One of the first things you teach someone in finance, or even economics, is that risk is related to return. You can only get higher returns by taking higher risk. True enough. But is it true 'on average': more risk, more return? If not, why not? A recent working paper downloadable at the SSRN, Why Risk is Uncorrelated with Return addresses this issue.

In finance there’s a specific definition of risk relating to the covariance of an asset with some nondiversifiable factor (eg, the market portfolio, a metric of total financial and human capital). Developed in the 1960’s, it’s the crowning achievement of finance, an integration of statistics with utility theory. It’s elegant, relatively simple, and slightly surprising (idiosyncratic risk is not priced). But it’s also empirically vacuous. Even die-hard efficient markets proponents agree that however betas are measured, they don’t generate a nice scatter plot with increasing returns (let alone linear in the factor sensitivity).

The failure of beta for cross-sectional equity pricing is but one example of the failure of the risk-return theory (assumption?). 30-year bonds have the same returns as 3-year bonds on average, in spite of considerably higher volatility, beta, and a negative correlation with inflation. Private investments that are intrinsically undiversified positions due to agency issues—franchises and the like—produce no premium over the S&P500. Recent papers have documented that traditional high risk areas—distressed securities in danger of bankruptcy, high idiosyncratic volatility, or firms with greater earnings forecast dispersion—generate lower returns than average. Corporate bonds show no reward for taking on credit risk (current B-rated yield spreads are below their expected loss and therefore should generate below AAA-rated net returns). Add to that diverse findings, such as that lower variance G-rated movies generate higher returns and less variance than R-rated movies, or that long-shots have the lowest net payout at the racetrack, or that long-shot lotteries are more popular than lower-risk/higher-payout lotteries, and it appears that there is either no correlation with 'risk' as traditionally defined, or a negative one.

This all reminds me of the theory of aether, a substance that supposedly permeated the universe and was consistently found absent. In the late 19th century a good way to academic success was to invent refinements that explained why it couldn't be measured, much like current papers that prove that under certain conditions, there's no beta correlation to return (of course, these then fail in their other implications, such as Roll and Ross's critique that mismeasuring the market generates no return correlation to beta, but as the correlation between idiosyncratic variance and returns is actually negative, this wrecks that angle because idiosyncratic variance should pick up mismeasured factor loadings). To these people, risk is like facial recognition, something common and intuitive yet exceedingly difficult to model abstractly. The Michelson-Morley experiment of our field was Fama-French in 1992, confirming what researchers all knew, and since then everyone accepts the empirical failure of CAPM as the rule, not the exception. Isn't data the ultimate arbiter of theory?

In the paper, my alter-ego explains this as a consequence of people caring about their relative status, rather than absolute wealth. In such an environment, nondiversifiable risk becomes like diversifiable risk in the traditional CAPM, avoidable, so unpriced. All you have to do is assume people care about relative wealth and using arbitrage or utility theory, risk is not related to returns. A beta=0 asset has the same risk as a beta=2 asset to someone benchmarked against the market. The paper presents a simple model, and goes over the empirical evidence with copious references.

There’s actually been quite a few models using a relative status approach for various parochial problems, so it’s not novel in that aspect, it just takes the approach to the general problem of risk and return. And all the general normative implications for volatility retain, including the desire to hedge, or buy insurance (though not, say, Global Warming insurance). There is one big seemingly counterfactual implication: that the equity risk premium is zero. I address this by noting that the equity risk premium used to be estimated at around 8%, and is now generally estimated around 3.5%, so another 3.5% is not farfetched. Further, that estimate ignores transaction costs, and peso-problems in equity indices, which takes this to zero (is the marginal investor the Vanguard500 investor? A high volume/expense day trader? A 5% front-load paying granny?). It should be noted that the traditional model generates only a 0.35% risk premium for plausible parameters, so this isn't as contrary as it seems (any outside-the-box refinement to the traditional model could well be applicable to this one).

Love of power over men (and the implied greater access to women regardless of aggregate wealth) is a base instinct no less petty or universal than greed. Economists should not shirk the implication because as dismal scientists, we draw the line at greed, not envy. It’s not a normative theory, just a positive one (ie, descriptive, not prescriptive). Not only can a relative status utility function explain the absence of the risk aether’s effects in markets, but it can potentially explain other issues, such as the home bias (people are more concerned about their income relative to their countrymen, not the world), endogenous instability (a world where ‘no risk’ is defined as what everyone else is doing has some arbitrariness), and why aggregate happiness is stagnant in countries 5 times as wealthy as 70 years ago (the rat race is unaffected). Rick Harbaugh has a paper where a similar approach generates the utility function of Prospect theory, which is typically just asserted as a funky preference. So there's much to be gained, and only empirical embarrassment to lose (plus all those canned presentation about CAPM given to students).