According to the three factor model, a fund's expected return can be explained by market excess return, a size factor, and a B/M factor. In terms of regression format, it can be written as follows:

 

Spread sheet file (PS2_Q8_FF_Raw Data_2023.xlsx) contains data for two mutual funds, excess market return, size factor and B/M factor for 30 months. Size factor is the difference of returns of small firms portfolio and large firms portfolio. B/M factor is the difference of returns of value firms portfolio and glamour (growth) firms portfolio. 

 

(a) (5%) Suppose you run Fama and French's three factor model regressions. Then you would like to check the sign of coefficient estimate of B/M factor. If coefficient estimate of B/M factor turns out to be negative and significant for a certain fund, can you identify whether this is a growth fund or a value fund? (For this question you don't have to run actual regressions) 

 

(b) (5%) Now using the whole sample, run three factor model regressions for each fund and tell me the characteristics of each fund. For example, which fund (between A and B) is heavily investing in large stocks? To answer this question, you need to check the sign of coefficient estimate of size and B/M factors and their t statistics. Use 10% significance level (p value) to answer the question.

r r = a + mi[rm. -rft]+PSMB [Smalls - Large]+BHML ["value, Growth,t+E -r.