Risk is not empirically correlated with return

The most widely appreciated finance theory is the Capital Asset Pricing Model. It basically says that diminishing marginal utility of absolute wealth implies that riskier financial assets should have higher expected returns than less risky assets and that only risk correlated with the market (beta risk) is a whole is important because other risk can be diversified out.

Eric Falkenstein argues that the evidence does not support this theory; that the riskiness of assets (by any reasonable definition) is not positively correlated with return (some caveats apply). He has a paper (long but many parts are skimmable; not peer reviewed; also on SSRN) as well as a book on the topic. I recommend reading parts of the paper.

The gist of his competing theory is that people care mostly about relative gains rather than absolute gains. This implies that riskier financial assets will not have higher expected returns than less risky assets. People will not require a higher return to hold assets with higher undiversifiable variance because everyone is exposed to the same variance and people only care about their relative wealth.

Falkenstein has a substantial quantity of evidence to back up his claim. I am not sure if his competing theory is correct, but I find the evidence against the standard theory quite convincing.

If risk is not correlated with returns, then anyone who is mostly concerned with absolute wealth can profit from this by choosing a low beta risk portfolio.

This topic seems more appropriate for the discussion section, but I am not completely sure, so if people think it belongs in the main area, let me know.

Added some (hopefully) clarifying material:

All this assumes that you eliminate idiosyncratic risk through diversification. Technically impossible, but you can get it reasonably low. The R’s are all *instantaneous* returns; though since these are linear models they apply to geometrically accumulated returns as well. The idea that E(R_asset) are independent of past returns is a background assumption for both models and most of finance.

Beta_portfolio = Cov(R_portfolio, R_market)/​variance(R_market)

In CAPM your expected and variance are:

E(R_portfolio) = R_rfree + Beta_portfolio * (E(R_market) - R_rfree)
Var(R_portfolio) = Beta_portfolio * Var(R_market)

in Falkenstein’s model your expected return are:

E(R_portfolio) = R_market # you could also say = R_rfree; the point is that its a constant
Var(R_portfolio) = Beta_portfolio * Var(R_market)

The major caveat being that it doesn’t apply very close to Beta_portfolio = 0; Falkenstein attributes this to liquidity benefits. And it doesn’t apply to very high Beta_portfolio; he attributes this to “buying hope”. See the paper for more.

Falkenstein argues that his model fits the facts more closely than CAPM. Assuming Falkenstein’s model describes reality, if your utility declines with rising Var(R_portfolio) (the standard assumption), then you’ll want to hold a portfolio with a beta of zero; or taking into account the caveats, a low Beta_portfolio. If your utility is declining with Var(R_portfolio—R_market), then you’ll want to hold the market portfolio. Both of these results are unambiguous since there’s no trade off between either measure of risk and return.

Some additional evidence from another source, and discussion: http://​​falkenblog.blogspot.com/​​2010/​​12/​​frazzini-and-pedersen-simulate-beta.html