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Decode the Greeks: Ancient Alphabet Helps You Trade Options

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July 11, 2012

The greeks can help measure how much an option might gain or lose—and help you decide how much risk you’re willing to take.

If you’ve been trading options, you’ve likely heard chatter on the “greeks”—delta, gamma, theta, vega, and rho. But, do you know what they are and how options traders use them? When buying stocks, you only make money when the stock moves higher than your purchase price, or lose when the stock moves below that price. With options, there are other variables, like volatility and time decay, that not only help you determine how much money you stand to potentially make or lose, but also why you’re about to grin or gripe.

Traders often mistakenly assume that the Greeks are used only to price an option. Not true. They’re also used to help measure the value of an option after something happens, such as time passing, volatility fluctuating, or direction changing. In other words, they take uncertain variables and attempt to quantify their impact, thereby allowing you to “stress-test” your own option strategy.

Nuts & Bolts

The greeks represent the many different risks in an options trade—namely direction, time decay, volatility, and interest rates. However, since potential reward only comes at the expense of risk, it helps to know which risks you are most and least willing to embrace.

Let’s set up a sample trade and then we’ll break down this trade using the greeks.

Suppose you are considering buying 1 call option at $1.60 each in stock XYZ, which trades at $50 a share, for a total investment of $160 (plus commissions and fees). For this example, this is also your maximum risk.

STOCK PRICEDELTAGAMMATHETAVEGARHO
$50.50.10-0.020.090.03

FIGURE 1: HYPOTHETICAL GREEKS ON ONE LONG XYZ 50 CALL FOR $1.60* WITH STOCK AT $50 PER SHARE. 
*The listed price of the option doesn't include commissions and fees. For illustrative purposes only. Past performance does not guarantee future results.

Before we answer the question of how much you can lose, we need to find out the sensitivities of your trade: What are the events that can cause your trade to change in value?

Delta and Gamma: How much might I make or lose if the stock moves?

Directional risk is familiar to most traders. Traders are used to either making or losing money depending on a stock move. Delta and gamma attempt to help you figure out how much reward or damage you’ll incur when the stock moves.

Delta is the measure of an option’s sensitivity to a $1 change in the underlying asset. In this case, if the stock moves up $1, the call option would gain $50.

Gamma is a measure of delta’s sensitivity to a $1 change in the underlying asset (i.e. the velocity of an options move). After the stock moves $1, what is the new delta for the next $1 move? In this case, if the stock moves up $1, the position’s new delta would be .60. If the stock moves down $1, the new delta would be .40.

Theta: How Much Might I Make or Lose as Time Passes?

All changes in option values assume that all else remains unchanged. In the real world, however, more than one factor can change at the same time. Time, always moving forward, is one variable that changes no matter what else happens to an investment. Options are time-sensitive assets and the value of your option position will change with the passage of time. The amount of this change is measured by the option greek theta.

In our example, the position’s total daily theta value is -0.02, meaning that our $160 position loses $2 each day simply due to the passage of time. If you take what you learned about delta and gamma, it means that you would need the stock to tick two dollars simply to make up for one day’s time decay. This is extremely important information because if you do not want to take on such a large time-decay risk, you may not want to enter a particular position, or you may want to reduce the size of the position.

Want More Options?

To learn more, log in to your TD Ameritrade account and log in to the Trade Architect platform. Then go to: Help > Education > Options

Vega: How Much Might I Make or Lose as Volatility Changes?

Of course, in order to perform a complete evaluation of an option position, you have to consider volatility and how it affects the value of your trade. An increase in option volatility typically leads to higher option premiums, while a drop in option volatility typically leads to lower option premiums. Premium is the total price of an option: intrinsic value plus time value.

The amount that an option position changes due to changes in volatility is referred to as the vega of the position. More specifically, vega is a measure of an option’s sensitivity to a 1% change in the implied volatility of the underlying asset. Our hypothetical example has a vega of 0.09 (or $9 per contract), meaning that if volatility rises by one percentage point, you can expect your position to increase in value from $160 to $169. On the other hand, if volatility drops by one percentage point, you can expect your position value to drop from $160 to $151.

As you can see, it can be important to know whether you are near the top or near the bottom of the volatility range when placing an option trade.

FIGURE 2: Log in to your account at tdameritrade.com and open the thinkorswim® platform. Under the “Trade” tab, select “All Products.” Enter the underlying stock ticker. Under “Option Chain” and “Layout”, select Delta, Gamma, Theta, Vega to display the greeks. For illustrative purposes only. Past performance does not guarantee future results.

Rho: How Much Might I Make or Lose as Interest Rates Change?

The position rho in our sample is .03 (or $3 per contract)—the amount that your position would make based on a one-percentage-point rise in interest rates. Given that current U.S. policymakers do not typically change interest rates by more than half a point at a time, this is a fairly inconsequential risk for all but the longest-term option positions. Still, it deserves some attention.

The option greeks help you break down the potential risks and benefits of an option position based on what you consider to be realistic market conditions (See Figure 2). The interpretation is a little more subjective; for example, a position may show a large delta risk, but if you do not foresee the stock price moving in an adverse manner, you may feel comfortable taking on that risk. Or, your position may have a relatively small vega exposure but if you think you’re about to experience a significant volatility crush, you may want to think twice about placing that trade.

Having a sound understanding of option greeks can potentially leave you in a better position to pursue the trades that suit your personal risk tolerance and market expectations.