VAR question

[srinu2singaraju]

Hi david,

FRM 2007 question:
A relative value hedge fund manager holds a long position in Asset A and a short position in Asset B of roughly equal principal amounts. Asset A currently has a correlation with Asset B of .97. The risk manager decides to overwrite this correlation assumption in the variance model to a level of 0.30. What effect will this change in correlation from 0.97 to 0.30 have on the resulting VAR measure?

A. It increases VAR.(Answer)
B. It decreases VAR.
C. It has no effect on VAR, but changes profit or loss of strategy.
D. Do not have enough information to answer.

Why VAR should increase? I am not clear on the concept.
Thanks in advance

Regards,
Srinivas

 

[David Harper CFA FRM]

Hi Srinivas,

It's an instructive question: If this were a two-asset portfolio, an increase in correlation would increase VaR; e.g., at perfect correlation (1.0), portfolio VaR = sum of individual VaRs.

Here is the two-asset VaR spreadsheet:
http://www.bionicturtle.com/premium/spreadsheet/4.a.1_two_asset_var_relative_vs_absolute/

please note that portfolio variance =
w1^2*variance(asset1) + w^2*variance(asset2)+2*w1*w2*Cov(asset1,asset2)

if you use an input of, say, -30% (-0.3) for the (1) weight, this will simulate a long + short position such that the portolio variance above is given by; i.e., a short is input with a negative weight:

w1^2*variance(asset1) + w^2*variance(asset2)+2*(negative for the short)*(positive for the long)*Cov(asset1,asset2)
... so the final term is (-x*covariance) rather than (+x*covariance) and now an increase in correlation is decreasing the portfolio variance!

and, intuitively, for a significant correlation, the short is a cross-hedge of the long; e.g., at 1.0 correlation, the short is an almost perfect hedge (if volatilties are =, then perfect hedge)

David