Let's say we have two stocks, Stock A and Stock B.
Both of them have the same standard deviation $\sigma$, and therefore have the same risk.
The only difference is that Stock A has a perfect positive correlation $\rho=1$ to the market ($\beta>0$), while Stock B has a perfect negative correlation $\rho=-1$ to the market of ($\beta<0$).
According to CAPM, Stock B should pay me less than the market risk-free rate while Stock A should pay me more. If both have the same amount of risk, i.e. standard deviation, then why does Stock B pay me less than Stock A?
I can only think of two reasons:
- There is less market supply of negative $\beta$ stocks than positive $\beta$ stocks, and therefore a higher price for negative $\beta$ stocks and lower returns.
- Since the market generally has positive returns (and a positive E[r]), a stock with a market correlation ($\rho$) of -1 has generally negative returns (and a negative E[r]).
Anyone care to give their opinion on this?