Increamental VAR

[rickm123]

Hi David:

In one of your practice questions, if we will wanted the incremental VAR of of the CAD positions why is USD removed?


2.6. C. $592,000 (component VaR) and $329,000 (incremental VaR)
Since beta = Cov/Var = (correlation * volatility * volatility) / variance --> correlation = beta (i, P) * portfolio volatility / position volatility. In this case,
Correlation = 0.60 * 10%/10% = 0.60; i.e., portfolio volatility = SQRT(60%^2*10%^2 40%^2*20%^2) = 10%.
Individual (position) VaR of CAD = $6 million * 10% * 1.645 = $986.91.
Component VaR = Individual VaR * correlation = $986.91 * 0.60 = $592,147
Incremental VaR (CAD) = Portfolio VaR - Individual VaR (USD); i.e., the difference if the CAD position is deleted! In this case,
Incremental VaR (CAD) = $1.645 million - ($4 million * 20 % * 1.645) ~= $329,000

thanks

Rick

 

[David Harper CFA FRM]

Hi Rick,

Yes, that can be confusing. Incremental VaR (CAD) = Portfolio VaR (with CAD) - Portfolio VaR (after removing the CAD position); i.e., the drop in Portfolio VaR if we exit the position, by full-repricing, not the approximation using marginal VaR.

But in the case of a portfolio with only two assets (CAD & USD):
Portfolio VaR (with CAD) - Portfolio VaR (after removing the CAD position) =
Portfolio VaR(CAD + USD) - Portfolio VaR (USD only), and since Portfolio VaR (USD) = Individual VaR (USD) =
Incremental VaR (CAD) = Portfolio VaR (CAD + USD) - Individual VaR (USD)

In case it helps, similar discussion on another related question:
http://forum.bionicturtle.com/threads/grinold-ch-14.5494/#post-15447
i.e.,
"In Jorion's case, when I subtract as follows:
257.738 Portfolio VaR - 165 Individual VaR = 92.738 Incremental VaR, I am relying on the fact there are only two assets, so the 165 Individual CAD VaR is the portfolio VaR after subtracting the EUR position!
Portfolio VaR [Portfolio] - VaR [Portfolio - EUR] = Incremental VaR due to elimination of EUR position; but in this case, equal to:
Portfolio VaR [CAD + EUR] - VaR [CAD only] = Incremental VaR due to elimination of EUR position
i.e., only b/c it's two assets can I use VaR [CAD only] to replace VaR[portfolio - EUR]"

Thanks,