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How to Find Expected Mean, Covariance, Standard Deviation and Correlation Coefficient
Question
Consider the following ex ante (expected) distributions for assets 1 and 2: marginal distributions
Asset 1 


Asset 2 


m 
R_{1m} 
f(R_{1m}) 
l 
R_{2l} 
f(R_{2l}) 
1 
12% 
0.45 
1 
4% 
0.09 
2 
6% 
0.55 
2 
8% 
0.17 



3 
10% 
0.35 



4 
14% 
0.39 
joint distribution (for above outcomes of return)
m 
L 
f(R_{1m}, R_{2l}) 
1 
1 
0.01 
1 
2 
0.03 
1 
3 
0.17 
1 
4 
0.24 
2 
1 
0.08 
2 
2 
0.14 
2 
3 
0.18 
2 
4 
0.15 
For question 3, consider the following data for assets 1, 2, and 3 (i = 1, 2, 3):
Asset i 
E[R_{i}] 
s_{i} 
1 
4% 
2% 
2 
10% 
3% 
3 
15% 
5% 
Also, S_{12}= 5, S_{13} = 9, and S_{23}= 3.
Question
Using the above data for assets 1, 2, and 3 and assuming that you have $1,000,000 to invest, answer the following:
A. If you have $400,000 invested in asset 1, $100,000 in asset 2, and the rest in asset 3, what is the expected return on your portfolio (E[R_{P}]) ?
B. Using the portfolio in part A of this question, what is the total risk of your portfolio's return in percentage terms (s_{P})?
Summary
The question belongs to Statistics and it is about finding expected return from the investment made in the assets. And also the risk of the portfolio has to be calculated.
Total Word Count 85
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