Question

The following data are available relating to the performance of High Variance Stock Fund and the market portfolio High Variance Market Portfolio 19% Average Return Standard Deviation of Returns 12% 35% 15% Beta 1.5 1.0 Residual standard deviation 3.0% 0.0% The risk-free return during the sample period was 6%. (1) Evaluate the performance of the High Variance Stock Fund relative to the market portfolio in terms of the Sharpe measure, the Treynor measure, the Jensen measure of performance evaluation, and the information ratio. (2) Comment on your findings, stating the investment situations in which each measure is the most appropriate measure

Please solve question 1 and 2.

Answer 1

(1)

Sharpe ratio = (fund return - risk free rate) / standard deviation of fund.

Sharpe ratio = (19% - 6%) / 35%

Sharpe ratio = 0.37.

Treynor ratio = (fund return - risk free rate) / beta of fund.

Treynor ratio = (19% - 6%) / 1.5

Treynor ratio = 0.087.

Jensen measure = fund return - (risk free rate + (beta * (market return - risk free rate))

Jensen measure = 19% - (6% + (1.5 * (12% - 6%))

Jensen measure = 4%.

Information ratio = (fund return - market return) / residual standard deviation

Information ratio = (19% - 12%) / 3%

Information ratio = 2.33

(2)

The Sharpe ratio is low (less than 1), which means that the excess return per unit of risk is low. It is not a good investment. This measure is most appropriate to determine whether return is adequate for the risk taken.

In this case, the Treynor measure needs to be compared against a benchmark to determine whether it is a good investment. The Treynor measure is most appropriate to measure the risk-adjusted return of a particular investment within a portfolio.

The Jensen measure is positive, which means that the fund has earned alpha, or excess returns. Jensen measure is most appropriate to use when the expected return of a fund can be calculated using CAPM model.

Information ratio is very high for this fund. A ratio of more than 1 is very rare. However, the market portfolio may not be the most appropriate benchmark in this case as the fund is a high variance fund. The information ratio is most appropriate to use when there is an appropriate benchmark and the residual standard deviation can be calculated.