An analyst who believes in the Treynor - Black Model has identified one active s

Question

An analyst who believes in the Treynor - Black Model has identified one active stock, stock A, which he/she wants to combine with the passive Market Index M to form their firm's optimal risky portfolio. A regression of the excess returns of stock A on the excess returns of the market index M, have discovered that stock A's alpha is 4%, its beta is 2.0, and the residual standard deviation of the error term for stock A is 17%. The standard deviation for the market index M is 14%, the expected return on M is 11%, the risk-free rate of return is 3%, and the expected return on stock A is 22%. Use this information to answer questions 14 through 17:

14. What is active stock A's information ratio?

15. What is the Sharpe Ratio for the passive market index M?

16. What is the Sharpe Ratio for the optimal risky portfolio formed by the optimal combination of the active stock A with the passive market index M?

17. What percentage of the optimal risky portfolio formed with A and M should be invested in active stock A?

Explanation / Answer

14)

Information ratio:

It is the ratio of portfolio returns in excess of returns of the benchmark.

(Return on portfolio-Return on index)/Tracking error

=(16.5-11)/14*100

=39%

Working note:

Return on portfolio is as follows:

Expected return on market + Return on stock/2

=22+11/2

=16.5

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