The current price of the BP stock is $53. The distribution of the BP’s stock pri

Question

The current price of the BP stock is $53. The distribution of the BP’s stock price over the 10-day period is given below. Compute the 99% 10-day VaR and the expected shortfall:
Price ($).        probability
40.                    0.003
42.                    0.005
49.                    0.1
50.                    0.2
55.                    0.522
60.                    0.1
65.                    0.07

a. Calculate the loss distribution on BP stock (i.e. calculate losses relatively to the current price).
b. What is a 10-day VaR?
c. What is the Expected shortfall?
d. Continue with the previous exercise, but suppose that the lowest price is changed to $30.
Will VaR change?
e. Will expected shortfall change? How?

Explanation / Answer

Ans) a. Calculate the loss distribution on BP stock (i.e. calculate losses relatively to the current price). Price Probability Probability * Price Deviation Square of Deviation Variance (P*Square of Deviation) 40 0.003 0.12 -14.49 210.0 0.62988 42 0.005 0.21 -12.49 156.0 0.78 49 0.1 4.9 -5.49 30.1 3.01401 50 0.2 10 -4.49 20.2 4.03202 55 0.522 28.71 0.51 0.3 0.135772 60 0.1 6 5.51 30.4 3.03601 65 0.07 4.55 10.51 110.5 7.732207 Expected Price 54.49 19.3599 BP Stock Price = $    54.49 Expected Price = $ (53.00) Total Profit $       1.49 2. What is a 10-day VaR? Ans) $                   19.3599 3. What is the Expected shortfall? Ans) Nill Because it will gain $1.49 profit 4. Continue with the previous exercise, but suppose that the lowest price is changed to $30. Will VaR change? Ans) Variable Change Is = 20.5284 19.3599 1.1685 Price Probability Probability * Price Deviation Square of Deviation Variance (P*Square of Deviation) 30 0.003 0.09 -24.46 598.3 1.794875 42 0.005 0.21 -12.46 155.3 0.776258 49 0.1 4.9 -5.46 29.8 2.98116 50 0.2 10 -4.46 19.9 3.97832 55 0.522 28.71 0.54 0.3 0.152215 60 0.1 6 5.54 30.7 3.06916 65 0.07 4.55 10.54 111.1 7.776412 54.46 20.5284 e .Will expected shortfall change? How? Ans)               If we accept the shortfall change then there is a change of Expected return of (0.03) ($54.49-$54.46)

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