Converting a Log-Price Hedge Ratio into Pair Share Weights

Summary

The document explains how to interpret a hedge ratio estimated by regressing one stock’s log price on another’s. The ratio describes the relative percentage sensitivity of the two stocks: for example, a ratio of two means that a one percent logarithmic move in stock B corresponds to a two percent move in stock A under the fitted relationship. This is not directly a ratio of share counts.

To translate the estimate into a pair position, first choose dollar exposures using a position-sizing rule. The example allocates twice as many dollars to B as to A so their modeled percentage moves offset in dollar terms. Divide each desired dollar exposure by that stock’s price to obtain its share count. The answer does not prescribe a universal sizing rule; it mentions using a fixed dollar amount for the more volatile stock or another rule. The resulting hedge depends on the estimated relationship, selected capital allocation, and prevailing prices.

Key ideas

• A log-price hedge ratio describes relative percentage sensitivity, not a direct share-count ratio.
• Under the stated regression interpretation, a ratio of two links a one percent move in B to a two percent move in A.
• Choose dollar exposures according to a separate position-sizing rule before converting them into shares.
• Divide each stock’s target dollar exposure by its price to calculate its share count.

Tags

# calculating the pair weights from log price hedge ratio


# calculating the pair weights from log price hedge ratio












I am calculating the hedge ratio using log prices:

$$ \ln(A) = \text{hedge_ratio} \cdot \ln(B) $$

How do I convert the `hedge_ratio` into a number of shares of A vs. a number of shares of B?

## Answer by Alex C (score 1)

https://quant.stackexchange.com/a/32139

Think in terms of dollars invested, not shares. A hedge ratio of 2 for example means that Stock A will go up 2% (on a logarithmic basis, i.e. $\ln P_{t+1}=\ln P_t+0.02$) when Stock B goes up 1%. That means you need twice as many dollars invested in B as in A for the movements to offset each other in dollar terms.

Once you decide what these amounts should be (based on a position size rule, say 10000 USD for the most volatile of the two stocks, or other more complicated rule) you just divide 10000 and 20000 by the respective prices to determine the number of shares (e.g. $10000/P_A$ and $20000/P_B$).

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.