Test Bank: Chapter 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 days? (ii) What is the standard deviation of the return from stock B over 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, P , and the return on the stock in one day, x (circle one) (a) P 12 x (b) P 1.2x (c) P 120x (d) P 22x In question suppose that the position has a gamma of Which of the following is the extra term that should be added to the right hand side of your answer to question (circle one) (a) 4(x ) (b) 2(x ) (c) 20(x ) (d) 200(x ) 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   09 is used Answer the following questions giving two decimal place accuracy (i) What is the 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? _ ... 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?... 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   09 is used Answer the following questions giving two decimal place accuracy (i) What is the estimate of the volatility per day of