Can VaR increase when correlation decreases?

For the sake of the argument, let's just take two risky assets in the portfolio.
Given that correlation between returns on those 2 risky assets decreased, (rho1,2), VaR should naturally decrease because the risk (volatility of portfolio) has just been decreased. However, an interview question asked me in what situation/portfolio can the VaR actually increase??? I'm all confused

Comments (6)

Best Response
Oct 29, 2013

One of the assets could have gotten riskier while the other stays the same. Consider a portfolio of two assets. One returns 5, 10 or 15, and the other returns 10, 20 or 30. Currently correlation=1 and VaR=0. Now let the first asset still return 5, 10, or 15, but now the second asset returns 0,-19.3, or-12. Correlation is now -.62 and VaR has increased.

A simpler example of this is a perfectly hedged portfolio of two assets. Say correlation=1 and the gains from the first asset will always perfectly offset losses from the second and vice versa, so VaR=0. If the correlation decreases there will now be some probability of a loss so VaR>0.

    • 2
Oct 29, 2013
mrme355:

A simpler example of this is a perfectly hedged portfolio of two assets. Say correlation=1 and the gains from the first asset will always perfectly offset losses from the second and vice versa, so VaR=0. If the correlation decreases there will now be some probability of a loss so VaR>0.

Just curious... Wouldn't you say that this is an example of correlation=-1, rather than 1?

Oct 29, 2013

You are correct

Oct 29, 2013

Thanks for the input mrme335!
I get the idea that if correlation decreases, then the SD of portfolio decreases as well, and hence VaR increases given the VaR formula: VaR=-(mu+1.65*SDportfolio) for 95% CI.
However, I'm confused at why does VaR=0 if correlation=1?

Oct 30, 2013

VaR is 0 in the correlation = -1 or 1 sense because you can just buy/sell the proper ratio to offset all gains and losses.

For example if you know with certainty, which you do because correlation=1 or -1, that whenever asset A increases in price by $1 asset B decreases in price by $3, then you could buy 3 of A and 1 of B. In this portfolio no matter what happens you will make, and lose no money, hence VaR = 0. The downside is obviously that you can't make money either.

Oct 30, 2013
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