Question

Please use the following information on the portfolio and its benchmark (S&P 500 index) to calculate...

  1. Please use the following information on the portfolio and its benchmark (S&P 500 index) to calculate

Portfolio

S&P 500

Average Annual Return

12%

10%

Standard Deviation

18%

15%

Beta

1.2

1

Risk-free rate =

2%

  1. Sharpe ratio for the portfolio and S&P 500 index
  2. Treynor ratio for the portfolio and S&P 500 index
  3. Jensen’s alpha based on Capital Asset Pricing Model.

Homework Answers

Answer #1

1) SHARPE RATIO:

Formula= RETURN OF PORTFOLIO - RISK FREE RATE

Standard deviation

= Portfolio = 0.12 - 0.02

0.18

Ans= 0.56

FOR S&P500 SHARPE RATIO WILL BE

=0.10 - 0

0.15

Ans =0.67

2) TREYNOR RATIO;

FORMULA:  Portfolio return - risk free rate

Portfolio beta

For portfolio

= 0.12 - 0.02

1.2

=0.083

For S&P500

= 0.10 - 0

1

=0.1

JENSENS ALPHA;

FORMULA = α = Rp – [Rf + (Rm – Rf) β]

Portfolio= 0.12-(0.02+(0.18-0.02)1.2)

= 0.12-(0.21)

= -0.092

S&P500

=0.10-(0+(0.15-0)1)

= 0.10-(0.15)

= -0.05

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