Question

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?

Answer #1

YEAR
X
Y
2009
1000
9000
2010
800
12500
2011
650
15000
2012
1200
11000
2013
1100
10500
2014
1300
12000
2015
1250
11000
2016
3000
8000
2017
4000
7500
2018
10000
5500
2019
15000
1000
2020
14000
1500
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