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. You are given returns data for a stock, AAPL, from March 2002 to Feburary 2007, with a monthly frequency.

1) Test whether CAPM holds for AAPL. 2) Does this stock offer a positive alpha, how large is it? 3) Please calculate the betas (exposures) of AAPL corresponding to these four factors. 4) How is the performance of the fourth factor UMD in explaining returns of AAPL.

The data below have already been converted to monthly percentage.
Date	AAPL	MKT	SMB	HML	UMD	RF	MKT-RF	APPL-RF
200203	9.124424	4.47	4.35	1.09	-1.7	0.13	4.34	8.994424
200204	2.533784	-4.96	5.78	4.23	7.92	0.15	-5.11	2.383784
200205	-4.03624	-1.05	-3.69	2.37	3.05	0.14	-1.19	-4.17624
200206	-23.9485	-7.02	3.5	1.55	6.17	0.13	-7.15	-24.0785
200207	-13.8826	-8.11	-5.11	-3.7	3.41	0.15	-8.26	-14.0326
200208	-3.27654	0.8	-2.17	2.15	1.68	0.14	0.66	-3.41654
200209	-1.76152	-10	2.73	1.13	9.09	0.14	-10.14	-1.90152
200210	10.75862	7.5	-2.99	-6.57	-5.17	0.14	7.36	10.61862
200211	-3.48692	6.13	3.16	-1.52	16.26	0.12	6.01	-3.60692
200212	-7.6129	-5.33	-0.54	3.85	9.63	0.11	-5.44	-7.7229
200301	0.27933	-2.34	1.37	-0.84	1.53	0.1	-2.44	0.17933