# The power of delta

Learn how this greek can help you assess the probability of making a profit.

- Fidelity Active Investor
- – 01/11/2019

Options traders have a number of resources at their disposal. Greeks, for example, can help analyze the effects of a number of factors on an option. The most widely used greek, which is delta, is one such potentially powerful tool. If you trade options, incorporating delta into your analysis can be a critical component of success.

### What is delta?

Essentially, delta is a measurement of an option's price sensitivity to a given change in the price of an underlying asset. As a result of each $1 move for a stock, option prices tend to adjust by the amount of the delta. So, if the delta is .30 for a specific option contract, for each $1 move the option price may move by $0.30.

However, an option price will not always move exactly by the amount of the delta. Delta is a dynamic greek that is constantly changing because it is impacted by other factors. For instance, another greek, called gamma—which is the rate of change of delta when the underlying security moves—impacts the delta of an option.

Here are a few other helpful principles about delta that are worth considering:

- All else being equal, an in-the-money call option's delta will move toward 1 at expiration, and an in-the-money put option delta will move toward –1 at expiration.
- Delta may be more sensitive to time until expiration and volatility the further in the money or out of the money the option is.

### Uses of delta

Another way that traders use delta is to measure their exposure to the underlying stock. For example, if a long call is showing a delta of .30, the trader might think of the position as if he were long 30 shares. This may simplify the analysis.

Yet another application of delta is that it can provide a probability estimate of the likelihood that the option will be in the money by expiration. If your long call is showing a delta of .30, some traders may think of this as having approximately a 30% probability of being in the money. This can be used as a risk management tool.

## Delta in application

To get a sense of how delta can assess the risk-reward profile of options, let's look at a hypothetical trade. Assume you anticipate that a stock might make a big move, and would like to construct a long strangle that has a 70% chance of being in the money, according to delta. Let's also assume that constructing a 70% probability of being in the money for a long strangle will require a 35% probability of being in the money by expiration for *each* leg.

For a particular stock, we can look at the option chain and find the appropriate deltas. The option chain presented below has call bid-ask prices on the left and put bid-ask prices on the right:

For a stock trading at $422.90, this option chain shows that the 450 call and the 400 put have deltas close to .35 (outlined in red). A multi-leg strategy using these two options may provide a roughly 70% probability of being in the money.

However, as traders we really want our position to be profitable. So, let's go a step further and find the probability of making a profit. We need to add in the costs of the trade, which are the premiums. This would be $13.95 for the call and $16.10 for the put, a total of $30.05. The breakeven above the current market price is roughly $480.05 ($450 exercise price + $30.05 cost of the options), and below the current market price the breakeven is $370 ($400 exercise price – $30.05 cost of the options). Note: These examples do not include commissions and other fees.

Look at the deltas for the options at these prices. The approximate probability of profit is 39% (480 call shows **.212** delta + 370 put shows a **.1816** delta = **.39**) for the long strangle (green outline).

## Delta goes both ways

What if you are looking to sell a strangle because you believe there will not be a lot of volatility, despite the market's expectation for it? In our example, the long strangle has an estimated 70% probability of being in the money. By inference, the short strangle for this same position should have a 30% probability of success. Because we have two legs, each leg of the short strangle should have about .15 delta (.30 ÷ 2).

Referring back to the options chain, we can find calls and puts with .15 delta. The 495 call and the 360 put (outlined in yellow) have deltas that add up to 30% (**.1576** delta for the calls + **.1423** delta for the puts = **.2999**).

To find the probability of profit for this trade, we add the $10.20 premium received (495 calls at a bid price of $5.40 + 360 puts at a bid price of $4.80) to the call and put strikes. Again, this provides the breakeven prices. Here, the breakeven price above the current market price is $505.20 ($495 exercise price + $10.20 cost of the options), and the breakeven price below the current market price is $349.80 (360 exercise price – 10.20 cost of the options). The deltas of the two breakevens (outlined in blue) are .1278 for the 505 calls and .1094 for the 350 puts, which add up to .2372. This reflects a 76% (1.00 – .2372 = .7628) probability of profit.

## Trading implications

Probability will be a moving target as well, because time and movement of the underlying security will adjust the percentages as you go. Nevertheless, the power of delta can be used in several ways to design your options strategies. Of course, delta is just one piece of the puzzle when looking at trading options. For the experienced options trader, accessing an approximation of the probability of profit can be a powerful tool.

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Greeks are mathematical calculations used to determine the effect of various factors on options.

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