how should I determine the return on a dollar neutral investment strategy? that is, the amount invested in the long position is equal to the amount invested in the short position. therefore, the net investment is zero.should i take the sum of the returns of the individual positions?

Your second sentence olny explains that you have a hedge position . Not all hedge positions are dollar neutral. Could you explain more about what you like to do so that we can be more of help.

well I buy options on a certain stock A, and sell options on a stock B. I want the amount I sell to equal the amount I buy, to be equal in dollars that is. so let's say I buy option A for 4 dollars at time t, and its value rises to 10 at time t+1.I sell option B for 4 dollars at time t, and its value declines to 2 at time t+1.and at time t+1, I unwind my position.So at time t, my net investment is 0 (=4-4), and at time t+1 my proceeds are 10-2=8Now how should I calculate my return on this investment?

Wbenard,You are trading different underlyings you can't treat them as Credit/Debit Spreads. I suggest calculating separately. However I am not an expert on options I would be interested to know the reasonning behind the opposing idea if any. Since this is a student forum, I want to mention for beginners that calculating the return on selling options is not that straight forward. This is often confused among many people. For a short put position return is calculated on the initial margin. Required minimum margin is the largest of 20 percent of the stock price plus the put premium less the amount by which the put is out of the money or 10 percent of the stock price plus the put premium.

"Return" is not a well-defined concept. An investment strategy typically has two major inputs, the cash that must be put up (or taken out) and the capital that is put at risk. "Economic capital" is an attempt to convert those both to a single standardized input.In most cases, it doesn't matter. If you use a smaller denominator, your return goes up, but your risk goes up just as much. Usually it's the ratio of return to risk that matters.A reasonable solution is to use a pro-forma risk-based capital. If your strategy has a dollar standard deviation of $1,000 per year, that's about the same as $5,000 invested in the S&P500.Another solution is to use the net margin posted. There's no real theory behind this, unless your strategy is constrained by your funds available for margin. However, it can give reasonable answers.

The idea is based on an article by Hogan et al: Testing Market Efficiency Using Statistical Arbitrage with Applications to Momentum and Value Strategies (http://papers.ssrn.com/sol3/papers.cfm? ... _id=386440).They propose a methodology to test if a certain strategy meets the criteria of statistical arbitrage, that is a zero net investment and in the long run no risk of a loss (although in the short run, there is a probability of loss since it is no pure arbitrage, but statistical arbitrage based on statistical relationship).They do this for instance using momentum strategies, where they buy losers and sell the winners. They generate a series v(t) of discounted trading profits, which consists just of absolute values, so no returns. But I think it would also be nice to calculate returns, to give a measure of profitability that is more comparable with other trading strategies.So indeed as with momentum strategies, I am not buying and shorting the same securities. I therefore also think it is correct to calculate returns individually from the long and short position, but then there are a lot of different ways to do this. I was wondering if there is some sort of 'generally accepted' method to do this.

If you are planning to use the idea mentioned in that paper I have some suggestions that might help you improve the results.Rather than trading options stick to stocks, create a linear relationship among your long stocks and also short stocks. When you have 2 linear relationships check weather they are co integrated, if not try finding a linear relationship that is co integrated .If you don't have any experience in statistical arb trading make sure your spread is stationary when looking for a co integration relationship, that will take care of many risks you can't calculate for now. Other wise spread does not need to be stationary but it requires different type of risk management and trading. From that point you can start using ideas like stochastic structural break for co integration and stochastic volatility estimations. It becomes much like a pairs trading strategy. You don't have to take only convergence /divergence trades, with little creativity and modeling you can come up with new strategies and improve results very much. Also if you can, create a risk management system to control your volatility of any single trade within the consistency boundaries of the relationship you created. That will allow you realize much faster when the trade will lose money..

The two common approaches are to use the required margin amounts or some measure of economic capital (say a multiple of standard deviation to keep it simple).