# Calculating % Return in Pairs Trading Strategy

Hi guys Could you help me here?

I would like to calculate the return of a Pairs Trading strategy. For example:

18/11 - Open the Trade: I will go long on A and Short on B:

Stock A : $$32.24 Stock B :$$ 29.82

Ratio: $$\frac{(Price of StockA)}{(Price of StockB)} = 1,0812$$

I will buy: $$\frac{(30.000)}{32.24} = 900$$ (approximately)) units of Stock A. The cost is: $$900*32.24 = \29,016.00$$

And Sell: $$\frac{(30.000)}{29.82} = 1000$$ (approximately)) units of Stock B : $$= 1000*29.82 = \29,820.00$$

The Cost of Open the Trade:$$\29,820.00 - \29,016.00 = \804$$

At 20/11 I will Close the Trade:

Price of Stock A At 20/11: $$\32.63$$ Price of Stock B At 20/11: $$\30.08$$

Ratio: $$\frac{(Price of StockA)}{Price of StockB} = 1,0848$$

I will sell $$900$$ units of Stocks A: $$900*32.63 = \29,367$$ and I will buy $$1000$$ units of Stock B: $$1000*30.08 = \30,080$$

The cost of Close the Trade: $$\29,367 - \30,080 = -\713$$

To calculate Profit/Loss of this strategy I just sum the The cost of Open the Trade and The cost of Close the Trade which is $$\91$$ on this case.

My question is: How can I calculate the $$\%$$ return of this strategy?

But I've been reading and it got a little confusing for me.

Many thanks!

• Short answer is that the return equals P&L divided by your equity. Long answer = longwinded proof of concept gladly given, if required :-) Had you doubled the size of your pairs trade, would that change the % return? Done millions rather than thousands? If not, you’re getting into concepts of return that have no intuitive meaning to mainstream investors. Happy to explain, if useful. – demully Nov 19 '19 at 21:31
• @demully you mean by shor answer this: $\frac{(\$91)}{\$29,016.00}$ ? I didnt understand the long answer part. – Laura Nov 19 '19 at 21:33
• The problem you face is that the long and the short are self-financing. You borrow X to sell X worth of the short to give you X cash to finance X's worth of your long. Which gives you a profit or loss of Y. This is only meaningful in % terms compared to the Z capital you have to risk this P&L. The same Y P&L for investors with more or less Z to support this position leads to different "% returns". – demully Nov 19 '19 at 22:43
• Ah OK... his "returns" are expressed in unit terms, not % terms ;-) His nice chart is just my Y, ie P&L, given his position sizing. The % return you seek is a function of this AND how much capital you have to bear said risk. That is the ungiven, for all of us. – demully Nov 19 '19 at 23:29
• Now that's the basis for a question in it's own right, to which I promise I will attempt a proper answer, beyond comments to clarify comments :-) – demully Nov 20 '19 at 1:21