A pension fund manager is considering three mutual funds. The first is a stock f

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 5.8%. The probability distributions of the risky funds are:

Suppose now that your portfolio must yield an expected return of 17% 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.)

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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 5.8%. The probability distributions of the risky funds are:

Explanation / Answer

Answer:

E(RS ) = 19%,   E(RB )= 9%,   S = 48%, B = 42%, P= 0.1065

From the standard deviation and correlation coefficient we generate the covariance matrix:

Stock

Bond

Stock

48*48= 2304

48*42*0.0762 = 153.62

Bond

153.62

42*42 = 1764

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)}

              = {1764 – 153.62} / {2304+1764- 2*153.62} = 1610.38/ 3760.76 = 0.4282

Therefore,   Wmin(B) = 1- 0.4282 = 0.5718

Standard deviation of portfolio is:

B1.) To find proportion of funds invested in T-Bill we have mean of the portfolio as 19% which is the average of T-bill rate and combination of risky assets like stock and bonds. Let y be the proportion of risky assets in the portfolio. The mean of portfolio alon any optimal CML is:

Here rf = 5.8% and E(RC) = 19%

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) = (19-5.8)(1764) – (9-5.8)(153.62) / (19-5.8)(1764) +(9-5.8)(2304)-(19+9-

                                                                                                                                  11.6)(153.62)

W (S) = 0.81 and therefore W (B)= 1-0.81 =0.19

E(RC) = (1-y)rf + y E(Rp) =

So, E(Rp) = (0.81)(19%) + (0.19)(9%) = 17.1

Now use this in this formula

E(RC)= (1-y) rf + y E(Rp) = 5.8 + y(17.1- 5.8) = 17 solve this for y.

Hence, y = 0.9911

Therefore proportion of T bills = 1- 0.9911 =0.0088 = 0.88%

       B2.) Proportion invested in two risky assets, like stock and bond is given as under:

Proportion in Stock = Wmin(S) = 0.4282

Proportion in Bond = Wmin(B) = 0.5718

Stock

Bond

Stock

48*48= 2304

48*42*0.0762 = 153.62

Bond

153.62

42*42 = 1764

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