Rick,
Doesn't that assume she works until she dies? If she retires her earned income will go to zero. SSI (if it even exists in 25 years) would only provide a percentage of her original earned income. So, to maintain $50K in total income she would need even more support from her unearned income than before retirement.
____
"As much effort as we put into investing, is it fair to call it unearned income?"
The Lowest rate of return may have been 8.1% over 30 years, but Will's point that the volatility of the 8.1% is still on target. Many times over 30 years this would negative, IMO. There would be many occurances the small cap would be negative, and if those years occurred early in the cycle, it would compound problems even more.
But average arithmetic returns are misleading. It is the volatility that matters when you are drawing down, especially early on as Jim pointed out. Remember that you're in a non-commutative regime if you are drawing down - order matters.
n was 1000 in this case.
The probabilities tested were not near zero or one.
There were ~440 trials with a positive outcome, and ~550 with a negative outcome.
Given that the simulation does not use fat tails, I'd guess that the results are optimistic.
I admit 1000 trials sounds low, but it sounds like you are suggesting it only ran ~10 trials.
-Will
Fair enough. But there is another important caveat of the Monte Carlo simulator: it assumes that the distribution of returns does not change over time. In fact, if you use a Hodrick-Prescott filter (that provides a better trendline than just the average), you may appreciate that the average return of the small cap value portfolio has been increasing over time (not by much, but even small changes mean a lot when composed many years). Also, the volatility of these returns have decreased somewhat: the largest volatility of small cap value stocks returns were in the first 11 years of the sample (the 1927-1937 period). The absolutely-worst yearly performance of small cap value stocks was in
1931 -a decline of 51.86 percent- while the best performance was in 1933 -a return of 118.31 percent-. In the last 30-yr period (1966-2005), the worst performance was in 1973 (minus 27.32 percent) and the best was 1967 (69.17 percent). Since the 1973-1974 period, there has been only one year with a double digit decline in small cap value returns - 1990, with a 24 percent decline, which was followed by a (positive) return of 40.64 percent the next year-I don't think that the Monte Carlo simulator -that uses only the average and the standard deviation for the whole sample- takes into account changes in the distribution in different subsample periods, as well as the fact that in almost every case very bad outcomes one year were immediately followed by excellent returns the next year.
These are the small cap value returns data downloaded from the Ken French website (they are not inflation-adjusted):
High
1927 36.26 1928 41.17 1929 -36.05 1930 -46.15 1931 -51.64 1932 1.54 1933 118.31 1934 8.97 1935 52.36 1936 73.92 1937 -51.21 1938 26.1 1939 -3.64 1940 -9.39 1941 -4.81 1942 35.1 1943 92.27 1944 50.58 1945 72.67 1946 -7.59 1947 5.16 1948 -2.22 1949 20.72 1950 50.01 1951 12.54 1952 8.14 1953 -6.55 1954 62.37 1955 23.54 1956 6.71 1957 -15.77 1958 69.77 1959 18.13 1960 -5.75 1961 30.61 1962 -9.26 1963 28.93 1964 22.78 1965 41.31 1966 -8.02 1967 69.17 1968 46.43 1969 -25.75 1970 6.21 1971 14.46 1972 7.13 1973 -27.34 1974 -18.33 1975 58 1976 59.67 1977 23.21 1978 21.63 1979 37.93 1980 21.78 1981 17.41 1982 41.18 1983 47.58 1984 8.43 1985 33.04 1986 14.3 1987 -6.14 1988 30.72 1989 17.08 1990 -24 1991 40.64 1992 35.28 1993 26.55 1994 0.43 1995 32.29 1996 23.52 1997 38.42 1998 -1.14 1999 8.13 2000 21.83 2001 22.41 2002 -8.8 2003 64.01 2004 22.74 Average 19.9 Standard dev 31.8 Max 118.31 Min -51.64Just checked/updated the information provided by the Ken French data library
Average Value Weighted Returns -- Annual Small Big Low 2 High Low 2 High
1927 31.59 26.74 33.79 44.26 23.55 31.79 1928 31.88 40.42 42.43 46.51 31.79 25 1929 -46.73 -30.7 -36.81 -19.54 0.76 -4.4 1930 -35.79 -32.19 -45.38 -26.38 -29.29 -43.35 1931 -41.33 -48.31 -51.66 -35.88 -60.22 -57.89 1932 -5.04 -8.53 3.61 -7.32 -16.73 -4.33 1933 166.14 119.96 125.42 44.23 89.36 114.81 1934 34.17 19.78 8.03 10.75 -2.9 -21.77 1935 47.95 75.87 53.8 42.06 47.13 50.77 1936 38.34 48.9 74.95 26.42 37.94 48.55 1937 -48.77 -48.65 -50.44 -34.35 -31.93 -40.71 1938 46.68 43.98 25.54 33.12 20.33 25.69 1939 10.08 1.24 -3.97 7.59 -3.46 -13.17 1940 -1.68 -1.65 -10.49 -9.67 -3.87 -2.5 1941 -16.58 -10.83 -4.68 -12.58 -5.31 -1.18 1942 16.94 27.98 35.26 13.54 17.41 33.4 1943 46.31 54.97 93.32 21.61 33.96 43.81 1944 40.41 40.22 50.44 16.03 21.76 42.58 1945 63.62 60.02 72.48 31.72 38.71 49.84 1946 -12.44 -9.64 -7.44 -7.18 -1.65 -8.18 1947 -8.52 -2.3 5.18 3.54 4.55 8.81 1948 -7.86 -6.96 -2.69 3.71 1.6 4.75 1949 24.51 22.67 21.51 23.38 15.9 16.95 1950 31.1 31.9 51.05 22.64 31.37 56.99 1951 16.78 15.19 12.33 20.02 25.13 13.4 1952 7.18 9.97 9.23 13.04 13.39 20.26 1953 0.42 -0.97 -6.4 2.26 0.53 -7.96 1954 42.9 61.1 63.28 47.77 48.2 77.77 1955 14.71 20.64 23.89 28.63 18.93 29.51 1956 7.96 7.76 5.98 6.57 13 4.32 1957 -16.93 -14.8 -16.18 -8.9 -8.15 -23.19 1958 76.07 57.72 69.42 41.45 45.58 72.04 1959 20.02 20.38 17.96 13.12 9.97 18.98 1960 -2.72 -0.93 -5.74 -2.2 8.16 -8.68 1961 21.08 30.37 31.35 26.38 26.61 29.18 1962 -19.92 -15.47 -9.35 -10.75 -5.8 -3.29 1963 7.56 16.57 28.96 21.9 17.15 32.81 1964 8.08 17.61 23.05 14.46 20.42 19.52 1965 35.72 33.31 41.83 13.46 10.04 22.69 1966 -5.81 -6.07 -7.35 -10.83 -5.87 -10.46 1967 89.73 72.72 67.92 29.16 15.8 31.84 1968 32.58 40.45 46.22 3.96 15.84 26.79 1969 -24.48 -22.98 -25.93 3 -16.96 -16.41 1970 -21.27 -7.89 6.52 -5.71 8.05 10.32 1971 26.22 21.15 14.52 24.22 5.86 13.41 1972 -0.06 7.84 7.1 21.48 11.01 18.71 1973 -45.51 -32.72 -27.51 -21.65 -8.83 -4.17 1974 -32.35 -26.39 -18.39 -29.3 -22.86 -23.1 1975 60.91 58.08 57.9 34.32 41.9 55.18 1976 38.51 47.13 60.18 17.35 41.07 44.22 1977 18.64 18.46 23.22 -9.57 -0.81 1.4 1978 17.5 21 22.05 6.96 6.89 3.74 1979 49.19 36.83 38.34 16.49 23.4 22.95 1980 52.4 30.62 22.33 35.41 36.55 16.45 1981 -10.88 13.78 17.28 -7.57 -7.44 14.16 1982 19.36 33.56 41.18 21.64 17.97 27.28 1983 19.58 40.26 48.07 14.59 25.23 27.2 1984 -13.87 2.35 8.32 -0.66 5.69 15.82 1985 28.87 34.89 32.75 32.5 32.22 31.49 1986 2.39 9.96 14.17 14.64 20.09 21.32 1987 -13.43 -4.14 -6.11 7.41 3.36 -2.2 1988 14.51 28.26 30.73 12.67 17.75 25.79 1989 19.63 17.97 16.46 36.2 25.36 29.33 1990 -18.7 -17.52 -23.57 1.14 -5.52 -13.49 1991 53.62 46.63 40.64 43.04 22.18 27.54 1992 4.65 22.53 35.19 6.31 9.77 23.53 1993 10.61 20.29 27.2 0.85 16.9 22.31 1994 -6.7 0.24 0.15 2.6 1.01 -5.71 1995 28.8 28.37 32.74 37.75 38.63 36.57 1996 9.28 22.43 24.07 22.58 25.53 14.67 1997 10.01 31.73 38.4 30.65 37.08 27.01 1998 -1.49 -5.58 -1.36 39.47 7.51 20.3 1999 46.6 21.71 7.75 26.79 5.82 -0.69 2000 -23.39 19.3 22.12 -13.51 16.9 20.9 2001 -0.12 16.8 22.51 -14.59 -1.28 -0.68 2002 -32.1 -11.72 -9.05 -22.57 -15.29 -25.13 2003 54.71 49.92 64.06 27.9 30.7 27.93 2004 15.11 20.37 21.38 7.48 14.76 20.05 2005 -0.66 8.85 9.16 4.06 8.26 11.62Average 13.9 17.5 19.9 11.5 12.8 15.7 STDEV 33.9 29.1 31.9 20.4 21.4 27.1 Max 166.14 119.96 125.42 47.77 89.36 114.81 Min -48.77 -48.65 -51.66 -35.88 -60.22 -57.89
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Thank you.
-HW "Skip" Weldon Columbia, SC
Hey, I was using your inputs. I don't claim to know how the distributions will change in the future. Do you want to assume lower volatility and lower returns?
....if I define "very bad" outcomes as losing money and "excellent returns" as > 10% then excellent returns followed losing years 57% of the time in the data series you presented in the previous post. But I would expect to get > 10% returns 62% of the time with a random draw against a normal distribution with the same mean and standard deviation as the series you presented. So it seems that a Monte Carlo would have excellent returns following very bad years more often than your series. Does this make the Monte Carlo optimistic?
Always, always, always check my math...
-Will
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