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2 June, 02:13

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

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  1. 2 June, 02:36
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    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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