Problem 1. In each of the following scenarios, estimate from historical data or

Question

Problem 1. In each of the following scenarios, estimate from historical data or compute the yearly Value at Risk of the portfolio at the confidence level of 80%. (a) (5 points) A portfolio with the following changes in its value (in millions of dollars) during the last 10 years: (b) (5 points) A $100,000 portfolio of stocks A and B, financed by a loan at zero interest rate, with 20% invested in A and 80% in B. Assume that the joint distribution of stock returns is normal and that their expectation, standard deviation and correlation are given by Ha = 12%, (Hint: Any linear combination of jointly normal random variables is still normal)

Explanation / Answer

If we arrange the given values of changes in the portfolio values as follows

To calculate the VaR at 80% Confidence level, we select the 2nd number from the sorted list of numbers. Here -0.3 is the 2nd In the above data -ve numbers indicate loss.

(A) For the given portfolio VaR at 80% is $0.3 millions

Sr. # Profits 1 -0.3 2 -0.3 3 -0.2 4 -0.2 5 -0.1 6 -0.1 7 -0.1 8 0.2 9 0.5 10 1

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