Delta Hedging

February 28, 2014
By Vlad Karpel

Over the last few months we have examined the Greek letters that make the life of option traders much easier. Delta, gamma, rho, vega, and theta are highly useful tools that correlate dimensions of risk in the price of an option to important factors such as the price of the underlying asset, interest rates, volatility, and time-to-maturity. By carefully analyzing each of these sensitivities, traders can choose the best options for their specific strategies and avoid the negative surprises that can lead to quick and big losses. Today we explore how a trader can use delta to hedge risk.

Delta measures the sensitivity of an option’s price to changes in the underlying asset price. A delta of 0.6 tells the trader that for each $1 the underlying asset rises, the option is going to rise $0.6. This measure helps us understand how the option will respond to underlying changes, which is the main driver for the option price, but it is also a key tool if one wants to build what is known as a “delta neutral portfolio.”

A delta neutral portfolio is a set of assets that doesn’t change (or changes very little) when the price of an underlying asset changes. The portfolio is built in a way that the change in one asset is offset by an opposite move in another asset. In the context of options, a delta neutral portfolio usually involves holding a long position in an underlying asset while holding a short position in an option, or holding a short position in a stock while holding a long position in a call option.

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Let’s look at an example. Assume you hold 1,200 shares of Monsanto at $100, which are worth $120,000. You want to protect your entire position without selling the stock (for tax reasons, for example), so you choose to sell call options. Let’s say you find a call on Monsanto’s stock with a delta of 0.6. That means for each $1 change in Monsanto’s stock, the option will change 0.6. Because you want to hedge, you need to sell the calls to counterbalance your stock position; thus the delta is actually -0.6. To completely offset the change in the stock you need to sell 1200/0.6 options, or 2,000 options. If Monsanto declines $2, you will lose $2,400 in your stock position, but the option position would appreciate 0.6 X $2 X 2,000, or $2,400.


By using the information provided by delta you are able to build a delta neutral portfolio and avoid risk temporarily. But note that, as indicated in our article about delta, the sensitivity of an option to the underlying price isn’t static, which means the hedge works for small changes in price. You would need to rebalance the portfolio to keep the hedge. Using the example in this article, assume delta changes to 0.8. The new number of call options you should hold short is 2000/0.8, or 2,500, which means you would have to sell 500 call options to keep the hedge.

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