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?