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
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%.
3. The current market price of General Eclectic is $10.50 and the distribution of General Eclectic’s...
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