# Value at Risk - Long/Short position

I have a simple question on the VaR for a portfolio that consists of a long and short position. Say I have a portfolio consisting of the following positions:

• long 1000 shares of stock X

• short 1000 shares of stock X

Let's assume the daily volatility for Apple stock is 2% and that the stock trades at 2 dollar/share so my investment is 4000 dollar in total. I want to calculate the VaR for each of the positions separately and for the full portfolio, but I am a little bit confused with the signs associated with long and short position. Intuitively, the portfolio should have VaR = 0 as the long and short position in the same stock with equal investment have a neutralizing effect.

(1) VaR for the long position VaR = 2%*2000*2.33 = 93.2

(2) VaR for the short position VaR = 2%*abs(-2000)*2.33 = 93.2

Now, for the combined position, my question is which signs to use? Do we say:

VaR = 2.33*sqrt((40)^2+(-40)^2+2*40*(-40)*corr) = 0 since corr = 1

VaR = 2.33*sqrt((40)^2+40^2+2*40*40*corr) = 0 since corr = -1

Since you have the same stock X, the correlation is simply equal to 1 or do we say it is equal to -1 because we have a short and long position in it? So generally my question is, do we take the absolut value if the position is short or?

Thanks!

• If your portfolio consists 1000 long and 1000 short share of same stock, it means that value of your portfolio will always be zero. Question can make more sense if it is two different securities. – Neeraj Nov 21 '17 at 19:19