Charting a Beta-Weighted Long-Short Stock Position
Summary
The document asks how to chart a long-short position when its two stocks have different capital weights or market sensitivities. One response says to combine each stock’s price or profit-and-loss contribution using the same weights as the position, so the resulting series reflects the portfolio’s weighted change rather than an unweighted price ratio.
A second approach estimates each stock’s beta by regressing its price on a sector equity index, then uses the estimated betas to size hedges against the index or against one another. These are practical suggestions, not a complete specification for constructing a return series. The discussion does not address estimation windows, changing betas, intercepts, or whether the desired hedge is dollar-neutral or market-neutral, so implementation requires additional choices.
Key ideas
- A price ratio alone does not represent a position with unequal weights.
- Weight each stock’s profit and loss consistently with its portfolio allocation to track the position.
- Regression against a relevant equity index can estimate stock betas for hedge sizing.
- Estimated betas can guide hedging one stock against an index or one stock against another.
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# dollar neutral ratio vs beta hedged ratio # dollar neutral ratio vs beta hedged ratio Hi guys i really hope you can help as i've been pulling out my hair for days on this!! OK so basically i understand the dollar neutral ratio, simply stocka/stockb = dollar neutral ratio. Works great because i can chart it and do a daily p/l update and it perfectly tracks the p/l of my whole long short position. My questions is how do i get the ratio when the spread is weighted differently due to differing beta values? For example stocka is very volatile and stockb is not. So i will for arguments sake weight 80% of my capital on stocka and 20% of my capital on stock. Now to get my ratio i can not simply divide the stocka by stockb as i did before because i get the same daily p/l swings. So guys how do i get a beta hedged ratio which i can chart and also track a daily p/l which perfectly represents my whole long short position. Appreciate all your time and energy, thank you! ## Answer by BCM (score 1) https://quant.stackexchange.com/a/30492 Wouldn't you just weight the p/l equation the same way your position is weighted? So: `(P(StockA)*0.8)/(P(StockB)*0.2) = Net % change in the position` ## Answer by rrg (score 0) https://quant.stackexchange.com/a/30526 Take BCM's approach, or, weight your exposure (and PNL) by the stock beta within the equity index. To do this, run the least squares regression to determine BetaA: ' ' StockPriceA = const + BetaA * SectorEquityIndex + residual StockPriceB = const + BetaB * SectorEquityIndex + residual You could then either trade one stock hedged at that beta against the index, or two stocks (A,B) hedged against one another with weights BetaA/BetaB.
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