Question

1.Sharpe Ratio:

a)We expect to have our stock portfolio to return 11% next year. The return on the risk-free T-bills is 3.2% and our portfolio has 5% standard deviation. What is the Sharpe ratio?

b)Stock portfolio A has a Sharpe ratio of 1.6 and an expected return of 10%. An alternative stock portfolio B has a Sharpe ratio of 1.2 and an expected return of 10%. In which one should you invest?

c)Stock portfolio A has a Sharpe ratio of 1.6 and an expected return of 10%. An alternative stock portfolio C has a Sharpe ratio of 1.6 and an expected return of 11%. In which one should you invest?

Answer 1

Sharpe ratio = (Mean portfolio return - Risk-free rate)/Standard deviation of portfolio return
Solution A
Sharpe ratio=	(11%-3.2%)/5%
Sharpe ratio=	1.56
Solution B
	Portfolio A	Portfolio B
Expected return	10%	10%
Risk free rate	Same	Same
Sharpe ratio	1.6	1.2
Since Numerator is going to be same for both companies, denominator which is standard deviation will be generating different
sharpe ratios. Since Portfolio A is having higher sharpe ratio which represents its denominator or SD is lower as compared to Portfolio B
and hence we should choose Portfolio A which is having same return but less standard deviation
Solution C
	Portfolio A	Portfolio C
Expected return	10%	11%
Risk free rate	Same	Same
Sharpe ratio	1.6	1.6
Since both portfolio is having same Sharpe ratio, it means the difference in numerator is compensated by denominator.
Higher numerator for Portfolio C would have given higher sharpe ratio but getting same sharpe ratio means its denominator is also higher. This
represents portfolio is high risk and high return portfolio
Now choice of portfolio will depend on risk apetite of investor. If risk apetite is high then choose portflio C else portfolio A