Question

explain why CAPM beta is thought to be a more relevant measure of risk than standard deviation for a well-diversified investor

Answer 1

Beta measures the volatility a stock adds to a diversified portfolio, standard deviation is the volatility if the stock is the only asset in your portfolio. So Beta is more important if you plan to hold a diversified portfolio, standard deviation is more important if you plan to put all your wealth into one stock.

Stock Beta (SB)
This indicates the volatility of a stock in relation to the overall market trend. A beta of less than 1 means that the security will be less volatile than the market. A beta of greater than 1 indicates that the security's price will be more volatile than the market. For example, if a stock's beta is 1.2, it's theoretically 20% more volatile than the market.

Standard Deviation (SD)
This is a historical report of the volatility of stock over a period of time in the past. It is usually used to predict future volatility


From the above, we can understand that SD is historical trend of SB.

Since you are interested in investing NOW, the current beta is more important than what happened in the past. The past (SD) may indicate how the SB will be, but if you have a sure method to know the SB, you are way much better off than those who invest by looking at SD and trying to predict future movement.