Foundation of Risk Management Quiz 1 Question 17

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

Foundation of Risk Management Quiz 1 Question 17

Postby kspoon » Wed Apr 04, 2012 12:35 am

I am a little confused with the solution of the following 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
Choose one answer.
a. St1: $3.2 billion
b. St2: $2.4 billion
c. St3: $1.9 billion
d. St4: $1.6 billion

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?



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

Re: Foundation of Risk Management Quiz 1 Question 17

Postby content.pristine » Wed Apr 11, 2012 2:42 pm

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 :)

Return to “FRM Part I”


Global Association of Risk Professionals, Inc. (GARP®) does not endorse, promote, review or warrant the accuracy of the products or services offered by EduPristine for FRM® related information, nor does it endorse any pass rates claimed by the provider. Further, GARP® is not responsible for any fees or costs paid by the user to EduPristine nor is GARP® responsible for any fees or costs of any person or entity providing any services to EduPristine Study Program. FRM®, GARP® and Global Association of Risk Professionals®, are trademarks owned by the Global Association of Risk Professionals, Inc

CFA Institute does not endorse, promote, or warrant the accuracy or quality of the products or services offered by EduPristine. CFA Institute, CFA®, Claritas® and Chartered Financial Analyst® are trademarks owned by CFA Institute.

Utmost care has been taken to ensure that there is no copyright violation or infringement in any of our content. Still, in case you feel that there is any copyright violation of any kind please send a mail to and we will rectify it.