The data in the figure has been collected to appraise the performance of four as

Question

The data in the figure has been collected to appraise the performance of four asset management firms: Fund 1 6,45% 0,88 2,74% Fund 2 8,96% 1,02 4,54% Fund 3 9,44% 1,36 3,72% Fund 4 5,82% 0,8 2,64% Market Index 6% 1,0 2,8% Return Beta Standard deviation Standard deviation of excess returns 5,6% 6,1% 12,5% 5,3% N/A The market index return and risk-free rate of return for the relevant period were 6% and 3% respectively. Calculate and rank the funds using Jensen's alpha, the Treynor ratio, the Sharpe ratio, the Information ratio and M.

Explanation / Answer

Jenson’s Alpha = Expected Return on Portofolio – [Risk free rate+ beta * (Expected market return – Risk Free Rate)]

Also Jenson’s alpha = Rp- [Rf+ Bp(Rm - Rf)]

Fund 1 :

Risk Free Rate = 3%

Expected return on Portfolio = 6.45%

Beta = 0.88

Market return = 6%

Jenson’s Alpha = 6.45% - [3% + 0.88 (6% - 3%)] = 0.0645 – [0.03 + 0.88 (0.03)] = 0.0645 – [0.03+0.0264] = 0.0645 – 0.0564 = 0.0081

Treynor Ratio = (Return on Portfolio – Risk free rate of return)/ Beta = (0.0645 – 0.03)/ 0.88 = 0.0345/0.88 = 0.0304091

Sharpe Ratio = (Expected return on portfolio – Risk free Rate)/ Standard Deviation of the portfolio

Sharpe Ratio = (0.0645-0.03)/0.056 = 0.0345/0.056 = 0.616071

Information Ratio = (Return on Portfolio – Return on Index)/Tracking Error

M Squared = Risk Free rate + Portfolio Sharpe Ratio * Market Standard Deviation

Msquare = 0.03 + 0.616071*0.028 = 0.03+0.01725 = 0.04725

Fund 2:

Jenson’s Alpha = Expected Return on Portofolio – [Risk free rate+ beta * (Expected market return – Risk Free Rate)]

Jenson’s Alpha = 0.0896 – [0.03+ 1.02(0.06-0.03) = 0.0896 – [0.03+0.0306] = 0.029

Treynor Ratio = (Return on Portfolio – Risk free rate of return)/ Beta = (0.0896-0.03)/1.02 = 0.0596/1.02 = 0.05843

Sharpe Ratio = (Expected return on portfolio – Risk free Rate)/ Standard Deviation of the portfolio = (0.0896 – 0.03)/0.0454 = 0.0596/0.0454 = 1.31277

Information Ratio = (Return on Portfolio – Return on Index)/Tracking Error = (0.0896-0.06)/0.061 = 0.0296/0.061 = 0.48525

M Squared = Risk Free rate + Portfolio Sharpe Ratio * Market Standard Deviation = 0.03 + 1.31277 * 0.028 = 0.03+0.03676 = 006676

Fund 3:

Jenson’s Alpha = Expected Return on Portofolio – [Risk free rate+ beta * (Expected market return – Risk Free Rate)] = 0.0944 – [0.03+1.36(0.06-0.03)] = 0.0944 – [0.03+ 0.0408] = 0.0944 – 0.0708 = 0.0236

Treynor Ratio = (Return on Portfolio – Risk free rate of return)/ Beta = (0.0944 – 0.03)1.36 = 0.0644/1.36 = 0.04735

Sharpe Ratio = (Expected return on portfolio – Risk free Rate)/ Standard Deviation of the portfolio = (0.0944-0.03)/0.0372 = 0.0644/0.0372 = 1.7312

Information Ratio = (Return on Portfolio – Return on Index)/Tracking Error = (0.0944-0.06)/0.124 = 0.2774

M Squared = Risk Free rate + Portfolio Sharpe Ratio * Market Standard Deviation = 0.03 + 1.7312 * 0.028 = 0.03+0.04847 = 0.07847

Fund 4:

Jenson’s Alpha = Expected Return on Portofolio – [Risk free rate+ beta * (Expected market return – Risk Free Rate)] = 0.0582 – [0.03 + 0.8(0.06 – 0.03)] = 0.0582-[0.054] = 0.0042

Treynor Ratio = (Return on Portfolio – Risk free rate of return)/ Beta = (0.0582-0.03)/0.8 = 0.0284/0.8 = 0.0355

Sharpe Ratio = (Expected return on portfolio – Risk free Rate)/ Standard Deviation of the portfolio = (0.0582 – 0.03)/0.0264 = 0.0284/0.0264 = 1.07576

Information Ratio = (Return on Portfolio – Return on Index)/Tracking Error = (0.0582-0.06)/0.053 = -0.0018/0.053 = -0.034

M Squared = Risk Free rate + Portfolio Sharpe Ratio * Market Standard Deviation = 0.03+ 1.07576*0.028 = 0.03+0.03012 = 0.0601

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