The Greeks: What They Are and How to Use Them

The Greeks have given us feta cheese, philosophy, mathematics, and the Oedipal complex. They also tell us how much risk our option positions have.

There are ways of estimating the risks associated with options, such as the risk of the stock price moving up or down, implied volatility moving up or down, or how much money is made or lost as time passes. They are numbers generated by mathematical formulas. Collectively, they are known as the "greeks", because most use Greek letters as names. Each greek estimates the risk for one variable: delta measures the change in the option price due to a change in the stock price, gamma measures the change in the option delta due to a change in the stock price, theta measures the change in the option price due to time passing, vega measures the change in the option price due to volatility changing, and rho measures the change in the option price due to a change in interest rates.

Delta

The first and most commonly used greek is "delta". For the record, and contrary to what is frequently written and said about it, delta is NOT the probability that the option will expire ITM. Simply, delta is a number that measures how much the theoretical value of an option will change if the underlying stock moves up or down $1.00. Positive delta means that the option position will rise in value if the stock price rises, and drop in value if the stock price falls. Negative delta means that the option position will theoretically rise in value if the stock price falls, and theoretically drop in value if the stock price rises.

The delta of a call can range from 0.00 to 1.00; the delta of a put can range from 0.00 to –1.00. Long calls have positive delta; short calls have negative delta. Long puts have negative delta; short puts have positive delta. Long stock has positive delta; short stock has negative delta. The closer an option's delta is to 1.00 or –1.00, the more the price of the option responds like actual long or short stock when the stock price moves.

So, if the XYZ Aug 50 call has a value of $2.00 and a delta of +.45 with the price of XYZ at $48, if XYZ rises to $49, the value of the XYZ Aug 50 call will theoretically rise to $2.45. If XYZ falls to $47, the value of the XYZ Aug 50 call will theoretically drop to $1.55.

If the XYZ Aug 50 put has a value of $3.75 and a delta of -.55 with the price of XYZ at $48, if XYZ rises to $49, the value of the XYZ Aug 50 put will drop to $3.20. If XYZ falls to $47, the value of the XYZ Aug 50 put will rise to $4.30.

Now, these numbers assume that nothing else changes, such as a rise or fall in volatility or interest rates, or time passing. Changes in any one of these can change delta, even if the price of the stock doesn't change.

Time Spreads & Diagonals

Long Call Time Spread:
Short 1 XYZ Sep 50 call @ $2.00, Long 1 XYZ Dec 50 call @ $5.00
Cost	$300 Debit
Maximum Loss:	$300
Maximum Profit:	Depends on value of Dec 50 call at time of Sep expiration
Short Call Time Spread
Long 1 XYZ Sep 50 call @ $2.00, Short 1 XYZ Dec 50 call @ $5.00
Cost	$300 Credit
Maximum Loss:	Depends on value of Dec 50 call at time of Sep expiration
Maximum Profit:	$300
Long Put Time Spread
Short 1 XYZ Sep 50 put @ $1.00, Long 1 XYZ Dec 50 put @ $3.00
Cost	$200 Debit
Maximum Loss:	$200
Maximum Profit:
Short Put Time Spread
Long 1 XYZ Sep 50 put @ $1.00, Short 1 XYZ Dec 50 put @ $3.00
Cost	$200 Credit
Maximum Loss:	Depends on value of Dec 50 put at time of Sep expiration
Maximum Profit:	$200

Explanation and Application

Time spreads are so called because they are positions with options in two different expiration months, with the options being either both calls or both puts. Time spreads involve buying an option in one expiration month and selling another option in a different expiration month but with the same strike as the first option. Specifically; a long call time spread is selling a call in a front month at a certain strike, and buying a call in a deferred month at the same strike. A put time spread is selling a put in a front month at a certain strike, and buying a put in a deferred month at the same strike. A short call time spread or put time spread is simply the reverse of the long time spread: long front month and short deferred month. In time spreads, one option in the position expires before the other. You have to keep this in mind because it does present certain risks and necessary adjustments that other types of positions might not.

Time spreads, whether they are call time spreads or put time spreads, maximize their value when the stock is at the strike price of the options, and the front month option is expiring. Time spreads have their minimum value when the stock is very far away from the strike price of the options. If you buy a time spread you want the stock price to be at the strike price at expiration. If you sell a time spread you want the stock price to be as far away as possible from the strike price at expiration.

Butterflies & Wingspreads

Long Call Butterfly
Long 1 XYZ Sep 50 call @ $2.00, Short 2 XYZ Sep 55 calls @ $1.00, Long 1 XYZ Sep 60 call @ $.50
Total Cost	Option premium paid, $50
Maximum Loss	Option premium paid, $50
Maximum Profit	Dollar value of difference between outside and middle strike prices minus premium paid, $450
Short Call Butterfly:
Short 1 XYZ Sep 50 call @ $2.00, Long 2 XYZ Sep 55 calls @ $1.00, Short 1 XYZ Sep 60 call @ $.50
Total Credit Received	Net option premium received, $50
Maximum Loss	Dollar value of difference between outside and middle strike prices minus credit received, $450
Maximum Profit	Net option premium received, $50
Long Put Butterfly:
Long 1 XYZ Sep 30 put @ $.25, Short 2 XYZ Sep 35 puts @ $.50, Long 1 XYZ Sep 40 put @ $1.00
Total Cost	Option premium paid, $25
Maximum Loss	Option premium paid, $25
Maximum Profit	Dollar value of difference between outside and middle strike prices minus premium paid, $475
Short Put Butterfly
Short 1 XYZ Sep 30 put @ $.25, Long 2 XYZ Sep 35 puts @ $.50, Short 1 XYZ Sep 40 put @ $1.00
Total Credit Received	Net option premium received, $25
Maximum Loss	Dollar value of difference between outside and middle strike prices minus credit received, $475
Maximum Profit	Net option premium received, $25

Explanation and Application

Butterflies, condors and "wingspreads" are so-called because with sufficient -- no, make that CONSIDERABLE imagination, their expiration date risk profiles look like something that could fly. That, and anything that can add a bit of color to the otherwise dreary world of option trading is welcome. When talking about butterflies et al., you'll hear self-proclaimed experts speak of options as "body" and "wings". The "body" refers to options with strikes in between the two exoskeletal outermost strikes. The "wings" refer to options at the diaphanous outermost strikes. We use the term "wingspreads" to identify option positions such as "condors", "pterodactyls" and "albatrosses", which look like butterflies that have been stretched out. Rather than come up with a myriad of names to identify these spreads, we use "wingspreads" because they all have similar risk/reward characteristics and sensitivities, and those flying creatures are much more threatening than butterflies.

The risks and potential rewards of butterflies and wingspreads are limited. If you buy a butterfly, the most you can lose is the amount you paid for it. The most you can make is the difference between the "body" strike and a "wing" strike minus the amount you paid for it. If you sell a butterfly, the loss and profit are the inverse of buying a butterfly.

Ratio & Back Spreads

Call Back Spread
Short 1 XYZ Sep 50 call @ $2.00, Long 2 XYZ Sep 60 calls @ $0.75
Cost	$50 Credit
Maximum Loss	$950
Maximum Profit	Unlimited
Call Ratio Spread
Long 1 XYZ Sep 50 call @ $2.00, Short 2 XYZ Sep 60 calls @ $0.75
Cost	$50 Debit
Maximum Loss	Unlimited
Maximum Profit	$950
Put Back Spread
Short 1 XYZ Sep 50 put @ $1.00, Long 2 XYZ Sep 40 puts @ $0.50
Cost	$0 Even Money
Maximum Loss	$1000
Maximum Profit	Unlimited
Put Ratio Spread:
Long 1 XYZ Sep 50 put @ $1.00, Short 2 XYZ Sep 40 puts @ $0.50
Cost	$0 Even Money
Maximum Loss	Unlimited
Maximum Profit	$1000

Explanation and Application

Back spreads and ratio spreads are simply the mirror image of each other. Back spreads and ratio spreads are comprised of either both calls or both puts at two different strike prices in the same expiration month. If the spread has more long contracts than short contracts, it is a Back Spread. If there are more short contracts, it is a Ratio Spread. Any ratio of long to short options is possible, but to keep it simple we will deal mainly with 1 by 2s in this article, i.e. long 1 option and short 2 option ratio spreads, and short 1 option and long 2 option back spreads. When naming this type of spread, the lower strike is generally stated first, whether it is long or short, so, it's the Sep 50/60 call back spread or ratio spread, and the 40/50 put back spread or ratio spread.

Back spreads and ratio spreads can be executed for debits (you pay money) or credits (you receive money) or Even Money when there is no debit or credit. This occurs because the amount you pay for the long options in the spread is sometimes less than, equal to, or more than the amount you receive for the short options in the spread. This can be a bit confusing at times, because you might be a credit bid for a back spread or ratio spread.

Straddles & Strangles

Long Straddle
Long 1 XYZ Sep 50 call @ $2.00, Long 1 XYZ Sep 50 put @ $1.75
Total Cost	Option Premium Paid, $375
Maximum Loss	Option Premium Paid, $375
Maximum Profit	Unlimited Potential
Short Straddle
Short 1 XYZ Sep 50 call @ $2.00, Short 1 XYZ Sep 50 put @ $1.75
Total Credit Received	Net option premium received, $375
Maximum Loss	Unlimited Potential
Maximum Profit	Net option premium received, $375
Long Strangle
Long 1 XYZ Sep 40 put @ $1.00, Long 1 XYZ Sep 60 call @ $.75
Total Cost	Option Premium Paid, $175
Maximum Loss	Option Premium Paid, $175
Maximum Profit	Unlimited Potential
Short Strangle
Short1 XYZ Sep 40 put @ $1.00, Short 1 XYZ Sep 60 call @ $.75
Total Credit Received	Net option premium received, $175
Maximum Loss	Unlimited Potential
Maximum Profit	Net option premium received, $175

Explanation and Application

The names "straddle" and "strangle" may give you clues about these option positions. Like your favorite politician trying to win both Democratic and Republican votes, these positions are on both sides of the issue. Long straddles and strangles make money if the stock price moves up or down significantly. Who cares which way the stock goes, so long as it GOES!

Straddles and strangles are essentially speculations on whether the price of the stock will move a lot or not or implied volatility is going to go up or down. If you think the stock is going to move big in one direction or another and/or if you think implied volatility is going to rise, you would buy a straddle or strangle. If you think the stock is going to sit still or not move very much and/or if you think implied volatility is going to fall, you would sell short a straddle or strangle.

A long straddle is long 1 call and long 1 put at the same strike price and expiration and on the same stock. A long strangle is long 1 call at a higher strike and long 1 put at a lower strike in the same expiration and on the same stock. Such a position makes money if the stock price moves up or down well past the strike prices of the strangle. Long straddles and strangles have limited risk but unlimited profit potential.

Verticals

Essentials

Long Call (Bull) Vertical
Long 1 XYZ Sep 50 call @ $2.00, Short 1 XYZ Sep 60 call @ $.75
Total Cost	Option premium paid, $125
Maximum Loss	Option premium paid, $125
Maximum Profit	Dollar value of difference between the strike prices minus premium paid, $875
Short Call (Bear) Vertical
Short 1 XYZ Sep 50 call @ $2.00, Long 1 XYZ Sep 60 call @ $.75
Total Credit Received	Net option premium received, $125
Maximum Loss	Dollar value of difference between the strike prices minus credit received, $875
Maximum Profit	Net option premium received, $125
Long Put (Bear) Vertical
Long 1 XYZ Sep 40 put @ $1.00, Short 1 XYZ Sep 35 put @ $.25
Total Cost	Option premium paid, $75
Maximum Loss	Option premium paid, $75
Maximum Profit	Dollar value of difference between the strike prices minus premium paid, $425
Short Put (Bull) Vertical
Short 1 XYZ Sep 40 put @ $1.00, Long 1 XYZ Sep 35 put @ $.25
Total Credit Received	Net option premium received, $75
Maximum Loss	Dollar value of difference between the strike prices minus credit received, $425
Maximum Profit	Net option premium received, $75

Explanation and Application

Verticals are the most basic option spread. You're hedging one option with another: when one makes money, the other loses money. The idea is that in exchange for relatively low risk, you're giving up the possibility of stratospheric gains. But don't scoff. Verticals (either a bull vertical or bear vertical) are popular with professionals because of their limited risk nature and their profit potential that, though limited, can still amount to many times the risk taken. In many stocks, option volatility and margin requirements are so high as to prohibit either buying or selling options outright, whereas verticals typically don't have such high cost or prohibitive margin requirements. Verticals can offer investors an efficient way of creating long or short exposure in a stock.

Before we proceed, understand that a bull vertical is always long a lower strike option and short a higher strike option, and can be either a long call vertical or a short put vertical. Conversely, a bear vertical is always short a lower strike option and long a higher strike option, and can be either a long put vertical or a short call vertical.

It's not enough to know a bull vertical spread is used when you are bullish and a bear vertical spread when you are bearish. Should you be considering a vertical that's in-the-money (ITM), at-the-money (ATM), or out-of-the money (OTM)? With respect to the stock's current price, a vertical might have one option ITM and one OTM making it an ATM vertical. Therefore, an ITM vertical is one where both options are currently ITM, and an OTM vertical is one where both options are currently OTM. Do you want the passage of time to help you, or are you willing to let it hurt you? Do you think implied volatility will rise, fall, or stay the same during your time frame? Verticals can be created to meet these requirements.

Calls, Puts & Covered Writes

Essentials

Long Call
Long 1 XYZ Sep 50 call @ $2.00
Total Cost	Option premium paid, $200
Maximum Loss	Option premium paid, $200
Maximum Profit	Unlimited
Short Call
Short 1 XYZ Sep 50 call @ $2.00
Total Credit Received	Option premium received, $200
Maximum Loss	Unlimited
Maximum Profit	Option premium received, $200
Long Put
Long 1 XYZ Sep 40 put @ $1.00
Total Cost	Option premium paid, $100
Maximum Loss	Option premium paid, $100
Maximum Profit	Unlimited
Short Put
Short 1 XYZ Sep 40 put @ $1.00
Total Credit Received	Option premium received, $100
Maximum Loss	Unlimited
Maximum Profit	Option Premium Received, $100

Explanation and Application

Before you can trade the more complicated option positions, it would be wise to understand their building blocks: calls and puts. Critics of option trading always point out how risky, speculative, and unnecessary options are. But what they either don't understand or point out is that options are designed to be a tool for transferring risk from one trader to another. It is imperative to understand that when buying calls or puts, the potential loss is limited to the amount paid for the calls or puts. When selling calls or puts, the potential loss is unlimited (short puts really have risk limited to their strike price, but are considered unlimited for all intents and purposes). Therefore, when you buy an option, you are limiting your risk by transferring it to whomever sold the option. When you sell an option short, you are accepting the risk from whoever bought the option. Options can offer a great deal of leverage, meaning that you can have the risk/reward exposure of a large position in stock for a relatively small amount of money.

It's important to understand that there are trade-offs in options. There are good points and bad points about every option strategy. You must isolate your speculation, i.e. precisely what do you think is going to happen to a stock and when is it going to happen? You must balance potential risk versus potential reward. Always keep in mind that in option trading, you never get anything for free.