The Capital Asset Pricing Model (CAPM) predicts that differences in the exposure to market returns should explain all cross-sectional expected return differences between different assets. In this question, you will evaluate CAPM using annual data on portfolios sorted by CAPM beta from 1964 to 2019.

a) Compute the average return, volatility, average beta, and the Sharpe ratio for each portfolio.

b) As a mean-variance investor who needs to pick one of the five beta-sorted portfolios, which portfolio would you choose?

c) Show graphically that CAPM does not hold. To do this, plot the security market line (SML) predicted by the data on the market return and the riskless rate along with the average returns and average betas of portfolios.

d) What does the relation between the expected portfolio returns and betas imply for mispricing under the assumption that the CAPM is the right model? Which portfolios are overpriced, and which portfolios are underpriced?

Annual Returns of Beta-sorted Portfolios (Low to High)						Macro Data
year	p1	p2	p3	p4	p5	mkt	rf
1964	16.87	19.84	17.56	8.73	12.4	16.08	3.54
1965	8.72	6.98	15.53	24.76	49.06	14.45	3.93
1966	-9.24	-12.18	-9.08	-2.94	-2.13	-8.75	4.76
1967	13.44	22.07	32.01	42.65	50.98	28.7	4.21
1968	15.83	9.16	13.53	12.41	24.61	14	5.21
1969	-12.59	-3.74	-6.72	-18.64	-22.6	-10.96	6.58
1970	8.69	2.59	-3.57	-6.64	-19.57	0.03	6.52
1971	11.67	17.23	21.89	20.28	22.93	16.17	4.39
1972	21.77	15.27	15.19	12.49	-1.15	16.89	3.84
1973	-11.4	-14.11	-23.68	-35.22	-42.51	-19.26	6.93
1974	-24.56	-27.26	-29.75	-34.83	-32.85	-27.75	8
1975	30.42	42.42	46.81	59.11	78.05	38.24	5.8
1976	29.67	19.63	30.55	31.77	32.05	26.99	5.08
1977	-1.7	-9.6	-1.21	3.33	8.48	-3.14	5.12
1978	6.13	6.03	11.14	10.2	23.8	8.21	7.18
1979	23.99	17.59	22.84	26.92	32.87	23.47	10.38
1980	29.59	31.81	31.15	42.11	45.77	33.37	11.24
1981	7.95	-9.57	-2.75	-3.26	-6.4	-3.42	14.71
1982	31.33	38.34	18.15	2.76	9.5	21.2	10.54
1983	15.94	29.46	25.13	29.17	16.47	22.54	8.8
1984	14.38	8.23	4.81	-4.28	-13.92	3.8	9.85
1985	37.22	37.25	27.69	25.88	24.2	32.63	7.72
1986	29.43	16.45	15.27	5.65	4.35	16.28	6.16
1987	2.45	7.6	2.78	1.92	-9.56	1.6	5.47
1988	18.51	16.44	16.4	22.86	12.93	17.9	6.35
1989	33.79	29.02	29.54	23.16	25.03	28.86	8.37
1990	-1.52	-3.32	-7.64	-8.45	-8.21	-6.14	7.81
1991	21.86	29.75	39.31	42.05	55.51	34.78	5.6
1992	4.5	5.4	13.04	19.17	17.07	9.74	3.51
1993	12	7.39	7.68	17.46	16.78	11.11	2.9
1994	-2.29	6.91	-2.4	-3.52	2.05	-0.2	3.9
1995	35.14	40.07	33.81	39.85	38.96	36.82	5.6
1996	16.33	18.72	26.4	24.43	29.24	21.17	5.21
1997	29.27	29.95	37.92	35.05	27.5	31.22	5.26
1998	18.66	30.68	22.2	23.61	27.21	24.32	4.86
1999	-4.86	19.82	14.63	29.78	52.57	25.25	4.68
2000	27.77	7.85	-7.56	-5.25	-28.04	-11.71	5.89
2001	-7.97	-6.28	3.38	-8.28	-24.56	-11.37	3.83
2002	-9.74	-13.64	-13.45	-25.04	-35.42	-21.11	1.65
2003	18.07	27.65	20.78	35.2	53.73	31.77	1.02
2004	10.81	15.25	15.47	12.99	5.15	11.92	1.2
2005	4.67	10.2	6.37	8.58	1.68	6.07	2.98
2006	15.55	16.73	12.38	21.95	8.31	15.4	4.8
2007	3.77	6.18	6.14	8.11	7.02	5.7	4.66
2008	-28.98	-33.45	-36.76	-48.59	-50.39	-36.74	1.6
2009	9.85	23.26	38.25	52.5	86.94	28.36	0.1
2010	11.81	13.37	20.14	27.59	33.69	17.49	0.12
2011	12.23	1.45	-2.11	-10.5	-18.08	0.48	0.04
2012	11.69	14.9	19.53	22.92	25.03	16.33	0.06
2013	27.56	40.86	33.47	37.48	44.35	35.22	0.02
2014	17.3	14.08	9.29	5.98	-1.36	11.73	0.02
2015	4.53	5.16	-3.66	-6.4	-15.4	0.1	0.02
2016	7.46	13.4	14.41	18.63	27.38	13.5	0.2
2017	18.76	24.68	23.18	21.42	23.47	22.31	0.8
2018	-1.17	-1.6	-4.43	-9.16	-16.94	-5.12	1.81
2019	27.02	29.68	30.35	37.5	31.61	30.42	2.14