Consider a portfolio with two assets. Asset A comprises 25% of the portfolio and has a standard deviation of 17.9%. Asset B comprises 75% of the portfolio and has a standard deviation of 6.2%. If the correlation of these two investments is 0.5, the portfolio standard deviation is closest to:
B is correct. The standard deviation of a two asset portfolio is given by the square root of the portfolio’s variance: σP= √(w1 2σ1 2 + w2 2σ2 2+ 2w1w2ρ1,2σ1σ2 )
Using the above formula, the existing standard deviation is calculated as follows:
√( 0.252×0.1792 + 0.752×0.0622+ 2×0.75×0.25×0.5×0.179×0.062)= 7.90%.