Beta Drift And When To Re-Hedge

You hedged a $10m position at a beta of 1.15 — $11.5m of index short. Three months later, the stock's estimated beta has drifted to 1.30. Your hedge is now under-sized relative to the position's current market sensitivity by roughly $1.5m of notional. Beta drift is normal and constant; the question is never whether it happens, it's how big a mismatch you'll tolerate before you spend money re-hedging it.

Why beta drifts

Beta isn't a fixed property of a stock, it's a rolling estimate, and it moves for real reasons: the company's business mix changes (a shift toward a more cyclical segment raises beta), leverage changes (more debt mechanically raises equity beta), or the broader market regime changes (correlations across stocks tend to rise in stressed markets, pulling individual betas toward 1). Some drift is also just estimation noise — the true beta hasn't moved, your estimate of it has wobbled.

The trade-off

Re-hedging every time the estimate ticks costs money — commissions, spread, and for a futures hedge, the friction of adjusting a position repeatedly. Not re-hedging at all leaves you increasingly exposed to a risk you thought you'd covered. The practical answer most desks use is a tolerance band: re-hedge only when the drift crosses a threshold meaningful relative to the position size, not on every recalculation.

Worked example

Position: $10m long. Hedge sized at inception using $\beta = 1.15$, so $11.5m short index. A desk policy sets the re-hedge trigger at a beta drift of more than 0.10 from the last hedge point, or a resulting notional mismatch exceeding $750,000, whichever comes first.

• Month 1: beta re-estimated at 1.19. Drift of 0.04, mismatch of $0.04 \times 10{,}000{,}000 = 400{,}000$. Below both triggers — no action.
• Month 2: beta at 1.24. Drift from the original 1.15 is 0.09, mismatch $900,000$. Crosses the $750,000 notional trigger even though the beta-drift trigger (0.10) hasn't quite been hit. Re-hedge: sell an additional $900,000 of index exposure, bringing the hedge to $12.4m and resetting the reference beta to 1.24.
• Month 3: beta at 1.30 relative to the new 1.24 reference. Drift of 0.06, mismatch $600,000$. Below trigger — hold.

Over three months, one re-hedge trade instead of three, and the notional mismatch never exceeded $900,000 on a $10m position — about 9 percent, which the desk judged an acceptable band to run rather than trade around continuously.

Setting the band

The right trigger size depends on the position's risk budget: a band of $750,000 mismatch on a $10m position is a reasonable 7.5 percent tolerance for a moderate risk budget, but the same absolute number would be far too loose on a $2m position. Express the trigger as a percentage of position size or of your risk budget, not as a fixed dollar figure, so it scales sensibly as positions change.