1+1+2rho

问题如下：

The AT&T pension fund has 68%, or about $13 billion invested in equities. Assume a normal distribution and volatility of 15% per annum. The fund measures absolute risk with a 95%, one-year VaR, which gives $3.2 billion. The pension plan wants to allocate this risk to two equity managers, each with the same VaR budget. Given that the correlation between managers is 0.5, the VaR budget for each should be

选项：

A.$3.2 billion

B.$2.4 billion

C.$1.9 billion

D.$1.6 billion

解释：

Call x the risk budget allocation to each manager.This should be such that:

Solving for:

we find x = $1.85billion.

Answer A is incorrect because it refers to the total VaR. Answer B is incorrect because it assumes a correlation of zero. Answer D is incorrect because it simply divides the $3.2 billion VaR by 2, which ignores diversification effects.