# What is the proper way to calculate returns for Pair Trading?

Edit

I am assuming that I don't need to use margin account to short here:

What is a standard way to calculate return for pairs trading strategy? For example, I bought 100 dollars worth of a loser (L) and shorted 100 dollars worth of winner (W), and when their prices converged I sold L for 110 dollars worth, and paid 90 dollars for W. At the end I made dollars 20, but what is my return? Normally I would divide profit by investment, but here my net investment is zero, so I can't do that. It seems reasonable to count each of my 100 dollars positions as separate investments, in that case I would have:

$$\mbox{return} = \frac{20}{100 + 100} * 100 \% = 10 \%$$

Is the above right? If not what is the proper method?

If I need to use a margin account:

Under Regulation T, it is mandatory for short trades that 150% of the value of the position at the time the short is created be held in a margin account. This 150% is comprised of the full value of the short (100%), plus an additional margin requirement of 50% or half the value of the position. (The margin requirement for a long position is also 50%.) For example, if you were to short a stock and the position had a value of \$20,000, you would be required to have the \$20,000 that came from the short sale plus an additional \$10,000, for a total of$30,000, in the account to meet the requirements of Regulation T

Investopedia

Then I would need to put 100 * 1.5 = 150 in the margin account for shorting a winner, and buy 100 dollars worth a loser, so my return is: $$\mbox{return} = \frac{20}{100 + 150} * 100\% = 8\%$$

I think the above is right, but a bit unsure.

Thank You

• You had to put-up money for the margin account, right? Mar 10 '13 at 20:37
• @chrisaycock, thanks for the pointer, I think thinking about margin account explicitly actually makes things easier. I updated my a question, I think I am calculating the return correctly now, is that right? Mar 10 '13 at 22:46
• It differs on which market you're investing, notice that Regulation T only applies in america. Other countries will have similar rules though. However, you're still not calculating it correctly. Notice that if you need a collateral of 150% of the value of the shorted stock, you'll still get cash from selling it. So the cash thats taken from your pocket is only 50% of the value of the stock. Also, I think you can use some percentage of the long position as collateral, but ofc this depends on what kind of player you are. Mar 11 '13 at 17:18