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Archives of Business Review – Vol. 8, No.6
Publication Date: June 25, 2020
DOI: 10.14738/abr.86.8484.
Samsa, G. (2020). The Impact of Market Drops is Different for Investors Before and After Retirement. Archives of Business Research,
8(6). 196-201.
The Impact of Market Drops is Different for Investors Before and
After Retirement
Gregory Samsa, PhD
Professor, Dept. of Biostatistics and Bioinformatics,
Duke University, Durham, USA.
ABSTRACT
As applied to investing for and during retirement, the popular financial
press has promulgated two memes about the impact of market drops:
(1) for those investing for retirement market drops aren’t problematic;
and (2) for those in retirement market drops are. We use simulation
to illustrate the logic behind these memes, to demonstrate that they are
mostly but not entirely true, and finally to restate them more precisely.
Although sequence of returns risk is not present during the
accumulation phase as an investor plans for retirement, it can have a
significant (and perhaps underestimated) impact during retirement.
This, however, can place the retiree in a predicament – namely, settle
for lower returns and lower distributions during retirement or gamble
on stocks. However, it does not necessarily imply that retirees must
abandon the expected returns associated with stocks, because of the
ability to write deep-in-the-money covered call options, which harvest
the expected market return (but no more than this) with limited
variability.
Key words: index fund; retirement planning; sequence of returns risk.
INTRODUCTION
As applied to investing for and during retirement, the popular financial press has promulgated two
memes about the impact of market drops: (1) for those investing for retirement market drops
aren’t problematic; and (2) for those in retirement market drops are. By implication, stocks are an
excellent asset class before retirement but not during it. We use simulation to illustrate the logic
behind these memes, to demonstrate that they are mostly but not entirely true, and finally to
restate them more precisely. The impact of two factors is considered: (1) the sequence of returns;
and (2) variability among returns. For concreteness, we assume that the stock portfolio in
question is entirely comprised of an S&P500 index fund. We assume that an investor has 30 years
until retirement, and also that retirement will last another 30 years.
IMPACT OF SEQUENCE OF RETURNS DURING THE ACCUMULATION PHASE BEFORE
RETIREMENT
In the popular press, the argument for investing in stocks while saving for retirement is essentially
this: “even though the returns of an index fund can be quite variable from year to year, and even
though its value will tend to drop in approximately one year out of every four, the average return
of stocks is approximately 10% per year, which significantly exceeds the expected returns of safer
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asset classes, and for planning purposes investors with a sufficiently long investment horizon can
treat this 10% as essentially being guaranteed”. To deconstruct this argument, consider Table 1 –
the annual returns (including dividends) of the S&P500 index from its inception in 1926 through
2019 [1], and Table 2 – this same information summarized by categories. Indeed, the S&P500
dropped 25 years out of 94, and so the assertion that the value of an index fund will tend to drop
approximately one year out of every four is accurate. Moreover, the arithmetic mean of the annual
returns is 12.1%, the standard deviation is 19.8%, and the geometric mean (that is, the return
which the investor who bought this index in 1926 and held it until the end of 2019 would receive)
is 10.2%. Thus, the 10% figure is historically accurate. So long as we assume that the historical
returns of stocks are likely to continue going forward, the premises of this argument (i.e., variable
returns, averaging 10%, losing money approximately one year out of every four, outperforming
other asset classes) can be considered to be sufficiently sound to proceed.
It is also true that the order of the returns has no impact on the value of a portfolio at the time of
retirement. During the accumulation period before retirement an initial investment of X0will grow,
in t years, to Xt=X0(1+r1)(1+r2)...(1+rt), where ri is the return in year i. Because they are all
embedded within the same set of product terms, the order of the returns has no impact on the final
value Xt.
Table 1: Annual S&P500 returns 1926-2019
Year Return (%) Year Return (%) Year Return (%)
1926 11.6 1958 43.4 1990 -3.1
1927 37.5 1959 12.0 1991 30.5
1928 43.6 1960 0.5 1992 7.6
1929 -8.4 1961 26.9 1993 10.1
1930 -24.9 1962 -8.7 1994 1.3
1931 -43.3 1963 22.8 1995 37.6
1932 -8.2 1964 16.5 1996 23.0
1933 54.0 1965 12.4 1997 33.4
1934 -1.4 1966 -10.1 1998 28.6
1935 47.7 1967 24.0 1999 21.0
1936 33.9 1968 11.1 2000 -9.1
1937 -35.0 1969 -8.5 2001 -11.9
1938 31.1 1970 4.0 2002 -22.1
1939 -0.4 1971 14.3 2003 28.7
1940 -9.8 1972 19.0 2004 10.9
1941 -11.6 1973 -14.7 2005 4.9
1942 20.3 1974 -26.5 2006 15.8
1943 25.9 1975 37.2 2007 5.5
1944 19.7 1976 23.8 2008 -37.0
1945 36.4 1977 -7.2 2009 26.5
1946 -8.1 1978 6.6 2010 15.1
1947 5.7 1979 18.4 2011 2.1
1948 5.5 1980 32.4 2012 16.0
1949 18.8 1981 -4.9 2013 32.4
1950 31.7 1982 21.5 2014 13.7
1951 24.0 1983 22.6 2015 1.4
1952 18.4 1984 6.3 2016 12.0
1953 -1.0 1985 31.7 2017 21.8
1954 52.6 1986 18.7 2018 -4.4
1955 31.6 1987 5.2 2019 31.5
1956 6.6 1988 16.6
1957 -10.8 1989 31.7
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Samsa, G. (2020). The Impact of Market Drops is Different for Investors Before and After Retirement. Archives of Business Research, 8(6). 196-201.
However, the conclusion of this argument, namely that a 10% return can be assumed for planning
purposes, doesn’t follow from these premises, as it ignores the impact of variability in returns. To
illustrate this impact, Table 3 presents the results of randomly sampling from the historical
distribution of annual returns, with replacement, for 30 years (i.e., the expected time until
retirement), 100 times. For example, to obtain the return in year 1 of sample 1 the randomly
chosen year might be 1967, and the return 24.0%. In year 2 of sample 1 the randomly chosen year
might be 2003, and the return 28.7%. Each selection is taken independently from the others, and
within a sample a particular year can appear multiple times, one time, or not at all. Consistent with
intuition, the average annualized rate of return across these 100 samples is 10.5%. However, the
standard deviation is 3.6%, and the returns ranged from a minimum of -2.8% to a maximum of
19.5%. Seven of the 100 samples had an annualized return of less than 5%. Thus, an annualized
return of 10% is by no means “guaranteed”. This isn’t due to the sequence of returns, but instead
to the impact of variability.
Table 2: Annual S&P500 returns categorized
Annual return Frequency Annual return Frequency
-50% to -55% 0 0 to 5% 6
-45% to -5% 0 5-10% 8
-40% to -45% 1 10-15% 7
-35% to -40% 2 15-20% 12
-30% to -35% 0 20-25% 11
-25% to -30% 1 25-30% 5
-20% to -25% 2 30-35% 11
-15% to -20% 0 35-40% 4
-10% to -15% 5 40-45% 2
-5% to -10% 8 45-50% 1
0 to -5% 6 50-55% 2
The same phenomenon occurs when the contribution is regular, rather than one-time (data not
shown). In essence, the terminal value Xt can be written as the sum of the terminal value, over 30
years, of a one-time contribution in year 1, plus the terminal value, over 29 years, of a one-time
contribution in year 2, etc. The case that is particularly problematic occurs when the final return
is strongly negative, because this reduces the terminal value of all of the above income streams.
Table 3: annualized returns for 100 random samples, 30-year accumulation period
Category Frequency Category Frequency
-3% to -2% 1 10%-11% 8
-2% to 2% 0 11%-12% 7
2%-3% 1 12%-13% 11
3%-4% 3 13%-14% 15
4%-5% 2 14%-15% 5
5%-6% 8 15%-16% 1
6%-7% 7 16%-17% 2
7%-8% 6 17%-18% 2
8%-9% 8 18%-19% 0
9%-10% 11 19%-20% 1