Sizing a Standard Beta Hedge Between Two Assets

Summary

The document asks how to size a short position in one asset to hedge a long position in another using their betas. The accepted answer gives a dollar-weighting rule: make each position’s market value inversely proportional to its beta. It illustrates the rule by describing equal dollar positions when both betas are one, and a smaller position in the asset with the higher beta when the other asset’s beta remains one.

This is a simplified sizing relationship, not a full hedge construction. The question provides covariance and standard deviations, but the answer does not work through the example to calculate the beta or share count. It also does not discuss estimation windows, changing betas, trading costs, or whether beta hedging addresses risks beyond the chosen market relationship. The sizing guidance therefore depends on the beta definitions and reference exposure used.

Key ideas

• The answer sizes hedge legs by making their dollar values inversely proportional to their betas.
• Equal betas imply equal dollar exposures under the stated rule.
• A higher beta calls for a smaller dollar position relative to a lower-beta leg.
• The answer does not calculate the requested share count from the example.

Tags

# How to "Standard Beta Hedge"?


# How to "Standard Beta Hedge"?












Let's say I have 2 time-series, how would I "standard beta hedge" them against each other? For example, what if the position in 1 timeseries is 100 shares at 16 USD per share. Another time-series is 25 USD per share. Covariance of the two is 50 and the standard deviation of time-series 1 is 5 and of time-series 2 is 7. So I know that:

```
beta = Cov(ts_1, ts_2)/(SD(ts_1)*SD(ts_2))
beta = 50/(7*5)
beta = 1.428
```

How would I determine the position of ts_2 that I should short?

## Answer by nbbo2 (score 2, accepted)

https://quant.stackexchange.com/a/33434

To "standard beta hedge" you would make your positions dollar values inversely proportional to their Betas. So if your standard position is 1000 USD long vs 1000 USD short when the Betas are 1, then you would have 909 long vs 1000 short when the betas are 1.1 and 1. In general $1000/\beta_1$ long of security 1 vs $1000/\beta_2$ short of security 2..

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