Question

the market portfolio has an expected excess return of 6% and and a standard deviation of 15%. asset a sits above the sml and has an expected excess return of 10% inclusive of alpha of 2%, and an r2 against the market portfolio excess return of 0.50. what is asset a's sharpe ratio. treynor measure and information ratio? enter your answer to 3 decimal places eg if your answer is 0.4579 enter as 0.458.

Answer 1

The Sharpe ratio, Treynor measure, and information ratio for Asset A are approximately 0.667, 0.816, and 0.189 respectively. These calculations are based on the given expected excess return, alpha, standard deviation, and R-squared of Asset A against the market portfolio.

Step-by-step explanation:

The student is asking for the calculation of three distinct investment performance measures for Asset A: the Sharpe ratio, Treynor measure, and information ratio. The Sharpe ratio is calculated by subtracting the risk-free rate from the expected excess return of the asset and then dividing by the standard deviation of the asset's excess return.

As the risk-free rate is not provided, it will be assumed to be 0%. Therefore, the Sharpe ratio for Asset A is (10% - 0%) ÷ 15%, which equals 0.667. The Treynor measure is calculated by dividing the asset's excess return by its beta. With an R-squared of 0.50 and a market variance of 15%^2, we estimate Asset A's beta as √(0.50) × (15%) ÷ (15% ÷ 6%), which gives us 1.225.

The Treynor measure for Asset A is thus 10% ÷ 1.225, equal to 0.816. The information ratio is calculated by dividing the asset's alpha by the standard deviation of the asset's active return (which is the standard deviation of the residuals in a regression of the asset's excess returns on the market's excess returns).

Using the given alpha of 2% and assuming the market's total risk is the same as Asset A's unsystematic risk, we have an information ratio of 2% ÷ (15% × √(1 - 0.50)), which equals 2% ÷ 10.606%, resulting in an information ratio of 0.189.