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

These questions help understand risk when trading options. That’s because “options are a multi-dimensional asset,” says Hans Albrecht, portfolio manager and options strategist at Horizons Investment Management in Toronto.

Options give you the right to buy or sell an underlying asset at a certain price on a certain day. A call option is the right to buy an underlying asset (e.g., a stock, bond or commodity) at a certain price at a certain time, while a put option is the right to sell it.

The value of options depends on things like how far you are from the expiration date and the agreed-upon strike price. 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. “Greeks give us those handy answers.”

Common Greeks include delta, gamma, theta and vega. Here, we’ll introduce you to one of the simpler, yet important, Greeks: delta.

## What is delta?

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.

Delta’s range is from 0 to 1 for calls, or 0 or -1 for puts. Put options have negative delta, whereas call options have positive delta. Traders 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 it 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 tells you 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.

Why does this matter? 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.

## In the money

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”: 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. Being in the money means the call option’s strike price is below the price of the underlying asset—indicating that exercising the option to buy is still worth it.

“For example, if Barrick was trading at \$100, maybe I’m owning a \$96 strike. So it’s already in the money by \$4,” says Albrecht.

## Time value

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—i.e., there’s only a 10% chance of being at the money.

“The stock is still the same price,” Albrecht says. “Nothing’s changed except we only have two weeks left in that option.”