Question:

A portfolio manager estimates that the volatility of her daily portfolio returns is 1.2%. She also expects this portfolio to bring a return of 6% per year. Assume that there are 252 trading days in a year. The current value of her portfolio is $10,000,000.

(a) Calculate a 5-day VaR ($) at the 97,5% confidence level (b) What is the 95% confidence interval of the value of this portfolio after 20 days?

(c) Suppose the value of a portfolio dropped by $555,000 in 10 days. What is the chance of this happening? (d) Up to what horizons (number of days) can she hold this portfolio with a 99% confidence that her total loss will not be more than 30%? Show your work. State your answer in number of days