Question

Consider the two (excess return) index-model regression results for stocks A and B. The risk-free rate over the period was 8%, and the market’s average return was 13%. Performance is measured using an index model regression on excess returns.

	Stock A	Stock B
Index model regression estimates	1% + 1.2(rM ? rf)	2% + 0.8(rM ? rf)
R-square	0.659	0.478
Residual standard deviation, ?(e)	11.7%	20.5%
Standard deviation of excess returns	23%	27.7%

a. Calculate the following statistics for each stock:

i) Sharpe ratio

ii) Treynor Measure

Answer 1

Sharpe Measure = (Return on Portfolio - Risk Free rate)/ Standard Deviation of Portfolio

Risk free rate = 8%

Market return = 13%

Return on Portfolio for Stock A = 1% + 1.2 * (13% - 8%)

Return on Portfolio for Stock A = 7%

Standard Deviation of stock A = 23%

Sharpe ratio = (7%)/ 23%

Sharpe ratio of Stock A = 0.3043

Return on Portfolio for Stock B = 2% + 0.8 * (13% - 8%)

Return on Portfolio for Stock B = 6%

Risk free rate = 8%

Sharpe ratio = (6%)/ 27.7%

Sharpe ratio of Stock B = 0.2166

Part B:

Beta of Stock A = 1.2

Treynor ratio of Stock A = 7%/ 1.2

Treynor ratio of Stock A = 5.83

Beta of Stock B = 0.8

Treynor ratio of Stock B = 6%/ 0.8

Treynor ratio of Stock B = 7.50