How to Delta Hedge an Options Portfolio - Shares, Options and Index Hedges

Reviewed by Leon Moyer - Published October 9, 2026 - Last reviewed October 9, 2026

Delta hedging is adding a position whose delta offsets your portfolio's net delta, so that small moves in the stock barely change the portfolio's value. A portfolio whose net delta is close to zero is called delta neutral. In one sentence: hedge size = the opposite of your net delta, in shares or share-equivalents.

What Is Portfolio Delta? gave the module's running example, the XYZ book, a net delta of +113.14: 100 XYZ shares at $50, one XYZ 55 call sold for $0.33, three XYZ 45 puts sold for $0.20, 30 days to expiration, 30% implied volatility. This lesson hedges that delta three ways and shows what each hedge does to everything else.

How do you delta hedge with shares?

Shares have a delta of exactly 1 and no gamma, theta or vega, so they change delta and nothing else. To hedge a net delta of +113, sell about 113 shares; to hedge -50, buy about 50.

For the XYZ book, the obvious share hedge is to sell the 100 shares it already owns. That leaves the two option positions, with a net delta of about +13.14.

Gamma, theta and vega are unchanged: -17.29, +$5.24 a day and -$10.66. The hedge only reset the starting point. As soon as XYZ moves, the sold options' delta changes again.

Why does a delta hedge drift?

A share hedge's delta is fixed. The options' delta is not, because of gamma. So a hedge that was neutral at $50 stops being neutral as XYZ moves.

How often to rebalance is a judgment call. Rebalancing often keeps delta closer to zero but runs up commissions and bid-ask spreads; rebalancing less often lets delta drift further from zero. One approach is to rebalance when net delta moves outside a band you set in advance, such as plus or minus 50 shares, rather than on a timetable; the right width depends on your account size and trading costs.

How do you delta hedge with options?

Buy options whose delta has the opposite sign. Bought puts have negative delta, so they cut a long book's delta. Two XYZ 50 puts, at $1.62 each ($324 for two), have a combined delta of about -93:

• Delta: +113.14 - 93.15 = about +20.
• Gamma: -17.29 + 18.49 = about +1.20.
• Theta: +$5.24 - $5.08 = about +$0.16 a day (about +$0.15 on the calculator's unrounded legs).
• Vega: -$10.66 + $11.40 = about +$0.74.

The puts hedge almost everything at once: delta, gamma and vega all move much closer to zero. The cost is plain in the theta line. The book was built to collect about $5.24 a day, and the hedge spends almost all of it. Option hedges bring their own Greeks, so they always change more than delta.

What does the option-hedged book look like at expiration?

With the two puts added, held to expiration:

• Maximum profit: $269, with XYZ at or above $55 (and also at exactly $45).
• Maximum loss: $8,731, if XYZ goes to zero.
• Break-evens: $43.66, $47.69 and $52.31 at expiration. It loses between $47.69 and $52.31, makes money from $43.66 to $47.69 and above $52.31, and loses below $43.66.

The risk is still large. The puts cut the loss at $40 from $2,407 to $731, but the three sold 45 puts still outnumber the two bought 50 puts, so below $45 the book still loses $200 for every $1 XYZ falls. A delta hedge is sized for today's Greeks; it is not a floor under the position.

How do you hedge delta with an index fund?

For an account with many stocks, hedging each one separately gets expensive. Instead, traders beta-weight the account, as in What Is Beta-Weighted Delta?, and hedge the total with an index fund or index options.

With a hypothetical beta of 1.2 and an index fund at $500, the XYZ book is about +13.58 index shares. Selling about 14 shares of the index fund would roughly offset its exposure to market moves. It would do nothing about an XYZ-specific move, such as an earnings surprise, and it depends on the beta estimate being right. Index hedges trade precision on each stock for one cheaper, broader hedge.

Should you delta hedge at all?

Not always. Delta hedging suits traders who want to earn from theta or volatility rather than direction, and who will monitor and rebalance. If your view is directional, a net delta that matches the view is the point, and hedging it away leaves you paying costs for no exposure you wanted. Hedges also cost money every time you trade them, and an imperfect hedge can give a false sense of safety. Decide what you are trying to hold before you decide what to hedge.