From: John Conover <email@example.com>
Subject: Chances of a down market, four years in a row?
Date: 3 Jan 2003 23:44:33 -0000
So far, in the last week, (CNBC, etc.,) I've heard that the last time we had four down years in row in the major US indices was the early Thirties in the Great Depression-implying that its almost a certainty that this year, (2003,) will finish up. What's the chances? The market indices increase at a little less than 10% per year, (over the Twentieth Century,) so, we would expect a four year gain of about 1.1^4 = 1.46. But about a 2% deviation per day in index values, (for the Nasdaq-a little less for the S&P and DJIA,) would be about e^(0.02 * sqrt (1012)) = 1.89 at four years, or 1.89 / 1.46 = 1.3 standard deviations, which has a chance of 0.0968, or about 0.1 = 10%, or about one chance in ten. So, the chances of the market indices finishing down at the end of 2003 is about one chance in 10-and a 90% chance of finishing up. John BTW, sanity check: If this year finishes down, then there will have been two times in 70 years-for a total of at least 8 years-or 8 / 70 = 11% that the possible combinations of years finished down in succession-approximately. Or, about 10%-which is reasonable. -- John Conover, firstname.lastname@example.org, http://www.johncon.com/