Part 1
Using data in Excel file comparison.xlsx, construct four graphs and one table as follows. Your
graphs and table will be based on the years 1945 to 2015, rather than the longer period in Siegel,
and include data on only two assets: S&P 500 total returns and US Gov. Bond total returns (and
cash in Graph 1). The CPI is also included so that you can construct real values and real returns.
Graph 1: Replicate Fig. 1.1 in Seigel, page 6, based on the real value of the S&P 500 total return
index, Government Bonds, and cash.
For stocks and bonds, construct the real value by dividing each index by the price level, the CPI
divided by 100. Then construct the real rate of return by the percent change from year to year.
You want all the investments to begin at the value 1. One way to do this is to start at 1 and then
increase the next year’s value by the real increase of that index. For example, if stocks increased
by 3% from 1945 to 1946, and 5 % from 1946 to 1947, the value would be 1 in 1945, 1.03 in
1946, and 1.03(1.05)=1.0815 in 1947.
For cash, just compute the real value of $1 with 1945 as the base year of the CPI.
Be sure to use the logarithmic scale, an option on the vertical axis menu of Excel.
Graph 2: Present a bar graph of the annual real total return to the S&P 500 and indicate on the
graph with three lines the average annual return, and plus and minus two standard deviations
from the average annual return. (This is the only graph not shown in Seigel, so an example will
be discussed in lecture.)
Graph 3: Replicate Figure 6-2 page 98 in Seigel for the S&P 500 total returns only for 1,2, 5,
and 10 year holding periods.
For this graph, first compute the annual real return based on continuous compounding.
(Continuous compounding works better here since the average return of the longer holding
periods is then just the average of the one year returns. For example, the average return to a 5-
year holding period is the average of 5 one-year holding periods.)
Allow holding periods to overlap. For example, the average return to the two year holding period
1946-1947 is simply the average of the returns in 1946 and 1947. The next two year holding
period is 1947-1948, and so forth.
Graph 4: Replicate Figure 6-4 page 102 in Seigel for only the 1 year holding period. Your graph
should show 11 distinct combinations of stocks and bonds, following the computations in
Estrada page 49, Table 5.2. (You are using the S&P 500 and government bonds instead of
Boeing and IBM, of course. Please use real returns here also.)
Table 1: Neatly summarize with clear labels the following information: the compound average
annual real return to stocks, bonds, and cash (as in the box on Fig 1.1 of Seigel).
Econ 135 Report 1 Due in class Wednesday, Feb 17
ALL GRAPHS SHOULD BE CLEAR AND LARGE (AT LEAST ½ PAGE), with neat titles
(including graph number), legends, and axes labels. You should be able to look at the graph
alone and know what it presents. Take the time to format all elements in the graph and tables,
like axes numbers and percentages, as simply as possible with no extraneous decimals. Use
Seigel’s graphs and tables as a guide. You must attend class and discussion sessions regularly
for further guidance. DO NOT TURN IN THE RAW DATA, JUST THE GRAPHS!
Part 2. Essay: Are stocks a good long-run investment?
In this part you will evaluate Seigel’s main argument that stocks are a good investment for the
long-run. Write a two-page essay (typed, double spaced) that explores this argument by
answering the following questions. Since this is an essay, do not include the questions or the
numbers, but be sure to address all the questions and points. (You may change the order if it
helps your essay.) A brief introduction that explains your main theme – stocks for the long run –
is a great way to start.
Refer to the graphs in your answers by their respective numbers. For example, you could write,
“As we can see from Graph 2, stock returns were highest in year x, when investors earned x %
return.” Your essay will be evaluated on clarity and originality, and should be in grammatically
correct English.
1. Suppose you invest in the stock market for one year only during the period from 1945 to 2015.
Based on Graph 2 what and when is the highest return you could have earned and the lowest
return you could have earned? Based on the normal distribution, what range would you expect
your return to fall in about 95 percent of the time? (See also Estrada page 27.)
2. Diversification reduces risk and one way to diversify is by investing in a longer period. Based
on Graph 3, summarize the advantages of a longer holding period in terms of reducing risk. If
you have a ten year holding period, what and when is the highest return you could have earned
and the lowest return you could have earned?
3. Another way to diversify is by holding a portfolio of different assets. Based on Graph 4 and
the discussion in Estrada Chpt. 4, identify and explain the minimum variance portfolio and the
efficient set.
4. The data in Graph 1 and Table 1 show the long run return to investing in stocks compared to
other assets in the past. Suppose you invest today $1000 in a diversified stock portfolio, $1000 in
bonds, and $1000 in a safe deposit box. Further suppose inflation averages 2 percent per year for
the next 50 years. Assuming real returns are the same as in the past, how much will each of these
investments be worth in 50 years in today’s dollars?
5. Do you agree with Seigal that stocks are a good investment for the long-run? In particular, do
you think past stock performance is a good guide to future returns? Why or why not?
Year Date CPUSAM_Close TRUSG10M_Close _SPXTRD_Close
1945 12/31/1945 18.2 215.0121416 2.9371946
1946 12/31/1946 21.5 215.8326526 2.6969206
1947 12/31/1947 23.4 212.8275291 2.8382415
1948 12/31/1948 24.1 218.6308455 2.9829645
1949 12/31/1949 23.6 229.4161097 3.521831
1950 12/31/1950 25 226.2626571 4.5987771
1951 12/31/1951 26.5 225.0084991 5.7279092
1952 12/31/1952 26.7 229.2454038 6.7876335
1953 12/31/1953 26.9 234.3316782 6.713057
1954 12/31/1954 26.7 241.7165637 10.2309499
1955 12/31/1955 26.8 238.9850925 13.4464101
1956 12/31/1956 27.6 232.5690885 14.3375005
1957 12/31/1957 28.4 246.3377313 12.7813799
1958 12/31/1958 28.9 241.1442065 18.3213981
1959 12/31/1959 29.4 238.4185337 20.5024572
1960 12/31/1960 29.8 266.2257269 20.6014928
1961 12/31/1961 30 271.8110076 26.1250431
1962 12/31/1962 30.4 287.6317353 23.8302102
1963 12/31/1963 30.9 292.3673573 29.2375866
1964 12/31/1964 31.2 303.1178226 34.0201508
1965 12/31/1965 31.8 305.3092875 38.2236182
1966 12/31/1966 32.9 321.9488962 34.3612885
1967 12/31/1967 33.9 312.0100944 42.5882308
1968 12/31/1968 35.5 331.560688 47.2739305
1969 12/31/1969 37.7 312.8747792 43.2719299
1970 12/31/1970 39.8 372.0636484 44.9966073
1971 12/31/1971 41.1 413.8790549 51.4425812
1972 12/31/1972 42.5 423.7502946 61.1835476
1973 12/31/1973 46.2 437.8743303 52.1337402
1974 12/31/1974 51.9 455.7808237 38.2980073
1975 12/31/1975 55.5 481.3878258 52.5640195
1976 12/31/1976 58.2 554.7864149 65.0083427
1977 12/31/1977 62.1 558.439742 60.2055422
1978 12/31/1978 67.7 554.1421345 64.082723
1979 12/31/1979 76.7 564.8003783 75.8437676
1980 12/31/1980 86.3 558.7422438 100.3158824
1981 12/31/1981 94 589.7685687 95.2469162
1982 12/31/1982 97.6 821.5991773 115.709087
1983 12/31/1983 101.3 843.3115598 141.7432587
1984 12/31/1984 105.3 969.9124013 150.4637031
1985 12/31/1985 109.3 1257.213784 198.0818463
1986 12/31/1986 110.5 1524.826122 234.9318738
1987 12/31/1987 115.4 1491.027037 247.0799963
1988 12/31/1988 120.5 1595.649448 288.116
1989 12/31/1989 126.1 1879.483718 379.409
1990 12/31/1990 133.8 2027.553979 367.631
1991 12/31/1991 137.9 2407.819313 479.633
1992 12/31/1992 141.9 2587.153881 516.178
1993 12/31/1993 145.8 2923.373837 568.202
1994 12/31/1994 149.7 2709.258099 575.705
1995 12/31/1995 153.5 3412.12823 792.042
1996 12/31/1996 158.6 3416.603331 973.897
1997 12/31/1997 161.3 3827.383535 1298.821
1998 12/31/1998 163.9 4380.536871 1670.006
1999 12/31/1999 168.3 4051.571595 2021.401
2000 12/31/2000 174 4749.11096 1837.365
2001 12/31/2001 176.7 5011.952402 1618.979
2002 12/31/2002 180.9 5782.470044 1261.176
2003 12/31/2003 184.3 5808.930267 1622.939
2004 12/31/2004 190.3 6076.712609 1799.548
2005 12/31/2005 196.8 6264.391346 1887.931
2006 12/31/2006 201.8 6402.542451 2186.13
2007 12/31/2007 210.036 7077.453117 2306.23
2008 12/31/2008 210.228 8509.13894 1452.98
2009 12/31/2009 215.949 7701.010715 1837.49
2010 12/31/2010 219.179 8260.300819 2114.29
2011 12/31/2011 225.672 9655.403786 2158.9399
2012 12/31/2012 229.601 9923.028 2504.44
2013 12/31/2013 233.049 9074.07 3315.59
2014 12/31/2014 234.812 10048.52 3769.44
2015 12/31/2015 237.336 10161.75 3821.6
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