Question

Is it possible that a security with a positive standard deviation of returns could have a beta of zero (excluding T-bills)? Explain. From the CAPM, what is the expected return on such an asset? Is it possible that a security with a positive standard deviation could have an expected return from the CAPM that is less than the risk-free rate? If so, what would its beta be? Would anyone be willing to purchase such a stock? Discuss.

Answer 1

Beta of a security is related to the riskiness of the asset. In case the secutiry has a positive standard deviation and a beta of zero, the rate of return would be

Rate of return = Rf +  Beta * (Rm-Rf)

Rm = Market rate of return , Rf = Risk free rate

Given that Beta is zero, the rate of return would be equal to risk free rate (typically T Bills). The security would not have a positiver standard derviation of returns since the rate of return is same as risk free rate.

It is also possible for a security with positive standard deviation to have a negative beta (Beta < 0) resulting in a return lower than the risk free rate. This would be a contra security with negative correlation to the markets e.g. Gold, which tend to appreciate in a negative markets. Investors would look to purchase such stocks as a hedge in their portfolio where in case the market declines, these stocks would appreciate and reduce the negative impact on the portfolio.