# Finance Portfolio Theory

• Oct 17th 2010, 11:28 PM
thekiterunner
Finance Portfolio Theory
consider the two (excess retrun) index model regression results from stocks A and B. The risk free rate over the period was 6% and the market's averge return was 14%. Performance is measured using an index model regression on excess return:

Stock A
inxel model regression equation: 1% + 1.2(rM-rf)
R-square: 0.576
residual standard deviation: 10.3%
standard deviation of excess returns: 21.6%

Stock B
inxel model regression equation: 2% + 0.8(rM-rf)
R-square: 0.436
residual standard deviation: 19.1%
standard deviation of excess returns: 24.9%

How do i calculate:

1) Alpha:
2) Information ratio:
3) Sharpe measure:
4) Treynor measure:

Can someone just show me how you determine the answers by showing me the full workings so i can sit down and properly understand it.

I have this information from the solution guide but i have no idea how to use it:

*To compute the Sharpe measure, note that for each stock, (rP – rf ) can be computed from the right-hand side of the regression equation, using the assumed parameters rM = 14% and rf = 6%. The standard deviation of each stock’s returns is given in the problem.
** The beta to use for the Treynor measure is the slope coefficient of the regression equation presented in the problem.
• Oct 21st 2010, 08:39 PM
dexteronline
Sharpe Measure

Stock A
$S = \frac{R_p-R_f}{\sigma}$
$R_p = 1\% + 1.2 (R_m - R_f )$
$R_m=14\%$
$R_f=6\%$
$\sigma=21.6\%$
$R_p=1\% + 1.2(14\%-6\%)$
$R_p=1\% + 1.2(8\%)$
$R_p=1\% + 9.6\%$
$R_p=10.6\%$
$S = \frac{10.6\%-6\%}{21.6\%}$
$S = \frac{4.6\%}{21.6\%}$
$S = 0.2129$

Stock B
$S = \frac{R_p-R_f}{\sigma}$
$R_p=2\% + 0.8(R_m-R_f)$
$R_m=14\%$
$R_f=6\%$
$\sigma=24.9\%$
$R_p=2\% + 0.8(14\%-6\%)$
$R_p=2\% + 0.8(8\%)$
$R_p=2\% + 6.4\%$
$R_p=8.4\%$
$S = \frac{8.4\%-6\%}{21.6\%}$
$S = \frac{2.4\%}{21.6\%}$
$S = 0.1111$

Treynor measure:

$T = \frac{R_p-R_f}{\beta}$

Stock A

$T = \frac{10.6\%-6\%}{1.2}$
$T = \frac{4.6\%}{1.2}$
$T = 0.038333$

Stock B

$T = \frac{8.4\%-6\%}{0.8}$
$T = \frac{2.4\%}{0.8}$
$T = 0.03000$

Jensen's Alpha

Stock A
$\alpha_p = 10.6\% - [6\% + 1.2 (14\% - 6\%)]$
$\alpha_p = 10.6\% - [6\% + 1.2 (8\%)]$
$\alpha_p = 10.6\% - [6\% + 9.6\%]$
$\alpha_p = 10.6\% - [6\% + 9.6\%]$
$\alpha_p = 10.6\% - 15.6\%$
$\alpha_p = -0.05$

Stock B
$\alpha_p = 8.4\% - [6\% + 0.8 (14\% - 6\%)]$
$\alpha_p = 8.4\% - [6\% + 0.8 (8\%)]$
$\alpha_p = 8.4\% - [6\% + 6.4\%]$
$\alpha_p = 8.4\% - [6\% + 6.4\%]$
$\alpha_p = 8.4\% - 12.4\%$
$\alpha_p = -0.04$