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Explanation:
Today’s stock price is $100 × (1 + 10%) = $110
The 95% VaR is given by the 14th worst return, i.e., -6.05%,
N/B: Using 260 days moving window of historical data, the 95% VaR will be r = 260(1 - 95%) + 1 = 14th observation
The new 95% VaR will be $110 × (-6.05/100) = -$6.655
Note. The latest return (10%) does not affect the left tail of the loss distribution. It is higher (more positive) than all the returns given and does not get a spot among the worst 16 observations. In addition, the examiner assumes that the oldest return pushed out the rolling window is not among the entries given. Therefore, today’s worst 16 observations will be the same as yesterday’s.
Things to Remember
Q.3037 You have been hired on the trading floor, and one of the traders comes over and asks about the impact of a price change on her VaR made of a long position in stock A, whose value stood at 100 as of yesterday. Assume you are using a 95% confidence historical VaR (based on 260 days moving window of historical data). Further, assume that the 16 worst 1-day returns of stock as of yesterday were as follows:
-9.5, -8, -7.6, -7.4, -7.2, -7.18, -7.1, -6.9, -6.57, -6.56, -6.45, -6.4, -6.25, -6.05, -5.99, -5.85.
Assume the price of the stock increased by 10% between yesterday and today. Further, assume that the oldest return is not among the returns given. What will the value of today’s 95% VaR (in absolute value) be?
A
$6.25.
B
$6.655.
C
$10.
D
$6.05.
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