Portfolio Margin: Understanding Options Greeks

11/21/17

There are a few key concepts you may want to be familiar with before you get started with portfolio margin. In this article we will provide an overview of the options Greeks, explore different types of Greeks, and explain how they relate to portfolio margin.

### Options Greeks

Within risk-based margin, it’s important to understand the different factors that contribute to your portfolio’s risk, including direction, volatility, and time. On any given day, as the market fluctuates, the options Greeks can help you measure changes in the value of your holdings. In other words, the Greeks—delta, gamma, theta, vega, and rho—help you determine how much an option may change in value, and why it may have changed.

### Delta

Delta tells you how much money you make or lose when the stock moves. Think of it as the speed at which an option moves. Options prices don’t usually change value one-for-one with stock prices; instead, they change by some percentage of the stock’s move, and delta tells you that percentage. The percentage can be any value from zero to 100. An option that’s completely worthless tends to have a delta near zero, while deep in-the-money options tend to have deltas near ±1.00, or ±100%. At-the-money options—those with a stock price equal to the strike price—tend to have delta values near ±0.50, or ±50%. The standard definition is of delta is:

 Change in the option price Change in the stock price

For example, suppose you were bullish on XYZ stock, currently trading for \$42 per share. You decide to buy a 40-strike call currently priced at \$3.20 showing a delta value of 0.58. What this means is if XYZ were to rise in value by \$1, from \$42 to \$43, your call option would rise in value by 58 cents, from \$3.20 to \$3.78. On the other hand, if XYZ were to drop by \$1, from \$42 to \$41, your call option would drop in value by \$0.58, from \$3.20 to \$2.62.

### Gamma

While delta measures how fast your option changes in value relative to how much the stock changes in value, gamma measures the change in the delta relative to the change in the stock price. Think of it as the rate at which your option changes speed. The standard definition of gamma is:

 Change in the delta Change in the stock price

Long options positions have positive gamma, while short options positions have negative gamma. To illustrate how gamma works, let’s take the earlier example in which you were bullish on XYZ stock trading for \$42 per share. You decided to buy a 40-strike call currently priced at \$3.20 and showing a delta value of 0.58. Let’s further assume that the 40-strike call shows a gamma value of 0.06.

If XYZ were to rise in value by \$1, from \$42 to \$43, your option value would change by \$0.58 (the delta value), from \$3.20 to \$3.78. However, with XYZ at \$43, your option delta would have increased by the value of the gamma (0.06), from 0.58 to 0.64.

Then, if the stock were to rise another dollar, say from \$43 to \$44, your option value would increase by the new delta value of 0.64, from \$3.78 to \$4.42.

### Theta

Options have a set expiration date. Prior to that date, a portion of an option’s value is referred to as time value, because the amount is largely dependent on the remaining time in the life of the option. As the option approaches expiration, it loses some of that time value. The rate at which the option loses time value is called theta. It’s defined as:

 Change in the option price One day change in time

Theta answers the question, “How much money will my option lose between today and tomorrow if nothing happens?” Going back to the earlier example in which you bought a 40-strike call priced at \$3.20, let’s suppose your option shows a theta value of -0.18. If all else is equal, at this time tomorrow, your option will drop in value from \$3.20 to \$3.02. As the days pass, the time value in your option will continue to drop, until it reaches a value of zero.

### Vega

Vega can be thought of as the exchange rate between volatility points and dollars. Higher volatility levels mean more expensive options. Vega is defined as:

 Change in the option price Percentage-point change in implied volatility

Vega tells you how much money you may make, or lose, as volatility changes. Going back to the earlier example of the 40-strike call priced at \$3.20, suppose your option shows a vega value of 0.25 and has an implied volatility level of 28%. If the implied volatility level were to rise a full point, from 28% to 29%, your option would be expected to rise in value by \$0.25, from \$3.20 to \$3.45.

The relationship works backwards as well. For example, if the market value of your option were to rise from \$3.20 to \$3.70 with nothing else changing, the \$0.50 rise would equal a two percentage-point rise in implied volatility. Thus, you’d expect to see the option’s volatility level rise from 28% to 30%.

### Rho

Rho measures the sensitivity of options prices to changes in interest rates. Rho is positive for calls and negative for puts. The standard definition of rho is:

 Change in the option price Percentage-point change in interest rates

Even though rho may be used less frequently in understanding options prices, it’s important to know that rho measures your interest rate risk.

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Examples in this article are for hypothetical purposes only and not a recommendation.