Sorry, if this has been posted, but I couldn't find a similar topic in any of the archives.Extremely basic question about sign convention in portfolios.When you sell something it seems to get a negative sign.When you buy something it gets a positive sign. I don't understand this sign convention. For example I am trying to prove by arbitrage that the value of a European call option, c, is bounded from above by S, the stock price. We assume that the exercise price is K and that at expiry time the stock price is St.My argument then goes as follows. Assume c > S. And construct a portfolio where you write a call and buy a share:At time = 0 you sell c and buy S so the porfolio is S-c<0.If St < K at expiry your call is worthless and you have St > 0If St < K the option expires in the money and it is exercised so you have -St + K from the call and St from the stock which leaves you K.I understand the basic arithmetic of the portfolios since it is 3'd grade math. What I really don't get is why is the initial portfolio value negative. It seems to me that if you sell the call and buy the stock you would have money c-S and your portfolio would be greater than zero.This is something very stupid, I know. And I am missing something so fundamental that it is obvious. What the heck is it?Thanks!

QuoteOriginally posted by: RiazASorry, if this has been posted, but I couldn't find a similar topic in any of the archives.Extremely basic question about sign convention in portfolios.When you sell something it seems to get a negative sign.When you buy something it gets a positive sign. I don't understand this sign convention. Sign convention illustrates only your "positions" on assets making up the portfolio. QuoteMy argument then goes as follows. Assume c > S. And construct a portfolio where you write a call and buy a share:At time = 0 you sell c and buy S so the porfolio is S-c<0. S-C => short call, long share (your positions)

Ah, thanks.I knew I was overlooking something extremely basic.

Simple, yes, but very important and a too-frequent problem. If you are not careful to be consistent in your signs, you can make a nonsense argument. Sloppy authors can be very confusing.One common problem is to use the same symbol (S, C or P for example) for the security and the price of a security. So you if buy S you have a cash flow of -S. This quickly leads to incomprehensible equations.Convention is not important, consistency is.