A pension fund manager is considering three mutual funds. The first is a stock f
ID: 2612685 • Letter: A
Question
A pension fund manager is considering three mutual funds. The first is a stock fund, the second is a longterm government and corporate bond fund, and the third is a T-bill money market fund that yields a sure rate of 5.5%. The probability distributions of the risky funds are: The correlation between the fund returns is 15. What is the expected return and standard deviation for the minimum-variance portfolio of the two risky funds? A pension fund manager is considering three mutual funds. The first is a stock fund, the second is a longterm government and corporate bond fund, and the third is a T-bill money market fund that yields a sure rate of 5.5%. The probability distributions of the risky funds are: The correlation between the fund returns is 15. What is the reward-to-volatility ratio of the best feasible CAL?Explanation / Answer
Particular
Expected Return
Standard Deviation
Stock Fund
15 %
32 %
Bond Fund
9 %
23 %
Correlation = 0.15
We will generate the covariance matrix as follows.
Bond Fund
Stock Fund
Bond Fund
529.00
110.4
Stock Fund
110.4
1024
Minimum Variance Portfolio Wmin (S) = [2 (B) – Cov (B,S)]/ 2 (B)+ 2 (S)- 2 Cov (B,S)
Wmin (S) =( 529-110.4)/ 1024+529-220.8
Wmin (S)= 0.3142
Hen Wmin (B) = 0.6858
Expected Return = 0.3142 x 15 + 0.6858 x 9
Expected Return= 10.8852 %
(min) = [ Ws2 2s + WB2 2B+ 2 WS WB Cov (B,S) ]0.5
Standard Deviation = 19.94 %
(2)
Optimal proportion of bond and stock fund will be as follows.
W(s) = A/B
Where
A = [(Es –Rf) 2B- (Eb –Rf) Cov (B,S)]
B= [(Es –Rf) 2B + (Eb –Rf) 2s- {Es- Rf + Eb –Rf } Cov (B,S)
W (S)= 0.6466
W(B)= 0.3534
Optimal CAL= (Expected return of portfolio – Risk Free return)/ Standard deviation of portfolio
Particular
Expected Return
Standard Deviation
Stock Fund
15 %
32 %
Bond Fund
9 %
23 %
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