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

standard deviation of your portfolio = 21.35%

Explanation:

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%

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