Another risk-reward calculus.

Photographer: Brent Lewin/Bloomberg

High Risk, High Returns? Not Quite.

Noah Smith is a Bloomberg View columnist. He was an assistant professor of finance at Stony Brook University, and he blogs at Noahpinion.
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For many years, investors have been told that risk and return are correlated. In a broad sense, history seems to bear that out -- the stock market, which fluctuates a lot more than the bond market, has yielded higher long-term returns. In a narrow sense, this principle -- the risk-return tradeoff -- is the basis of almost all academic theories of the value of financial assets. It makes sense, after all -- if something is risky, people generally won't buy it unless it also offers chances for big winnings. 

But how do you measure the riskiness of an asset? Finance theorists say that risk comes from big, broad factors, like the swings in the overall market. For example, take the capital asset pricing model, or CAPM. This is the most common and universal asset-pricing theory -- it garnered a Nobel Prize in economics, and it's where we get the terms "alpha" (marketing-beating returns) and "beta" (market-matching returns). This theory says that since you can diversify your portfolio, an asset's fluctuations don't really matter unless they also coincide with the fluctuations of other assets. If one of your stocks crashes but the other 39 do fine, you're safe, as long as that one stock wasn't a huge chunk of your portfolio. But if all 40 of your stocks crash together, you're in trouble (especially if you have to retire soon). An asset's true riskiness, therefore, is the degree to which it swings up and down when the whole market swings up and down. 

This same idea is present in most other asset-pricing theories, including the "multifactor models" that have replaced the CAPM as the industry standard in recent years. In all of these models, an asset's idiosyncratic volatility -- the amount that it fluctuates on its own, apart from other assets -- shouldn't matter, since you can just diversify your portfolio. 

There's just one problem with these theories: They don't seem to fit the data. A stock's idiosyncratic volatility matters a lot for how much it's worth. And weirdly, it seems to matter in the wrong direction. Stocks that fluctuate a lot, independently of the overall market, have worse returns than other stocks. 

This is called the low volatility anomaly, and it's been bedeviling financial economists for a decade. It all started in 2006, when Andrew Ang, Robert Hodrick, Yuhang Xing and Xiaoyang Zhang wrote a paper declaring that "[S]tocks with past high idiosyncratic volatility have abysmally low returns, but this cannot be explained by exposure to aggregate volatility risk." They found that none of the standard explanations for strange stock behavior -- for example, the ease with which it can be bought or sold -- altered the result. Three years later, the authors released a second paper, showing that the same result was true internationally. 

That idiosyncratic volatility is important would be troubling for finance theory, but not insurmountable;  the authors find that there are periods of time when low-volatility stocks tend to  do well and periods where they tend to do badly, implying that the pattern might be related in some way to overall business conditions. But the really weird thing is the way in which volatility matters. 

People ought to be compensated for taking risks. Higher risk should equal higher average return. But when it comes to volatility, low risk equals high return. You get paid more not to take risk! That flies in the face of everything finance theorists believe. 

Since those papers came out, a whole host of academics have tried to explain the anomaly in ways that make sense to finance theory as a whole. One team of academic and private-sector economists noted in 2013 that it's very hard to take advantage of the anomaly for practical trading purposes -- constantly buying and selling stocks as their recent volatility changes will rack up big transaction costs. A 2010 paper by two economists from the University of Texas-Dallas shows that although short-term volatility yields low returns, long-term volatility actually yields high returns. 

These findings seem to go together. If short-term volatility is something to avoid, then taking advantage of the low volatility anomaly would require frequent trading, which leads to high transaction costs. But if this really is the resolution of the puzzle, it means that markets aren't very efficient in the short run. If anomalous market behavior can't be traded away, it means that prices will tend to deviate from long-term fundamental value. 

In other words, any way you slice it, this finding is troubling for standard finance theory. All of our understanding of the field is based on the unifying theory of efficient markets and the risk-return tradeoff. But it looks as if that that understanding is not yet complete. 

This column does not necessarily reflect the opinion of the editorial board or Bloomberg LP and its owners.

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Noah Smith at

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