Question

Stock A has generated the following monthly rates of return over the preceding 6 months: 3%, 11%, 2%, 5%, -1%, 6% (annualized rates). You have estimated the stock’s beta to be 1.3. The risk-free rate is 1% and the market risk premium 8%. What is the expected rate of return on the stock in the next month? Find the stock’s Jensen’s alpha. Would you recommend buying or shorting this stock?

Answer 1

expected rate of return can be calculated as the arithmetic mean of the past returns

expected rate of return = Sum of returns / no. of returns

= (3+11+2+5-1+6)/6

= 26/6

= 4.33%

Using Capital Asset Pricing Model

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

Where,

Rf – Risk free return = 1%

b – Beta = 1.3

Rm – Expected return on market portfolio

Rm-Rf – Market risk premium = 8%

Required Rate of Return = 1+1.3*8

= 1+10.4

= 11.4%

Alpha = expected rate of return - Required Rate of Return

= 4.33-11.4

= -7.07%

Recommendation: Since alpha is negative, recommend to shorting this stock.