A pension fund manager is considering three mutual funds. The first is a stock f
ID: 2773737 • Letter: A
Question
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 4.7%. The probability distributions of the risky funds are:
Suppose now that your portfolio must yield an expected return of 15% and be efficient, that is, on the best feasible CAL.
What is the standard deviation of your portfolio? (Do not round intermediate calculations. Round your answer to 2 decimal places.)
What is the proportion invested in the T-bill fund? (Do not round intermediate calculations. Round your answer to 2 decimal places.)
What is the proportion invested in each of the two risky funds? (Do not round intermediate calculations. Round your answers to 2 decimal places.)
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 4.7%. The probability distributions of the risky funds are:
Explanation / Answer
Answer:
E(RS ) = 17%, E(RB )= 8%, S = 37%, B = 31%, P= 0.1065
From the standard deviation and correlation coefficient we generate the covariance matrix:
Stock
Bond
Stock
37*37= 1369
122.156
Bond
122.156
961
As the portfolio is a minimum variance portfolio so the portfolio weights can be found by using this formula:
Wmin(S) ={ B2 – Cov(B, S)} / {S2+B2- 2 Cov(B, S)}
= {961 – 122.156} / {1369+961- 2*122.156} = 838.844 / 1085.688 = 0.773
Therefore, Wmin(B) = 1- 0.773 = 0.227
Standard deviation of portfolio is:
B1.) To find proportion of funds invested in T-Bill we have mean of the portfolio as 15% which is the average of T-bill rate and combination of risky assets like stock and bonds. Ley y be the proportion of risky assets in the portfolio. The mean of portfolio alon any optimal CML is:
Here rf = 4.7% and E(RC) = 15%
For the calculation of E(Rp) which is mean of optimal risky portfolio, we have to calculate the proportion of stock and bond in this optimal risky portfolio:
W (S) = [E(RS)- rf] B2 - [E(RB)- rf] Cov(B, S) / [E(RS)- rf] B2+[E(RB)- rf] S2- [E(RB)- rf+ E(RS)-
rf] Cov(B,S)
W (S) = (17-4.7)(961) – (8-4.7)(122.156) / (17-4.7)(961) +(8-4.7)(1369)-(17+8-
9.4)(122.156)
W (S) = 0.79108 and therefore W (B)= 1-0.79108 =0.20891
E(RC) = (1-y)rf + y E(Rp) =
So, E(Rp) = (0.79108)(17%) + (0.20891)(8%) = 15.11964
Now use this in this formula
E(RC)= (1-y) rf + y E(Rp) = 4.7 + y(15.11964-4.7) = 15 solve this for y.
Hence, y = 0.9885
Therefore proportion od T bills = 1- 0.9885 =0.0115 = 1.15%
B2.) Proportion invested in two risky assets, like stock and bond is given as under:
Proportion in Stock = Wmin(S) = 0.773
Proportion in Bond = Wmin(B) = 0.227
Stock
Bond
Stock
37*37= 1369
122.156
Bond
122.156
961
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