You may have heard of them…you know, delta, gamma, theta, vega, and rho.
In fact, you maybe have even used them to explain options modeling and pricing.
But I am confident that you actually do not know what each of them are, what they represent, and even more importantly, how you can use these option greeks to do things such as make informed decisions when trading options (and stock), calculate expected return, or most importantly, use options greeks as tools to make you money!
That is the name of the game. While option greeks are really cool to talk about, the only reason we should know about them is that they can help us make money!
There is a lot of research in the investing community from Ph.D.’s that studied the ins and outs of these options greeks, but the truth is, there is actually very little you need to know about delta, gamma, theta, vega, and rho in order to stack the odds on your side and be able to tell what the market is predicting.
Our goal for this article is to not give you buzzwords or facts that you can rifle off to your friends at the next social gathering or investing club meeting, it is to give you the cold hard truth about each of these option greeks so that you can use ONLY what you need from them to make money.
At the end of this article, you will know exactly what delta, gamma, theta, vega, and rho are, as well as all the information about these options greeks you need to be successful (it is NOT that much).
And moving forward, I am willing to bet that you will be paying a lot more attention to these option greeks as they are an invaluable tool that every professional trader has their eyes on each and every day (and you will too).
The truth is, most of the investing information out there is worthless for individual investors like you and I. We don’t need to know everything under the sun about companies, sectors, market outlook, or what the Fed is going to do. Most of the boilerplate information out there is not actionable and cannot in any way shape or form add value to an investor. And when we say add value, we mean, make them money, because that is the only thing that matters.
However, there are occasions when these terms are incredibly beneficial for us investors. Delta, gamma, theta, vega, and rho are terms (and greeks) that can be an enormous difference maker for investors who know what they are.
My goal here is to teach you exactly what these option greeks are as well as give you actionable takeaways that you can start using as soon as the market is open next to be able to increase your profits, risk levels, and knowledge over night.
So here we go.
Our ultimate guide to the options greeks.
Delta, gamma, theta, vega, rho, and you.
Why I Care About Options Greeks
When I first started trading options, truth be told I started making money from the beginning. Not because I was so much smarter than anyone or had beginners luck. I had tried to make money in the markets day trading stocks, futures, and commodities.
I was able to make money trading options because I had learned an incredible amount of information from failing in what I had already done and seeing first hand what worked and what did not.
I was excited because I was finally making some money in the markets. I would have 10, 20, even sometimes 50 positions on at any given time. I was addicted and loved putting on more and more positions.
It was working, however, I had no idea what my total portfolio looked like at a given time. I had no idea my expected profit when the market went up 1% and I had no idea my expected loss if the market went down 1%. At that point, I would have called myself a lucky trader, one who was making money in the markets without having any clue as to what I was doing.
Because I had a lot of options positions on, I started to research. After all, I wanted to try to figure out first what I was doing and then second what I could do to improve on the positive results I was already getting.
I started to read up on options greeks. There is so much information out there on option greeks that it was an incredibly overwhelming experience.
But once I started to apply what I had learned to my portfolio and my day to day strategies and choices in trades, my profits skyrocketed. After learning about the option greeks delta, gamma, theta, vega, and rho, I had an understanding what my portfolio looked like, where my weaknesses were, and exactly how to improve on the positions I already had.
Understanding these option greeks was one of the turning points in my career that took me from a profitable investor solely by chance to an investor who could repeatedly earn profits over and over and over again.
This is why I am so excited to teach you all about option greeks, what they are, and how to use ONLY what you need from them to be able to have an understanding of what each options position and your entire portfolio look like at any given time.
Want to be able to tell how any shares of stock your options positions are worth? Option greeks can tell you that.
Want to know what your portfolio will look like if the market goes up or down 1%? Options greeks can tell you that.
Want to know how much value will be extracted from your options positions every single day (including weekends)? Option greeks can tell you that.
Want to know what will happen to your portfolio will look like if the Fed raises rates? Options greeks can tell you that.
What is more important than having reasonable expectations on your options positions and total portfolio? I can’t really think of any…
What Are These Option Greeks Anyway?
I just told you why these greeks are so important, but you probably want to know why I am so excited to teach you about them, right?
For starters, delta, gamma, theta, vega, and rho all measure different data points and factors that all affect the price of options in their own ways. These option greeks are used to calculate theoretical options pricing using the Black Sholes options pricing model.
Since there are five Greeks, we can think of it as there are five different ways options prices can be affected or change. For example, we can determine the pricing on an options contract based on a $1 move in a stock (delta) just as easily as we can figure out the change of an options contract if the Federal Reserve raises interest rates by 50 basis points (rho). Along the same lines, we can know that if a stock does not move at all, that there is a certain amount of value that will be extracted from an option contract every single day (theta).
Now, the moment you have all been waiting for, here is what each of the option greeks are and exactly how you can use them to make you more money.
Option Greeks: Delta
Option delta is the first of the option greeks and to me, is the most important by far. The other greeks add value, but delta is really what can make or break your account as well as your understanding of all of the positions in your portfolio (stock or option).
Delta, is its most simplistic form, measures the predicted price movement of an option per every $1 move in the underlying stock.
Since options are really no different than synthetic versions of stock, delta allows you to understand exactly how much synthetic stock you have in your options positions. This is crucial because options can be used as stock replacement, and there is no better way to tell how much stock replacement you have than simply looking at the delta’s of your options contracts.
Option delta for calls:
- Call options have a positive delta that can be anywhere from 0 to 1.00.
- The at the money options usually have a delta close to .50. At the money represents the options contracts closest to the current price strike of the underlying asset. If $AAPL is currently trading for $150 a share, then the $150 call is the at the money call and will typically have a .50 delta.
- As the price of the asset goes up, so does the delta of the call options. The delta for those call options will get closer to 1.00 (but never over) the further they are to the money (the current strike price of the underlying) as well as when they get deeper in the money (the strike price of the option is below the current price of the underlying).
- All option deltas who’s strike price is below the current price of the stock will gravitate more and more to a 1.00 delta the closer the option contract gets to expiring. The reason for this is because, on expiration, all in the money options have a delta of 1.00.
- All option deltas who’s strike prices are above the current price of the stock will gravitate more and more to a delta of 0 the closer the option contract gets to expiring. The reason for this is because, on expiration, all out of the money calls have a delta of 0.
But the most important thing about delta, and the only think you need to know about delta, is that is it the synthetic equivalent of stock.
But if we have purchased an at the money call (contract closest to the current strike price) with a 50 delta and the price of $SPY goes up $1, how much can we expect to make? Let's find out.
Here we can see we have 50 shares of $SPY.
You can clearly see we have 50 deltas as well. If $SPY goes up $1, we make $50.
But now we would like to have synthetic stock, maybe because it costs us less money, but whatever the case, we want to buy an at the money call which gives us an option delta of .50 (.51 to be exact).
And sure enough, what happen when $SPY is stressed up $1?
Pretty close to that $50 number. And what makes options cool is that to get that $50 gain, we would have to have invested $12,277.00 to get 50 shares of stock in a cash account or half of that ($6,138.50) in a margin account.
On the other hand, we only had to put up the price we paid for that option contract to get the same profit on a $1 move in the stock. In the example we showed, we paid $0.60 which is $60.
Now, just as easily as we can make roughly $50 from owning a call option that has a delta of .50 on a $1 move up in the stock...what do you think will happen if the stock goes down $1 and we own that at the money call option? That is correct, you guessed it, we will lose roughly $50.
To wrap up option delta, the number one thing you have to remember, and really, the only thing you have to remember, is that an options delta is its stock synthetic equivalent.
Own a .30 delta call and the stock goes up $1, how much money did you make on that contract? Roughly $30.
Own a .80 delta call and the stock goes down $2, how much money did you lose on that contract? Roughly $160.
Own a .50 delta call and two -.10 delta puts, and the stock goes up $1, how much money did you make on that day? Roughly $30.
Option delta is simple, however, incredibly powerful. Again, an options delta is its synthetic equivalent of stock for the underlying it is an option for.
Options Greeks: Gamma?
Gamma measures the change in the value of an options delta per $1 move in the underlying. Where delta is the synthetic equivalent of whatever type of underlying the option contract is for (usually stock), is it never a fixed number as delta can change if the stock goes up or down. That rate of change in the options contracts delta is known as the option greek gamma.
Again, delta is never static and always changing. If an option has a delta of .50 and the stock moves up $1, the delta will change, and we will be able to tell how much it will change depending on that options gamma.
It is challenging to speak about gamma by itself because it has such a strong relationship with delta. Here are some ways you can look at the relationship between delta and gamma.
- Delta is only accurate for exactly the moment you see it and it is almost never static (only static when the market is not open). As we mentioned above, if a call option has a delta of .50 (meaning it is the at the money call option), and the price of the stock goes up $2, that option contract will no longer have a delta of .50. It will be greater than .50, and we will be able to know exactly what our new synthetic share equivalent (delta) is based on that contracts gamma.
- The change in delta of an option is known as the option's gamma.
- An option's delta cannot ever be greater than 1.00, and as an option's delta approaches 1.00 (becomes further in the money), gamma decreases. This is true on the other side of the coin where an option's delta cannot ever be less than -1.00, and as an option's delta decreases towards -1.00, the gamma of the option increases.
As we stand right now, $SPY is trading for $243.87, making the at the money call the $244 strike.
The $244 call option expiring in 37 days currently has a delta of .49 and a gamma of .07. This would mean that assuming delta and gamma are accurate, a $1 move up in $SPY would result in this 244 call having a roughly .56 delta. And what do we see?
There we go. After we stress this call up $1, we see the new delta will be .5593, or as we mentioned earlier, a new delta of .56. This is exactly how gamma works with delta.
The same can be said if the stock were to go down $1. Right now, with the $244 call having a delta of .49 and a gamma of 7.29, we would expect a $1 down move in $SPY to change the delta of the @44 call to roughly .42. And what do we see?
Sure enough, right again! A $1 drop in $SPY for an option with a .49 delta and a 7.21 gamma results in a decrease of roughly 7 deltas.
Now, some of you might be asking, "but should I care about gamma?"
That is an excellent question. And the truth is, yes and no.
Yes, you need to care about gamma, however, there is one rule you can follow so that you never have to worry about gamma.
And that is...
Never be holding an option that has less than 10 days to expire.
The reason we never want to be holding an option anywhere within 10 days to expiration is that that is the only time gamma becomes a risk. The closer we get to expiration, the larger gamma is, and thus, the more sensitive delta is. We call this gamma risk.
Here is the at the money $SPY call option expiring in two days. We can see that is has a 31 gamma.
However, here is the gamma of that same strike expiring 37 days from now.
In the first example of the $244 call expiring in two days, the gamma risk is more than three times greater that when the option expires at a later date. This is a situation we do not ever want to be in and should avoid at all costs. Holding these options so close to expiration turns options from in the money with a delta of 1.00 to out of the money with a delta of 0 during very small price movement. This is a risk we do not have to take.
However, if you are not holding any options within 10 days of their expiration, you do not ever need to look at or worry about gamma. All you have to do is get rid of your options contracts when you are approaching the 10 days to expiration mark or roll them out to another expiration cycle. Gamma risk is nasty and we want to avoid it, and then completely forget about the need to know what gamma is.
Where delta is incredibly important when deciding which option greeks to know, gamma is not, especially if we follow the rule that we will not be holding any options contracts that are 10 or less days away from expiring.
Options Greeks: Theta?
I have bad news for all of option buyers out there...
Unless you have a call with a 1.00 delta, or a put with a -1.00 delta, every single option you own will lose value every single day.
Yes, you are owning something that is losing value every single day (even on weekends).
Theta measures the change in price of an option from one day to the next. Theta tells you how much the extrinsic value is going to be extracted or removed from the price of the option each day.
Extrinsic value is the value added on to an option given for a time. The more time an option has before it expires, the more extrinsic value will be assigned to it and added on to the price of the option. The closer an option is to expiring, the less extrinsic value it has, but either way, it is losing value every single day due to its theta component.
- If all other factors remain the same (delta, gamma, vega, rho), theta measures the amount of value that is removed from the price of an option every single day.
- Theta is non-linear, meaning theta in the options closest to the money (the current price of the stock) increases as the option's expiration approaches while theta in the options contracts further away from expiring increases as expiration approaches.
- While theta decreases at different rates depending on the distance of the option contract from the current price of the stock, all options with an extrinsic value remaining in them have a positive theta that increases as the option gets closer to expiring.
We care about delta because it tells us our synthetic stock equivalent of our options positions.
We do not care about gamma because we will not hold any options within 10 days of expiring which allows us to never worry about gamma risk.
But what about theta? What do we need to take away from theta?
There are actually a few things to take away from theta, and they can be broken down by option buyers and option sellers.
As an option buyer:
- Every single day, value from the options you own is removed
- Owning options with the least amount of extrinsic value helps remove the theta drag against you. For you to do this, purchasing options with a delta of greater than .80 will allow for limited extrinsic value to be removed every day. However, the prices of these options are higher than those with more extrinsic value and thus, a greater theta component.
- Owning options that are further away from expiring allows you to own options when theta is at its lowest and the least amount of value is removed daily.
- If you buy options anywhere near their expiration, you are crazy as theta is as it's greatest when options are close to expiring.
As an option seller:
- Every single day, value from the options you have sold is removed. This is a good thing.
- Selling options with the most amount of extrinsic value helps you as theta is highest for those options with the most extrinsic value
We mentioned that theta is higher the closer we are to the current price of the stock. For example, right now, $SPY is trading for $244.66, making the $245 strike the strike closest to the current price of the stock. If we look at the theta value for that strike price, we see a value of $3.34. This means that every single day, assuming all of the other option greeks remain the same, this contract will lose $3.34 in value.
On the other hand, if we were the sell a $250 call, our theta would be less as it is further away from the current price of the stock ($5 to be exact).
The $245 call decays at a rate that is double that of the $250 call because it is closer to the current strike price of the stock.
If theta increases the closer we are to the current price of the stock, what does that say for option sellers? It says that as option seller, we should be selling options closer to the current strike price of the stock. On the other hand, as option buyers, we should never be buying any options close to the current price of the stock as the most amount of theta decay is removed from those contracts every day.
So what is the takeaway here? What do we need to know about theta that can help us make money with options?
There are two takeaways.
- If you must buy options, only buy options with greater than a .80 delta. This way, there is little extrinsic value that can be removed via theta decay from the price you paid for the contract.
- If we are going to sell options, sell options close to the current price of the stock as theta decay is at its greatest for those strike prices.
Option Greeks: Vega
Most other articles you will read will gloss over the options greek vega, but the reality is vega is actually quite an important greek to have a strong understanding of.
Vega measures the change in the price of the option per every 1% change in the implied volatility of the underlying stock.
Implied volatility is the expected move for a stock. The larger the expected move of the stock, the higher the prices its options contracts will be. And the same is true for the reverse, the lower the expected move for the stock, the smaller the prices for that stocks options.
So vega measures the rate of change for every 1% move up or down in implied volatility for a stock.
- Vega measures how the expected move or implied volatility of the stock affects the prices of the options for that stock
- As implied volatility increase (and vega increases), so do the prices for all of the options contracts for that stock
- As implied volatility decreases (and vega increases), so do the prices for all of the options contracts for that stock
Let's check out an example of how vega can predict the price of options depending on the increase or decrease of the stocks implied volatility.
We have simulated purchasing a $244 call in $SPY. Here is what that looks like.
We can see that call currently has a vega of ~28.70.
If the implied volatility of $SPY goes up by 1%, we would expect the value of the option to go up by roughly ~.29. Here is what the price looks like if we simulate that 1% increase in the implied volatility of the stock.
We can see we had about a $28 increase in the value of the option. This is an excellent example of vega at work.
So...you might be asking now, "what do I need vega for?"
If you are long options, vega does not matter at all.
However, if you are short options, vega does matter. If we are short options we are looking to make money when the prices of the options decrease or vega/implied volatility decreases.
If we are short options, we will begin to lose money if vega increases. For this reason, we have set up a rule for you!
The rule is, for however many short delta's you are (if you are selling options), you must have 50% of the value of vega for every short delta.
If you are short 100 deltas (recall: synthetic stock), you should not have a vega number of over 50.
If these two numbers are our of whack, you must change one to get this rule in line.
This is what you need vega for and nothing else. However, if we are short options and have short synthetic stock (delta) via options, we must make sure our vega is never greater than half our short delta number.
Option Greeks: Rho
Rho measures the rate of change for an options price per every 1% change in interest rates.
- As interest rates increase, so does the value of options
- As interest rates decrease, so does the value of options
A lot of you might be asking, "do I need to care about rho?"
And the answer is...absolutely not.
Delta, gamma, theta, and vega are all moving targets as the values for those option greeks change by the second. When compared to rho, they move like lightening.
Rho changes very infrequently, and because interest rates/rho change so infrequently, there is absolutely no reason at all the pay any attention to it!
Wrapping Up Options Greeks
There you have it, folks. Option greeks from the viewpoint of a professional trader. For those who have skimmed directly to the bottom, here is a recap of what we spoke about.
- Delta is the synthetic stock equivalent we get from trading options. If we buy a call with a .50 delta, we are synthetically long 50 shares of the stock we bought the call in.
- Gamma is the rate of change of delta. Delta is never static, and gamma will be able to tell us our new delta for our options for every $1 move in the stock. If a call option has a .50 delta with a 10 gamma that goes up $1, the new delta on that call option will be .60.
- Theta is the amount of money that is removed from the value of the option every single day (including weekends). The closer our option contract is to the current price of the stock, the greater theta is. The closer we are to the date of our option expiration, the greater the pace of theta. As an option buyer, to avoid getting hurt by theta, we recommend buying options with a delta above .80 as theta is very low for those options.
- Vega measures the rate of change of an option for every 1% increase or decrease in implied volatility for the stock. As vega goes up, so do options prices. As vega goes down, so do option prices.
- Rho measures the rate of change in option prices for every 1% increase or decrease in interest rates. As rho goes up, so do option prices. As rho goes down, so do option prices.
But learning all of this information about option greeks is great and all, but what parts about these option greeks should we are about. Here is a summary of exactly what you need to know about these option greeks.
- Delta is your synthetic equivalent of stock.
- Gamma does not matter unless you are holding options that expire within 10 days. Don't hold options that expire within 10 days.
- If you buy options, buy options where theta is at its least. Buy options who's deltas are .80 or greater.
- If you are an option seller, make sure your vega levels are no greater than 1/2 your deltas.
- Don't worry about rho.
There you have it, folks. The ultimate guide to option greeks. What do you guys think?