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 5.5%. The probability distributions of the risky funds are: Expected Return and Standard DeviationStock fund (S) 15% and 32% Bond fund (B) 9 and 23 The correlation between the fund returns is 0.15. Draw a tangent from the risk-free rate to the opportunity set. What does your graph show for the expected return and standard deviation of the optimal risky portfolio?

can someone explain the calculation of E(r) and standard deviation

Answer 1

Expected return for stock fund = 15%-sure rate = 0.15-0.055 = 0.095

Expected return for bond fund = 9%-sure rate= 0.09-0.055 = 0.035

Standard deviation of stock fund,S = 32% = 0.32

variance of stock fund = (standard deviation of stock fund)² = (0.32)² = 0.1024

standard deviation of bond fund, B = 0.23

variance of bond fund = (standard deviation of bond fund)² = (0.23)² = 0.0529

covariance, C = correlation coefficient* standard deviation of stock fund*standard deviation of bond fund = 0.15*0.32*0.23 = 0.01104

now we will find optimal portfolio weights

substituting the values to find W_D

W_D = [(0.15*0.0529)-(0.09*0.01104)]/((0.15*0.0529)+(0.09*0.1024)-((0.15+0.09)*0.01104))

= 0.0069414/0.0145014 = 0.478671

W_E = 1 - W_D = 1-0.478671 = 0.521329

Expected return of portfolio of stock fund and bond fund = Ep

Ep = (W_D *Expected return of stock fund) + (W_E *expected return of bond fund) = (0.478671*0.15)+(0.521329*0.09) = 0.11872026

Variance of optimal portfolio = (Wd*S)² + (We*B)² + (2*Wd*We*C) = (0.478671*0.32)² + (0.521329*0.23)²+(2*0.478671*0.521329*0.01104)

= 0.0234625 + 0.014377 + 0.00550996 = 0.04334982

a)Standard deviation of optimal portfolio = (Variance of portfolio)^(1/2) = (0.04334982 )^(1/2) = 0.2082062 or 20.82062% or 20.82%