Question

You manage a risky portfolio with an expected rate of return of 19% and a standard deviation of 34%. The T-bill rate is 8%. Your client chooses to invest 70% of a portfolio in your fund and 30% in a T-bill money market fund.

What is the reward-to-volatility (Sharpe) ratio (S) of your risky portfolio? Your client’s?(round answers to 4 decimal places

Reward-to-volatility ratio?

Clients reward-to-volatility ratio?

Answer 1

Sharpe ratio(reward to variability)

=(Return-risk free rate)/std dev

=(19-8)/34

=0.3235

Expected return%=	Wt Risky poltfolio*Return Risky poltfolio+Wt Risk free*Return Risk free
Expected return%=	0.7*0.19+0.3*0.08
Expected return%=	15.7
Variance	=( w2A*σ2(RA) + w2B*σ2(RB) + 2*(wA)*(wB)*Cor(RA, RB)*σ(RA)*σ(RB))
Variance	=0.7^2*0.34^2+0.3^2*0^2+2*0.7*0.3*0.34*0*0
Variance	0.05664
Standard deviation=	(variance)^0.5
Standard deviation=	23.8%

Sharpe ratio(reward to variability)

=(Return-risk free rate)/std dev

=(15.7-8)/23.8

=0.3235