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A way to meet your mother's income objective is to invest in a
portfolio of small value stocks.
On average, the rate of return of such a portfolio has been 12.13
percent in REAL terms during the last 78 yrs (see
http://www.moneychimp.com/articles/index_funds/small
_value.htm)
Of course, the down side is that you need to accept relatively volatile
returns (for instance., you may get a return of 60 percent one year and
minus 20 percent the next year)
This should provide the desired income, even after accounting for taxes.
Jose Bailen wrote:
> A way to meet your mother's income objective is to invest in a
> portfolio of small value stocks.
> On average, the rate of return of such a portfolio has been 12.13
> percent in REAL terms during the last 78 yrs (see
> http://www.moneychimp.com/articles/index_funds/small
_value.htm)
> Of course, the down side is that you need to accept relatively volatile
> returns (for instance., you may get a return of 60 percent one year and
> minus 20 percent the next year)
> This should provide the desired income, even after accounting for taxes.
But for how long? The Monte Carlo retirement simulator at the same site
above only gives a 44% chance that her money will last 30 years. The
volatility of returns is killer when you're drawing down...
-Will
The results of the Monte Carlo simulation are too pessimistic. An
exercise I made some time ago is to download the historical data
supporting these results (they are available at the Ken French website:
http://mba.tuck.dartmouth.edu/pages/faculty/ken.fren
ch/data_library.html)
and, for 30 yrs periods, the lowest average real rate of return of the
typical small cap value portfolio was 8.1 percent (that was the 30-yr
period from 1946 to 1975) -the highest was the 30-yr period that ended
in 1961-. There are 49 30-year period observations -all the 30 year
periods starting the one that ended in 1956, so the results are
statistically significant.
This webpage at Harvard describes the caveats of the Monte Carlo
simulation:
http://www.eecs.harvard.edu/~ellard/Q-97/HTML/root/n
ode38.html
"A few very important caveats about these equations:
They should not be used with small n. The assumptions upon which they
are based break down when n is less than 30.
Similarly, they should not be used with probabilities that are
extremely near zero or one unless a large number of samples are drawn.
One rule of thumb is that the estimate should be based on at least 5
trials with both outcomes- so if you are estimating the probability of
an event that has a very low true probability, you may have to take a
large number of samples before you have any evidence at all that the
probability is non-zero- but if you happen to draw a positive sample in
one of the first trials and stop soon thereafter, your probability
estimate may be wildly high.
These equations are pessimistic. Assumming that the previous two
conditions are met, they generally give margins of errors that are too
wide (or suggest that you should perform more trials than you really
need to). Personally, this is the direction I prefer to err in- I would
rather believe that my estimate is less accurate than it is, instead of
thinking that it is more accurate than the facts would support.
However, if you are trying to perform the absolute minimum number of
trials necessary to achieve a given level of confidence, you may wish
to find a tighter bound.
>
> But for how long? The Monte Carlo retirement simulator at the same site
> above only gives a 44% chance that her money will last 30 years. The
> volatility of returns is killer when you're drawing down...
>
> -Will
Jose Bailen wrote:
> and, for 30 yrs periods, the lowest average real rate of return of the
> typical small cap value portfolio was 8.1 percent (that was the 30-yr
> period from 1946 to 1975) -the highest was the 30-yr period that ended
> in 1961-. There are 49 30-year period observations -all the 30 year
> periods starting the one that ended in 1956, so the results are
> statistically significant.
>
> >
> > But for how long? The Monte Carlo retirement simulator at the same site
> > above only gives a 44% chance that her money will last 30 years. The
> > volatility of returns is killer when you're drawing down...
> >
> > -Will
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.
Jose Bailen wrote:
> The results of the Monte Carlo simulation are too pessimistic. An
> exercise I made some time ago is to download the historical data
> supporting these results (they are available at the Ken French website:
> http://mba.tuck.dartmouth.edu/pages/faculty/ken.fren
ch/data_library.html)
> and, for 30 yrs periods, the lowest average real rate of return of the
> typical small cap value portfolio was 8.1 percent (that was the 30-yr
> period from 1946 to 1975) -the highest was the 30-yr period that ended
> in 1961-. There are 49 30-year period observations -all the 30 year
> periods starting the one that ended in 1956, so the results are
> statistically significant.
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.
> "A few very important caveats about these equations:
>
>
> They should not be used with small n. The assumptions upon which they
> are based break down when n is less than 30.
n was 1000 in this case.
>
> Similarly, they should not be used with probabilities that are
> extremely near zero or one unless a large number of samples are drawn.
The probabilities tested were not near zero or one.
> One rule of thumb is that the estimate should be based on at least 5
> trials with both outcomes- so if you are estimating the probability of
> an event that has a very low true probability, you may have to take a
> large number of samples before you have any evidence at all that the
> probability is non-zero- but if you happen to draw a positive sample in
> one of the first trials and stop soon thereafter, your probability
> estimate may be wildly high.
There were ~440 trials with a positive outcome, and ~550 with a negative
outcome.
>
> These equations are pessimistic.
Given that the simulation does not use fat tails, I'd guess that the
results are optimistic.
> Assumming that the previous two
> conditions are met, they generally give margins of errors that are too
> wide (or suggest that you should perform more trials than you really
> need to). Personally, this is the direction I prefer to err in- I would
> rather believe that my estimate is less accurate than it is, instead of
> thinking that it is more accurate than the facts would support.
> However, if you are trying to perform the absolute minimum number of
> trials necessary to achieve a given level of confidence, you may wish
> to find a tighter bound.
I admit 1000 trials sounds low, but it sounds like you are suggesting it
only ran ~10 trials.
-Will
> 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.
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 -51.64
Just checked/updated the information provided by the Ken French data
library
(http://mba.tuck.dartmouth.edu/pages/faculty/ken.fre
nch/data_library.html).
These are the returns of different investment styles from 1927-2005.
They are not inflation-adjusted. "Low" means low book-to-market
portfolios (i.e., growth portfolios) while "high" means high book to
market portfolios. These are annual data for average value-weighed
portfolios (equally weighted portfolios give even better average
returns, but also greater volatility):
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 11.62
Average 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
Jose Bailen wrote:
> 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.
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?
> 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
True, but...
> , as
> well as the fact that in almost every case very bad outcomes one year
> were immediately followed by excellent returns the next year.
....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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