|
|
|
|
|
|
From: Stephen Gould
Affiliation:
Address: srg@ms.com
Date: 02 Jul 1998
Time: 15:51:55
Short answer : CAPM states expected return is sum of risk-free rate and (stock beta times market risk premium), hence for zero beta, stock return equals the risk-free rate.
More intuitively, suppose we have a large number of independently performing (i.e. uncorrelated) assets that behave therefore like pure random variables (like dice) and would therefore have zero betas. As more and more assets are acquired (portfolio diversification) the effect of individual out/underperformances (high/low rolls) is swamped by the total returns of all the assets (throwing a 6 on one of 2 dice has a major impact on the total expected sum, but throwing a 6 on one of 100 dice has almost no effect on the total expected sum). If we call each specific under- or over- an "error" (this is specific risk) then total (expected) error as a proportion of the total return declines as more dice are thrown/assets acquired, tending to zero in the limit. (This last paragraph is a non-rigorous intepretation of the central limit theorem)
If all these random assets individually had expected returns higher than the risk-free rate then buying enough different assets to eliminate the effect of individual specific risk would give us a risk-free portfolio with expected returns higher than the risk-free rate, which is theoretically impossible and in practice would give arbitrage opportunities. So efficient investors would buy the assets until the prices had risen so that the expected returns would not exceed risk-free. Hence zero beta assets have expected returns equal to risk-free IN THEORY.
In practice, low-beta high-specific risk stocks do tend to show higher than expected returns, possibly because enough investors are not sufficiently diversification-efficient,or because there is no law of physics that requires that CAPM or APT actually work in real markets.
|
|
