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 4.2%. The probability distributions of the risky funds are:

Suppose now that your portfolio must yield an expected return of 11% 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 4.2%. The probability distributions of the risky funds are:

Explanation / Answer

PART -A

E(Rs) = 12%

E(Rb) =5%

Rf =4.2%

Ss = Std.deviation of stcok =33%

Sb = std.deviation of bond = 26%

Covariance (Rs,Rb) = Corr(rs,rb)*Ss*Sb = 0.0308*33*26 = 26.4264

Weight of S = Ws ={ [E(Rs) - Rf]*Sb^2 - [E(Rb) -Rf]*Cov(Rs, Rb)} / { [E(Rs) -Rf]*Sb^2 + [E(Rb) -Rf]*Ss^2 - [E(Rs) -Rf +E(Rb) -Rf]*Cov(Rs,Rb)}

Hence Ws = {(12-4.2)*676 - (5-4.2)*26.4264}/{(12-4.2)*676 + (5-4.2)*1089 -(12-4.2+5-4.2)*26.4264}

Ws = 0.8876

Wd = 1-Ws = 0.1124

Std.deviation of Potfolio Sp is given by

Sp = sqrt[ 0.8876^2*(1089) + 0.1124^2*(676) + 2*0.08876*0.1124*(26.4264)]

Sp = 29.53%

Therefore Standard deviation of portfolio = 29.53%

PART -B

TheSince the expected Return is 11% . Now let the Porportion in the porfolio by "y"

E(Rc) = (1-y)rf +yE(Rp)

E(Rp) = 0.8876 *12 + 0.1124*5 =11.21%

E(Rc) =11

Rf + y(E(Rp) -rf) =11

4.2 +y(11.21-4.2) =11

Hence y = 0.97

Hence 1-y =0.03

Hence Proportion in T bill is 3%

Proportion in Stock fund = 0.8876* 0.97 = 0.86 = 86%

Proportion in Bond fund = 0.1124* 0.97 = 0.11 =11%

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

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