Calculating the Geometric Average Return Calculate the geometric average return for S&P 500 large-cap stocks for the first five years in Table 12.1, 1926–1930.

Question

Calculating the Geometric Average Return

Calculate the geometric average return for S&P 500 large-cap stocks for the first five years in Table 12.1, 1926–1930.

First, convert percentages to decimal returns, add 1, and then calculate their product:

Table 12.1, Year-to-Year Total Returns: 1926–2010.

Consumer Price Index	.U.S Treasury Bills	Long-Term	-Large Company Stocks	Year	Consumer Price Index	.U.S Treasury Bills	Long-Term Government Bonds	Large Company- Stocks	Year
6.2	6.9	5.63-	8.43-	1969	1.12%-	3.30%	5.69%	13.75%	1926
5.57	6.5	18.92	3.94	1970	2.26-	3.15	6.58	35.7	1927
3.27	4.36	11.24	14.3	1971	1.16-	4.05	1.15	45.08	1928
3.41	4.23	2.39	18.99	1972	58.	4.47	4.39	8.8-	1929
8.71	7.29	3.3	14.69-	1973	6.40-	2.27	4.47	25.13-	1930
12.34	7.99	4	26.47-	1974	9.32-	1.15	2.15-	43.6-	1931
6.94	5.87	5.52	37.23	1975	10.27-	88.	8.51	8.75-	1932
4.86	5.07	15.56	23.93	1976	76.	52.	1.92	52.95	1933
6.7	5.45	0.38	7.16-	1977	1.52	27.	7.59	2.31-	1934
9.02	7.64	1.26-	6.57	1978	2.99	17.	4.2	46.79	1935
13.29	10.56	1.26	18.61	1979	1.45	17.	5.13	32.49	1936
12.52	12.1	2.48-	32.5	1980	2.86	27.	1.44	-35.45	1937
8.92	14.6	4.04	4.92-	1981	2.78-	06.	4.21	31.63	1938
3.83	10.94	44.28	21.55	1982	0.0	04.	3.84	1.43-	1939
3.79	8.99	1.29	22.56	1983	71.	04.	5.7	10.36-	1940
3.95	9.9	15.29	6.27	1984	9.93	14.	47.	12.02-	1941
3.8	7.71	32.27	31.73	1985	9.03	34.	1.8	20.75	1942
1.1	6.09	22.39	18.67	1986	2.96	38.	2.01	25.38	1943
4.43	5.88	3.03-	5.25	1987	2.3	38.	2.27	19.49	1944
4.42	6.94	6.84	16.61	1988	2.25	38.	5.29	36.21	1945
4.65	8.44	18.54	31.69	1989	18.13	38.	54.	8.42-	1946
6.11	7.69	7.74	3.1-	1990	8.84	62.	1.02-	5.05	1947
3.06	5.43	19.36	30.46	1991	2.99	1.06	2.66	4.99	1948
2.9	3.48	7.34	7.62	1992	2.07-	1.12	4.58	17.81	1949
2.75	3.03	13.06	10.08	1993	5.93	1.22	98.-	30.05	1950
2.67	4.39	7.32-	1.32	1994	6	1.56	20.-	23.79	1951
2.54	5.61	25.94	37.58	1995	75.	1.75	2.43	18.39	1952
3.32	5.14	0.13	22.96	1996	75.	1.87	2.28	1.07-	1953
1.7	5.19	12.02	33.36	1997	74.-	93.	3.08	52.23	1954
1.61	4.86	14.45	28.58	1998	37.	1.80	73.-	31.62	1955
2.68	4.8	7.51-	21.04	1999	2.99	2.66	1.72-	6.91	1956
3.39	5.98	17.22	9.1-	2000	2.9	3.28	6.82	10.5-	1957
1.55	3.33	5.51	11.89-	2001	1.76	1.71	1.72-	43.57	1958
2.38	1.61	15.15	22.1-	2002	1.73	3.48	2.02-	12.01	1959
1.88	94.	2.01	28.89	2003	1.36	2.81	11.21	47.	1960
3.26	1.14	8.12	10.88	2004	67.	2.40	2.20	26.84	1961
3.42	2.79	6.89	4.91	2005	1.33	2.82	5.72	-8.75	1962
2.54	4.97	28.	15.79	2006	1.64	3.23	1.79	22.7	1963
4.08	4.52	10.85	5.49	2007	97.	3.62	3.71	16.43	1964
09.	1.24	41.78	37-	2008	1.92	4.06	93.	12.38	1965
2.72	15.	25.61-	26.46	2009	3.46	4.94	5.12	10.06-	1966
1.5	14.	7.73	15.06	2010	3.04	4.39	2.86-	23.98	1967
					4.72	5.49	2.25	11.03	1968

Accepted Answer

First, convert percentages to decimal returns, add 1, and then calculate their product:

Product	S&P 500 Returns
1.1375	13.75
×1.3570	35.7
×1.4508	45.08
×.9120	-8.80
×.7487	-25.13
1.5291

Notice that the number 1.5291 is what our investment is worth after five years if we started with a $1 investment. The geometric average return is then calculated as follows:

Geometric average return = [latex] 1.5291^{1/5} -1=.0887, [/latex] or 8.87%

Thus, the geometric average return is about 8.87 percent in this example. Here is a tip: If you are using a financial calculator, you can put $1 in as the present value, $1.5291 as the future value, and 5 as the number of periods. Then, solve for the unknown rate. You should get the same answer we did.

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