Problem 1: Standard Deviation – A portfolio has an annual variance of .0420. What is the standard deviation of a two month period?
Problem 2: Normal Probabilities - The probabilities that a normal random variable X is less than various values of x are 5%, 2.5%, and 1%..What are these values of x?
Problem 3: Asset Allocation Fill in the missing information assuming a correlation of -.20.
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Portfolio Weights
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Expected
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Standard
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|
Stocks
|
Bonds
|
Return
|
Deviation
|
|
1.00
|
0.00
|
13%
|
22%
|
|
0.80
|
0.20
|
|
|
|
0.60
|
0.40
|
|
|
|
0.40
|
0.60
|
|
|
|
0.20
|
0.80
|
|
|
|
0.00
|
1.00
|
6%
|
9%
|
Problem 4: Value-at-Risk (VaR) Statistic Your portfolio allocates equal amounts to three stocks. All three stocks have the same mean annual return of 18%. Annual return standard deviations for these three stocks are 35%, 45%, and 55%. The return correlations among all three stocks are zero. What is the smallest expected loss for your portfolio in the coming year with a probability of 1 percent?