Explanation:
The total VaR of the fund can be calculated using the formula for the VaR of a portfolio with two components:
Given that (since each manager gets the same VaR budget), VaR_{Total} = \`3.4545 \text{ billion}$, and $\rho = 0.5$, we can substitute these into the formula: $3.45`45 = \sqrt{x^2 + x^2 + 2 \times 0.5 \times x \times x}$$
$3.4545 = \sqrt{2x^2 + x^2} = \sqrt{3x^2} = x\sqrt{3}$$
Solving for :
Therefore, the VaR budget for each manager should be $1.9945 billion. Option A is correct.
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Q.62 The BC&C pension fund has 60%, or about $21 billion, invested in equities. The fund measures absolute risk with a 95%, one-year VaR, which gives $3.4545 billion, assuming a normal distribution and volatility of 10% per annum. The fund would like to allocate this risk to two of its experienced equity managers, each with the same VaR budget. Determine what the VaR budget for each manager should be, given that the correlation between them is 0.5.
A
$1.9945 billion
B
$3.4545 billion
C
$2.4427 billion
D
$1.0731 billion