probability Question

Question

According to the January Theory. If the stock market is up for the month of January, it will be up for the year. If it is down in January, it will be down for the year. According to an article in the Wall Street Journal, this Theory held for 29 out of the last 34 years. Suppose there is no truth to this Theory; that is, the probability it is either up or down is .50. What is the probability this could occur by chance?

Answer 1

IF it's just random chance, then P(UY/UJ) = 1/2 = P(DY/DJ)

DY = down for the year, DJ = down in January

Odds then of 29 out of 34 is the same as flipping a coin 34 times and gettng 29 heads. Very unlikely, but possible.

But you have a sample of 1 out of 12 months, and that alone does move the odds a little above 1/2 for the stocks to go up for the year.

There's also a theory that whenever the former AFL team wins the superbowl that the stock market goes down. and vice versa. It seemed to have a good track record too.

For those 5 years when stocks didn't follow the January results, check and see if they had an AFL team losing the superbowl.