# Options 101: Delta

Delta is a term you might hear in the discussion around options. It is one of the options “Greeks” — a group of values that describe the individual risk factors affecting the price of an options contract.

Delta measures how much an option’s price should change if the value of the underlying security changes by \$1. The values of delta will range from 0 to 1 for call options and 0 to -1 for put options.

Delta is calculated using a complex formula grounded in options pricing theory. Many options exchanges offer free calculators that provide estimates for delta. The values change continuously as the markets move. Delta is highest for deep in-the-money options. It decreases as the strike prices moves out of the money from the market price of the underlying security.

Options traders should never expect actual price moves to precisely follow the predictions made by delta. Or any of the options Greeks, for that matter.

As an example, let’s say a trader is thinking about buying a call option on the SPDR S&P 500 (NYSE: SPY) ETF. Before he purchases the call, he calculates the option’s delta to be 0.68. This means that if SPY’s price increases by \$1, the price of the option should increase by \$0.68. Conversely, if SPY’s price falls by \$1, the value of the call option should fall by \$0.68.

For a put with the same strike price and expiration date, the delta would be -0.32. So if SPY’s price increases by \$1, the put option should fall by \$0.32. If SPY falls by \$1, the put option should increase by \$0.32.

### How Traders Use Delta

Traders use delta to identify options contracts that should provide the largest gains. This assumes, of course, the underlying stock moves in the direction expected.

Using high-delta options, traders can participate in market moves with a smaller investment than they would if they simply bought or sold the underlying security. This can significantly increase profits.

To understand this, let’s look at a theoretical example.

Stock XYZ is trading for \$170 a share. One trader believes that XYZ is going to move higher. So she buys 100 shares of XYZ for an investment of about \$17,000.

Another trader also believes XYZ is going to move higher. But instead of buying shares of XYZ, he buys one contract for the \$155 calls at \$15. The total investment is about \$1,500. This in-the-money call has a delta of 0.98. So if XYZ’s price increases by \$1, the trader can expect the value of his call to gain roughly \$0.98 (or \$98 per contract).

Let’s say XYZ reaches \$175. The trader who simply bought 100 shares of the stock would make \$500 for a 2.9% return on the investment. The trader who bought the deep in-the-money call for \$1,500 would make \$4.90 per share (\$0.98 * 5). That’s \$490 a contract, or a return of 32.7% on his smaller investment.

In this case, nothing except delta would have a significant impact on the option’s price if XYZ continued moving higher. However, the trader could buy 11 options contracts for less than the price of 100 shares of XYZ and significantly increase profits.

The further out of the money an option is, the lower the delta and the lower the price of the option. A trader buying an out-of-the-money call with a strike price of \$175 when XYZ is trading at \$170, may only have a delta of 0.38. But they might only pay \$0.34 for the option. When delta is low, most of the option premium would be paid for the time value of the option.

Some traders use options to implement a delta-neutral strategy. The goal of this strategy is to buy puts and calls on the same underlying security so that the deltas on the contracts add up to zero. In this way, the trader has no directional risk since changes in price should be cancelled out by changes in the prices of the options.

With this strategy, the trader is hoping to make money based on the time value of the options or on changes in market volatility. Delta-neutral strategies require constant rebalancing and a very large amount of trading capital.

### Why Delta Matters To Traders

Delta is the part of an options price that is most related to the price of the underlying security. Traders can use delta to identify options that should act just like the stock they want to trade.

If a trader expects a large price move in the underlying security, then a high-delta option contract could offer them the most “bang for the buck.” Buying several low-priced call options could deliver much larger gains than buying 100 shares of the stock if you believe a stock is going up. And buying several low-priced put options could deliver much larger gains (and carry less risk) than shorting 100 shares of a stock you believe is going down.

With a delta near 1 for calls (generally above 0.90) or near -1 for puts (generally below -0.90), the trader is minimizing the impact of time and volatility.

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