Why is gamma considered the 'hidden risk' for delta-hedged option sellers?

Gamma is often called the 'hidden risk' because it determines how quickly your delta hedge becomes stale and how expensive rebalancing will be. Here's why it matters so much.

Gamma Basics:

Gamma (G) = dDelta / dS = the second derivative of the option price with respect to the underlying price.

• Long options = positive gamma (delta moves in your favor when the stock moves)
• Short options = negative gamma (delta moves against you when the stock moves)

Why Negative Gamma Is Dangerous:

If you've sold options and are delta-hedging (like Redstone Capital in our previous example), negative gamma means:

• When the stock rises, your delta becomes more negative → you must buy shares at higher prices
• When the stock falls, your delta becomes less negative → you must sell shares at lower prices

You're forced into a buy-high, sell-low cycle. The larger the stock moves and the more frequently they occur, the more money you lose on rebalancing.

When Is Gamma Highest?

Gamma peaks when an option is at-the-money and near expiration. This is intuitive: a small stock move can flip the option from worthless to valuable (or vice versa), causing dramatic delta shifts.

Numerical Illustration:

Consider a portfolio at Ashford Trading that is short 500 at-the-money call contracts (50,000 shares equivalent) on Veritas Corp at $100 with 5 days to expiration.

• Gamma per option: 0.08 (high because ATM + near expiry)
• Portfolio gamma: -500 x 100 x 0.08 = -4,000

If Veritas moves $2 in one day:

• Delta change: -4,000 x $2 = -8,000
• You need to buy 8,000 shares at $102 (stock went up) or sell 8,000 at $98 (stock went down)
• Either way, you're rebalancing at unfavorable prices

The Gamma-Theta Trade-off:

There's a beautiful symmetry in options: gamma and theta are two sides of the same coin.

• Long gamma = negative theta (you pay time decay but profit from moves)
• Short gamma = positive theta (you earn time decay but lose from moves)

As an option seller, the theta you collect is compensation for bearing gamma risk. If realized volatility exceeds the implied volatility priced into the options, your gamma losses will exceed your theta gains.

Exam tip: CFA Level II loves testing the relationship between gamma, delta hedging frequency, and the cost of hedging. Remember that higher gamma means more frequent rebalancing and higher hedging costs.

For more on Greek risk management, check out our CFA Level II derivatives course on AcadiFi.