Question

You have been given the following return information for a mutual fund, the market index, and the risk-free rate. You also know that the return correlation between the fund and the market is .97.

Year	Fund	Market	Risk-Free
2015	-16.4%	-32.5%	3%
2016	25.1	20.3	4
2017	13.2	11.8	2
2018	6.2	8.0	5
2019	-1.68	-3.2	3

What are the Sharpe and Treynor ratios for the fund? (Do not round intermediate calculations. Round your answers to 4 decimal places.)

Sharpe ratio	?
Treynor Ratio	?

Answer 1

1.

Sharpe Ratio is given by the formula

Where, R = expected return of the fund

R_f = Risk Free Rate

σ = Standard Deviation of the fund

Sharpe Ratio can be calculated from the above information by the following steps

- Calculate expected return of the fund by calculating the average of all the fund return values using the AVERAGE function in spreadsheet

- Calculate expected risk free return by calculating the average of all the fund return values using the AVERAGE function in spreadsheet

- Calculate the excess return as the difference between the fund return and risk free rate for each year

- Calculate the standard deviation of the excess return (R-R_f) using the STDEVA function in spreadsheet

- Calculate Sharpe Ratio from the expected return of fund, risk free return and standard deviation using the sharpe ratio formula given above

The calculations are as shown below.

From the above image,

Expected Fund Return, R = 5.2840%

Risk Free Return, R_f = 3.4000%

Standard Deviation, σ = 15.432151%

Sharpe Ratio = (R-R_f)/σ = (5.2840% - 3.4000%)/15.432151% = 0.1221

2.

Treynor Ratio is given by the formula

Where, R = expected return of the fund

R_f = Risk Free Rate

β = Beta of the fund

Beta of the fund is given by the formula

β = Covariance (Fund, Market) / Variance(Fund)

Treynor Ratio can be calculated from the above information by the following steps

- Calculate expected return of the fund by calculating the average of all the fund return values using the AVERAGE function in spreadsheet

- Calculate expected risk free return by calculating the average of all the fund return values using the AVERAGE function in spreadsheet

- Calculate the variance of the fund from all the fund returns using VARA function in spreadsheet

- Calculate the covariance of the fund and market from all the fund and market returns using COVAR function in spreadsheet

- Calculate beta from covariance and variance using the above formula

- Calculate Treynor Ratio from the expected return of fund, risk free return and beta using the treynor ratio formula given above

The calculations are as shown below.

From the above image,

Expected Fund Return, R = 5.2840%

Risk Free Return, R_f = 3.4000%

β = Covariance (Fund, Market)/ Variance (Fund) = 2.460033% / 2.437173% = 1.009380

Treynor Ratio = (R-R_f)/β = (5.2840% - 3.4000%)/1.009380 = 0.0187