Choosing Price Ratios or Hedge-Adjusted Spreads for Pairs Trading
Summary
The document compares two ways to measure a relationship between two stocks for pairs trading. A price ratio represents a dollar-neutral position: the trader invests equal dollar amounts in each asset. A regression-based spread instead uses a hedge ratio, such as the slope relating their prices, to set the number of shares in one leg relative to the other. The choice depends on whether the objective is dollar neutrality or hedging the assets’ price movement relationship; cointegration alone does not ensure equal betas.
The discussion also explains why a ratio is not a direct measure of trade profit and loss. Changes in the long asset affect the ratio differently from changes in the short asset, so the ratio can overstate short-leg gains and understate short-leg losses. The examples illustrate this asymmetry. The material gives conceptual guidance rather than a tested trading rule, and it does not specify how to estimate or update the hedge ratio, test cointegration, or account for costs and other risks.
Key ideas
- A price ratio supports equal-dollar exposure, while a regression-based spread uses a hedge ratio to relate the two legs.
- Cointegration does not imply that the two assets have equal betas.
- A hedge ratio can be used to determine the relative share quantities in a spread position.
- Ratio changes do not map consistently to pair-trade profit and loss, especially for moves in the short leg.
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Full text
# Calculate spread for pairs trading # Calculate spread for pairs trading What is the best way to begin calculations for pairs trading? I have seen two ways: 1) Start from the price ratio `StockAPrice/StockBPrice` and calculate mean, standard deviation and z-score from a times series of that. 2) Start with the spread calculated as `StockAPrice-StockBPrice*Hedge ratio` (where hedge ratio is just the beta of the regression). You then purchase `x` shares of stockA an short `x*hedge ratio` of stock B, for example. What is the right way to do it? If #1 is acceptable, how do you incorporate hedge ratio in that? ## Answer by Jacques Joubert (score 5) https://quant.stackexchange.com/a/23004 It depends on if you are trying to do a Dollar neutral hedge or a beta neutral hedge. Method 1 is a Dollar neutral hedge and Method 2 is the Beta neutral hedge ratio. Remember that even if you find a cointegrated pair, share A can have a higher beta than share B. ## Answer by vibhu_singh (score 2) https://quant.stackexchange.com/a/45830 The first method is dollar neutral and the second one is based on the relationship of price movement between two assets. For the first method of dollar neutral Let's say you want to keep the amount invested in stock A and stock B same. Then, simply divide $1000 with the price of A and B. The number you get is the number of shares of A and B you need to buy/sell to make the pair dollar neutral. For the second method, you need to find the relationship between two stocks A and B. Use that to calculate the spread. For example, the spread can be formed as 1 * stock A - slope * stock B. Where the slope of the line resulting from regressing A and b prices becomes the number of shares of stock b to buy for every 1 share of stock A. ## Answer by Nomad Trader (score 1) https://quant.stackexchange.com/a/43318 It's worth noting that once you take a position in a pair-trade the subsequent change in the ratio does not always equate to the same change in your P&L. It depends on whether you are winning/losing on the long position or the short position. Specifically, while the ratio will change commensurately with a change in your long position, it will not change commensurately for changes in your short position. For winning short positions the change in the ratio overstates the winnings, and for losing short positions the change in the ratio understates the losses. As such, you can't set your take-profit and stop-loss levels at percent changes in the ratio. Example follows: Long StockA @ 100 Short StockB @ 100 Ratio = 1 Long StockA now 120 Short StockB now 100 Ratio = 1.2 We can see that a 20% increase in the long stock equates to a 20% increase in the ratio. Great. Long StockA @ 100 Short StockB @ 100 Ratio = 1 Long StockA now 100 Short StockB now 80 Ratio = 1.25 We can see that a 20% fall in the short stock equates to a 25% increase in the ratio. Ratio has overstated the win. Long StockA @ 100 Short StockB @ 100 Ratio = 1 Long StockA now 100 Short StockB now 120 Ratio = 0.83 We can see that a 20% increase in the short stock equates to a 16.6% decrease in the ratio. Ratio has understated the loss.
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