Question

The Sharpe ratio of an asset Alpha is 0.8. Alpha has and expected return of 12% and a standard deviation of 20%. Youhavebeen tasked to arrive at the expected return of an asset Gamma. Themarketreturn in this economy is 14% and the beta (systematic risk) of Gamma with market return is 1.4. What is the expected return of asset Gamma?

Answer 1

Sharphe Ratio = (Expected Return - Rf) / S.D.

Rf = Risk free Return

S.D. =Standard deviation

We have Sharpe ratio(0.8)' expected return(12%) and S.D. of asset alpha(20%), therefore we can calculate Rf

0.8 = (12% - Rf) / 20%

Rf = 16% - 20% = -4%

As we can see, the rf is coming to negative, which is not the usual case.

We will calculate the expected return of Gamma using CAPM. As per CAPM model,

Expected Return = Rf + (Rm - Rf)*B

Rm =Market Return = 14%

B = Beta =1.4

Rf( as calculated above) = -4%

Expected return = -4% + (14% - (-4%))*1.4

= -4% + 25.2%

Expected return of gamma = 21.2%