Question

A well-diversified portfolio P has an expected return of 5% and a beta of 1.3. The risk-free rate is 2.3% and the expected return on the S&P 500 is 8%.

a) What is the portfolio's expected alpha? Enter your answer as a decimal.

b) What should you do? Buy the security or Short-sell the security? Why?

Answer 1

a) What is the portfolio's expected alpha?

Step 1: Calculation of Required Rate of Return using Capital Asset Pricing Model

Using Capital Asset Pricing Model

Required Rate of Return = Rf + b ( Rm – Rf )

Where,

Rf – Risk free return = 2.3%

b – Beta = 1.3

Rm – Expected return on market portfolio = 8%

Required Rate of Return = 2.3+1.3*(8-2.3)

= 2.3+7.41

= 9.7%

Alpha = Expected portfolio return - Required Rate of Return

= 5-9.7

= -4.7%

b) What should you do? Buy the security or Short-sell the security? Why?

Negative alpha means the portfolio is under performing. It indicates that the investment are not optimally diversified. Alpha is only one among the various techniques for evaluating portfolio. So take a comprehensive view and take decision.

That is all cases of negative alpha does not imply that the stock should sell. It is an indicator.