At the Belmont Stakes horse race coming up June 9, I’ll Have Another will attempt to become the 12th horse to win the Triple Crown. Now, I’m not a huge fan of horse racing, but the economist in me is always intrigued by what sporting events can teach us about investor behavior. In particular, I’m interested not in which horse wins the race but in how those who follow the races place their bets. Let me explain why – and how it applies to minimum volatility portfolios.
In an earlier blog post, I argued that equity minimum volatility portfolios are potentially a good replacement for a traditional equity investment in a cap-weighted market portfolio. Key to this claim is the fact that a wide range of empirical studies show that minimum volatility portfolios have performed equally well, if not better, than the market but have done so with lower risk.
Still, no matter the strength of the historical observation, I am continually asked whether minimum volatility portfolios can continue to perform as they have in the past. One way of answering the question is to focus on what are the sources of the performance of minimum volatility portfolios and make an assessment of their likely persistence
Today I want to discuss “behavioral” sources for the low-risk anomaly. “Behavioral” is a catch-all term that encompasses a wide range of theories of how people’s behavior appears to deviate from the theoretically ideal behavior when dealing with uncertainty.
My favorite example is what has been known since the 1950s as the “favorite/long-shot bias”[1]. This is the finding that people who bet on horse races bet on the long-shot horses more than would be justified by the actual odds of winning (and conversely bet less than they should on the favorite horses). The story generally goes like this: Horse-racing bettors have difficulty evaluating small differences in outcome probabilities, for example the difference between a 1-in-50 odds horse and a 1-in-100 odds horse. That’s a 2% probability of winning versus a 1% probability of winning. This results in a large proportion of bettors placing too high of a bet on the longer odds because the potential winnings appear larger in that case[2].
If I replace horses with stocks, you can see where this leads: Stocks with high beta (or high risk) may be “overbought” (leading to future underperformance) and vice-versa for low-beta (or low risk) stocks. While the various theories around this behavior can get complicated (as theory always does), there is a common theme: Investors have difficulty evaluating small differences in probabilities, particularly when large outcomes are possible. This results in an apparent preference for risky assets of various kinds, thus leading to their underperformance[3].
Why is this explanation interesting? It tells us that the “hurdle” for thinking that the low-risk effect may persist in the future could be similar to other factors that equity investors have already come to rely on, like momentum investing, which are tied to behavioral explanations.
There is an additional reason that the low-risk effect may persist. This is the fact that the widespread use of active-management benchmarks may induce money managers to prefer high-beta stocks even in the absence of any behavioral biases. More on this on my next post.
Daniel Morillo, PhD is the iShares Head of Investment Research and a regular contributor to the iShares Blog. You can find more of his posts here.
Past performance does not guarantee future results.
[1] Griffith, R. M. 1949. “Odds Adjustments by American Horse-Race Bettors.” American J. Psychology 62 (August): 290–94
[2] See, for example, “Explaining the Favorite-Long Shot Bias: Is it Risk-Love or Misperceptions?” Journal of Political Economy 2010, vol 118, no 4.
[3] See, for example, Barberis N. and Huang M. “Stocks as Lotteries: The implications of Probability Weighting for Security Prices”. American Economic Review 2008, 98:5 2066-2100.
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As with most “behavioural” explanations, I don’t like this one. It is purely descriptive: people favour highly skewed bets. The interesting part is why people behave this way. Is it rational or irrational?
Personally I prefer the relative-wealth concerns explanation for the minimum volatility anomaly because it also fits in with many other anomalous results in finance and economics (Easterlin, Zizzo & Oswald, etc.)
The “badly designed incentives for money managers” explanation may hold some water, but I don’t think it’s a real explanation either. They are not given money out of nowhere, and their incentives aren’t designed in a vacuum: investors actually value this approach to investing.
The above ideas are supported by the Mitton & Vorkink (2007) results that show that retail investors knowingly and deliberately sacrifice mean-variance optimality for increased skewness.
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Dan M: I can certainly relate to the concern that behavioral explanations are difficult to pin down in terms of linking a specific empirical result (say the low risk anomaly) and any one of the various potential behavioral theory candidates. However, the evidence for the presence of various forms of behavioral bias in the experimental economics literature is quite strong. So in general, I find it difficult to dismiss the potential link in the absence of competing explanations showing an ability to uniquely explain the phenomenon.
A preference for skewness does have some advantages to more traditional “prospect-type” explanations as you mention. But it is not obvious to me that it is straightforward to empirically distinguish it as the major cause of the low-volatility anomaly… Note that I make no value judgment as to whether prospect theory or skewness preferences represent “irrational” behaviour or not. Either way the result is the ability for some investors to benefit from the effect (implicitly in this analysis the investors who benefit evaluate their outcomes in a mean-variance way).
Among competing explanations, I find the broad category of “delegated asset management” explanations compelling partly because they allow for an extended form of the CAPM to still be useful in understanding market equilibria. That is something that is generally more difficult to do with explanations such as various forms of limits to arbitrage (e.g. the “leverage effect” whereby high beta securities act as a form of leverage in the absence of full access to shorting or leverage markets). These explanations are in a strict sense “rational” and the market can generally still be understood as efficient given the limits to arbitrage or the institutional setup that leads to delegated asset management choices.
As above, however, I see no reason to impose a “value judgement” on whether, for example, delegated asset management (and the attendant economic incentives for all involved) is good or not. After all, in the context of my original post I simply want to highlight that for investors who have mean-variance preferences and care about total returns and total risk, taking advantage of the low risk anomaly can potentially be an important component of their investment strategy.