Question

1. Consider the following data for a particular sample period when returns were high.

	Portfolio A	Market M
Average return	35%	28%
Beta	1.2	1
Standard deviation	42%	30%

Required

Calculate the three performance measures (sharpe, Jensen or alpha, and Treyner’s ratios) for portfolio A and the market. The Treasury bill rate during the period was 6%. By which measures did portfolio A outperform the market?                        [9 marks]

Answer 1

Solution:

a)Sharp Ratio

=(Expected Portfolio return-Risk free rate)/Portfolio standard deviation

Therefore,Sharp ratio of

Portfolio A=.35-.06/.42

=.69

=69%

Market M=.28-.06/.30

=.73

=73%

Higher the sharpe ratio,better the performance.Since the sharpe ratio of Portfolio is less than the Market,hence performance of Portfolio is not better than Market.

b)Treynor Ratio

=(Expected return-Risk free rate)/Beta

Therefore,Treynor ratio of

Portfolio A=.35-.06/1.2

=.24

=24%

Market M=.28-.06/1

=.22

=22%

Higher the treynor ratio,better the portfolio.

Accordingly,on the basis of treynor ratio,Portfolio A perform better than Market.

C)Jensen or Alpha

=Expected return-Risk free rate-beta(Market Return-Risk free rate)

Thus Jensen Alpha

=.35-.06-1.2(.28-.06)

=.03

=3%

Since Jensen's Alpha is positive(i.e.3%),hence the Portfolio has outperformed the market.