Question

Let X denote the percentage increase in the Dow Jones Index in the coming year and...

Let X denote the percentage increase in the Dow Jones Index in the coming year and let Y denote the percentage increase in the S&P500 Index in the coming year. Suppose that X and Y obey a joint normal distribution and that the mean of X is 11% and its standard deviation is 13%, and the mean of Y is 10% and its standard deviation is 12%. Suppose that corr(X,Y) = 0.43.

1. What is the probability that the Dow Jones Index will increase by more than 11% in the coming year?

2. What is the probability that the Dow Jones Index will decrease by more than 11% in the coming year?

3. What is the probability that the S&P500 Index will increase in the coming year by an amount less than 15%?

4. Suppose that a person places 30% of a portfolio in the Dow Jones Index and the remaining 70% of the portfolio in the S&P500 Index. What is the expected return of the combined portfolio? What is the standard deviation of this return? 5. What is the distribution of X ? Y? What is the probability that X is greater than Y?

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