Sorry for this dumb question but what are the mathematical-finance /academic conventions for calculating portfolio weights in a long/short portfolio where the longs are fully funded by the shorts? Note that I am asking for the 'academic' conventions, I'm aware that in reality one needs to hold margin etc.
Suppose I am long USD200 of Apple, and I have shorted USD200 of Google stock. What is the portfolio weight of apple and google?
- w_apple = 200/200 = 1 and w_google = -200/200 = -1?
- w_apple = 200/(200 + abs(-200)) = 0.5 and w_google = -200/(200+abs(-200)) = -0.5?
- something else?