Theta Explained

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Theta Explained (A Simple Options Guide)

As an options contract gets closer to expiration, it naturally decreases in value. That rate of decrease is called theta.

Theta is one of “the Greeks,” or statistical values identified by Greek letters that traders use to evaluate stock options.

Other Greeks include:

  • Delta – the option’s sensitivity to the price of the underlying security
  • Vega – the option’s sensitivity to the volatility of the underlying security
  • Gamma – the option’s sensitivity to Delta as it responds to price changes

Theta is different from the other Greeks in that it’s not dependent on changes in the underlying security. Instead, it’s dependent on how close the option is to expiration.

In this guide, I’ll explain theta so you’ll know how to use it when you consider trading stock options.

What Is Theta?

In a nutshell, theta is a measurement of time decay.

As a rule of thumb, the closer an option gets to its expiration date, the more it will drop in value.

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Of course, if the underlying stock price drops dramatically or rises significantly, that will affect the option price as well. That’s why options analysts frequently use the phrase “all other things being equal” when discussing theta (or any of the other Greeks).

“All other things being equal,” in this context, means that if the stock price and implied volatility remain the same, then you can expect the price of an option to drop every day as it gets closer to expiration.

That’s not a linear drop, though. Time decay will increase as the contract gets closer to its expiration date.

When Would You Care About Theta?

You’ll almost always take a long, hard look at theta when you’re buying options in a single-leg order.

Why? Because, all other things being equal, you’ll lose money every day when you buy an option.

That’s why it’s a great idea to go long on an option when you have a reason to believe that the stock price will move significantly one way or the other.

On the other hand, if you think that a stock price is going to stay relatively flat, you can short an option and let time decay work in your favor. As the value of the option decreases, you make money.

It should be noted, though, that you’ll need a margin account if you want to short stock options.

So to summarize:

  • Time decay works against you when you’re long an option
  • Time decay works in your favor when you’re short an option

Wasting Assets

Wasting assets are assets that tend to decrease in value over time. Options are wasting assets.

Why? Because as a contract nears expiration, it’s easier to determine the value of the underlying stock at expiration.

In other words, there’s less opportunity for a wild swing in the price of the security.

Time decay is especially noticeable on options that are out-of-the-money.

An out-of-the-money option is one in which the underlying stock is lower than the strike price (if it’s a call) or higher than the strike price (if it’s a put).

When out-of-the-money options near expiration date, it becomes less likely that they’ll ever get in-the-money. As a result, there’s less demand for them on the open market because nobody wants to buy an option that will probably expire worthless.

When there’s less demand for an option, with all other things being equal, its price will drop.

Real Life Example of Using Theta

Let’s say that Tesla is currently trading at $346 per share. You think it’s going to stay the same over the next month, so you’d like to make some money off of time decay.

You fire up your trading platform and check out the options chains. You see that next month’s $346 call option is trading for $21.15 right now.

But you’re curious about how much money you can make quickly if the price of Tesla stays the same. You check out the details of the call option that you’re thinking about purchasing.

Fortunately, your online brokerage lists all the Greeks for every option. You notice that the theta for next month’s $346 call option is -0.2836.

Why is it measured as a negative? For a very good reason.

Remember: theta is a measurement of time decay. It shows you how much the call option is likely to decrease in value every day, all other things being equal.

A theta of -0.2836 means that the call option will decrease about 28 cents in value every day.

There’s a caveat, though. The theta will decrease even more as you get closer to expiration.

In other words, just because the theta is -0.2836 today, that doesn’t mean it will be the same two weeks from now.

In fact, that option is likely to have a theta below -0.4 in a couple of weeks.

For now, if you sell the call option, you stand to make about $28 per day with all other things being equal.

You like the sound of that so you move forward with the trade. You sell one call option contract for $21.15. That earns you $2,115 because options are sold in groups of 100 shares ($21.15 x 100).

Now you have an extra $2,115 in your account. Don’t get too excited, though, because you’re on the hook to buy 100 shares of Tesla if the call option stays in the money. That will cost you a lot more than $2,115.

However, there’s still a month until expiration. You’re confident that time decay will lower the value of the call option. Then, you can buy it back at a lower price and pocket a profit.

Let’s say everything stays the same with Tesla over the next day. You check your account and notice that the call option that you sold for $21.15 is now worth $20.87.

In other words, the price dropped about $0.28, just as theta predicted. So far so good.

Next, let’s say that after a couple of weeks that Tesla is still trading around $346 per share. Your call option is now worth $17.00.

That’s good news because now it’s much lower than the price you paid for it. Should you ride it out for more profit or not?

You remember that pigs get fat and hogs get slaughtered, so you decide not to be too greedy and take your win. You buy back the call option for $17.00.

That buy-back costs you $1,700 ($17.00 x 100). But you already earned $2,115 from the sale of the call in the first place. So your total profit is $415 ($2,115 – $1,700).

Congratulations! You made money by letting time decay work in your favor.

That’s why it’s important to pay attention to theta when evaluating options.

Theta

What is Theta?

Theta is a measure of the rate of decline in the value of an option due to the passage of time. It can also be referred to as an option’s time decay. If everything is held constant, the option loses value as time moves closer to the maturity of the option. Theta is generally expressed as a negative number and can be thought of as the amount by which an option’s value will decline every day.

Theta is drawn from the Greek alphabet and has numerous meanings across different fields. In the world of economics, theta can also refer to the reserve ratio of banks in economic models.

Theta

Understanding Theta

Theta is part of the group of measures known as the Greeks, which are used in options pricing. The measure of theta quantifies the risk that time poses to option buyers, since options are only exercisable for a certain period of time.

Key Takeaways

  • Theta refers to the rate of decline in the value of an option over time.
  • If all other variables are constant, and option will lose value as time draws closer to its maturity.
  • Theta, usually expressed as a negative number, indicates how much the option’s value will decline every day up to maturity.

Options give the buyer the right to buy or sell an underlying asset at the strike price before the option expires. If two options are similar, but one has a longer time until it expires, the longer-term option will have more value since there is a greater chance (given more time) that the option could move beyond the strike price.

Differences Between Theta and Other Greeks

The Greeks measure the sensitivity of options prices to their respective variables. The delta of an option indicates the sensitivity of an option’s price in relation to a $1 change in the underlying security. The gamma of an option indicates the sensitivity of an option’s delta in relation to a $1 change in the underlying security. Vega indicates how an option’s price theoretically changes for each one percentage point move in implied volatility.

Theta for Option Buyers vs. Option Writers

If all else remains equal, the time decay causes an option to lose extrinsic value as it approaches its expiration date. Therefore, theta is one of the main Greeks that option buyers should worry about since time is working against long option holders. Conversely, time decay is favorable to an investor who writes options. Option writers benefit from time decay because the options that were written become less valuable as the time to expiration approaches. Consequently, it is cheaper for option writers to buy back the options to close out the short position.

Put a different way, option values are composed of both extrinsic and intrinsic value (if applicable). At option expiration, all that remains is intrinsic value, if any, because time is a significant part of the extrinsic value.

Key Takeaways

  • Theta measures the daily rate of price decline in an option’s value as it nears its expiration date.
  • Option writers are the main beneficiaries of the decline in an option’s value because it becomes cheaper for them to buy back the options to close out short positions.

Theta Example

Assume an investor purchases a call option with a strike price of $1,150 for $5. The underlying stock is trading at $1,125. The option has five days until expiration and theta is $1.

In theory, the value of the option drops $1 per day until it reaches the expiration date. This is unfavorable to the option holder. Assume the underlying stock remains at $1,125 and two days have passed. The option will be worth approximately $3. The only way the option becomes worth more than $5 again is if the price rises above $1,155. This would give the option at least $5 in intrinsic value ($1,150 – $1,150 strike price), offsetting the loss due to theta or time decay.

Theta

The option’s theta is a measurement of the option’s time decay. The theta measures the rate at which options lose their value, specifically the time value, as the expiration date draws nearer. Generally expressed as a negative number, the theta of an option reflects the amount by which the option’s value will decrease every day.

Example

A call option with a current price of $2 and a theta of -0.05 will experience a drop in price of $0.05 per day. So in two days’ time, the price of the option should fall to $1.90.

Passage of time and its effects on the theta

Longer term options have theta of almost 0 as they do not lose value on a daily basis. Theta is higher for shorter term options, especially at-the-money options. This is pretty obvious as such options have the highest time value and thus have more premium to lose each day.

Conversely, theta goes up dramatically as options near expiration as time decay is at its greatest during that period.

Changes in volatility and its effects on the theta

In general, options of high volatility stocks have higher theta than low volatility stocks. This is because the time value premium on these options are higher and so they have more to lose per day.

The chart above illustrates the relationship between the option’s theta and the volatility of the underlying security which is trading at $50 a share and have 3 months remaining to expiration.

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