Deck 20: Value at Risk

Question 1

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)

A) $4 ( \Delta x ) ^ { 2 }$
B) $2 ( \Delta x ) ^ { 2 }$
C) $20 ( \Delta x ) ^ { 2 }$
D) $200 ( \Delta x ) ^ { 2 }$

Answer 1

$200 ( \Delta x ) ^ { 2 }$

Question 2

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 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? _ _ _ _ _ _ _

Answer 2

i): 2.12% ii): 0.95% iii) 0.45

Question 3

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? _ _ _ _ _ _

Answer 3

i): 2.4%
ii): 3.6%
iii): $47,000

Question 4

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)

A) $\Delta P = 12 \Delta x$
B) $\Delta P = 1.2 \Delta x$
C) $\Delta P = 120 \Delta x$
D) $\Delta P = 22 \Delta x$

Question 5

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? _ _ _ _ _ _