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Question B.1 [3 + 3 + 3 + 4 + 6 + 6 = 25pts, 20min] You have been approached with an investment offer in the PLC fund. To support your decision, you analyse past performance of the fund based on a sample of 216 monthly observations of the fund's return in excess of the risk-free rate. You fit the Fama-French 3-factor version of the APT model to the returns. In the below output: MKT_RF is the value-weighted market return in excess of the risk-free rate, SMB is the Small-minus-Big factor HML is the High-minus-Low factor You obtain the following results from your Excel Regression tool. SUMMARY OUTPUT Regression Statistics Multiple R 0.96043583 R Square 0.922436984 Adjusted R Square 0.921339394 Standard Error 0.108105799 Observations 216 ANOVA of 55 MS F Significance F Regression 3 29.46563896 9.821879652 840.4204775 2.2526E-117 Residual 212 2.477615125 0.011686864 Total 215 31.94325408 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept -0.069582574 0.007458244 -9.329618941 1.46377E-17 -0.084284392 -0.054880757 Mkt RF 1.264393021 0.032840954 38.50049563 1.21884E-97 1 199656373 1329129569 SMB 18.3583406 1.09015E-45 0.788341708 0.97800191 HML -0.139959078 -3.123359193 0.002037775 -0.228290165 -0.05162799 a) What is the standard error of the HML coefficient estimate? b) What proportion of the variance of the returns on PLC is systematic according to the Fama- French model? c) The agent selling you this investment claims that PLC is a low-beta investment. Do you agree with them? Why (not)? 3 d) Has PLC performed well or poorly on a risk-adjusted basis according to your analysis? Why? e) Compute the SMB coefficient estimate and the corresponding standard error. f) Based on the regression output and without knowing the composition of the portfolio of stocks that the PLC fund invests in, would you infer that the PLC fund invests in a small number or a large number of stocks? Why