Question

Check my work mode: This shows what is correct or incorrect for the work you have completed so far. It does Problem 7-7 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 rate of 6%. The probability distribution of the risky funds is as follows: Expected Return 16% Standard Deviation Stock fund (5) Bond fund (5) 35$ 15 The correlation between the fund returns is 0.13 Solve numerically for the proportions of each asset and for the expected return and standard deviation of the optimal risky portfolio (Do not round Intermediate calculations. Enter your answers as decimals rounded to 4 places.) % Answer is complete but not entirely correct. Portfolio invested in the Stock Portfolio invested in the bond 0.1300 0.8000® 12.6533 15.8700® Expected return Standard deviation < Prev 2 of 4 !!! Next > EN

Answer 1

The Optimal Risky portfolio weights for a two security (A and B) portfolio is given by

WA = [(E(RA) – Rp) *0% - (E(RB) – Rp)*0A * OB* PA,B]/[(E(RA) - Rp)*03+ (E(RB) - Rf)*04- (E(RA) - R+E(RB) - Rp)*0A*OB*PA,B]

and W_B= 1 - W_A

These weights correspond to the point on the Capital allocation line which is tangent from the Risk free Asset point (0,RFR)

Let A be the stock fund and B be the bond fund

Here, E(R_A) = 16%, stdev(A) = 35%

E(R_B) = 12%, stdev(B) = 15%

R_f= 6% , Correlation coefficient = 0.13

So, W_A = [(0.16-0.06)*0.15² - (0.12-0.06)*0.13*0.35*0.15] / [(0.16-0.06)*0.15² +(0.12-0.06)*0.35² - (0.16-0.06+ 0.12-0.06)*0.13*0.35*0.15]

=[0.00225-0.00041]/[0.00225+0.00735-0.001092]

=0.001841/0.008508

=0.2163 =21.63%

and W_B = 1-0.2163=0.7837 =78.37%

This is the optimal portfolio weights i.e. 0.2163 invested in Stock fund and 0.7837 invested in Bond fund

The return of a portfolio is the weighted return of the two stocks

So Return of this portfolio = 0.2163 * 16% +0.7837 *12% = 12.8653%

The standard deviation of a two security portfolio is given by

Op = W;*W, *0; * 0;* Pij

So, standard deviation of portfolio =sqrt (0.2163²*0.35²+0.7837²*0.15²+2*0.2163*0.7837*0.15*0.35*0.13)

=sqrt(0.021865)

=0.147868 =14.7868%