Suppose that a portfolio has a beta of 1.15. Over the period of one year, the portfolio had a return of 12.4% with a standard deviation of 16.2%.
1. If the T-bill return for the year was 1.2% and the return on the S&P500 was 10.2%, calculate the following performance measures for the portfolio.
a. Jensen's alpha
b. Treynor's index
c. Sharpe's index

Answer and Explanation:

Given:

Weighted average β = 1.15

Average return (r) = 12.4%

Risk free return (Rf) = 1.2%

Market return (Rm) = 10.2%

Standard deviation (SD) = 16.2%

Computation of Jensen's α :

Jensen's α = r - [Rf + β(Rm - Rf)]

Jensen's α = 12.4% - [1.2% + 1.15(10.2% - 1.2%)]

Jensen's α = 12.4% - [1.2% + 10.35%]

Jensen's α = 12.4% - 11.55%

Jensen's α = 0.85%

Computation of Treynor's index :

Treynor's index (Ratio) = (r - Rf) / β

Treynor's index (Ratio) = (12.4% - 1.2%) / 1.15

Treynor's index (Ratio) = 11.2% / 1.15

Treynor's index (Ratio) = 9.73913043%

Treynor's index (Ratio) = 9.74% (Approx)

Computation of Sharpe's index :

Sharpe's index (Ratio) = (r - Rf) / SD

Sharpe's index (Ratio) = (12.4% - 1.2%) / 16.2%

Sharpe's index (Ratio) = 11.2% / 16.2%

Sharpe's index (Ratio) = 0.69 13%

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