Swedroe: Risk & The Two Faces Of Beta

How investors experience risk fuels different, but related, versions of beta, Swedroe says.

There’s a growing body of evidence that beta is actually a two-sided, not a one-sided, “coin,” and those two faces are separated by perceptions of risk.

Being risk averse, most investors care more than just about the standard deviation of returns (volatility), assigning more weight to downside deviations from the mean than to upside deviations. They also care about when that volatility appears.

Thus, assets that do poorly in bad times, such as in recessions when labor capital risk increases, should carry large risk premiums. In other words, that’s a risk-based explanation for the value premium, as well as the momentum premium. And that’s what the research is showing.

Thierry Post, Pim Van Vliet and Simon Lansdorp, authors of the 2009 study “Sorting Out Downside Beta,” found that depending on which of the three measures they used to measure downside risk, from 1963 through 2009, the downside beta was estimated to be 3.6 to 7.6 percent per year for downside beta, compared with 0.8 to 4.6 percent for regular beta.

The authors concluded: “When properly defined and estimated, [downside beta] is a driving force behind stock prices. Risk aversion thus not only helps to explain why stocks yield higher average returns than safer asset classes, but also why high-risk stocks yield higher average returns than low-risk stocks, ceteris paribus.”

Similarly, Joseph Chen, Andrew Ang and Yuhang Xing, authors of the 2006 study “Downside Risk,” found the downside risk premium to be about 6 percent per year. And it wasn’t simply compensation for regular market beta—nor was it explained by co-skewness or liquidity risk, or size, book-to-market, and momentum characteristics. The exception to their findings was that the highest-volatility stocks—about 4 percent of the market—had poor returns regardless of their exposure to downside risk. It seems to me the likely explanation is the well-known investor preference for “lottery tickets.”

A new study by Peter Xu and Rich Pettit, “No-Arbitrage Condition and Expected Returns When Assets have Different B’s in Up and Down Markets,” that appears in the February issue of the Journal of Asset Management, adds to the body of evidence on downside beta being an independent-priced risk.

Using data from 1985 through 2012, they found that “the risk premium on the downside β is 6.6 per cent per year, with a t-statistic of 18.8. The positive and very significant risk premium on the downside β indicates that investors demand higher returns for holding stocks with larger downside β’s.”

They also found that the different beta premiums can be expressed in terms of the price and expected payoff of a call and a put option, respectively, on the market index. For the upside β, the higher the price of the call option relative to its expected payoff, the smaller the risk premium; but for the downside β, the higher the price of the put option relative to its expected payoff, the larger the risk premium.

They concluded that their model provides a useful perspective on what systematic risks are and how they are priced.

All of the evidence is consistent with the economic theory that investments that perform poorly in bad times should carry larger risk premiums. The higher return to stocks with high downside betas is compensation for accepting that risk.

Larry Swedroe is director of Research for the BAM Alliance, a community of more than 130 independent registered investment advisors throughout the country.