Question

please I want it to step by step and in word posted so I can read them.

Q:

If the average realized return of a portfolio is 27.5% per year, the standard deviation of returns is 50%, the portfolio beta is 1.25, the average return of Treasury bills over the same period is 2.5% per year, and the average return on the market is 12.5% per year

Calculate i) the Sharpe; ii) Treynor and iii) Jensen    

Answer 1

- Average Realized Return of Portfolio = 27.5%

- Standard Deviation of returns =50%

As per CAPM,

Rf = Risk free Return/Average return of Treasury bills = 2.5%                                                    

Rm = Market return/Average Return on the market = 12.5%

Portfolio Beta = 1.25

Expected Return = 2.5% + 1.25(12.5%-2.5%)

= 15%

i). Sharpe ratio = (Return of Portfolio - Risk free Return)/Standard Deviation of Portfolio

= (27.5% - 2.5%)/50%

= 0.50 times

ii). Treynor Ratio = (Return of Portfolio - Risk free Return)/Portfolio Beta

=(27.5% - 2.5%)/1.25

= 20 times

iii). Jensen's alpha = Average Realized Return of Portfolio - Expected Return of Portfolio

= 27.5% - 15%

= 12.5%

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