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%
