Question

Consider the following information: Portfolio Expected Return Beta Risk-free 8 % 0 Market 10.2 1.0 A 8.2 0.7 a. Calculate the expected return of portfolio A with a beta of 0.7. (Round your answer to 2 decimal places.) Expected return % b. What is the alpha of portfolio A. (Negative value should be indicated by a minus sign. Round your answer to 2 decimal places.) Alpha % c. If the simple CAPM is valid, is the above situation possible? Yes No

Answer 1

Following Information provided -

Portfolio	Portfolio Return	Beta
Risk Free	8%	0
Market	10.20%	1
A	8.20%	0.7

Under CAPM, Required Return(expected Return) of an Assets can be calculated with following equation -

$\textup{Required Return = Risk free return + Beta*(Market Return - Risk Free Return)}$

a.

Expected Return of Portfolio A -

$\textup{Expected Return of A = 0.08 + 0.7*(0.102 - 0.08)}$

$\textup{Expected Return of A = 0.08 + 0.0154}$

Expected Return of A 0.0954

Expected Return of Portfolio A = 9.54%

b.

Alpha is measure of excess return of an assets over its expected return under CAPM.

$\textup{Alpha = Portfolio Return - Expected Return of Portfolio under CAPM}$

Thus,

$\textup{Alpha of A = 0.082 - 0.0954}$

$\textup{Alpha of A = -0.0134}$

Therefore,

Alpha of A = - 1.34%

c.

Yes, above situation is possible, When portfolio or assets is under performing than market then alpha would be negative.

Hope this will help, please do comment if you need any further explanation. Your feedback would be appreciated.