Using the Hedge Ratio to Choose Pair-Trade Legs and Sizing
Summary
The answer explains how the sign of a hedge-adjusted spread can guide the direction of a pair trade. Under the stated spread definition, a positive spread prompts a short position in the first asset and a long position in the second; a negative spread reverses those legs. The answer frames the spread as a deviation from an equilibrium relationship and treats the hedge ratio as the coefficient linking the two asset prices.
It says that prices alone do not determine the share quantities: the hedge ratio determines relative exposure. In its example, a positive spread corresponds to selling a fixed dollar amount of the first asset and buying a hedge-ratio-scaled dollar amount of the second. The hedge ratio is commonly estimated by regression on historical data, with the described specification regressing one price on the other and setting the intercept to zero. This is a simplified account: it does not detail entry and exit thresholds, costs, changing hedge ratios, or how to validate the assumed reversion relationship.
Key ideas
- The spread’s sign determines which asset is bought and which is sold under the specified spread convention.
- The hedge ratio sets the relative exposure of the two legs rather than the assets’ prices alone.
- The answer expresses position sizes in dollar exposure, scaling the second leg by the hedge ratio.
- A historical regression can be used to estimate the hedge ratio, with a zero-intercept specification described here.
- The method assumes a reversion relationship and does not explain threshold selection or transaction costs.
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Full text
# How buying/selling pairs and entering/exiting trade works in pairs trading? # How buying/selling pairs and entering/exiting trade works in pairs trading? Lets say I have two stocks x and y and their corresponding stock price p(x) and p(y). consider HR as hedge ratio. Then we can calculate the spread using this equation. $spread=p(x)-HR*p(y)$ from this step what rationale should we use for buying and selling pairs? This is my logic Pairs trading works for two highly correlated stocks. We then sell the costlier stock and buy cheaper stock simultaneously. If spread is positive the price of `x` is higher than price of `y` so we will sell x and buy y . if spread is negative y is costlier than x then we sell y and buy x simultaneously. So the total return on pairs trading can be return as $TotalReturn=sell(return of asset 1)-HR*buy( return of asset2)$ pseudocode ``` if(spread>0 and entry_threshold=True) TotalReturn=sell(x)-HR*buy(y) elif(spread<0 and entry_threshold=True) TotalReturn=sell(y)-HR*buy(x) exit_trade(exit_threshold=True) ``` is this rationale correct? another question? If price of `x` is 13 dollar and price of `y` is 63 dollar then how many shares of x and y should we buy and sell simultaneously in a pairs trading? ## Answer by Slug Pue (score 1) https://quant.stackexchange.com/a/28192 Your reasoning is correct. To answer your last question: the current prices alone don't decide how many shares to sell and buy in each of the stocks. That is decided by the hedge ratio. In fact, the whole point of the hedge ratio is to assume that it is the ratio that the stocks will revert back to over time. So if we denote the spread at time $t$ by $s_t$ and the hedge ratio as $\beta$, we have $$ s_t = p(x_t) - \beta p(y_t) + \epsilon_t $$ where $\epsilon_t$ is the deviation from the equilibrium state. When you get your signal and let's say $s_t>0$, you sell \$1 worth of $x$ and buy \$ $\beta$ worth of $y$. How do you decide $\beta$? Well, usually by doing a linear regression using some past data. In the stated model it is natural to regress $x_t$ on $y_t$ and force the intercept to be $0$.
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