Question

Congratulations! Your portfolio returned 9.1​% last​ year, 2.3​% better than the market return of 6.8​%. Your portfolio had a standard deviation of earnings equal to 21​%, and the​ risk-free rate is equal to 4.1​%. Calculate​ Sharpe's measure for your portfolio. If the​ market's Sharpe's measure is 0.38​, did you do better or worse than the market from a​ risk/return perspective?

The​ Sharpe's measure of your portfolio is ____ (Round to two decimal​ places.)

Your​ portfolio's performance is ___

equal

inferior

superior

to the​ market's performance. ​ (Select from the​ drop-down menu.)

Answer 1

​

Sharpe Ratio=​(Rp​−Rf)

​​                           σp

where:-

R_p is the expected return on the asset or portfolio;

R_f is the risk-free rate of return; and

σ_p is the standard deviation of portfolio’s excess return

The Sharpe ratio is calculated by subtracting the risk-free rate from the return of the portfolio and dividing that result by the standard deviation of the portfolio’s excess return.

As per the given question,

Rp​=return of portfolio i.e. 9.1%

Rf​=risk-free rate i.e. 4.1%

σp​=standard deviation of the portfolio’s excess return i.e. 21%

Sharpe Ratio=​(Rp​−Rf)   =    (9.1%-4.1%) = 5%      = 0.24

​​    σp     21% 21%

Therefore, Sharpe’s measure of our portfolio is 0.24

It is given in the question that market's Sharpe's measure is 0.38​.

Higher the Sharpe’s measure, more it is considered as good. Since, our Sharpe’s measure is 0.24 which is less than the market’s Sharpe’s measure 0.38, therefore, we did worse than the market from a risk/return perspective. Therefore, Our Portfolio’s performance is inferior to the market’s performance.

Notes:-

• Usually, any Sharpe ratio greater than 1.0 is considered acceptable to good by investors.
• A ratio under 1.0 is considered sub-optimal.