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 4.49%. 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

E(R) = Expected Return
Market return = (R_m) 10%
Beta = 1.4
R_f = Risk free rate = 4%
alpha = 4.49%
Using CAPM model R_p = R_f + Beta * (R_p - R_f ) = 4% + 1.4 * ( 10% - 4%) = 12.4%
Return for Informed traders = R_if= alpha + R_f + Beta * (R_m- R_f) = 4.49% + 4% + 1.4 * ( 10% - 4%) = 16.89%
(Return on portfolio ) R_p is combination of Return of fad followers and Return of informed followers
Fad followers weights = W_ff = (20/25) = 0.8
Informed followers weights =W_if = (05/25) = 0.2
R_p = W_ff *R_ff + W_if * R_if
12.4% = 0.8 * R_ff + 0.2 * 16.89%
R_ff = 11.28%
Alpha _ff = R_ff - Rf - Beta * ( R_m - R_f) = 11.28% - 4% - 1.4 *( 10% - 4%) = -1.12%
Answer Alpha of fad followers = -1.12

Best of Luck