Will the standard deviation of returns on the mutual fund that has a beta equal to 0.75 be less than the standard deviation of market returns?
The beta of a mutual fund is the correlation between the return given by the market and that given by the mutual fund. A mutual fund with a beta equal to 1, would give a return equal to the market return. The loss incurred by an investor in the mutual fund is also the same as the loss incurred by the market.
A higher value of beta implies a larger gain than the market when the market rises and a larger loss than the market when the market falls. The standard deviation of returns increases with the value of beta.
For a mutual fund with a beta equal to 0.75, the return of the mutual fund is lower than the return of the market, but the standard deviation of returns of the mutual fund is also lower than that of the market.