In this question, you are to use historical return data to estimate means and std deviations Rates of Return 1926 2008 World Portfolios U S Markets Year Equity Return in U S Dollars Bond Return in U S Dollars Small Stocks Large Stock Long Term T Bonds T Bills Inflation Real T bill Rates 1926 25 24 8 10 8 91 12 21 4 54 3 19 1 12 4 36 1927 23 15 9 62 35 48 35 99 8 11 3 13 2 26 5 51 1928 28 62 2 44 51 31 39 29 0 93 3 54 1 16 4 76 1929 12 56 3 45 48 35 7 66 4 41 4 74 0 59 4 13 1930 22 6 6 04 48 36 25 90 6 22 2 43 6 40 9 43 1931 39 94 12 32 53 17 45 56 5 31 1 09 9 32 11 48 1932 1 46 18 26 8 58 9 14 11 89 0 95 10 27 12 50 1933 70 81 29 26 153 18 54 56 1 03 0 30 0 76 0 46 1934 0 15 3 87 34 78 2 32 10 15 0 18 1 52 1 32 1935 22 44 1 41 72 87 45 67 4 98 0 14 2 99 2 77 1936 18 84 0 49 77 01 33 55 6 52 0 18 1 45 1 25 1937 17 7 0 96 55 05 36 03 0 43 0 29 2 86 2 50 1938 6 21 0 65 15 46 29 42 5 25 0 04 2 78 2 82 1939 5 6 5 11 6 79 1 06 5 90 0 01 0 00 0 01 1940 7 97 11 32 14 15 9 65 6 54 0 02 0 71 0 72 1941 13 26 5 61 13 42 11 20 0 99 0 04 9 93 9 00 1942 0 56 3 69 39 66 20 80 5 39 0 28 9 03 8 03 1943 19 3 2 76 108 74 26 54 4 87 0 36 2 96 2 53 1944 13 49 3 02 61 46 20 96 3 59 0 33 2 30 1 93 1945 13 72 0 08 81 98 36 11 6 84 0 32 2 25 1 89 1946 16 91 13 50 13 17 9 26 0 15 0 36 18 13 15 04 1947 1 09 8 46 1 91 4 88 1 19 0 50 8 88 7 70 1948 3 06 5 59 6 50 5 29 3 07 0 81 2 73 1 87 1949 17 35 1 83 21 20 18 24 6 03 1 12 1 83 3 00 1950 24 44 2 52 46 88 32 68 0 96 1 22 5 80 4 33 1951 28 69 0 60 6 68 23 47 1 95 1 49 5 97 4 23 1952 14 21 4 73 5 12 18 91 1 93 1 65 0 91 0 73 1953 5 37 3 74 5 60 1 74 3 83 1 83 0 60 1 22 1954 48 2 7 66 63 70 52 55 4 88 0 86 0 37 1 23 1955 22 94 0 20 24 62 31 44 1 34 1 57 0 37 1 20 1956 8 62 4 28 4 30 6 45 5 12 2 47 2 83 0 35 1957 6 86 2 97 13 99 11 14 9 46 3 15 3 04 0 11 1958 36 78 0 42 65 52 43 78 3 71 1 53 1 76 0 23 1959 24 96 0 47 21 84 12 95 3 55 2 98 1 52 1 44 1960 7 71 10 46 4 72 0 19 13 78 2 67 1 36 1 29 1961 19 86 1 99 29 48 27 63 0 19 2 12 0 67 1 44 1962 7 2 9 59 11 56 8 79 6 81 2 73 1 23 1 48 1963 14 35 2 76 18 51 22 63 0 49 3 11 1 65 1 44 1964 11 05 3 20 19 05 16 67 4 51 3 53 1 20 2 30 1965 10 49 2 84 39 27 12 50 0 27 3 92 1 92 1 96 1966 6 47 5 36 6 90 10 25 3 70 4 75 3 36 1 34 1967 23 75 3 28 104 15 24 11 7 41 4 21 3 28 0 90 1968 19 92 2 11 50 43 11 00 1 20 5 22 4 71 0 49 1969 6 21 2 35 31 38 8 33 6 52 6 57 5 90 0 63 1970 2 94 9 76 17 95 4 10 12 69 6 52 5 57 0 90 1971 19 22 15 01 17 96 14 17 17 47 4 39 3 27 1 08 1972 25 23 7 90 0 20 19 14 5 55 3 84 3 41 0 42 1973 15 81 4 39 38 33 14 75 1 40 6 93 8 94 1 85 1974 25 48 5 08 27 40 26 40 5 53 8 01 12 10 3 65 1975 36 65 7 44 59 51 37 26 8 50 5 80 7 13 1 24 1976 17 89 11 26 49 03 23 98 11 07 5 08 5 04 0 04 1977 4 95 16 04 27 63 7 26 0 90 5 13 6 68 1 45 1978 21 28 13 56 24 96 6 50 4 16 7 19 8 99 1 65 1979 8 52 0 41 41 32 18 77 9 02 10 38 13 26 2 54 1980 28 07 2 84 40 26 32 48 13 17 11 26 12 35 0 97 1981 2 86 3 78 1 71 4 98 3 61 14 72 8 91 5 33 1982 12 49 21 95 27 84 22 09 6 52 10 53 3 83 6 45 1983 24 61 1 73 34 34 22 37 0 53 8 80 3 79 4 83 1984 6 97 7 50 10 49 6 46 15 29 9 84 4 04 5 57 1985 40 98 34 12 29 22 32 00 32 68 7 72 3 79 3 79 1986 45 1 30 56 3 59 18 40 23 96 6 16 1 19 4 91 1987 23 11 18 86 14 30 5 34 2 65 5 47 4 33 1 09 1988 22 61 5 24 18 61 16 86 8 40 6 36 4 41 1 87 1989 16 83 6 48 9 01 31 34 19 49 8 38 4 64 3 57 1990 17 85 12 07 27 24 3 20 7 13 7 84 6 26 1 49 1991 18 89 18 58 49 09 30 66 18 39 5 60 2 98 2 54 1992 5 24 4 65 21 11 7 71 7 79 3 50 2 97 0 51 1993 25 94 20 22 19 01 9 87 15 48 2 90 2 81 0 09 1994 6 08 1 67 5 59 1 29 7 18 3 91 2 60 1 28 1995 16 88 26 61 34 01 37 71 31 67 5 60 2 53 2 99 1996 13 1 3 68 16 54 23 07 0 81 5 20 3 38 1 76 1997 13 37 6 78 23 82 33 17 15 08 5 25 1 70 3 49 1998 21 64 17 21 7 36 28 58 13 52 4 85 1 61 3 19 1999 32 7 5 60 40 55 21 04 8 74 4 69 2 68 1 96 2000 15 41 8 22 6 20 9 10 20 27 5 88 3 44 2 36 2001 16 21 0 34 29 25 11 89 4 21 3 86 1 60 2 22 2002 16 81 22 91 11 77 22 10 16 79 1 63 2 48 0 83 2003 37 82 11 81 74 75 28 69 2 38 1 02 2 04 1 00 2004 17 19 12 67 14 36 10 88 7 71 1 19 3 34 2 08 2005 14 39 0 03 3 26 4 91 6 50 2 98 3 39 0 40 2006 21 52 3 00 17 69 11 78 1 21 4 81 2 57 2 18 2007 18 94 2 30 8 26 3 53 10 25 4 67 4 12 0 53 2008 44 00 1 20 34 97 38 49 1 34 1 55 0 10 1 45 (i) Calculate the averge return of the large cap, small cap, and the T bills using the Excel function AVERAGE (ii) Calculate the std dev of the large cap and small cap using the Excel function STDEVP (iii) Calculate the Sharpe ratio of the large cap using the formula (Ave ret of large cap Avg ret of T bills) Std dev of large cap Calculate the Sharpe ratio of the small cap in the similar fashion Which asset class has the highest Sharpe ratio

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Question: In this question, you are to use historical return data to estimate means and std deviations. Rates of Return 1926-2008 World Portfolios U.S. Markets Year

In this question, you are to use historical return data to estimate means and std deviations.

Rates of Return 1926-2008
	World Portfolios		U.S. Markets
Year	Equity Return in U.S. Dollars	Bond Return in U.S. Dollars	Small Stocks	Large Stock	Long-Term T-Bonds	T-Bills	Inflation	Real T-bill Rates
1926	25.24	8.10	-8.91	12.21	4.54	3.19	-1.12	4.36
1927	23.15	9.62	35.48	35.99	8.11	3.13	-2.26	5.51
1928	28.62	2.44	51.31	39.29	-0.93	3.54	-1.16	4.76
1929	-12.56	3.45	-48.35	-7.66	4.41	4.74	0.59	4.13
1930	-22.6	6.04	-48.36	-25.90	6.22	2.43	-6.40	9.43
1931	-39.94	-12.32	-53.17	-45.56	-5.31	1.09	-9.32	11.48
1932	1.46	18.26	8.58	-9.14	11.89	0.95	-10.27	12.50
1933	70.81	29.26	153.18	54.56	1.03	0.30	0.76	-0.46
1934	0.15	3.87	34.78	-2.32	10.15	0.18	1.52	-1.32
1935	22.44	-1.41	72.87	45.67	4.98	0.14	2.99	-2.77
1936	18.84	-0.49	77.01	33.55	6.52	0.18	1.45	-1.25
1937	-17.7	-0.96	-55.05	-36.03	0.43	0.29	2.86	-2.50
1938	6.21	0.65	15.46	29.42	5.25	-0.04	-2.78	2.82
1939	-5.6	-5.11	-6.79	-1.06	5.90	0.01	0.00	0.01
1940	7.97	11.32	-14.15	-9.65	6.54	-0.02	0.71	-0.72
1941	13.26	5.61	-13.42	-11.20	0.99	0.04	9.93	-9.00
1942	-0.56	-3.69	39.66	20.80	5.39	0.28	9.03	-8.03
1943	19.3	2.76	108.74	26.54	4.87	0.36	2.96	-2.53
1944	13.49	3.02	61.46	20.96	3.59	0.33	2.30	-1.93
1945	13.72	0.08	81.98	36.11	6.84	0.32	2.25	-1.89
1946	-16.91	-13.50	-13.17	-9.26	0.15	0.36	18.13	-15.04
1947	-1.09	-8.46	-1.91	4.88	-1.19	0.50	8.88	-7.70
1948	3.06	5.59	-6.50	5.29	3.07	0.81	2.73	-1.87
1949	17.35	1.83	21.20	18.24	6.03	1.12	-1.83	3.00
1950	24.44	2.52	46.88	32.68	-0.96	1.22	5.80	-4.33
1951	28.69	0.60	6.68	23.47	-1.95	1.49	5.97	-4.23
1952	14.21	4.73	5.12	18.91	1.93	1.65	0.91	0.73
1953	5.37	3.74	-5.60	-1.74	3.83	1.83	0.60	1.22
1954	48.2	7.66	63.70	52.55	4.88	0.86	-0.37	1.23
1955	22.94	0.20	24.62	31.44	-1.34	1.57	0.37	1.20
1956	8.62	-4.28	4.30	6.45	-5.12	2.47	2.83	-0.35
1957	-6.86	2.97	-13.99	-11.14	9.46	3.15	3.04	0.11
1958	36.78	-0.42	65.52	43.78	-3.71	1.53	1.76	-0.23
1959	24.96	0.47	21.84	12.95	-3.55	2.98	1.52	1.44
1960	7.71	10.46	-4.72	0.19	13.78	2.67	1.36	1.29
1961	19.86	1.99	29.48	27.63	0.19	2.12	0.67	1.44
1962	-7.2	9.59	-11.56	-8.79	6.81	2.73	1.23	1.48
1963	14.35	2.76	18.51	22.63	-0.49	3.11	1.65	1.44
1964	11.05	3.20	19.05	16.67	4.51	3.53	1.20	2.30
1965	10.49	2.84	39.27	12.50	-0.27	3.92	1.92	1.96
1966	-6.47	5.36	-6.90	-10.25	3.70	4.75	3.36	1.34
1967	23.75	-3.28	104.15	24.11	-7.41	4.21	3.28	0.90
1968	19.92	2.11	50.43	11.00	-1.20	5.22	4.71	0.49
1969	-6.21	-2.35	-31.38	-8.33	-6.52	6.57	5.90	0.63
1970	-2.94	9.76	-17.95	4.10	12.69	6.52	5.57	0.90
1971	19.22	15.01	17.96	14.17	17.47	4.39	3.27	1.08
1972	25.23	7.90	0.20	19.14	5.55	3.84	3.41	0.42
1973	-15.81	4.39	-38.33	-14.75	1.40	6.93	8.94	-1.85
1974	-25.48	5.08	-27.40	-26.40	5.53	8.01	12.10	-3.65
1975	36.65	7.44	59.51	37.26	8.50	5.80	7.13	-1.24
1976	17.89	11.26	49.03	23.98	11.07	5.08	5.04	0.04
1977	4.95	16.04	27.63	-7.26	0.90	5.13	6.68	-1.45
1978	21.28	13.56	24.96	6.50	-4.16	7.19	8.99	-1.65
1979	8.52	0.41	41.32	18.77	9.02	10.38	13.26	-2.54
1980	28.07	2.84	40.26	32.48	13.17	11.26	12.35	-0.97
1981	-2.86	-3.78	-1.71	-4.98	3.61	14.72	8.91	5.33
1982	12.49	21.95	27.84	22.09	6.52	10.53	3.83	6.45
1983	24.61	1.73	34.34	22.37	-0.53	8.80	3.79	4.83
1984	6.97	7.50	-10.49	6.46	15.29	9.84	4.04	5.57
1985	40.98	34.12	29.22	32.00	32.68	7.72	3.79	3.79
1986	45.1	30.56	3.59	18.40	23.96	6.16	1.19	4.91
1987	23.11	18.86	-14.30	5.34	-2.65	5.47	4.33	1.09
1988	22.61	5.24	18.61	16.86	8.40	6.36	4.41	1.87
1989	16.83	6.48	9.01	31.34	19.49	8.38	4.64	3.57
1990	-17.85	12.07	-27.24	-3.20	7.13	7.84	6.26	1.49
1991	18.89	18.58	49.09	30.66	18.39	5.60	2.98	2.54
1992	-5.24	4.65	21.11	7.71	7.79	3.50	2.97	0.51
1993	25.94	20.22	19.01	9.87	15.48	2.90	2.81	0.09
1994	6.08	-1.67	-5.59	1.29	-7.18	3.91	2.60	1.28
1995	16.88	26.61	34.01	37.71	31.67	5.60	2.53	2.99
1996	13.1	3.68	16.54	23.07	-0.81	5.20	3.38	1.76
1997	13.37	6.78	23.82	33.17	15.08	5.25	1.70	3.49
1998	21.64	17.21	-7.36	28.58	13.52	4.85	1.61	3.19
1999	32.7	-5.60	40.55	21.04	-8.74	4.69	2.68	1.96
2000	-15.41	8.22	-6.20	-9.10	20.27	5.88	3.44	2.36
2001	-16.21	-0.34	29.25	-11.89	4.21	3.86	1.60	2.22
2002	-16.81	22.91	-11.77	-22.10	16.79	1.63	2.48	-0.83
2003	37.82	11.81	74.75	28.69	2.38	1.02	2.04	-1.00
2004	17.19	12.67	14.36	10.88	7.71	1.19	3.34	-2.08
2005	14.39	-0.03	3.26	4.91	6.50	2.98	3.39	-0.40
2006	21.52	-3.00	17.69	11.78	-1.21	4.81	2.57	2.18
2007	18.94	2.30	-8.26	3.53	10.25	4.67	4.12	0.53
2008	-44.00	1.20	-34.97	-38.49	1.34	1.55	0.10	1.45

(i) Calculate the averge return of the large cap, small cap, and the T-bills using the Excel function AVERAGE

(ii) Calculate the std. dev. of the large cap and small cap using the Excel function STDEVP;

(iii) Calculate the Sharpe ratio of the large cap using the formula: (Ave ret of large cap - Avg ret of T-bills)/Std dev. of large cap; Calculate the Sharpe ratio of the small cap in the similar fashion. Which asset class has the highest Sharpe ratio?

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