Question

Assume that the economy has three types of people. 20% are fad followers, 75% are passive investors, and 5% are informed traders. The portfolio consisting of all informed traders has a beta of 1.4 and an alpha of 3.8%. The market has an expected return of 10% and the risk-free rate is 4 %. What is the alpha for the fad followers? Enter your answer as a percentage to two decimal places (i.e. 0.12% rather than 0.0012; the percent sign is not necessary).

Answer 1

The portfolio return = Risk free return + Beta * ( Market return - Risk free return)

= 4% + 1.4* (10% -4%)

= 12.4%

Required rate of Return for the informed investors = 3.8% + 12.4% = 16.2%

Portfolio return = Weight of fad followers * Required return + Weight of informed traders * Required return

12.4% = 20 / 25 * Required return + 5/ 25 * 16.2%

Required return = 11.4%

Alpha of fad followers = Required Return - [Risk free return + Beta * ( Market return - Risk free return)]

= 11.4% - [ 4% + 1.4* (10% -4%)]

= -1%