Use the Fama-French 3 factor model to evaluate how risk factor sensitivity is estimated at the portfolio level.

Rei,t=i+i,MReMKT+i,SMBSMBt+i,HMLHMLt+ei,tRi,te=i+i,MRMKTe+i,SMBSMBt+i,HMLHMLt+ei,t

To simplify notation in the regression notice that:

Rei,t=Ri,tRF,t=Ri,te=Ri,tRF,t= is stock or portfolio ithith excess return and ReMKT=RMtRF,t=RMKTe=RMtRF,t= is the excess return on a "stock market portfolio".

SMB = Small Minus Big, i.e., the return of a portfolio of small stocks in excess of the return on a portfolio of large stocks.

HML = High Minus Low, i.e., the return of a portfolio of stocks with a high book-to-market ratio in excess of the return on a portfolio of stocks with a low book-to-market ratio.

Consider the monthly returns from Nov-2007 to October 2017 produced by a popular mutual fund: Fidelity Magellan (FMAGX). This fund seeks capital appreciation. The fund invests primarily in common stocks. It invests in either "growth" stocks or "value" stocks or both.

DATE	MKT	SMB	HML	RETX_TRMCX
2007M11	-4.83	-2.63	-1.18	-4.24
2007M12	-0.87	0.2	-0.52	-13.52
2008M01	-6.36	-0.89	3.65	10.28
2008M02	-3.09	-0.23	-0.95	-2.93
2008M03	-0.93	0.94	-0.15	-0.93
2008M04	4.6	-1.64	-0.96	4.06
2008M05	1.86	3.21	-1.38	2.29
2008M06	-8.44	1.27	-2.43	-8.15
2008M07	-0.77	2.47	5.81	-0.25
2008M08	1.53	3.61	1.56	1.81
2008M09	-9.24	-1.13	6.33	-8.48
2008M10	-17.23	-2.33	-2.89	-19.70
2008M11	-7.86	-2.99	-5.94	-8.23
2008M12	1.74	3.59	-0.24	0.35
2009M01	-8.12	-0.01	-11.1	-4.49
2009M02	-10.1	0.17	-7.25	-8.78
2009M03	8.95	-0.09	3.53	9.34
2009M04	10.19	4.83	5.46	16.66
2009M05	5.21	-2.33	-0.21	4.81
2009M06	0.43	2.61	-2.71	0.86
2009M07	7.72	2.07	5.28	9.14
2009M08	3.33	-0.9	7.76	5.50
2009M09	4.08	2.45	0.92	6.23
2009M10	-2.59	-4.22	-4.17	-4.62
2009M11	5.56	-2.49	-0.17	5.16
2009M12	2.75	6.11	0.01	3.69
2010M01	-3.36	0.38	0.31	-2.34
2010M02	3.4	1.2	3.16	3.25
2010M03	6.31	1.42	2.1	6.32
2010M04	2	4.98	2.81	3.76
2010M05	-7.89	0.05	-2.38	-6.93
2010M06	-5.56	-1.97	-4.5	-6.70
2010M07	6.93	0.16	-0.27	6.25
2010M08	-4.77	-3	-1.95	-5.23
2010M09	9.54	3.92	-3.12	9.56
2010M10	3.88	1.15	-2.59	2.05
2010M11	0.6	3.7	-0.9	0.75
2010M12	6.82	0.7	3.81	5.41
2011M01	1.99	-2.47	0.81	2.75
2011M02	3.49	1.52	1.09	4.42
2011M03	0.45	2.6	-1.55	0.31
2011M04	2.9	-0.34	-2.51	2.51
2011M05	-1.27	-0.7	-2.06	-0.66
2011M06	-1.75	-0.18	-0.31	-1.80
2011M07	-2.36	-1.31	-1.23	-1.99
2011M08	-5.99	-3.06	-2.44	-8.35
2011M09	-7.59	-3.48	-1.46	-8.08
2011M10	11.35	3.41	-0.17	10.04
2011M11	-0.28	-0.17	-0.35	-1.32
2011M12	0.74	-0.71	1.74	-4.89
2012M01	5.05	2.15	-1.09	10.83
2012M02	4.42	-1.75	0.09	4.14
2012M03	3.11	-0.61	0.87	1.84
2012M04	-0.85	-0.52	-0.47	-0.59
2012M05	-6.19	0.02	-0.62	-6.80
2012M06	3.89	0.77	0.44	4.48
2012M07	0.79	-2.58	-0.25	1.99
2012M08	2.55	0.41	1.28	3.43
2012M09	2.73	0.5	1.52	2.66
2012M10	-1.76	-1.14	3.79	-0.49
2012M11	0.78	0.59	-0.96	0.79
2012M12	1.18	1.47	3.55	-4.16
2013M01	5.57	0.39	0.92	12.64
2013M02	1.29	-0.45	0	1.57
2013M03	4.03	0.79	-0.26	4.26
2013M04	1.55	-2.44	0.59	0.41
2013M05	2.8	1.67	2.55	2.11
2013M06	-1.2	1.22	-0.19	-1.30
2013M07	5.65	1.86	0.55	5.39
2013M08	-2.71	0.3	-2.78	-3.52
2013M09	3.77	2.94	-1.18	4.51
2013M10	4.18	-1.49	1.15	4.11
2013M11	3.12	1.24	0.24	1.33
2013M12	2.81	-0.5	-0.3	-1.67
2014M01	-3.32	0.87	-2.08	2.20
2014M02	4.65	0.33	-0.39	5.00
2014M03	0.43	-1.89	5.09	1.73
2014M04	-0.19	-4.25	1.14	0.48
2014M05	2.06	-1.83	-0.26	1.98
2014M06	2.61	3.06	-0.74	3.19
2014M07	-2.04	-4.23	0.01	-2.88
2014M08	4.24	0.37	-0.57	4.37
2014M09	-1.97	-3.82	-1.22	-3.98
2014M10	2.52	4.23	-1.69	1.25
2014M11	2.55	-2.06	-2.99	1.23
2014M12	-0.06	2.54	2.07	-12.35
2015M01	-3.11	-0.57	-3.47	13.17
2015M02	6.13	0.53	-1.77	5.05
2015M03	-1.12	3.05	-0.45	-0.40
2015M04	0.59	-2.97	1.85	0.61
2015M05	1.36	0.94	-1.33	1.44
2015M06	-1.53	2.81	-0.81	-1.82
2015M07	1.54	-4.15	-4.14	-1.51
2015M08	-6.04	0.49	2.69	-4.51
2015M09	-3.08	-2.64	0.53	-3.47
2015M10	7.75	-1.98	-0.09	5.67
2015M11	0.56	3.64	-0.51	0.88
2015M12	-2.17	-2.81	-2.57	-13.26
2016M01	-5.77	-3.39	2.1	6.91
2016M02	-0.07	0.78	-0.48	1.65
2016M03	6.96	0.89	1.14	9.19
2016M04	0.92	0.67	3.25	3.27
2016M05	1.78	-0.26	-1.8	1.41
2016M06	-0.05	0.65	-1.49	-0.45
2016M07	3.95	2.64	-1.13	3.99
2016M08	0.5	1.17	3.34	0.29
2016M09	0.25	2.01	-1.49	0.12
2016M10	-2.02	-4.36	4.16	-1.85
2016M11	4.86	5.48	8.27	7.45
2016M12	1.82	0.08	3.61	-4.81
2017M01	1.94	-1.05	-2.68	7.64
2017M02	3.57	-1.99	-1.79	2.11
2017M03	0.17	1.2	-3.17	0.04
2017M04	1.09	0.73	-1.91	-0.22
2017M05	1.06	-2.54	-3.75	-1.90
2017M06	0.78	2.15	1.32	1.84
2017M07	1.87	-1.42	-0.28	1.87
2017M08	0.16	-1.71	-2.26	-1.60
2017M09	2.51	4.53	3.02	2.47
2017M10	2.25	-1.94	-0.09	0.30

This exercise asks you to apply the Fama-French 3 factor model to evaluate how risk factor sensitivity is estimated at the portfolio level. RE = di + Bim RM + Bi,SMB SMB: + BiHmL HML: + lint it MKT To simplify notation in the regression notice that: RR = Rijt RF, = is stock or portfolio ith excess return and RUKT = RMt RF,1 = is the excess return on a "stock market portfolio". SMB = Small Minus Big, i.e., the return of a portfolio of small stocks in excess of the return on a portfolio of large stocks. HML = High Minus Low, i.e., the return of a portfolio of stocks with a high book-to-market ratio in excess of the return on a portfolio of stocks with a low book-to-market ratio. Consider the monthly returns from Nov-2007 to October 2017 produced by a popular mutual fund: Fidelity Magellan (FMAGX). This fund seeks capital appreciation. The fund invests primarily in common stocks. It invests in either "growth" stocks or "value" stocks or both. Question: The estimated model is: RE = 0.17 +0.89 Rukt + 0.15 SMB: + 0.15 HML RO = 0.32 + 1.63 RMKT + 2.02 SMB: + 0.32 HML RO = 1.01 + 1.00 RMKT - 0.19 SMB; 0.32 HML; R = -1.08 + 1.26 RMKt + 1.02 SMB: + 0.11 HML, R = -0.43 + 1.19 RMKT 0.19 SMB: + 1.18 HML; Question: Choose the appropriate hypotheses to test the joint hypothesis that the coefficients on both the "SMB" and "HML" risk factors are zero. O H. : $smb = 0 and Bumu 0 vs H : at least one + 1 O H. : BSMB 0; vs H1 : Bhml 0 Ho : BSMB 1 Ho : BSMB O and BHML 0; VS H1 : at least one # 0 O Ho : BsMB 2 0 and Bhul > 0; vs Hi : at least one 1 Ho : BSMB O and BHML 0; VS H1 : at least one # 0 O Ho : BsMB 2 0 and Bhul > 0; vs Hi : at least one