Question

A measure of risk-adjusted performance that is often used is the Sharpe ratio. The Sharpe ratio is calculated as the risk premium of an asset divided by its standard deviation. The standard deviation and return of the funds over the past 10 years are listed in the following table. Calculate the Sharpe ratio for each of these funds. Assume that the expected return and standard deviation of the company stock will be 17 percent and 70 percent, respectively. Calculate the Sharpe ratio for the company stock. How appropriate is the Sharpe ratio for these assets? When would you use the Sharpe ratio? A risk free rate is not given.

Bledsoe S&P 500 index fund 10yr return= 6.88% standard deviation= 10.75%

Bledsoe small-cap fund 10yr return= 9.29 standard deviation= 12.81

Bledsoe large-company stock fund 10yr return=3.56 standard deviation=10.99

Bledsoe bond fund 10yr return=5.27 standard deviation=7.12

Answer 1

Sharpe ratio = (expected return- risk free rate)/std dev

---- since risk free rate is not given, we can take it as zero

Sharpe ratio of company stock= .17/.7 =.242

Sharpe ratio of Bledsoe S&P 500 index fund= .0688/.1075=.64

Sharpe ratio of Bledsoe small-cap fund= .0929/.1281=.7252

Sharpe ratio of large-company stock fund= .0356/.1099=.3239

Sharpe ratio of Bledsoe bond fund = .0527/.0712=.74

----- Sharpe ratio is used to find out the risk adjusted performance of the fund. Portfolio managers use sharpe ratio to optimise their portfolio and compare the performance of the portfolio. Portfolios are optimised such that from a given set of portfolio, the portfolio weights that give the optimum sharpe ratio is selected. Generally it will show the degree of diversification, it is not that much useful for non diversified funds and in that case we can use Treynors ratio.