Question

Assume that the economy has three types of people. 15% are fad followers, 75% are passive investors, and 10% are informed traders. The portfolio consisting of all informed traders has a beta of 1.3 and an alpha of 4.98%. The market has an expected return of 12% 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

Answer :

Here, we need to calculate the Alpha of Fad followers . Fad followers are those investors who invested in short period of time with high risk.

Therefore we calculate the beta for Fad followers on the basis of the weight to fad followers and the beta of the informed investors ( as these are calculated the risk factor and take risk )

Here it is given that there are 10% informed investors and 15% fad followers

therefore, the beta for fad investors be calculated as follows

= beta of informed investors X Weight of Fad followers / Weight of informed investors

= 1.3 x 0.15 / 0.10 = 1.95

Now, we calculate the expected return to fad followers by using CAPM model and calculated beta

=

r = R_f + Beta X ( R_m - R_f )

here ,

r = Expected return of Fad Followers

R_f = Risk free rate of Return

R_m = Market Return

r = 0.04 + 1.95 ( 0.12-0.04) = 0.196 i.e. 19.60%

Alpha for the Fad Follower = Expected return of fad followers from market - Actual Market Return = 0.1960 - 0.12 = 0.076 i.e 7.6%