I'm uncertain how to think about the rate of return on hedged positions, and I suspect part of the problem has to do with the difference between theoretical scenarios (such as in put-call parity demonstrations) versus actual short positions in the real world. But regardless of the source of my confusion, here's the problem:Suppose I have some method of evaluating stocks, which I believe gives me an advantage over the typical investor. Let's say I use my method to rank the S&P 1500. Now because I believe in my method, I think that the expected return on, say, the top 100 stocks (as ranked by my method) exceeds the expected return on the entire S&P 1500. So if I had, say, $1 million to invest, I might spread it (perhaps in a cap weighted fashion) over those top 100. If I wanted a higher return (but more risk), I might spread it over 50 or 25 of the top stocks (as ranked by my method).However, an alternate approach would be to go long on the top X stocks, and go short on the bottom Y. This way, I'm really isolating the information contained in my method of ranking. But in this approach, how do I calculate the rate of return on the portfolio? For example, suppose I buy $1 million worth of the top 50 stocks, and short $1 million worth of the bottom 50. If I wait one year, close out the position, and have $1.1 million, is it right to say I earned 10%? I see at least two complications, and maybe there are more:(1) The rate of interest on the $1 million raised by shorting.(2) The fact that if the bottom 50 (which I shorted) had risen during the year, I would have had to put in more to satisfy the broker (right?). Even if the bottom 50 collectively never rose, nonetheless they *could* have, and so in a sense more of my wealth could have been exposed to the portfolio.I'm sure my concerns aren't even phrased in the right way, but any discussion (even if you dispute some of my premises) would be very helpful.

Make it simpler:Suppose at time t=0, you fund a portfolio with 100 and instantaneously go long 100 and short -100. In period 1, both the long and short positions appreciate 10%. Assume also that your cash return is 5%, no leverage is used and no additional flows occurred during the period (broker did not call you to pony up more cash). t=0 Per1 t=1Long +100 +10% +110Short -100 +10% -110Cash +100 +5% +105Total +100 +105Return on portfolio = 105/100 - 1 = 5%. Here, your short bet offset the long bet, and the return is on interest from investing the short sale proceeds (I think this goes into a restricted bucket until the short position is unwound and you may not get any interest).In the next scenario, assume that you hit both bets and the short value loses 10% t=0 Per1 t=1Long +100 +10% +110Short -100 -10% -90Cash +100 +5% +105Total +100 +125Your periodic return is 25%.Note a seemingly odd result in both situations -- in situation one the total return is at the lower bound of the underlying component returns, and in situation two the total return is outside the underlying component returns. This is a natural consequence of a long/short strategy.Finally, one last oddity to discuss. In situation one, the short position lost money for you. The return is positive! In situation two, the short position helped you, but the asset class return is negative! To alleviate this, some recommend dividing by the absolute value of the average capital employed in the period (the Beg MV here). Don't do this! It makes intuitive sense to do so, but the multiperiod compounding gets screwed up.Suppose 1 share of stock has a t=0 price of 100 initially, and is priced at 120 (t=1), 130 (t=2), 120 (t=3) and at 110 (t=4).A long position has returns returns of 20%, 8.33%, -7.69% and -8.33%. The compounded return is 10%, which is exactly what we expect: 100 increases to 110. The short position is exactly the same. If we take the absolute value of the denominator to calculate the returns, we have -20%, -8.33%, 7.69% and 8.33%. Compounding gives us a -14.44% rate of return. The short value went from -100 to -110 and there was no additional activity. No way can this return be reconciled with the values. In each period, the adjustment "made sense" and followed the valuation impact to the portfolio, but the multiperiod return is incorrect.Sorry for the long post. I veered a bit from the topic, but the return calculation is really no different long vs. short.

Thanks for the help. I think though it's not so much hedging that's confusing me, but shorting itself. So let's make it even simpler than your scenario. Suppose I short $10,000 of a particular stock. What exactly happens at that point? In textbook discussions, they make it sounds (sometimes) as if you can go buy pizza with that money. But in reality, what happens? The broker keeps track of it, and it earns interest for you (?) but you can't touch it until you close out the position?Also, if the stock rises in the meantime, you have give the broker money, right? The idea is that at any time, you have enough on deposit with the broker so that you could close out the short position?OK, assuming that's how it works, here's my problem. Suppose I short $10,000 worth of the stock when it's selling at $100, and then it drops to $90. I close out the position and have $1000 more than I started with. So what's my rate of return from this? If the stock never rose (after I shorted it), I didn't have to put in a penny. So my rate of return is infinite? But if the stock had risen in the meantime from $100 to $105, I would have had to kick in $500. So my rate of return is now only 200% for the period in question?I understand that something is wrong with this reasoning, but I'm not sure exactly what. Also, if anyone tries to enlighten me, please try to be clear on what things are merely real world complications, versus those things that even in a textbook would blow up my faulty arguments above.

The thing is that the amount that you keep on deposit with the broker (called a margin account) has to be 150% of the proceeds of the short sale (which includes the proceeds of the short sale itself). So in your example, if you made a 10000 short sale, you would also have to put up 5000 of your own money into the margin account. So you would say that the initial margin requirement is 150%.This is to start off; as time goes on, there is a maintenance margin requirement of somewhere between say 120% and 140%, such that if the stock price moves up against you and the value of your margin account moves below the maintenance margin, then you have to put up more money to meet the maintenance margin.On the other side of the coin, if the stock price moves down in your favor, then the maintenance margin stays at 150%, but you'll have excess money in your margin account, which can be released to you.It is also worth noting that the same can be more or less done when it comes to going long on a stock---you only need to put up 50% of your own money, and then there is a similar maintenance margin which you'll have to put up more money for if the stock price moves down against you.Here is a good explanatory link about short sales.