## Foundation of Risk Management Quiz 1 Question 17

kspoon
Posts: 6
Joined: Wed Apr 04, 2012 12:33 am

### Foundation of Risk Management Quiz 1 Question 17

I am a little confused with the solution of the following question:

Question:

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
a. St1: \$3.2 billion
b. St2: \$2.4 billion
c. St3: \$1.9 billion
d. St4: \$1.6 billion

Solution:
The answer is St3.

Call x the risk budget allocation to each manager. This should be such that x2 + x2 +2*rho xx = \$3.22. Solving for x, 1 + 1 + 2*rho= x sqrt(3) = \$3.2, we find x = \$1.85 billion. Answer St1) is incorrect because it refers to the total VAR. Answer St2) is incorrect because it assumes a correlation of zero. Answer St4) is incorrect because it simply divides the \$3.2 billion VAR by 2, which ignores diversification effects.

Where does this formula: x2 + x2 +2*rho xx come from? I searched though the slides and handbook but I don't see any term explaining what "rho" is. Could anyone please help?

Thanks

content.pristine
Finance Junkie
Posts: 356
Joined: Wed Apr 11, 2012 11:26 am

### Re: Foundation of Risk Management Quiz 1 Question 17

Hi KSpoon,

"rho" is ρ. This is your correlation coefficient.
In this question ρ is 0.5
"x2 + x2 +2*rho xx" is basically: (x1)^2 + (x2)^2 + 2ρ(x1)(x2)
Since the risk is divided equally between the two fund managers x1=x2=x

I hope this helps