Monthly realized returns for two mutual funds, the market and the risk-free secu

Question

Monthly realized returns for two mutual funds, the market and the risk-free security are provided below.
Month Fund1 Fund2 Market Risk-free
Jan 8:5669% 4:0237% 2:5302% 0:0489%
Feb -4:9697% 5:6860% 1:6806% 0:0749%
Mar -0:5001% 2:9540% -1:9386% 0:0824%
Apr 13:6661% 17:9551% 13:5449% 0:0832%
May 3:3059% 2:4608% 8:8257% 0:0822%
Jun -2:3716% -2:4764% -0:9055% 0:0938%
Jul 7:8584% 5:4698% 5:2323% 0:0877%
Aug 5:5479% 1:7605% -0:0560% 0:0865%
Sep -3:8608% -13:7448% -6:7318% 0:1034%
Oct -10:1137% -7:1444% -10:4689% 0:0977%
Nov 8:5709% 3:7174% 7:5441% 0:0996%
Dec -3:4970% 9:7989% -0:4110% 0:1112%
Evaluate the performance of the two funds using Sharpe and Treynor ratios and Jensen's alpha.

Explanation / Answer

Jensen's alpha = Portfolio Return ? [Risk Free Rate + Portfolio Beta * (Market Return ? Risk Free Rate)]

Sharpe ratio = (Mean portfolio return ? Risk-free rate)/Standard deviation of portfolio return

Treynor ratio =(Average Return of a Portfolio – Average Return of the Risk-Free Rate)/Beta of the Portfolio

detailed solution :

Month Fund1 Fund2 Market Risk-free Jan 8.5669% 4.0237% 2.5302% 0.0489% Feb -4.9697% 5.6860% 1.6806% 0.0749% Mar -0.5001% 2.9540% -1.9386% 0.0824% Apr 13.6661% 17.9551% 13.5449% 0.0832% May 3.3059% 2.4608% 9.8257% 0.0822% Jun -2.3716% -1.4764% -0.9055% 0.0938% July 7.8584% 5.4698% 5.2323% 0.0877% Aug 5.5479% 1.7605% -0.0560% 0.0865% Sep -3.8608% -13.7448% -6.7318% 0.1034% Oct -10.1137% -7.1444% -10.4689% 0.0977% Nov 8.5709% 3.7174% 7.5441% 0.0996% Dec -3.4970% 9.7989% -0.4110% 0.1112% Average Return 1.8503% 2.6217% 1.6538% 0.0876% Standard Deviation 0.0710946 0.0790974 0.0674448 0.00016 Beta 0.8715225 0.9004458 1 Sharpe Ratio 0.2479289 0.3203759 Treynor Ratio 0.0202249 0.0281426 Jensen's Alpha 0.0039766 0.0112381

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