A pension fund manager is considering three mutual funds. The first is a stock fund, the second is a long-term government and corporate bond fund, and the third is a T-bill money market fund that yields a sure rate of 4.1%. The probability distributions of the risky funds are: Expected Return Standard Deviation Stock fund (S) 11 % 33 % Bond fund (B) 8 % 25 % The correlation between the fund returns is .1560. Suppose now that your portfolio must yield an expected return of 9% and be efficient, that is, on the best feasible CAL. a. What is the standard deviation of your portfolio

Without mincing words, let's dive straight into the solution to this particular question. The following parameters are given in the question and they are:

The expected Return Standard Deviation Stock fund (S) = 11 % with standard deviation of 33%[=0.33] and the expected Return Standard Deviation Stock fund is 8% with standard deviation of 25 %[=0.25]. Also, it is given that the correlation between the fund returns = .1560.

STEP ONE: Determine the proportion of stock in minimum risky portfolio.

Therefore, the proportion of stock in minimum risky portfolio = [( 0.25)² - ( 0.33 × 0.25 ×.1560)] ÷ [ (0.33²) + (0.25²) - ( 2 × 0.33 × 0.25 × 0.156)] = 34.07%[=0.3407].

STEP TWO: Determine the proportion of bond fund in minimum risky portfolio.

The proportion of bond fund in minimum risky portfolio = 1 - 0.3407 = 0.6593 = 65.93.

STEP THREE: Determine the expected return of minimum risky portfolio.

The expected return of minimum risky portfolio = 0.3407 × 0.11 + 0.6593 × 0.08 = 0.0902= 9.02%.

STEP FOUR: Determine the standard deviation of your portfolio.

The standard deviation of your portfolio = [(0.6593²) × (0.25²) × (0.3407²) × (0.33²) + ( 2 × 0.6593 × 0.340 × 0.33 × 0.25 × 0.156)]^0.5 = 0.2135 = 21.35%