DATA TO COPY

	AAPL	MKT	SMB	HML	UMD	RF
200203	9.124424	4.47	4.35	1.09	-1.7	0.13
200204	2.533784	-4.96	5.78	4.23	7.92	0.15
200205	-4.03624	-1.05	-3.69	2.37	3.05	0.14
200206	-23.9485	-7.02	3.5	1.55	6.17	0.13
200207	-13.8826	-8.11	-5.11	-3.7	3.41	0.15
200208	-3.27654	0.8	-2.17	2.15	1.68	0.14
200209	-1.76152	-10	2.73	1.13	9.09	0.14
200210	10.75862	7.5	-2.99	-6.57	-5.17	0.14
200211	-3.48692	6.13	3.16	-1.52	16.26	0.12
200212	-7.6129	-5.33	-0.54	3.85	9.63	0.11
200301	0.27933	-2.34	1.37	-0.84	1.53	0.1
200302	4.5961	-1.54	-0.35	-1.54	1.29	0.09
200303	-5.85885	1.03	0.88	-1.71	1.5	0.1
200304	0.565771	8.28	1.21	-0.08	-9.48	0.1
200305	26.30098	6.35	4.71	0.27	10.79	0.09
200306	6.124722	1.63	1.47	0.64	-1.06	0.1
200307	10.59811	2.31	5.64	-2.11	-0.35	0.07
200308	7.305503	2.49	2.64	1.78	-0.55	0.07
200309	-8.39965	-0.91	0.56	0.99	-0.07	0.08
200310	10.42471	6.03	2.91	1.75	3.7	0.07
200311	-8.65385	1.66	2.23	1.39	1.63	0.07
200312	2.296651	4.55	-2.87	2.76	-5.67	0.08
200401	5.519177	2.31	2.6	1.66	2.58	0.07
200402	6.028369	1.55	-1.2	0.37	-1.14	0.06
200403	13.04348	-1.07	1.85	-0.01	0.2	0.09
200404	-4.65976	-2.42	-2.53	-1.69	-5.33	0.08
200405	8.844065	1.41	-0.12	-0.31	1.64	0.06
200406	15.96579	2.16	2.25	1.72	2.08	0.08
200407	-0.61463	-3.77	-3.82	4.42	-2.32	0.1
200408	6.679035	0.27	-1.56	1.13	-1.54	0.11
200409	12.34783	2.06	2.82	0.4	5.28	0.11
200410	35.19092	1.78	0.49	-0.95	-1.54	0.11
200411	27.9771	4.82	4.11	1.96	3.24	0.15
200412	-3.9666	3.52	0.18	-0.35	-2.82	0.16
200501	19.40994	-2.66	-1.67	2.52	3.12	0.16
200502	16.671	2.27	-0.76	2.85	3.19	0.16
200503	-7.11101	-1.69	-1.37	1.71	0.93	0.21
200504	-13.4629	-2.52	-3.95	-0.49	-0.84	0.21
200505	10.26068	3.79	3.01	-1.16	0.46	0.24
200506	-7.41952	1.15	2.58	2.84	2.1	0.23
200507	15.86525	4.33	2.77	-0.47	0.05	0.24
200508	9.941383	-0.59	-0.88	1.44	2.24	0.3
200509	14.33141	1.06	-0.64	1.22	3.5	0.29
200510	7.423988	-2.08	-1.05	-0.74	-1.37	0.27
200511	17.7635	4.04	0.98	-1.75	0.39	0.31
200512	6.00118	0.35	-0.47	0.51	0.77	0.32
200601	5.035471	4.01	5.32	1.18	2.77	0.35
200602	-9.29678	-0.16	-0.31	-0.76	-1.8	0.34
200603	-8.42459	1.91	3.51	0.04	1.22	0.37
200604	12.22895	1.3	-1.22	3.07	0.65	0.36
200605	-15.0874	-3.1	-3	2.75	-3.66	0.43
200606	-4.1827	-0.04	-0.47	1.51	1.52	0.4
200607	18.66597	-0.19	-3.9	3.25	-2.24	0.4
200608	-0.16186	2.51	0.8	-1.66	-3.48	0.42
200609	13.45615	1.95	-1.21	-0.49	-0.98	0.41
200610	5.326059	3.71	1.68	0.49	-0.18	0.41
200611	13.04884	2.37	0.7	0.39	-1	0.42
200612	-7.44054	1.08	-0.93	2.56	0.81	0.4
200701	1.049033	1.94	0.02	0	0.22	0.44
200702	-1.30643	-1.4	1.38	0.32	-1.32	0.38

Question 1) Carhart (1997) extends the Fama French three factor model to a four factor model. That is, there are four factors in the markets, which are MKT, SMB, HML and UMD. The risk free rate is RF. MI You are given returns data for a stock, AAPL, from March 2002 to Feburary 2007, with a monthly frequency. a) Test whether CAPM holds for AAPL. b) Does this stock offer a positive alpha, how large is it? c) Please calculate the betas (exposures) of AAPL corresponding to these four factors. d) How is the performance of the fourth factor UMD in explaining returns of AAPL. The data below have already been converted to monthly percentage. AAPL MKT SMBHMLUMDRF 200203 9.124424 4.471 4.35| 1.09 -1.70.13 2002042.533784) -4.96 5.78 4.23 7.92 0.15 200205 -4.03624 -1.05 -3.69 2.37 3.050.14 200206 -23.9485 -7.02 3.5 1.55 6.170.13 200207-13.8826 -8.11 -5.11 -3.71 3.410.15 200208)-3.27654 0.8-2.17 2.15 1.680.14 2002091-1.76152 -10 2.73 1.13 9.09 0.14 200210 10.75862 7.5 -2.99 -6.57 -5.17|0.14 200211 -3.486921 6.13 3.16-1.52 16.26 0.12 200212 -7.61291-5.33 -0.54 3.85 9.63 0.11 200301 0.27933 -2.341 1.371 -0.84 1.53 0.1 200302 4.5961] -1.54 -0.35 -1.54 1.290.09 200303-5.85885 1.03 0.88 -1.71 1.51 0.1 200304|0.565771 8.28| 1.21 -0.08 -9.48 0.1 ||200305 26.30098 6.35 4.71 0.27 10.790.09 2003066.124722 1.63 1.47 0.64 -1.06 0.1 ||200307 10.59811 2.31 5.641 -2.11 -0.350.07 ||200308 7.305503| 2.49 2.64 1.78 -0.550.07 200309 -8.39965 -0.91 0.56 0.991 -0.0710.08 200310 10.42471 6.03 2.91] 1.75 3.710.07 200311-8.65385 1.66 2.23 1.39 1.630.07) 200312 2.296651 4.55 -2.87 2.76 -5.6710.08 200401 5.519177 2.31 2.6 1.66 2.580.07) 20040216.028369 1.550 -1.2 0.37 -1.14 0.06 200403 13.04348 -1.07) 1.85 -0.01 0.210.09 200404 -4.65976 -2.42 -2.53 -1.69-5.330.08 200405 8.844065 1.41 -0.12 -0.31 1.640.06 20040615.96579 2.16 2.25 1.72] 2.080.08 2004071 -0.61463)-3.77 -3.82 4.42) -2.32 0.1 20040816.679035 0.27 -1.56 1.13) -1.54|0.11 20040912.34783 2.06 2.82 0.4 5.28 0.11 200410 35.19092 1.78 0.491-0.951 -1.54 0.11 200411 27.9771| 4.82 4.11 1.96 3.240.15 200412) -3.9666 3.52 0.18-0.35 -2.8210.16 200501 19.40994) -2.66 -1.67 2.52 3.12 0.16 200502 16.671) 2.27 -0.76 2.85 3.19 0.16 200503) -7.11101 -1.69 -1.37 1.71 0.93|0.21 200504|-13.4629 -2.52-3.95 -0.491 -0.840.21 200505 10.26068 3.79 3.01 -1.16 0.46 0.24 200506 -7.41952 1.15 2.58 2.84 2.10.23 200507 15.86525] 4.33 2.77 -0.47] 0.050.24 2005089.941383/-0.59 -0.88 1.44 2.24 0.3 20050914.33141] 1.06 -0.64 1.22 3.510.291 20051017.423988)-2.08 -1.05 -0.74 -1.370.27| 200511] 17.7635| 4.04 0.98 -1.75 0.39 0.31 200512 6.00118 0.35 -0.47 0.51 0.77 0.32 200601 5.035471 4.01 5.321 1.18 2.77 0.35 200602 -9.29678) -0.16 -0.31 -0.76 -1.8|0.34 200603) -8.42459 1.91 3.51 0.04 1.220.37| 200604 12.22895 1.3 -1.22 3.071 0.650.36 200605 -15.0874 -3.1 -3 2.75 -3.66 0.43 200606 -4.1827 -0.04 -0.47 1.51) 1.52 0.4 200607 18.66597 -0.19 -3.9 3.25 -2.24 0.4 200608-0.16186 2.51 0.8 -1.66 -3.480.42 200609 13.45615 1.95 -1.21 -0.49 -0.980.41 200610 5.326059 3.71 1.68 0.491 -0.18 0.41 200611 13.04884 2.37 0.71 0.39 -110.421 200612 -7.44054 1.08 -0.93 2.56 0.81 0.4 200701 1.049033| 1.94 0.02 0 0.22 0.44 200702 -1.30643 -1.4 1.38 0.32 -1.32 0.38