Question

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.

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