Exam 20: Value at Risk

The gain from a one-year project is uniformly distributed between −$2 million and +$8 million. i) What is the one-year 99% value at risk? _ _ _ _ _ _ ii) What is the one-year 99% expected shortfall? _ _ _ _ _ _

Stock A has a daily volatility of 1.2% and stock B has a daily volatility of 1.8%. The correlation between the two stock price returns is 0.2. i) What is the standard deviation of the return from stock A over 4 days? _ _ _ _ _ _ ii) What is the standard deviation of the return from stock B over 4 days? _ _ _ _ _ _ iii) What is the standard deviation to the nearest $'000) of the 4-day change in the value of a portfolio consisting of a $1 million investment in stock A and a $1 million investment in stock B? _ _ _ _ _ _

Consider a position in a single option on a stock. The position has a delta 12. The stock price is 10. What is an approximate relationship between the change in the portfolio value in one day, $\Delta P$ , and the return on the stock in one day, $\Delta x$ ? choose one)

In question 3, suppose that the position has a gamma of 4. Which of the following is the extra term that should be added to the right hand side of your answer to question 3? choose one)

At the end of Thursday, the volatility of asset A is 2% per day and the volatility of asset B is 1% per day. Also, the covariance between the assets is 0.0001. During Friday, asset A produces a return of 3% and asset B produces a return of zero. An EWMA model with $\lambda = 0.9$ is used. Answer the following questions giving two decimal places. i) What is an estimate of the volatility per day of asset A at the end of Friday? _ _ _ _ _ _ _ ii) What is an estimate of the volatility per day of asset B at the end of Friday? _ _ _ _ _ _ iii) What is an estimate of the correlation between the assets at the end of Friday? _ _ _ _ _ _ _