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Lesson 7 - The Greeks

by Uncle Bob Williams

The Greeks

The Greeks are important to understand when we trade Options, and they are not hard to understand. Think of The Greeks like the gauges in a car: We have a speedometer to tell us how fast we are going. A gasoline gauge to tell us how much further we can drive before we have to get more gas. An engine temperature gauge will tell us if our engine will overheat and we need to stop.

With Options, the Greeks are our gauges that tell us what will happen to the price of our Options when certain market factors change:

Delta & Gamma

Delta & Gamma describe how the Option price will change when the PRICE of the underlying changes.
IE: If the price of Acme goes up or down $1.00 in price, the Delta & Gamma tell us how much that $1.00 Acme price change will affect the price of our Option.


Theta

Theta describes how the Option price will change when 1 day of TIME has passed, and we are now 1 Day closer to Expiration of this Option.


Vega

Vega describes how the Option price will change if the VOLATILITY of the underlying changes by 1%.

Rho

Rho describes how the Option price will change if the INTEREST RATE changes by 1%.

We normally won't need to follow the Rho. We don't use Rho in any of the monitoring indicators at Uncle Bob's Money. Any change in the Interest rate will affect all Options prices equally, and the Interest rate generally does not change fast enough to become a significant factor for Options positions that are held for around a month.

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Delta

Delta as the Option Price Change:

Delta describes how much the price of an Option will change when the price of the Underlying changes by $1.00. The Delta will be a value between 0 to 1. Sometimes the Delta is expressed as a number between 0 and 100, and it can be expressed as a negative number for Puts.

For example:

The current price of Acme stock is $50 per share.

This Option: ACME | JUNE | 52 | CALL | Option price = $1.00 per share | Delta = .24

If the price of Acme goes UP by $1.00, then this 52 CALL Option price will go up by $0.24: The new Option price will be $1.24 per share. And likewise, if the price of Acme goes down by $1.00, then the price of this Option will go down $0.24, and the new Option price will be $0.76.

NOTE: A share of stock has a Delta of 1. IE: A $1.00 change of price in the underlying will result in a $1.00 price change of our share; thus our share price will always exactly mirror the price change of the Underlying.

Delta as the Probability:

The Delta is also known as the Probability that that the Underlying price will reach the Strike price on that Option. This is an important trick to remember because we can quickly scan down an Option Price Chain and use the Delta column to understand the different probabilities for specific Options trades.

For example:

The current price of Acme stock is $50 per share.

This Option: ACME | JUNE | 52 | CALL | Option price = $1.00 per share | Delta = .24

The Delta for this Option is .24, and this means that the probability that the ACME stock will go from $50 to $52 by EXPIRATION of this Option is approximately 24%, or about 1 out of 4.

One of the strategies we trade at Uncle Bob's Money are called Condors / Iron Condors, and a critical factor that we look at when selecting our trade positions is the Delta of our Short Strike. With a Condor, we don't want the Market price to hit our Short Strike: we want the Short Strike to be as far away from the current price as possible, but with the maximum amount of profit.

If for example, 2 different trades have similar amounts of profit:

a) Trade A: the Delta of the Short Strike is .08 (8% probability that Market price will reach this Strike)

b) Trade B: the Delta of the Short Strike is .07 (7% probability that Market price will reach this Strike)

In this case where the profit amount is same, we would go with Trade B, where the Delta of the Short strike is .07 because the risk is less for the same profit.

NOTE: With a Condor we might think that it makes sense to always take the position with the lowest Delta, except the amount of profit for each trade can vary depending on the demand for specific Option Strikes. In some cases, the more 'risky' position might have enough extra profit to justify the slight change in risk.

Delta Neutral:

Delta Neutral is a term when trading multiple Option positions, and we want to keep our portfolio hedged so that we won't lose money if the market fluctuates slightly up or down. Delta Neutral means that when we add up all Delta values of our Options positions, the total number is close to zero, and therefore a $1.00 change in the underlying won't make any change to the total value of the Options we have right now. Managing your Options positions using the Greeks is an advanced trading technique; however it important to understand the Delta value because it is a very important indicator of what will happen to our Options values when the price of the underlying changes.

If we have multiple Options positions, we can add up the Delta values of each individual Option position to get an overall Delta value for the combinations of all our Options.

CALLS have a Positive Delta value: as the price of the underlying goes UP, your CALL Option will be more valuable.

PUTS have a Negative Delta value: as the price of the underlying goes DOWN, your PUT Option will be more valuable.

If the combined value of our Delta's is positive, we call that LONG DELTA. When we are LONG DELTA, our Options will Increase in value if the price goes UP, and drop in value if the Price goes down.

If the combined value of our Delta's is negative, we call that SHORT DELTA. When we are SHORT DELTA, our Options will Increase in value if the price goes DOWN, and drop in value if the Price goes UP.

Example A: Single CALL Option Position

The current price of Acme stock is $50 per share.

We BOUGHT 1 | ACME | JUNE | 52 | CALL | Option price = $1.00 per share | Delta = .24

(We are LONG Delta by .24)

If the price of Acme goes up $1.00 to $51 per share, then the value of our CALL Option goes up to $1.24 per share. We could turn around and sell that Option for $1.24 and make a profit of 24%!

If the price of Acme goes down $1.00 to $49 per share, then the value of our CALL Option goes down to $0.76 per share. We could turn around and sell that Option for $0.76, and have a loss of 24%! Ouch.

Example B: Single PUT Option Position

The current price of Acme stock is $50 per share.

We BOUGHT 1 | ACME | JUNE | 48 | PUT | Option price = $1.00 per share | Delta = -.24 (remember PUT Delta's are negative)

(We are SHORT Delta by -.24)

If the price of Acme goes up $1.00 to $51 per share, then the value of our PUT Option goes to down to $0.76 per share. We could turn around and sell that Option for $0.76, and have a loss of 24%! Ouch.

If the price of Acme goes down $1.00 to $49 per share, then the value of our PUT Option goes up to $1.24 per share. We could turn around and sell that Option for $1.24 and make a profit of 24%!

Example C: 2 Option Positions, 1 CALL and 1 PUT

The current price of Acme stock is $50 per share.

We BOUGHT 1 | ACME | JUNE | 52 | CALL | Option price = $1.00 per share | Delta = .24

We BOUGHT 1 | ACME | JUNE | 48 | PUT | Option price = $1.00 per share | Delta = -.24 (remember PUT Delta's are negative)

(We are DELTA NEUTRAL. Combined Delta = 0. [.24 plus -.24 = 0])

If the price of Acme goes up $1.00 to $51 per share, then the value of our CALL Option goes up to $1.24 per share, and the value of our PUT Option goes down to $0.76 per share. Our Net Profit = $0.

If the price of Acme goes down $1.00 to $49 per share, then the value of our CALL Option goes down to $0.76 per share, and the value of our PUT Option goes up to $1.24 per share. Our Net Profit = $0.

This Delta Neutral example shows how a change in price of the underlying made no difference to the overall value of our Options positions.

Then how do we make money? Easy, if our Options positions are Delta Neutral, we can focus on making money by the other Greeks: Vega and Theta (and possibly Rho).

SIDE NOTE: We can understand a little more clearly now how stock trades have a Delta of 1. Every $1.00 movement in the Stock price will produce a $1.00 value change of our position.

At Uncle Bob's Money, we provide the combined Delta value (along with all of the Greeks) for all the positions you have for a Stock / Index, as well as the values for specific strategies and for specific spreads. It's important to note here that we don't 'play' the Greeks with the core strategies at Uncle Bob's Money. We have specific Greeks that we monitor as part of the Trading Checklist for each strategy, but our goal is to provide an easy way to profitably trade Options that doesn't require constant Market attention. We feel it's important to have a solid understanding of the Greeks and how we use them as monitoring tools.

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Gamma

Gamma is a Greek on a Greek. Gamma is an estimate that describes how much the DELTA will change with a $1 price change of the Underlying. In other words, the Gamma is the Delta of the Delta.

For example:

The current price of Acme stock is $50 per share.

This Option: ACME | JUNE | 52 | CALL | Option price = $1.00 per share | Delta = .24 | Gamma = .04

DELTA: If the price of Acme changes by $1.00, then the price of the Option will change by $0.24.

IE: If Acme stock goes up to $51, this Option price will be $1.24. If Acme stock goes down to $49, this Option price will be $0.76.

GAMMA: If the price of Acme changes by $1.00, then the new Delta value will change by .04.

IE: If Acme stock goes up to $51, the Delta of this Option will be .28. If Acme stock goes down to $49, the Delta of this Option will be .20.

THEREFORE: If the price of Acme goes up $1.00, then the new price and the new Delta of this Option would look like this:

New price of Acme stock is $51 per share.

This Option: ACME | JUNE | 52 | CALL | Option price = $1.24 per share | Delta = .28 | Gamma = .04

The new Delta is .28 because of the Gamma increase of .04.

Just as the Delta changes, the Gamma will also change with the price movements of the underlying. Gamma is used to understand how volatile the price of this Option is: A small Gamma means the Options price is fairly stable and will only have a small price change if the underlying changes in price.

"Gamma Trading" or "Gamma Scalping" is a common term to describe a speculative strategy used by advanced traders which has very costly commission charges and requires constant attention. Read more about it here: Schwab Gamma Scalping Explaination

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Theta

Theta describes how the Option price will go down when 1 day of TIME has passed. Remember that Options have a finite lifespan that end at Expiration, and the Theta describes how much the value of that Option goes down for 1 day of time, assuming there is no change in the underlying price and that the Implied Volatility stays the same.

For example:

The current price of Acme stock is $50 per share.

This Option: ACME | JUNE | 52 | CALL | Option price = $1.00 per share | Theta = -.04

THEREFORE, if the price of Acme stays the same and the Implied Volatility stays the same, then tomorrow the Theoretical price of this Option will be: ACME | JUNE | 52 | CALL | Option price = $0.96 per share | Theta = -.04

As we get closer to expiration, the value of the Option will get smaller and smaller: the amount of Theta increases.



We see from the graph above, that when the Option is more than 30 days away from Expiration, the amount of Theta is very small.

A Calendar spread is one of the strategies we trade at Uncle Bob's Money, and the source of most of the profit is from a drop Theta. We usually put on Calendar spreads around 30 days before Expiration, and we hold them around 14 to 21 days when the drop in Theta is high. We explain Calendar Spreads thoroughly later in the book.

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Vega

Vega describes how the Option price will change if the VOLATILITY of the underlying changes by 1%.

The Vega is highest for Options that are ATM (At The Money - meaning the Strike of the Option is the same as the underlying price: A 52 CALL Option, when the price of the underlying is $52/per share).

For example:

The current price of Acme stock is $50 per share.

This Option: ACME | JUNE | 52 | CALL | Option price = $1.00 per share | Vega = .14

If the price of Acme goes up $1.00, then the new price would look like this:

New price of Acme stock is $51 per share.

This Option: ACME | JUNE | 52 | CALL | Option price = $1.14 per share | Vega = .22

Note that the VEGA also increased because this Option strike is now closer to the underlying price.

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