Question

3. The current market price of General Eclectic is $10.50 and the distribution of General Eclectic’s stock price is described below:

Price ($) 5 8 9 10 11 12 15
Probability 0.01 0.03 0.2 0.52 0.20 0.03 0.01

a. Construct the distribution of losses/profits on this stock
b. Compute the 95% VaR and the expected shortfall.
c. Continue with the previous exercise, but suppose that the lowest price is changed from $5 to $0. Will VaR change?
d. Will expected shortfall change? If it does change, calculate the new expected shortfall

Answer 1

price	prob(p)	loss/profit(q)	p*q	q^2	p*q^2
5	0.01	-5.5	-0.055	0.003025	0.00003025
8	0.03	-2.5	-0.075	0.005625	0.00016875
9	0.20	-1.5	-0.3	0.09	0.018
10	0.52	-0.5	-0.26	0.0676	0.035152
11	0.2	0.5	0.1	0.01	0.002
12	0.03	1.5	0.045	0.002025	0.00006075
15	0.01	4.5	0.045	0.002025	0.00002025
	Mean		-0.5		0.055432
	Standard deviation		0.23544
	95% VAR be		0.388476
	95% var value		4.08
Expected shortfall @100%		=Mean	-0.5

Standard deviation will be calculated by taking the square root of last column and expected shortfall will be calculated by using the column =p*q and summation of the column.

Lowest price if changed from $5 to $0

refer the table :

price	prob(p)	loss/profit(q)	p*q	q^2	p*q^2
0	0.01	-10.5	-0.105	0.011025	0.00011025
8	0.03	-2.5	-0.075	0.005625	0.00016875
9	0.20	-1.5	-0.3	0.09	0.018
10	0.52	-0.5	-0.26	0.0676	0.035152
11	0.2	0.5	0.1	0.01	0.002
12	0.03	1.5	0.045	0.002025	0.00006075
15	0.01	4.5	0.045	0.002025	0.00002025
	Mean		-0.55		0.055512
	Standard deviation		0.23561
	95% VAR will be		0.388756
	95% var value		4.08
Expected shortfall @100%		= mean	-0.55

As we can see the expected shortfall also got changed by changing the lowest value 1.3% per day estimated volatility price = $300,net value change due to volatility =$3.9.

volatility estimate at $298=3.9/298=1.31%.