Journal Papers

The Surprising Alpha From Malkiel's Monkey and Upside-Down Strategies

By Rob Arnott Jason Hsu Vitali Kalesnik

AUGUST 2013 Read Time: 30 min


Executive Summary

The authors provide empirical evidence to reach the surprising conclusion that, contrary to popular wisdom, the investment beliefs on which many well-established strategies are based play little or no role in their outperformance vis-à-vis capitalization-weighted benchmarks. The authors reach this striking result by inverting the popular strategies’ weighting algorithms and find these inverted strategies produce equal or better outperformance. Interestingly, so does any random stock selection strategy, even a monkey throwing darts at the Wall Street Journal to select stocks!

The implication of these findings is that many of the plausible investment beliefs held by investment professionals are nothing more than good stories. The key insight is that many active portfolio returns are largely driven by value and small-cap exposures, which are naturally occurring characteristics unless the portfolio, like the cap-weighted benchmark, is explicitly designed to have a positive relationship between security prices and weights. These results have an important practical implication: investors should make investment decisions based on strategy factor exposure as well as implementation characteristics rather than on the stories told about the strategies.

The authors’ research design is straightforward. Restricting the US universe to the 1,000 largest stocks by market capitalization, they construct three sets of portfolios. The first set simulates high-risk/high-reward strategies, including volatility-weighted, market beta-weighted, and downside semi-deviation weighted portfolios. The second set contains optimization-based strategies, including minimum-variance, maximum-diversification, risk-efficient, and equal-weighted risk cluster portfolios. The third set includes strategies that weight holdings on the basis of accounting measures, including book value, five-year average earnings, earnings growth, and the classic fundamental indexation method described in Arnott et al. (2005). In addition, the authors construct two reference portfolios, one cap-weighted, representing the market, and the other equal-weighted. Using the merged CRSP/CompuStat database, the authors back-test the hypothetical US portfolios with annual rebalancing over the period 1964–2012.

The researchers invert the portfolios’ weighting algorithms in two ways: they construct inverse ratio portfolios by normalizing the inverse weights (1/w) and inverse complement portfolios by normalizing the original portfolios’ complementary weight (max(w)-w).

In his classic 1973 book, A Random Walk Down Wall Street (now in its 12th edition), Burton Malkiel states that “a blindfolded monkey throwing darts at a newspaper’s financial pages could select a portfolio that would do just as well as one carefully selected by experts.” To test this claim, the authors ape Malkiel’s monkeys by annually picking 100 random, equal-weighted 30-stock portfolios.

In summary:

  • The equal-weight reference portfolio’s annualized rate of return over the 49-year measurement period outpaced the cap-weighted benchmark return by 1.80%.
  • The high-risk/high-reward portfolios’ return exceeded the cap-weighted benchmark returns by 2.23% to 2.49%, while the corresponding inverse portfolio returns surpassed the benchmark returns by 2.78% to 3.81%.
  • The optimization-based portfolios beat the cap-weighted benchmark by 1.51% to 2.83%; their inverses, by 2.67% to 3.57%.
  • The fundamentals-based portfolios’ returns outperformed the cap-weighted benchmark by 1.52% to 2.76%; their inverses, by 0.59% to 4.39%.
  • The 100 random portfolios (the simulated simian portfolios) earned, on average, a value-added return of 1.60% over the cap-weighted benchmark return.


Paradoxically, the upside-down strategies generally performed better than the sensible right-side-up strategies, achieving not only higher returns but also higher Sharpe ratios, information ratios, and CAPM alphas.  

To explain these results, the authors conduct performance attribution analyses of the original and inverted portfolios using the Fama–French four-factor model (FF4). The factors are market beta, size (SMB), value (HML), and momentum (UMD). In all but one of the portfolio sets, the analysis reveals meaningful value and/or small-cap tilts with no statistically significant net FF4 alpha. The exception was that a few of the inverted fundamentals-based strategies delivered statistically significant alpha, net of the factor effects. The significant alphas in these cases may be outliers, or they could reflect a risk factor that is missing from the FF4 model.

Using the Worldscope and Datastream databases, the authors extend their research to global developed markets for the period 1991–2012. With only one exception (market beta-weighted), all the original strategies added value; and again with but one exception (inverse-ratio earnings growth-weighted), the upside-down strategies also added value. Eighteen of the 22 inverted portfolios outperformed the underlying originals.

In view of the compelling US and global evidence that both sensible and nonsensical strategies outperform for the same reasons (value and small-cap biases), the authors conclude that potential investors would do well to base strategy selections largely on a comparison of explicit and implicit implementation costs due to portfolio turnover. 

Summarized by Philip Lawton, CFA

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