<THE FOOLISH FOUR>
Fun with Statistics, Take 2
by Ann Coleman
([email protected])
Reston, VA. (November 6, 1998) -- Time to tackle the big question: Does the Foolish Four really work? We know the returns are far higher than the market, but questions about statistical flukes or the probability of getting the same returns with four randomly selected Dow stocks keep cropping up. After all, a stopped clock is right twice a day. Have we just been lucky, or is something REAL happening here?
If you look at the table of annual returns below, you will see years where the strategies did better than the market and years where it did worse. It is a bewildering array of numbers. To make sense of it, we have to look at statistics.
[By the way, some of you may tend to agree with those old sayings "There are three kinds of lies -- lies, damned lies and statistics" or "You can prove anything with statistics (and therefore statistics are meaningless)." You can "prove anything with statistics" only to people who don't know much about statistics. Conversely, one can miss out on the truth by distrusting ALL statistics. It's a worthwhile field of study.]
So the question of the day is: Are the higher average returns for our strategies actually "statistically significant?"
I did a Z Test comparing the average returns for the High Yield 10 (Dogs of the Dow), the Foolish Four, and the RP4 with the average returns for Standard & Poor's 500. ( For "average" I used the mean instead of our usual Compounded Average Growth Rate because that's the appropriate "average" for this test.)
The Z Test is a tough one to pass. You can pass it a different levels, however. The lowest level (kind of a C+) generally accepted as statistically significant is the 90% confidence level. That level tells you that there is only a 10% chance that the difference you are observing is due to chance. The level more commonly associated with statistical validity is the 95% confidence level. At that level, there is only a 5% chance that the difference could be due to chance.
Alas, our Dogs of the Dow failed to pass this test at even the lowest level. The Z value was 0.828 (for those who are counting) which is not even close to 1.28, the level needed to pass the Z test at the 90% confidence level for a one tailed test.
Now, before anyone gets excited, please understand that this is a tough test. There is an observable and consistent difference in the returns of the High Yield 10 vs. the S&P 500, but I cannot say that the difference is great enough to be considered statistically significant.
I looked at two time periods, by the way: The past 25 years and the past 37 years (our entire data base). The Z value for the High Yield 10 was about the same in both time periods -- no help from our recent bull market here!
When it comes to the Foolish Four and the RP4, however, things look much more impressive. For the more recent time period, the Foolish Four's Z value is 1.664, comfortably above the critical value of 1.28 needed to pass the test of statistical significance at the 90% confidence level and close to, but not quite at, the 95% significance level of 1.96. The RP4 does much better, though, with a Z value of 2.434, which puts it well above the 99% confidence level. This is gold standard statistical significance.
For the longer time period, our full data base, the strategies still look good. Surprisingly, given the miserable '60s, the Foolish Four's significance level didn't change much. Its Z value for the 37 year time period is 1.658, still just below the 95% significance level. The RP4 variation drops to the 95% confidence level (z=1.965).
Whew! Still here? Congratulations. It was a tough road, but you made it.
Now, for the numbers.
HY10 Fool 4 RP4 S&P500
1963 21.06% 17.42% 18.62% 22.80%
1964 20.28% 26.79% 24.66% 16.48%
1965 19.34% 12.40% 15.84% 12.45%
1966 -17.90% -17.65% -22.89% -10.06%
1967 25.68% 40.91% 34.07% 23.98%
1968 14.68% 14.09% 18.34% 11.06%
1969 -12.77% -6.66% -8.41% -8.50%
1970 4.73% -5.92% -14.20% 4.01%
1971 5.71% 19.74% 19.74% 14.31%
1972 23.79% 24.91% 16.59% 18.98%
1973 3.89% 25.74% 17.28% -14.66%
1974 1.04% 5.25% 20.00% -26.47%
1975 52.17% 68.71% 68.71% 37.20%
1976 33.24% 36.92% 37.93% 23.84%
1977 1.17% 5.32% -2.96% -7.18%
1978 2.44% 9.89% 9.89% 6.56%
1979 9.69% 2.17% 17.70% 18.44%
1980 32.95% 48.18% 24.20% 32.42%
1981 4.87% -4.63% 9.66% -4.91%
1982 20.87% 41.58% 56.88% 21.41%
1983 38.43% 41.74% 36.72% 22.51%
1984 7.45% 10.24% 10.30% 6.27%
1985 30.61% 22.85% 49.82% 32.16%
1986 29.43% 27.30% 29.67% 18.47%
1987 8.56% 18.75% 17.89% 5.23%
1988 17.96% 13.62% 22.08% 16.81%
1989 29.64% 15.28% 47.35% 31.49%
1990 -10.01% -17.61% -17.61% -3.17%
1991 35.24% 81.61% 34.81% 30.55%
1992 6.35% 29.94% 29.94% 7.67%
1993 23.54% 26.22% 30.26% 9.99%
1994 2.43% 4.72% 7.59% 1.31%
1995 37.10% 30.42% 47.05% 37.43%
1996 27.47% 24.34% 26.56% 23.07%
1997 20.39% 22.31% 19.49% 33.36%
HY10 Fool 4 RP4 S&P500
37 yr. mean 16.33% 20.48% 21.53% 13.29%
25 yr. mean 18.68% 23.63% 26.05% 14.39%
37 yr. SD 15.78% 21.16% 20.07% 15.74%
25 yr. SD 15.64% 21.88% 19.13% 17.12%
37 yr. Z 0.828 1.658 1.965
25 yr. Z 0.924 1.664 2.434
Fool on and prosper!
Current Dow Order | 1998 Dow Returns
11/06/98 Close
Stock Change Last -------------------- UK - 3/16 44.88 IP - 3/8 46.13 MO - 9/16 53.00 EK +1 5/16 78.00 |
Day Month Year
FOOL-4 -0.08% 4.30% 15.68%
DJIA +0.67% 4.46% 13.49%
S&P 500 +0.63% 3.85% 17.58%
NASDAQ +1.06% 4.81% 18.22%
Rec'd # Security In At Now Change
12/31/97 206 Eastman Ko 60.56 78.00 28.79%
12/31/97 276 Philip Mor 45.25 53.00 17.13%
12/31/97 289 Int'l Pape 43.13 46.13 6.96%
12/31/97 291 Union Carb 42.94 44.88 4.51%
Rec'd # Security In At Value Change
12/31/97 206 Eastman Ko 12475.88 16068.00 $3592.13
12/31/97 276 Philip Mor 12489.00 14628.00 $2139.00
12/31/97 289 Int'l Pape 12463.13 13330.13 $867.00
12/31/97 291 Union Carb 12494.81 13058.63 $563.81
CASH $754.73
TOTAL $57839.48
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