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Probability: Stock Market

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Over the 48 years from 1950 through 1997, 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.

1) Based on historical data, what is the probability the stock market will go up in January?

2) Based on historical data, what is the probability the stock market will go up for the whole year?

3) What is the conditional probability that the stock market wil go up for the year given the stock market has already gone up in the month of January?

4) 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.

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Over the 48 years from 1950 through 1997, 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.

1) Based on historical data, what is the probability the stock market will go up in January?

Probability (stock market will go up in January) = No of years in which the stock market goes up in January / Total no of years= 31 / 48
Answer: Probability = 31 / 48

2) Based on historical data, what is the probability the stock market will go up for the whole year?

Probability (stock market will go up for the whole year) = No of years in which the stock market goes up for the whole year / Total no of years= 36 / 48
Answer: Probability = 36 / 48

3) What is the conditional probability that the stock market will go up for the year given the ...

Solution Summary

Answers questions on probability.

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See Also This Related BrainMass Solution

Investment/maxium probability
One of your friends has $ 2000.00 available to invest. Assume that all the money must be placed in one of three investments; a money market fund, a stock, or gold. Each dollar that your friend invests in the money market fund earns a virtually guareanteed 12%. Each dollar that is invested in stock earns an annual return characterized by the probability distribution provided.
Each dollar that is invested in gold earns an annual return characterized by the probability distribution provide.

A) If your friend must place all the available funds in a single investment, which investment should he choose to maximize his expected earnings of the next year?

Please see the attached file(s).
Problem One of your friends has $ 2000.00 available to invest. Assume that all the
money must be placed in one of three investments; a money market fund, a
stock, or gold. Each dollar that your friend invests in the money market fund
earns a virtually guareanteed 12%. Each dollar that is invested in stock
earns an annual return characterized by the probability distribution provided.
Each dollar that is invested in gold earns an annual return characterized by
the probability distribution provide.

A) If your friend must place all the available funds in a single investment, which
investment should he choose to maximize his expected earnings of the next
year?

Investment data

Distribution of Annual Returns for Given Stock
Return Probability
0.00 0.10
0.06 0.20
0.12 0.40
0.18 0.20
0.24 0.10

Distribution of Annual Returns for Gold
Return Probability
-0.36 0.10
-0.12 0.20
0.12 0.40
0.36 0.20
0.60 0.10

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