Consider the following information in relation to a portfolio composed of Fund A and Fund B:
| Fund A | Fund B | |
| Portfolio weights(%) | 70 | 30 |
| Expected returns(%) | 10 | 16 |
| Standard deviations(%) | 7 | 13 |
| Correlation between the returns of Fund A and Fund B | 0.80 | |
The portfolio standard deviation of returns is closest to:
B is correct. First, calculate the covariance between Fund A and Fund B given the standard deviation of returns and the correlation between the two funds:
where
σ(RA) = 7%. This is the standard deviation of returns of fund A
σ(RB) = 13%. This is the standard deviation of returns of fund B
ρ(RA, RB) = 0.80. This is the correlation between the returns of Fund A and Fund B.
Cov(RA, RB) = 0.80 × 7% × 13%= 0.00728.
Then calculate the portfolio standard deviation of returns as follow:
where
WA= 70%. This is the weight of Fund A in the portfolio
WB = 30%. This is the weight of Fund B in the portfolio.
Alternatively, use correlation directly in the formula for portfolio standard deviation:
