Test bank fundamentals of futures and options markets 7e by hull chapter 20

Test Bank: Chapter 20
Value at Risk
1. 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 _ _ _ _ _ _
2. 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?
______
3. 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
4. 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 (circle one)
(a) 4(x ) 2
(b) 2(x ) 2
(c) 20(x ) 2
(d) 200(x ) 2

5. 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?
_______