How does delta hedging work in practice, and why does it need constant rebalancing?

Delta hedging is one of the most testable topics in CFA Level II Derivatives. Let's walk through the mechanics step by step.

What Is Delta?

Delta measures how much an option's price changes for a $1 change in the underlying. For calls, delta ranges from 0 to 1. For puts, delta ranges from -1 to 0.

Setting Up the Hedge:

Suppose you're a market maker at Redstone Capital and you sell 100 call option contracts (each covering 100 shares) on Trident Industries. The call has a delta of 0.60.

Your option position delta: -100 contracts x 100 shares x 0.60 = -6,000 delta

To be delta-neutral, you need +6,000 delta from the stock:

Buy 6,000 shares of Trident Industries

Now your total portfolio delta is: -6,000 + 6,000 = 0 (delta-neutral)

Why Rebalancing Is Necessary:

Delta itself is not constant — it changes as the stock price moves (this is gamma). If Trident rises from $50 to $53:

• Call delta might increase from 0.60 to 0.68
• Your new option delta: -100 x 100 x 0.68 = -6,800
• Your stock position: still +6,000
• Net delta: 6,000 - 6,800 = -800 (no longer hedged!)

You need to buy 800 more shares to restore delta-neutrality. This continuous adjustment is why delta hedging requires dynamic rebalancing.

The Cost of Rebalancing:

Notice the pattern: when the stock goes up, you buy more shares. When it drops, you sell. You're systematically buying high and selling low — this is the cost of maintaining the hedge and represents the theta (time decay) you earn from selling the options.

In practice, the P&L of a delta-hedged short option position approximately equals the theta earned minus the realized gamma cost.

Exam tip: The CFA Level II exam often presents a scenario where a hedger sets up a delta-neutral position and then the stock moves. You'll need to calculate the new delta exposure and determine how many shares to buy or sell. Remember: for a short call position, a stock price increase requires buying more shares.

Explore more derivatives hedging strategies in our CFA Level II course on AcadiFi.