Question

B. Consider the following data for the year 2019.

​​​​​​​ Portfolio X ​​​ Market M

Average return ​​​​​​28% ​​​​24%

Beta ​​​​​​​ ​1.20 ​​​ ​1.00

Standard deviation ​​​​​​35% ​​​​25%

The T-bill rate during the period was 4%.

i. Calculate the following performance measures for portfolio X and the market:

- Sharpe Index,

- Jensen (alpha), and

- Treynor Index.

Answer.

ii. By which measures did portfolio X outperform and underperform the market?

Answer.

iii. Explain any inconsistency in the rankings between the different measures.

Answer.

iv. Based on your analysis, would you prefer an investment in portfolio X or in the market? Explain the reason(s) for your choice.

Answer 1

i)

T-bill(risk-free)	4%
	Portfolio X	Market
Average return	28%	24%
Beta	1.2	1
Standard deviation	35%	25%
Sharpe Index	68.57%	80.00%
Jensen Alpha	0	0.2
Treynor Index	0.2	0.2

Sharpe ratio = (Portfolio return-Risk-free rate)/ Standard deviation of portfolio

Treynor ratio =  (Portfolio return-Risk-free rate)/ Beta of portfolio

Jensen Alpha = Portfolio return - (Risk free rate + Beta*(Market return-risk-free rate))

ii)

Portfolio X underperformed the market in the Sharpe Index measure and Jensen alpha measure.

Portfolio X performed at par when Treynor's Index is used

iii)

According to the Sharpe Index measure and Jensen alpha measure, Market performs better than Portfolio X, while according to the Treynor's Index, both perform at par. This is the inconsistency in the rankings between the different measures

iv) I would prefer investment in the market. This is because the Sharpe's ratio suggest that portfolio X underperforms the market. Also, Jensen's alpha suggests that Portfolio X does not provide any excess returns over its estimated return using CAPM model. On the other hand, market is returning relatively better than its predicted returns using the CAPM model (in the Jensen alpha equation).