# 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. Commented Nov 19, 2019 at 21:31
• @demully you mean by shor answer this: $\frac{(\$91)}{\$29,016.00}$ ? I didnt understand the long answer part. Commented Nov 19, 2019 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". Commented Nov 19, 2019 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. Commented Nov 19, 2019 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 :-) Commented Nov 20, 2019 at 1:21