Explanation:
First, calculate the variance of the initial portfolio in dollar terms: Var(initial) = (W_A * Vol_A)^2 + (W_B * Vol_B)^2 + 2 * W_A * W_B * Vol_A * Vol_B * Corr(A,B) Var(initial) = (200 * 0.20)^2 + (100 * 0.25)^2 + 2 * (200 * 0.20) * (100 * 0.25) * 0.2 Var(initial) = 40^2 + 25^2 + 2 * 40 * 25 * 0.2 Var(initial) = 1600 + 625 + 400 = 2625 Annual volatility of initial portfolio ($) = sqrt(2625) = 51.2348
Next, calculate the variance of the new portfolio:
He sells $100 of A and buys $100 of B, meaning new weights are W_A = 100 and W_B = 200.
Var(new) = (100 * 0.20)^2 + (200 * 0.25)^2 + 2 * (100 * 0.20) * (200 * 0.25) * 0.2
Var(new) = 20^2 + 50^2 + 2 * 20 * 50 * 0.2
Var(new) = 400 + 2500 + 400 = 3300
Annual volatility of new portfolio ($) = sqrt(3300) = 57.4456
Change in annual volatility = 57.4456 - 51.2348 = 6.2108 Change in daily volatility = 6.2108 / sqrt(260) = 6.2108 / 16.1245 = 0.38517 Change in daily 99% VaR = 2.33 * 0.38517 = 0.897.
Ultimate access to all questions.
Q.100 John Wick, FRM, manages two assets – A and B. The correlation between A and B is 0.2. The table below outlines further details on the two assets:
| Asset | Annual Volatility | Value |
|---|---|---|
| A | 20% | $200 |
| B | 25% | $100 |
If Wick sells $100 worth of A and buys $100 worth of B, what would be the change in the daily VaR at the 99% level of confidence? Assume 260 trading days.
A
8.000
B
0.897
C
7.403
D
0.102
No comments yet.