Question

Please use the excel function data on stocks, bonds, bills to start discussion on time value.

First question:

Using the data and $100 invested in stocks, bonds and bills, confirm the values at 2011.

Terminal value at 2011= $100(1+r1)(1+r2)...(1+r84)

where r1= actual return given for 1928

r2=actual return given for 1929

r84=actual return given for 2011 for stocks, bonds and bills

Second Question:

Investing over 84 years is a little far fetched unless your grandfather was like Donald Trump's G.PA. Now consider dividing 1928-2011 to three sub-period of 1928-56 (28 years), 1956-1984 28 yr) and 1984-2011 (27 yr). Let's see how investment of $100 in stocks, bonds, bills using again the actual returns provided in each asset class (stocks, bonds, bills) perform? Compare, the future value of each investment as if in the second 28 years, and last 27 years you start with $100 investment in stocks, bonds, bills. What are the lessons we learn in this exercise as far as your future contribution to your own 401K is concerned?

	Annual returns stocks bonds bills				compound value of $100					DATE	VALUE	GDP growth rate											1929-69	1970-1999	2000-2010			43.81%	0.3458	7.2317E-08
	Year	Stocks	T.Bills	T.Bonds	Stocks	T.Bills	T.Bonds	skewness		1929	976.1	-0.086159205	-0.086159205	1		-0.086159205		0.060599779		0.010796691			-0.086159205	0.033565385	0.010796691			-8.30%	-0.1753	-9.42131E-09
1	1928	43.81%	3.08%	0.84%	$143.81	$103.08	$100.84	7.2317E-08		1930	892	-0.064798206	-0.064798206	2		-0.064798206		0.043716203		0.018134509			-0.064798206	0.053135276	0.018134509			-25.12%	-0.3435	-7.08836E-08
2	1929	-8.30%	3.16%	4.20%	$131.88	$106.34	$105.07	-9.42131E-09		1931	834.2	-0.130664109	-0.130664109	3		-0.130664109		0.057865169		0.025409119			-0.130664109	0.057926698	0.025409119			-43.84%	-0.5307	-2.61404E-07
3	1930	-25.12%	4.55%	4.54%	$98.75	$111.18	$109.85	-7.08836E-08		1932	725.2	-0.012961942	-0.012961942	4		-0.012961942		0.064200153		0.034681153			-0.012961942	-0.005516203	0.034681153			-8.64%	-0.1787	-9.9802E-09
4	1931	-43.84%	2.31%	-2.56%	$55.46	$113.74	$107.03	-2.61404E-07		1933	715.8	0.108829282	0.108829282	5		0.108829282		0.065178819		0.030709812			0.108829282	-0.002108193	0.030709812			49.98%	0.4075	1.18345E-07
5	1932	-8.64%	1.07%	8.79%	$50.66	$114.96	$116.44	-9.9802E-09		1934	793.7	0.088824493	0.088824493	6		0.088824493		0.025272637		0.026578468			0.088824493	0.053636625	0.026578468			-1.19%	-0.1042	-1.97865E-09
6	1933	49.98%	0.96%	1.86%	$75.99	$116.06	$118.60	1.18345E-07		1935	864.2	0.130525341	0.130525341	7		0.130525341		0.048410845		0.019130301			0.130525341	0.045981039	0.019130301			46.74%	0.3751	9.23011E-08
7	1934	-1.19%	0.32%	7.96%	$75.09	$116.44	$128.05	-1.97865E-09		1936	977	0.051279427	0.051279427	8		0.051279427		0.031066128		-0.003369578			0.051279427	0.055777856	-0.003369578			31.94%	0.2271	2.04841E-08
8	1935	46.74%	0.18%	4.47%	$110.18	$116.64	$133.78	9.23011E-08		1937	1027.1	-0.034368611	-0.034368611	9		-0.034368611		0.001902212		-0.030694657			-0.034368611	0.031254407	-0.030694657			-35.34%	-0.4457	-1.54844E-07
9	1936	31.94%	0.17%	5.02%	$145.38	$116.84	$140.49	2.04841E-08		1938	991.8	0.08076225	0.08076225	10		0.08076225		0.033565385		0.023914594			0.08076225	-0.00275209	0.023914594			29.28%	0.2005	1.40964E-08
10	1937	-35.34%	0.30%	1.38%	$94.00	$117.19	$142.43	-1.54844E-07		1939	1071.9	0.087694748	0.087694748	11		0.087694748		0.053135276		0.018073949			0.087694748	0.02538567	0.018073949			-1.10%	-0.1033	-1.92782E-09
11	1938	29.28%	0.08%	4.21%	$121.53	$117.29	$148.43	1.40964E-08		1940	1165.9	0.170769363	0.170769363	12		0.170769363		0.057926698		0.173364361	0.015760396		0.170769363	-0.019424617	0.173364361	0.015760396		-10.67%	-0.199	-1.37824E-08
12	1939	-1.10%	0.04%	4.41%	$120.20	$117.33	$154.98	-1.92782E-09		1941	1365	0.184468864	0.184468864	13		0.184468864		-0.005516203					0.184468864	0.045176358				-12.77%	-0.22	-1.86223E-08
13	1940	-10.67%	0.03%	5.40%	$107.37	$117.36	$163.35	-1.37824E-08		1942	1616.8	0.163718456	0.163718456	14		0.163718456		-0.002108193					0.163718456	0.071865468				19.17%	0.0994	1.71761E-09
14	1941	-12.77%	0.08%	-2.02%	$93.66	$117.46	$160.04	-1.86223E-08		1943	1881.5	0.080786606	0.080786606	15		0.080786606		0.053636625					0.080786606	0.041375637				25.06%	0.1583	6.93759E-09
15	1942	19.17%	0.34%	2.29%	$111.61	$117.85	$163.72	1.71761E-09		1944	2033.5	-0.011212196	-0.011212196	16		-0.011212196		0.045981039					-0.011212196	0.034646521				19.03%	0.098	1.64605E-09
16	1943	25.06%	0.38%	2.49%	$139.59	$118.30	$167.79	6.93759E-09		1945	2010.7	-0.109414632	-0.109414632	17		-0.109414632		0.055777856					-0.109414632	0.031989266				35.82%	0.2659	3.28792E-08
17	1944	19.03%	0.38%	2.58%	$166.15	$118.75	$172.12	1.64605E-09		1946	1790.7	-0.008990897	-0.008990897	18		-0.008990897		0.031254407					-0.008990897	0.041111263				-8.43%	-0.1766	-9.63247E-09
18	1945	35.82%	0.38%	3.80%	$225.67	$119.20	$178.67	3.28792E-08		1947	1774.6	0.044009918	0.044009918	19		0.044009918		-0.00275209					0.044009918	0.03572837				5.20%	-0.0403	-1.14467E-10
19	1946	-8.43%	0.38%	3.13%	$206.65	$119.65	$184.26	-9.63247E-09		1948	1852.7	-0.005181627	-0.005181627	20		-0.005181627		0.02538567					-0.005181627	0.018770941				5.70%	-0.0353	-7.6929E-11
20	1947	5.20%	0.57%	0.92%	$217.39	$120.33	$185.95	-1.14467E-10		1949	1843.1	0.087407086	0.087407086	21		0.087407086		-0.019424617					0.087407086	-0.002342066				18.30%	0.0907	1.30493E-09
21	1948	5.70%	1.02%	1.95%	$229.79	$121.56	$189.58	-7.6929E-11		1950	2004.2	0.077387486	0.077387486	22		0.077387486		0.045176358					0.077387486	0.0339273				30.81%	0.2158	1.7576E-08
22	1949	18.30%	1.10%	4.66%	$271.85	$122.90	$198.42	1.30493E-09		1951	2159.3	0.038299449	0.038299449	23		0.038299449		0.071865468					0.038299449	0.02852657				23.68%	0.1445	5.27678E-09
23	1950	30.81%	1.17%	0.43%	$355.60	$124.34	$199.27	1.7576E-08		1952	2242	0.04603033	0.04603033	24		0.04603033		0.041375637					0.04603033	0.04073413				18.15%	0.0892	1.24125E-09
24	1951	23.68%	1.48%	-0.30%	$439.80	$126.18	$198.68	5.27678E-09		1953	2345.2	-0.006310762	-0.006310762	25		-0.006310762		0.034646521					-0.006310762	0.025149214				-1.21%	-0.1044	-1.99006E-09
25	1952	18.15%	1.67%	2.27%	$519.62	$128.29	$203.19	1.24125E-09		1954	2330.4	0.072004806	0.072004806	26		0.072004806		0.031989266					0.072004806	0.037398195				52.56%	0.4333	1.42276E-07
26	1953	-1.21%	1.89%	4.14%	$513.35	$130.72	$211.61	-1.99006E-09		1955	2498.2	0.019774237	0.019774237	27		0.019774237		0.041111263					0.019774237	0.044569161				32.60%	0.2337	2.23225E-08
27	1954	52.56%	0.96%	3.29%	$783.18	$131.98	$218.57	1.42276E-07		1956	2547.6	0.020097347	0.020097347	28		0.020097347		0.03572837					0.020097347	0.043551123				7.44%	-0.0179	-1.00306E-11
28	1955	32.60%	1.66%	-1.34%	$1,038.47	$134.17	$215.65	2.23225E-08		1957	2598.8	-0.009004156	-0.009004156	29		-0.009004156		0.018770941					-0.009004156	0.048273916				-10.46%	-0.1969	-1.33507E-08
29	1956	7.44%	2.56%	-2.26%	$1,115.73	$137.60	$210.79	-1.00306E-11		1958	2575.4	0.071717015	0.071717015	30		0.071717015		-0.002342066					0.071717015	0.041380783				43.72%	0.3449	7.17539E-08
30	1957	-10.46%	3.23%	6.80%	$999.05	$142.04	$225.11	-1.33507E-08		1959	2760.1	0.024781711	0.024781711	31		0.024781711		0.0339273					0.024781711	0.988694005	0.032956467			12.06%	0.0283	3.96392E-11
31	1958	43.72%	1.78%	-2.10%	$1,435.84	$144.57	$220.39	7.17539E-08		1960	2828.5	0.023298568	0.023298568	32		1.170101873	0.036565684	0.02852657					0.023298568					0.34%	-0.0889	-1.22877E-09
32	1959	12.06%	3.26%	-2.65%	$1,608.95	$149.27	$214.56	3.96392E-11		1961	2894.4	0.060599779	0.060599779	33				0.04073413					0.060599779					26.64%	0.1741	9.22916E-09
33	1960	0.34%	3.05%	11.64%	$1,614.37	$153.82	$239.53	-1.22877E-09		1962	3069.8	0.043716203	0.043716203	34				0.025149214					0.043716203					-8.81%	-0.1804	-1.02678E-08
34	1961	26.64%	2.27%	2.06%	$2,044.40	$157.30	$244.46	9.22916E-09		1963	3204	0.057865169	0.057865169	35				0.037398195					0.057865169					22.61%	0.1338	4.18923E-09
35	1962	-8.81%	2.78%	5.69%	$1,864.26	$161.67	$258.38	-1.02678E-08		1964	3389.4	0.064200153	0.064200153	36				0.044569161					0.064200153					16.42%	0.0719	6.50058E-10
36	1963	22.61%	3.11%	1.68%	$2,285.80	$166.70	$262.74	4.18923E-09		1965	3607	0.065178819	0.065178819	37				0.043551123					0.065178819					12.40%	0.0317	5.57113E-11
37	1964	16.42%	3.51%	3.73%	$2,661.02	$172.54	$272.53	6.50058E-10		1966	3842.1	0.025272637	0.025272637	38				0.048273916					0.025272637					-9.97%	-0.192	-1.23785E-08
38	1965	12.40%	3.90%	0.72%	$2,990.97	$179.28	$274.49	5.57113E-11		1967	3939.2	0.048410845	0.048410845	39				0.041380783					0.048410845					23.80%	0.1457	5.40934E-09
39	1966	-9.97%	4.84%	2.91%	$2,692.74	$187.95	$282.47	-1.23785E-08		1968	4129.9	0.031066128	0.031066128	40				0.010796691					0.031066128					10.81%	0.0158	6.89822E-12
40	1967	23.80%	4.33%	-1.58%	$3,333.69	$196.10	$278.01	5.40934E-09		1969	4258.2	0.001902212	0.001902212	41				1.39770264	0.035838529				0.001902212					-8.24%	-0.1747	-9.32491E-09
41	1968	10.81%	5.26%	3.27%	$3,694.23	$206.41	$287.11	6.89822E-12		1970	4266.3	0.033565385	0.033565385	42									1.591612386	0.038819814				3.56%	-0.0567	-3.18797E-10
42	1969	-8.24%	6.56%	-5.01%	$3,389.77	$219.96	$272.71	-9.32491E-09		1971	4409.5	0.053135276	0.053135276	43														14.22%	0.0499	2.17304E-10
43	1970	3.56%	6.69%	16.75%	$3,510.49	$234.66	$318.41	-3.18797E-10		1972	4643.8	0.057926698	0.057926698	44														18.76%	0.0953	1.51372E-09
44	1971	14.22%	4.54%	9.79%	$4,009.72	$245.32	$349.57	2.17304E-10		1973	4912.8	-0.005516203	-0.005516203	45														-14.31%	-0.2354	-2.28131E-08
45	1972	18.76%	3.95%	2.82%	$4,761.76	$255.01	$359.42	1.51372E-09		1974	4885.7	-0.002108193	-0.002108193	46														-25.90%	-0.3513	-7.58229E-08
46	1973	-14.31%	6.73%	3.66%	$4,080.44	$272.16	$372.57	-2.28131E-08		1975	4875.4	0.053636625	0.053636625	47														37.00%	0.2777	3.74536E-08
47	1974	-25.90%	7.78%	1.99%	$3,023.54	$293.33	$379.98	-7.58229E-08		1976	5136.9	0.045981039	0.045981039	48														23.83%	0.146	5.44282E-09
48	1975	37.00%	5.99%	3.61%	$4,142.10	$310.90	$393.68	3.74536E-08		1977	5373.1	0.055777856	0.055777856	49														-6.98%	-0.1621	-7.44929E-09
49	1976	23.83%	4.97%	15.98%	$5,129.20	$326.35	$456.61	5.44282E-09		1978	5672.8	0.031254407	0.031254407	50														6.51%	-0.0272	-3.51943E-11
50	1977	-6.98%	5.13%	1.29%	$4,771.20	$343.09	$462.50	-7.44929E-09		1979	5850.1	-0.00275209	-0.00275209	51														18.52%	0.0929	1.40221E-09
51	1978	6.51%	6.93%	-0.78%	$5,081.77	$366.87	$458.90	-3.51943E-11		1980	5834	0.02538567	0.02538567	52														31.74%	0.2251	1.99477E-08
52	1979	18.52%	9.94%	0.67%	$6,022.89	$403.33	$461.98	1.40221E-09		1981	5982.1	-0.019424617	-0.019424617	53														-4.70%	-0.1393	-4.72736E-09
53	1980	31.74%	11.22%	-2.99%	$7,934.26	$448.58	$448.17	1.99477E-08		1982	5865.9	0.045176358	0.045176358	54														20.42%	0.1119	2.45051E-09
54	1981	-4.70%	14.30%	8.20%	$7,561.16	$512.73	$484.91	-4.72736E-09		1983	6130.9	0.071865468	0.071865468	55														22.34%	0.1311	3.9407E-09
55	1982	20.42%	11.01%	32.81%	$9,105.08	$569.18	$644.04	2.45051E-09		1984	6571.5	0.041375637	0.041375637	56														6.15%	-0.0308	-5.10996E-11
56	1983	22.34%	8.45%	3.20%	$11,138.90	$617.26	$664.65	3.9407E-09		1985	6843.4	0.034646521	0.034646521	57														31.24%	0.2201	1.86477E-08
57	1984	6.15%	9.61%	13.73%	$11,823.51	$676.60	$755.92	-5.10996E-11		1986	7080.5	0.031989266	0.031989266	58														18.49%	0.0926	1.38867E-09
58	1985	31.24%	7.49%	25.71%	$15,516.60	$727.26	$950.29	1.86477E-08		1987	7307	0.041111263	0.041111263	59														5.81%	-0.0342	-6.99591E-11
59	1986	18.49%	6.04%	24.28%	$18,386.33	$771.15	$1,181.06	1.38867E-09		1988	7607.4	0.03572837	0.03572837	60														16.54%	0.0731	6.83153E-10
60	1987	5.81%	5.72%	-4.96%	$19,455.08	$815.27	$1,122.47	-6.99591E-11		1989	7879.2	0.018770941	0.018770941	61														31.48%	0.2225	1.92644E-08
61	1988	16.54%	6.45%	8.22%	$22,672.40	$867.86	$1,214.78	6.83153E-10		1990	8027.1	-0.002342066	-0.002342066	62														-3.06%	-0.1229	-3.24654E-09
62	1989	31.48%	8.11%	17.69%	$29,808.58	$938.24	$1,429.72	1.92644E-08		1991	8008.3	0.0339273	0.0339273	63														30.23%	0.21	1.61966E-08
63	1990	-3.06%	7.55%	6.24%	$28,895.11	$1,009.08	$1,518.87	-3.24654E-09		1992	8280	0.02852657	0.02852657	64														7.49%	-0.0174	-9.21326E-12
64	1991	30.23%	5.61%	15.00%	$37,631.51	$1,065.69	$1,746.77	1.61966E-08		1993	8516.2	0.04073413	0.04073413	65														9.97%	0.0074	7.08697E-13
65	1992	7.49%	3.41%	9.36%	$40,451.51	$1,101.98	$1,910.30	-9.21326E-12		1994	8863.1	0.025149214	0.025149214	66														1.33%	-0.079	-8.62277E-10
66	1993	9.97%	2.98%	14.21%	$44,483.33	$1,134.84	$2,181.77	7.08697E-13		1995	9086	0.037398195	0.037398195	67														37.20%	0.2797	3.82686E-08
67	1994	1.33%	3.99%	-8.04%	$45,073.14	$1,180.07	$2,006.43	-8.62277E-10		1996	9425.8	0.044569161	0.044569161	68														23.82%	0.1459	5.43165E-09
68	1995	37.20%	5.52%	23.48%	$61,838.19	$1,245.15	$2,477.55	3.82686E-08		1997	9845.9	0.043551123	0.043551123	69														31.86%	0.2263	2.02684E-08
69	1996	23.82%	5.02%	1.43%	$76,566.48	$1,307.68	$2,512.94	5.43165E-09		1998	10274.7	0.048273916	0.048273916	70														28.34%	0.1911	1.22053E-08
70	1997	31.86%	5.05%	9.94%	$100,958.71	$1,373.76	$2,762.71	2.02684E-08		1999	10770.7	0.041380783	0.041380783	71														20.89%	0.1166	2.77244E-09
71	1998	28.34%	4.73%	14.92%	$129,568.35	$1,438.70	$3,174.95	1.22053E-08		2000	11216.4	0.010796691	0.010796691	72														-9.03%	-0.1826	-1.0648E-08
72	1999	20.89%	4.51%	-8.25%	$156,629.15	$1,503.58	$2,912.88	2.77244E-09		2001	11337.5	0.018134509	0.018134509	73														-11.85%	-0.2108	-1.63824E-08
73	2000	-9.03%	5.76%	16.66%	$142,482.69	$1,590.23	$3,398.03	-1.0648E-08		2002	11543.1	0.025409119	0.025409119	74														-21.97%	-0.312	-5.31165E-08
74	2001	-11.85%	3.67%	5.57%	$125,598.83	$1,648.63	$3,587.37	-1.63824E-08		2003	11836.4	0.034681153	0.034681153	75														28.36%	0.1913	1.22436E-08
75	2002	-21.97%	1.66%	15.12%	$98,009.73	$1,675.96	$4,129.65	-5.31165E-08		2004	12246.9	0.030709812	0.030709812	76														10.74%	0.0151	6.02139E-12
76	2003	28.36%	1.03%	0.38%	$125,801.18	$1,693.22	$4,145.15	1.22436E-08		2005	12623	0.026578468	0.026578468	77														4.83%	-0.044	-1.48979E-10
77	2004	10.74%	1.23%	4.49%	$139,315.72	$1,714.00	$4,331.30	6.02139E-12		2006	12958.5	0.019130301	0.019130301	78														15.61%	0.0638	4.5418E-10
78	2005	4.83%	3.01%	2.87%	$146,050.90	$1,765.59	$4,455.50	-1.48979E-10		2007	13206.4	-0.003369578	-0.003369578	79														5.48%	-0.0375	-9.22273E-11
79	2006	15.61%	4.68%	1.96%	$168,853.19	$1,848.18	$4,542.87	4.5418E-10		2008	13161.9	-0.030694657	-0.030694657	80														-36.55%	-0.4578	-1.678E-07
80	2007	5.48%	4.64%	10.21%	$178,114.34	$1,933.98	$5,006.69	-9.22273E-11		2009	12757.9	0.023914594	0.023914594	81														25.94%	0.1671	8.16009E-09
81	2008	-36.55%	1.59%	20.10%	$113,009.37	$1,964.64	$6,013.10	-1.678E-07		2010	13063	0.018073949	0.018073949	82														14.82%	0.0559	3.05493E-10
82	2009	25.94%	0.14%	-11.12%	$142,318.62	$1,967.29	$5,344.65	8.16009E-09		2011	13299.1		2.753670752	0.033581351														2.07%	-0.0716	-6.41955E-10
83	2010	14.82%	0.13%	8.46%	$163,411.79	$1,969.84	$5,796.96	3.05493E-10																						-9.47347E-08
84	2011	2.07%	0.03%	16.04%	$166,787.51	$1,970.44	$6,726.52	-6.41955E-10
						Risk Premium		-9.47347E-08
	Arithmetic Average					Stocks - T.Bills	Stocks - T.Bonds
	1928-2011	11.20%	3.66%	5.41%		7.55%	5.79%
	1962-2011	10.60%	5.22%	7.24%		5.38%	3.36%
	2002-2011	4.93%	1.81%	6.85%		3.12%	-1.92%
						Risk Premium
	Geometric Average					Stocks - T.Bills	Stocks - T.Bonds
	1928-2011	9.23%	3.61%	5.14%		5.62%	4.10%
	1962-2011	9.20%	5.19%	6.85%		4.02%	2.35%
	2002-2011	2.88%	1.80%	6.49%		1.08%	-3.61%

Answer 1

1928-2011: Mean, Standard Deviation and Return / Risk

1928: 1956 compound value of $100

1957: 1984 compound value of $100:

1985: 2011 compound value of $100:

In All:

Returns of the stocks for period 1928-2011 and of all sub- periods are approximately same. Standard Deviation of stocks is highest (Risk-reward)