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 5.4%. The probability distributions of the risky funds are:

Expected Return Standard Deviation

Stock fund (S) 15% 44%

Bond fund (B) 8% 38%

The correlation between the fund returns is .0684. Suppose now that your portfolio must yield an expected return of 13% and be efficient, that is, on the best feasible CAL.

1.What is the proportion invested in each of the two risky funds? (Do not round intermediate calculations. Round your answers to 2 decimal places.) Proportion Invested Stocks % and Bonds %

Explanation / Answer

Answer:

             The parameters which are provided in the question are as under:

E(RS ) = 15%,   E(RB )= 8%,   S = 44%, B = 38%, P= 0.0684

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

Stock

Bond

Stock

44*44= 1936

44*38*0.0684 = 114.3648

Bond

114.3648

38*38 = 1444

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)}

              = {1444 – 114.3648} / {1936+1444- 2*114.3648} = 1329.6352/3151.2704 = 0.42194

Therefore,   Wmin(B) = 1- 0.42194 = 0.57806

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

Proportion in Stock = Wmin(S) = 0.42194

Proportion in Bond = Wmin(B) = 0.57806

Stock

Bond

Stock

44*44= 1936

44*38*0.0684 = 114.3648

Bond

114.3648

38*38 = 1444

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.