Explanation:
To find the allocated VaR budget for each manager, we can use the portfolio variance/VaR formula for two correlated components. Let the total VaR be and each manager's allocated VaR be ().
The formula for portfolio VaR is:
Given that , , and :
$3.4545 = \sqrt{x^2 + x^2 + 2(0.5)(x)(x)}3.4545 = \sqrt{2x^2 + x^2}$
$3.4545 = x\sqrt{3}$
Solving for :
Thus, each manager should be allocated a VaR budget of approximately $1.9945 billion.
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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