What portfolio beta measures
Beta is how much a stock has tended to move for each 1% move in the market index. A beta of 1.3 means it has moved about 1.3% for every 1% in the index; 0.8 means 0.8%. A portfolio’s beta is the value-weighted average of its holdings’ betas.
portfolio beta = Σ(position value × beta) ÷ Σ|position value|
The top line of that formula, Σ(value × beta), is the beta-weighted exposure: the amount of index your portfolio behaves like. It is the number that matters for hedging, because it is already in dollars.
A worked example
| Holding | Value | Beta | Value × beta |
|---|---|---|---|
| Tech stock | $40,000 | 1.3 | $52,000 |
| Consumer staples | $30,000 | 0.8 | $24,000 |
| Industrials | $20,000 | 1.1 | $22,000 |
| Short: growth ETF | −$10,000 | 1.5 | −$15,000 |
| Total | $80,000 net, $100,000 gross | $83,000 |
The portfolio beta is $83,000 ÷ $100,000 = 0.83. The portfolio behaves like $83,000 of the index: a 1% fall in the index would be expected to cost about $830. To offset that with an index ETF at $550, you would short about $83,000 ÷ $550 ≈ 151 shares.
Notice what the short position does. It is only $10,000 of market value, but its high beta removes $15,000 of index exposure. Short positions are entered as negative values, and they count at their full size in the gross total that the beta is averaged over.
Where to find a beta
Most broker platforms and finance sites publish a beta for each stock, usually calculated against the S&P 500 from five years of monthly returns or two years of weekly returns. Different sources use different windows, so the same stock can show 1.1 on one site and 1.3 on another. Pick one source and use it for every holding, and make sure the betas are measured against the index you would hedge with.
For ETFs and funds, use the fund’s own beta rather than averaging its holdings. For cash, the beta is zero; leave it out of the table rather than entering it with a beta, or it will dilute the average.
From beta to a hedge
The calculator sizes a hedge two ways. Index ETF shares to short offset the beta-weighted exposure directly. Put contracts assume 100 shares per contract and a delta of 1, which is what a deep in-the-money put, or any put at expiry, approaches. Out-of-the-money puts protect less at first, because their delta is smaller, and that is the trade-off between the cost of a hedge and how soon it starts working. The beta-weighted hedge calculator sizes hedges in index futures too, and the guide to beta-weighted hedging explains what a hedge does and does not remove.
What beta cannot tell you
- It is backward-looking. A stock’s relationship with the market changes, and betas often rise in sell-offs, when everything falls together.
- It only covers market risk. An earnings miss, a lawsuit or a takeover moves a stock regardless of the index. A beta hedge leaves all of that in place.
- It assumes a straight-line relationship. Options, leveraged ETFs and very small companies often do not move in proportion to the index.