The most fundamental aspect of classic Standard Asset Pricing theory is that there is a positive correlation between risk and reward in capital markets. In other words, it is generally believed that in order to achieve a reward that is higher than the average market return a given investor must assume a risk level (known as “beta”) that is higher than the average market risk level (known as “alpha”). This theory is a basic tenet of both single factor models such as CAPM (Capital Asset Model), multi-factoral models such as ICAPM (Inter-temporal Capital Asset Pricing Model) and even arbitrage models such as the Arbitrage Pricing Theory.


Yet in a recent piece Lionel Martellini, Professor of Finance at EDHEC Business School, discusses the fact that some recent empirical research does not support the positive risk-ward correlation.

As Martellini notes:

…a number of older as well as more recent papers have reported a series of puzzling, or at least, contrasted findings from an empirical perspective. First, the “low beta anomaly” stipulates that the relationship between systematic risk as measured by a stock beta and return is much flatter than predicted by the CAPM (see early papers by Black (1972), Black, Jensen, and Scholes (1972), as well as Haugen and Heins (1975), who claims that the relationship was not merely flat in their sample period, but actually inverted).

More recently, Ang, Hodrick, Xing, and Zhang (2006, 2009) have drawn new attention to these results with a focus on the specific risk component, finding that high idiosyncratic volatility stocks have had “abysmally low returns” in longer U.S. samples and in international markets. This result is now widely known as the “idiosyncratic puzzle” or “iv puzzle” in short. Yet other papers have documented a rather flat or even negative relationship between total (as opposed to specific) volatility and expected return, an anomaly that some call the “total volatility puzzle”, or “tv puzzle” in short.

In Finance, this result is almost equivalent to physicists finding that acceleration and gravity are no longer related. If it holds true, then it would call into question an endless number of investment strategies that base their existence on the principle that an investor must be willing to assume higher levels of specific risk in order to expect a higher-than-average return. Furthermore, it would suggest that there may be some intrinsic flaw in our most basic understanding of how capital markets function. As Martellini notes with some understatement:

That we are left with such a puzzling picture regarding the exact nature of the risk-return relationship, and that we do not have a clear idea regarding whether it is positive, flat or even negative, is rather surprising, and somewhat embarrassing, given that a fair understanding of this question is of central importance in both asset pricing theory and investment practice.

So what is the explanation, or possible explanation, for what is commonly referred to as the “low beta anomaly”? Martellini points out that there are two general approaches to dealing with these unexpected observations. The first approach tries to explain the puzzle, i.e., this group of researchers tries to understand and explain why high risk strategies did not yield higher than average returns. The second group argues that the studies (and/or their data) are simply wrong, and that the low-beta anomaly is just that — an anomaly caused by flawed or incomplete data/research that, with the proper methods, can be made to fit the traditional risk-reward paradigm.

Personally, I would find the existence of a negative or even neutral risk-reward paradigm amazing. It’s easy to understand that most high-risk strategies will not yield high-returns, precisely because they are high risk. But to conclude that capital markets systemically do not reward higher risk taking with higher rewards would be a remarkable conclusion to accept. That said, the positive paradigm is not an absolute, then the answer to the puzzle might lie in some dynamic which we have not considered before. For example, perhaps there is some “risk concentration point” where too much risk begins to turn on itself, inverting the risk-reward relationship. This would be kind of like a financial “black hole” — a place where forces that normally produce outcome A suddenly produce outcome -A.

Whatever the answer, this is both a fascinating problem for risk specialists and, and it will be interesting to see how this research unfolds. As the EDHEC article notes:

The debate about the low volatility puzzle has important practical implications. Different priors, such as “all stocks have the same expected returns”, or “more risky stocks have lower expected returns” or “more risk stocks have higher expected returns”, will indeed lead to different proxies for the optimal tangency portfolio every rational risk-averse investors will want to hold according to modern portfolio theory.

Any time empirical data do not support one of a field’s fundamental theories, eyebrows will be raised and questions asked. The risk-return question is so basic to modern Finance and investment that one hopes further work will proceed quickly to settle this issue once and for all. In the meantime, everything we know about risk-reward may not be everything we thought it was.

Read more:


Posted by Carlos Alvarenga

Carlos Alvarenga is the Executive Director of World 50 ThinkLabs and an Adjunct Professor at the University of Maryland's Smith School of Business.

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