk parameters, such as leads to a natural skepticism. It’s hard to believe that they variances and covariances, using the previous five years could all work, in light of the longstanding literature on of monthly data. For example, for a covariance-based the mean-variance efficiency of the cap-weighed bench- strategy portfolio for 2003, we will use the sample cova- mark and the underperformance of active management. riance matrix from 1998 to 2002.10 Appendix B contains However, the empirical evidence from domestic and a strategy summary. global market data, which extend back as far as data are We break our analysis into five categories. available, suggests a robust outperformance.4 Our examination of this puzzle starts with portfo- Reference Portfolios lios formulated from an array of arguably sensible invest- ment beliefs. We then invert these beliefs to create less We establish two reference portfolios. Our first intuitive strategies. In inverting the strategies, we tacitly reference portfolio is the cap-weighted portfolio, which examine whether these strategies outperform because most people consider a reasonable representation of they are predicated on meaningful investment theses and the market. Exhibit 1 summarizes key attributes of the deep insights on capital markets, or for reasons unrelated U.S. cap-weighted portfolio, using data from 1964 to to the investment theses. If the investment beliefs are 2012. the source of outperformance, then contradicting those The second line of Exhibit 1 displays the equal- beliefs should lead to underperformance. weighted (EW) portfolio, which represents perhaps For each of the investment beliefs, we create long- the strongest level of investor naiveté, tacitly believing only equity portfolios using simple weighting heuristics. that all stocks have identical expected returns and risk We then turn them upside down. For each quasi-index attributes. This makes EW an interesting and sensible strategy, we form two inverse portfolios: 1) an inverse secondary reference portfolio. One might also interpret ratio portfolio, formed by normalizing the inverse weight EW as an effective approach for capturing stock-price 1/w and 2) an inverse complement portfolio, formed mean reversion where, at each rebalancing, the portfolio by normalizing the original portfolio’s complementary mechanically buys stocks that have fallen in price relative 5 weight (max(w)-w). Except for some special situations, to others—unless they’ve fallen so far that they no longer the two inverse portfolios generally have comparable make the size cut for the country—and sells stocks that characteristics. We also compute portfolios based on have risen in price relative to others. 6 Malkiel’s blindfolded dart-throwing monkey. The EW portfolio produces 180 basis points To ensure that we invest in sufficiently liquid stocks, (bps) per year of incremental performance over the we restrict our universe to the largest 1,000 U.S. stocks by cap-weighted reference benchmark. This incremental 7 market capitalization. We extend the analysis to global performance is almost entirely due to substantial size markets at both an individual country level and a global and value factor loading; EW delivers a 0.15 percent portfolio level. For the global country portfolios, we use annualized FF4 alpha, with no statistical or economic the largest stocks by market capitalization, matching the significance. Throughout this article, it will become number of stocks to the most popular local cap-weighted increasingly clear why the EW portfolio is a sensible 8 benchmark indices. The global country results are gen- reference benchmark for other non-price-weighted erally qualitatively similar to the U.S. results, but often strategy indices. with a considerably larger magnitude of CAPM and Fama–French Four Factor model (FF4) alpha.9 The SurPriSing alPha froM Malkiel’S Monkey and upside-down STraTegieS Summer 2013 1 i b i t H x e Strategies, Inverse and Random Portfolios: United States (1964–2012) Performance Summary, Source: Research Affiliates, based on CRSP/Compustat data. Summer 2013 The Journal of PorTfolio ManageMenT Favoring High-Risk Stocks in our Portfolios variance, with roots dating back to the late 1960s, is the first among many.11 The CAPM Capital Market Line is Given the theoretical and empirical links between empirically flatter than theory would predict. Indeed, risk and return, one might expect a link between higher empirically, it often is downward sloping: in many mar- returns and higher-risk stocks. A naive way to act on this kets, we find that low-volatility stocks produce higher belief, for investors willing to accept higher risk in the returns than do high-volatility stocks. The minimum- quest for higher returns, would be to build a portfolio variance (MinVar) portfolio represents a simple strategy that tilts toward more volatile stocks, or higher-beta for capturing this anomaly. stocks, or stocks with higher downside semi-deviation. Well-respected quantitative index providers We might expect these strategies to earn higher port- have introduced two other new strategies, which lean folio returns, rewarding us for our willingness to bear heavily on the Markowitz mean-variance optimization one of these types of incremental risk. This investment framework. The risk-efficient index assumes, among belief anchors our second set of strategies: weighting a other things, that stock returns are related to downside portfolio proportional to conventional risk measures, semi-variances. The maximum-diversification index such as market beta, volatility, or downside semi- portfolio, on the other hand, assumes a linear relation- variance of the constituent stocks. The second block ship between stock returns and volatility. These differ of Exhibit 1—labeled “High Risk = High Reward”— from our earlier exploration of weighting in propor- explores these three strategies and their inverted forms.