As we are all aware, the market has been down for the last three years, 2000-2002. Some market “experts,” including a well-known mutual fund manager whose fund has outperformed the S&P in each of the past dozen years, looked at what had happened in the past and noted that there was only one time in the 20th Century that there were four consecutive down years, namely 1929-32. So they said and wrote that we are highly unlikely to have another down year in 2003 because the chances were only 1% of having four consecutive down years. Since stocks did not move a whole lot in the first quarter, those same pundits might well say that it is still quite unlikely, based on that reasoning, that 2003 will be a down year.
Having taught basic probability many times during my college teaching days, I should not be surprised that many fail to grasp it. The historical data do support the idea that if we choose a four year period at random, there will be only a 1% chance that all four years are down. However, choosing 2000-03 at the end of 2002 is hardly making a random choice of four years. The appropriate historical comparison is to find all instances when the market was down for three years and see what happened in the following year. (For those of you who did understand the elementary course, this is what was called conditional probability.) There have been three such instances based on the annual changes in the Dow: 1929-31, 1930-32, and 1939-41. In one of the following years, 1932, the Dow fell yet again, so the best estimate based on that information says there is a 1/3 chance 2003 will be a down year.
As I have pointed out many times, making an estimate based on so few data points is not a good idea. Can we do better? Looking at the Dow over the past 100 years, 1903-2002, we see it was up in 64 of them and down in the other 36. That means the probability that a randomly chosen single year will see a higher Dow is 64%, and the chance of a down year is 36%. Interestingly, the last value is close to the 1/3 estimate that 2003 will be a down year based on the performance after three down years.
Assuming a 64% probability any year will see a higher Dow, we can carry things a bit further. The probability of four consecutive down years is 1.68%, so in a hundred year period, we would expect to see one or two such four year periods, which is consistent with history. The chances of three straight down years is 4.67%, so the four instances over the past hundred years is about what would be expected.
What about consecutive up years? We saw nine from 1991-99. The probability that happens based on a 64% chance of an up year is 1.80%, so the fact that it happened once over a century is hardly shocking. The next longest distinct sequence of up years was five, which happened twice, 1924-28 and 1985-89. It also happened five times during the nine year run, so there were a total of seven five-year all up periods. That is somewhat under the expected 10.7% chance of five straight up years.
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