Over the 48 years from 1960 through 2007, the stock market has gone up in the mo

Question

Over the 48 years from 1960 through 2007, the stock market has gone up in the month of January for 31 times: it has gone up for the whole year for 36 times, and it has gone up both for the year and in January for 29 times. Based on historical data, what is the probability the stock market will go up in January? Based on historical data, what is the probability the stock market will go up for the whole year? What is the conditional probability that the stock market will go up for the year given the stock market has already gone up in the month of January? Are the stock market's January performance and its annual performance independent events? What is the meaning of this conclusion to a financial analyst? Please use statistical analysis (not simple verbal narration!) to justify your answer.

Explanation / Answer

P(market going up in January) = 31/48

P(market will go up for whole year) = 36/48 = 3/4

P(market will go up for whole year | the market went up in January) = P(market going up in January and in whole year) / P(market going up in January) = 29/31

Let A = P(market going up whole year)x P(market going up in January) = 31/48 x 3/4 = 31/64

B = P(market going up in January and in whole year) = 29/48

The events are independent only if A = B

So, here the events are dependent. this means that the performance of market for the whole year is dependant on the performance of the market in January.

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