How fast am I driving? And, when I press the gas pedal, how quickly will I speed up?

These questions have nothing to do with investment, but they’re helpful analogies for understanding risk when trading options. That’s because “options are a multi-dimensional asset,” says Hans Albrecht, portfolio manager and options strategist at Horizons ETFs Management (Canada) Inc. in Toronto. Options pricing depends on several factors. Since options give you the right to buy or sell an underlying asset at a certain price on a certain day, their value depends on things like how far you are from the expiration date (time value) and the strike price (intrinsic value). These and other factors are quantified using measures known as the Greeks.

“Greeks are handy because they tell us what happens when certain market conditions change,” says Ioulia Tretiakova, vice-president and director of quantitative strategies at PUR Investing in Toronto. How will an option’s price change if implied volatility rises? “Greeks give us those handy answers.”

Common Greeks include delta, gamma, theta and vega. Their formulas aren’t for the faint of heart but, fortunately, software can calculate them for you (results varies by model). So what does each measure mean, and how can they help you become a better investor?

We asked Albrecht and Tretiakova to walk us through the most common Greeks.

## Delta

### Technical definition

Delta measures the rate of change in an option’s value for every one-point increase in the underlying asset. A delta of 50, for instance, means that for every dollar the price of the underlying asset (a.k.a. the “underlying”) goes up, a call will gain by $0.50. A delta of -20 means that for every dollar the underlying goes up, a put will go down by $0.20.

### Range

0 to 1 or -1. Put options have negative delta, whereas call options have positive delta. People will often say “50” or “25,” which actually means a delta of 0.5 or 0.25, respectively; they also tend to omit the sign because call deltas are always positive, whereas put deltas are always negative.

### Everyday analogy

Delta is like speed, says Albrecht, because the measure tells you whether you’re driving 20 kilometres per hour or 50 kilometres per hour. But, in trading terms, speed is measured per dollar.

Delta shows how much your position will gain or lose for every $1 move in the underlying—in other words, how quickly you’ll gain or lose money.

### Pricing examples

**Assume:**

- You own five call options trading at $10, with a strike price of $202
- Delta is 50 (or 0.5)
- Underlying stock is trading at $200

If the stock rises to $201, the call option trades at $10.50. How did we calculate that? Since delta is 0.5, for every $1 increase, the call goes up by $0.50. Since you bought five call options, you’ve just made $2.50.

**Now assume:**

- You own five call options trading at $10, with a strike price of $210
- Delta is 30 (or 0.3)
- Underlying stock is trading at $200

If the stock rises to $201, the call option would trade at $10.30, since, for every $1 increase, the call goes up by $0.30. You’ve gained $1.50 on the five call options.

**Now assume:**

- You own five call options trading at $10, with a strike price of $202
- Delta is 50 (or 0.5)
- Underlying stock is trading at $200

The stock rises to $201.50, so the call option would trade at $10.75 ($10 + [$1.50*0.5]). You’ve earned $3.75 on the five options.

### Why it matters

Since delta “helps describe how something is going to behave, it gives you an idea of risk,” says Albrecht.

Investors look at delta when they want to know how much the options will return relative to the underlying. “If I own 100 shares of Barrick Gold, I know that, if it goes up a dollar, I’m going to make $100.” But a 100-share call on Barrick with 50 delta would make $50, says Albrecht, since a 50-delta call goes up $0.50 for every dollar the stock goes up.

If the investor wants her 50-delta call to behave as if she owned 100 shares of Barrick, she must buy two calls. “Now, each one is moving up $50, and therefore I’ve made my $100,” Albrecht explains.

Delta also tells you about “moneyness,” or how close a strike price is to the actual price of the underlying. A 50 delta is considered “at the money”: it’s when the option’s strike price is identical to the price of the underlying security. At that point “it’s a coin flip,” says Albrecht: the delta indicates a 50% chance the asset goes either up or down. As a result, delta tells you the current probability of an option being in the money by expiry.

A call option with a 70 delta is in the money, and has about a 70% chance of still being in the money by expiry. “For example, if Barrick was trading at $100, maybe I’m owning a $96 strike. So it’s already in the money by $4.”

A 20-delta call, however, is “quite a ways out of the money,” he says, and has about a 20% chance of being in the money by expiry.

What “quite a ways” means can differ by type of stock.

“If you’re trading Tesla, which is a volatile stock, a 20 delta might be 15% out of the money,” he says. “If you’re trading [a blue chip like] Royal Bank, a 20 delta might [only] be 4% out of the money.” In this example, the chances of a blue chip jumping 4% are about the same as a tech stock jumping 15%. “So implied volatility has a direct effect on your delta,” Albrecht says.

Another point about delta and probability: time matters, too. If you’re two weeks into a one-month call option that had a 20 delta, and the underlying hasn’t moved, the delta and the probability of meeting the strike price by deadline would then be lower. “We had a 20% chance of that option being in the money. If we only have two weeks left, we [no longer have] a 20% chance of that being in the money, even though the stock hasn’t moved,” Albrecht says. Instead, the option might have fallen to 10 delta—that is, there’s only a 10% chance of being at the money. “The stock is still the same price,” Albrecht notes. “Nothing’s changed except we only have two weeks left in that option.”

## Gamma

### Technical definition

Gamma is related to delta. It measures the rate of change in an option’s delta for every one-point move in the underlying asset’s price. If a call on Barrick has 30 delta and 5 gamma, for instance, and Barrick goes from $100 to $101, the call’s new delta is 35.

### Range

0 to 1, with the same caveat about decimal places (e.g., 20 gamma is technically 0.2 gamma). Gamma is highest when the underlying is at the option’s strike price (at the money), and decreases as the underlying moves away from the strike price in either direction.

### Everyday analogy

Gamma is like acceleration, says Albrecht. It tells you how quickly delta will change as the stock moves around. “With a $1 move in the stock, will I go from 20 kilometres per hour to 40 kilometers per hour, or 20 kilometres per hour to 100 kilometres per hour? There’s a big difference,” he explains. “The latter has larger gamma.”

### Pricing example

**Assume:**

- You own a call option trading at $10, with a $202 strike price
- Delta is 50 (or 0.5)
- Gamma is 10 (or 0.1)
- Underlying stock is trading at $200

If the stock rises to $201, the call option would trade at $10.50, and the new delta would be 60 (since for every $1 increase in the stock, delta goes up by gamma, which is 10).

If the stock rises to $203, the call option would trade at $11.50, and the new delta would be 80.

### Why it matters

There’s a big difference between accelerating gradually and accelerating quickly. To avoid (or benefit from) investment whiplash, you need to understand how fast your positions will change.

“Gamma is something that gives you warnings as to where something might start to hurt or help you,” says Albrecht.

Gamma is highest when an option is near the money and close to expiry, says Albrecht, because a jump in the underlying is likely to cause the option to expire in the money (a drop would cause the option to expire worthless). Bill Feingold, an American options trader, has explained this using a basketball analogy: if the game is tied in the last minute, each team’s delta is 50. “When Team A scores right before the end of the game, its delta goes up from 50 to 98, a much higher rate of increase, or gamma, than when it scored the first basket of the game,” he writes in Forbes. Albrecht agrees with this analogy. “With two minutes left on Friday of expiry, an option becomes very binary,” he says. “It could close 5 cents in money, or 5 cents out of the money. That’s why binary options are so dangerous.”

And don’t be fooled by options on low-volatility stocks, which people rarely expect to move by much. They can still have a lot of gamma, because “when there’s [even a small] move, you can get hurt.” He adds that “gamma is important if you’re short options. If there’s a big move in the stock, they can start to hurt you exponentially.”

## Theta

### Technical definition

Theta measures how much an option’s value decreases over the course of a day.

Generally, as time passes, an option’s value falls because there is more certainty about whether it will be in the money. That value is typically stable at the beginning of an option’s life. But, says Tretiakova, as an at-the-money option approaches expiration, “the value will take a fast dive.” Theta therefore increases as an option closes in on its expiry.

### Range

Since theta always subtracts from an option’s value, it is always negative for long options and measured in units of value (e.g., cents). It starts at zero and its magnitude cannot exceed the value of the option premium. For a short call or put, theta is said to be positive, since you gain value through time.

### Everyday analogy

According to CARFAX, a new car will lose 60% of its total value over the first five years of its life (10% when driven out of the dealership). Theta behaviour is the inverse of that: for an at-the-money option, the time value of an option is stable until it gets close to the expiration, when it drops precipitously. (In-the-money options lose value more linearly.)

### Pricing example

Source: The Options Industry Council

### Why it matters

Traders need to know the point at which an option’s time value starts to nosedive, explains Tretiakova. Traditionally, the sweet spot of maximum value prior to the drop “is about a month.”

When Tretiakova is writing covered calls on stocks owned in a taxable account, and the stock has a low cost base, she usually wants to avoid having to sell the stock (being called) because that would trigger unwanted capital gains taxes. Instead, “If the option gets in the money or at the money [before expiry], we might want to close out our option position.” She would do this by buying back the option (so she’s relieved of the obligation to sell her shares). If possible, she’ll wait until theta peaks (and the option’s value is low) so she can get the option at a cheaper price. But that’s not always possible, and she may lose money when buying back the option.

Time decay can also work in your favour if you’re short options, since that decay turns into value accumulation: you’re earning theta. But there’s also a higher likelihood of those options becoming in the money, which is generally not what someone short a call option wants.

When he’s short, Albrecht monitors the theta-to-gamma ratio to ensure his theta accumulation compensates for his gamma risk. “Once there’s almost no theta left, why would I want to carry a lot of gamma risk? The Fed [could] come out and say something, and the market jumps up 3% tomorrow.

“I thought I was going to collect all this money, and now my calls are in the money and I’m going to get killed.”

## Vega

### Technical definition

“Vega describes how much you can make or lose from a 1% move in implied volatility,” says Albrecht. “Vega becomes more pronounced as an option has a longer lifespan.” That’s because the longer the lifespan, the more chances for volatility to affect the option.

### Range

Vega is positive when you buy options and negative when you sell them. Commonly, vega moves between 0 and +/-1.

“If we’re selling an option, we want higher sensitivity to volatility, so we would be looking for a higher number—it means we’ll get more premium up front,” says Tretiakova. “We would look for lower vega if we’re buying an option.”

### Everyday analogy

While there’s no easy analogy for vega, there is a good one that illustrates implied volatility: car insurance pricing. Let’s say there’s a rash of car thefts in your area and your premiums go from $300 a year to $500 a year, even though your car is worth the same. That’s purely a response to the increased risk (volatility).

### Pricing example

**Assume:**

- You own a call option trading at $10, with a $210 strike price
- Vega is 10 (or 0.1)
- Underlying volatility is 14%

If the underlying volatility increased by a percentage point to 15%, the option price would be $10.10. On the other hand, if the underlying volatility decreased by three percentage points to 11%, the option price would be $9.70.

### Why it matters

“Vega is one of the most important Greeks to options traders, especially as you start to trade longer-term options,” explains Albrecht.

Traders typically look at implied volatility for a given option relative to where it’s been over the past year. “If it tends to be in the higher end of the range, what you’re risking is that the prices will come down. If implied volatility comes down, you could lose money, all else being equal.”

Volatility tied to an expected event—for instance, an election or referendum—is particularly concerning. “You’re at risk that after the event, implied volatility comes down a lot. So vega is going to give you an idea of how much you’re going to get hurt.” He adds a tech stock like Tesla tends to have a higher vega than a blue-chip financial, for instance.

Traders need to know their risk if volatility changes. “If I want to buy a six-month option, and Barrick volatility is in its 80th percentile for the year, I’m taking on a lot of vega risk,” he says, because that volatility is more likely to fall. “If that volatility drops ten points, I’m going to get very hurt. Let’s say my vega is $500 per point of implied volatility. I could lose $5,000, and the stock doesn’t even have to move.” Another example: “If an option typically trades at a 30 vol, and it’s trading at a 40, you’ve got about 10 vol points of vega exposure,” says Albrecht. “What if vol goes back to 30? I could lose 10 vol points times the vega.”

On the flipside, Tretiakova says traders can use vega to find stocks that will make outsized moves on positive news. “If you expect volatility in a stock to pick up—so an earnings announcement, or ideally something you know that the market doesn’t—you would want an option with the highest sensitivity to that (i.e., with the highest vega), because it means you’ll make the most money.” But she cautions this would be a specific, speculative bet.

Albrecht adds that the relationship between implied volatility and options pricing isn’t linear. Triple the implied volatility can push up an out-of-the-money put by 15 times, he says.

## Beta

Beta is the sensitivity of the investment relative to the benchmark, and ranges from 0 to 1, with 1 meaning the investment mimics the benchmark perfectly. But Ioulia Tretiakova, director of quantitative strategies at PUR Investing, says people have incorrectly conflated volatility and beta. “A beta of zero does not mean that the investment has no volatility. It can have very high volatility, but [that volatility] is completely unrelated to the benchmark.”

## Short versus long

- When you’re trading short-term options, focus on delta and gamma.
- When you’re trading long-term options, focus more on vega.

## Moneyness

In-the-money options have intrinsic value as well as time value (e.g., an option that’s $4 in the money has an intrinsic value of $4, plus time value). Out-of-the-money options, however, have only time value and no intrinsic value.

In-the-money options react more to moves in the underlying stock. Hans Albrecht of Horizons says that calls with at least 70 delta work well in stock replacement strategies, since those calls behave almost like the stock itself.