Question

You must choose one of the following: a stock fund, a bond fund, or a portfolio of 50% stock and 50% bond. The expected returns are 13% and 8% for the stock and bond fund, respectively, and the standard deviations are 20% and 16%, with a correlation of 0.40 between the two funds. You can also borrow or lend at 5%. Relying on mean-variance analysis, determine the order of your preference from most preferred to least preferred.

Answer 1

Sharp Ratio is indicator of Reward/Risk Ratio

Sharp Ratio =(Return-Risk Free Return)/ Standard Deviation

Risk Free Return =5%

Sharp Ratio of Stock Fund=(13-5)/20=0.4000

Sharp Ratio of Bond Fund=(8-5)/16=0.1875

Portfolio Return=w1*R1+w2*R2

w1=Weight of Stock Fund in the portfolio=0.5

w2=Weight of Bond Fund in the portfolio=0.5

R1=Return of Stock Fund=13%

R2=Return of Bond Fund=8%

Rp=Portfolio Return=0.5*13+0.5*8=10.5%

Portfolio Variance=Vp=(w1^2)*(S1^2)+(w2^2)*(S2^2)+2*w1*w2*Cov(1,2)

w1=Weight of Stock Fund in the portfolio=0.5

w2=Weight of Bond Fund in the portfolio=0.5

S1=Standard Deviation of Stock Fund=20%

S2=Standard Deviation of Bond Fund=16%

Cov(1,2)=Covariance of returns of Stock fund and Bond fund=Corr(1,2)*S1*S2

Corr(1,2)=Correlation between Stock Fund and Bond Fund=0.4

Cov(1,2)=0.4*20*16=128%%

Portfolio Variance=Vp=(0.5^2)*(20^2)+(0.5^2)*(16^2)+2*0.5*0.5*128=228%%

Portfolio Standard Deviation =Sp=Square Root(Vp)=SQRT(228)=15.10%

Sharp Ratio of the Portfolio=(10.5-5)/15.10=0.3642

Preference from most preferred to least preferred;

Stock Fund=Sharp Ratio=0.4000

Portfolio= Sharp ratio=0.3642

Bond Fund=Sharp Ratio=0.1875