The Greeks
While most casual investors will probably be unfamiliar with the term “the greeks” in the context of markets, anyone who has really done their homework or dabbled with options will at least be loosely acquainted with their meaning and significance.
Not all the greeks I will be discussing are exclusive to the options or derivatives markets, but a good portion of them might as well be. For simplicity’s sake, you can consider five of the greeks I’ll be outlining as the language of the options market and the fundamental variables used in determining every option’s value.
Yet despite the relevance of most of the greeks finding a home in the options market, the first two greeks I’ll get into, Alpha and Beta, are applicable to all areas of the market and investing more broadly. Even the more option-specific greeks have general market uses and implications that make learning about them helpful to any investor looking to understand the different market dynamics that all contribute to price action.
With all that being said, let’s start off with the most basic greek, Alpha.
ALPHA
Alpha is just a term used by the investing community to describe an asset or strategy’s ability to beat the market. To generate Alpha is to generate returns in excess of a basic market index like the S&P 500. In that sense, then, every active investor is seeking to generate Alpha in some way. Presumably, the extent to which any investor generates Alpha will be proportionate to their edge in the market, so Alpha could be thought of as just that; your edge.
Any asset or portfolio with positive Alpha is outperforming the market and any asset or portfolio with negative Alpha is underperforming the market, so Alpha is the most basic metric by which we judge investor performance. If you are a passive index investor, which most investors should pursue as a strategy, you are not in the business of generating Alpha because you are aiming to mirror the benchmark, which would have an Alpha of zero.
Generating long-term Alpha in the market is extremely difficult, so investors shouldn’t view a zero Alpha or even a small positive Alpha as anything to complain about. Very few investors are capable of generating consistent Alpha through some edge in the market, so the vast majority of market participants should stick to an Alpha-neutral strategy by just investing in a benchmark index.
However, if you are an investor trying your luck in the market with some proprietary or discretionary strategy, generating Alpha is your ultimate goal and the best indicator of the profitability or efficacy of your strategy.
BETA
The next greek is Beta. Beta is essentially a volatility metric with the baseline it references being the overall market or a generic index like the S&P 500. Any stock or other financial asset with a Beta of 1.0 is expected to move in line with the overall market. Any asset with a Beta of 1.5 would be more volatile than the overall market and expected to move 1.50% for every 1.00% the broader market moves. And an asset with a Beta of 0.5 would be less volatile than the overall market, moving 0.50% for any 1.00% overall market move.
Another important thing to keep in mind about Beta is an asset inversely correlated to the market will have a negative Beta. An inverse S&P 500 ETF, for example, would have a Beta of -1.0. However, if it was a 3x levered inverse S&P 500 ETF, its Beta would be -3.0.
As a general rule of thumb, investors like to hold high-Beta assets during strong bull markets because their returns exceed that of the overall market, and they like to hold low-Beta assets during market declines as their drawdowns are smaller than high-Beta assets and the market as a whole. For this reason, Beta is often synonymous with risk. If you want to know how risky your portfolio is, add up the Betas for each individual asset. If your total Beta is 1.0, your portfolio is just as risky as the S&P 500. And if your total Beta is 4.5, your portfolio is 4.5x riskier (more volatile) than the S&P 500.
Though the average investor has a general understanding of diversification and its benefits, diversifying one’s Beta exposure is all too often overlooked. Just because you hold 15 different assets doesn’t mean your portfolio is properly diversified. The market often transitions from periods of low volatility to high volatility, so a properly diversified portfolio will make sure to balance the overall Beta exposure such that the overall volatility of the portfolio stays relatively constant.
Now, unfortunately, neither individual asset nor overall market volatility is constant, so you may have to adapt and rebalance your portfolio’s Beta exposure just like you would your asset weightings. Just keep in mind that managing your exposure to volatility can be even more important than managing weightings during tumultuous market conditions. Managing Beta is just another way to manage risk, thus it should absolutely be a consideration when constructing any portfolio.
Now that I’ve dug into Alpha and Beta, let’s get into the more option-specific greeks starting with Delta.
Delta
Delta refers to the total amount an option’s price is expected to move for every $1 change in the underlying asset. In simpler terms, Delta just tells you the sensitivity of your option’s value to price moving up or down. If an option’s Delta is high, its sensitivity to price moves in the underlying asset will also be high, and if its Delta is low, its sensitivity to price moves in the underlying will be low.
Delta is usually referenced on a scale from +1.00 to -1.00 with 0 being neutral to price moves, +1.00 being a 1:1 increase in value per dollar increase of the asset, and -1.00 being a 1:1 increase in value per dollar decrease of the asset.
For example, if you have a call with a Delta of +.60, the value of your option would increase by $0.60 for every $1 increase in the underlying asset. If your call option was worth $5.00, a $1 increase in the underlying would translate to a new value of $5.60. And because every option contract represents 100 shares, a $1 increase in the underlying asset would mean a $60 increase in the call’s actual value.
Another use of Delta is it tells traders their directional risk, and thus what their hedging ratio needs to be to become Delta neutral (market neutral). This is very important to market makers who prefer not to have a directional bias, as their goal is to make money by capturing spreads between the bid and the ask as a liquidity provider, not through price swings.
If you were long one call with a +0.10 Delta and long another call with a +0.30 Delta, your total book's Delta would be +0.40. If you then bought a -0.40 Delta put, the position would become Delta-neutral. In other words, you would be fully Delta hedged and unaffected by market moves one way or the other.
Though Delta is mostly referenced in options, it technically applies to stocks as well. Any long position has a Delta of +1.00 and any short position has a Delta of -1.00. This can be a useful heuristic to keep in mind when assessing your portfolio’s directional bias. The beta of each asset will also be a huge factor in the magnitude of any directional susceptibility of your portfolio, but your portfolio’s Delta will still be quite instructive in terms of its long/short bias.
Most retail investors have a tendency to be almost exclusively long equities, so they are far from market neutral. And that isn’t necessarily a problem, as equities tend to appreciate in value most of the time, especially over the long term, but the less Delta-hedged you are, the more your portfolio will live and die with the secular bullish or bearish trend of the market.
Gamma
The next greek is Gamma. Gamma is a bit different than the other greeks because it is a derivative of Delta rather than an entirely unique measurement. Gamma measures the rate of change in an option’s Delta, so it’s used to help forecast what the future Delta might be. More specifically, Gamma estimates the change in an option’s Delta with a $1 change in the price of the underlying asset. If an option’s Gamma is higher, its value (price) will be more volatile.
Gamma is also an important measure of convexity, which refers to the curvature of an asset’s price move. If you imagine a straight line moving diagonally on a graph that represents price or returns, convex price action or returns would have the ends of that diagonal line curving up or down like a half-circle. The reason for that curvature is the rate of change for an option’s Delta is not constant and can increase or decrease as price increases or decreases.
If the Delta of an option was constant, its value would move in a relatively straight diagonal line because it would increase by the same amount for every $1 increase in the underlying, but that is rarely, if ever, the case. Option value sensitivity to Delta will widen or narrow with price moves in the underlying, meaning its value, if depicted as a diagonal line, would curve up or down on either end as the Delta’s rate of change (Gamma) accelerates or decelerates with those price changes.
So, because an option’s Delta is only valid for a short period of time, Gamma and convexity will give traders a better idea of how an asset’s value will change in the future. Plotting option values with a constant Delta (as a diagonal line) is easier, but including Gamma in your calculation will be a more accurate representation of the asset’s potential future value.
A helpful analogy is Gamma is to Delta what acceleration is to speed. Delta will tell you the magnitude of an option’s value increase or decrease for every $1 change in the underlying (the speed of a moving car), but it won’t tell you how that magnitude itself changes for every $1 change in the underlying (how fast that car is accelerating). This makes Gamma extremely relevant in predicting option price swings.
In terms of Gamma’s relation to the price of the underlying asset, as an option gets deeper in-the-money (ITM) and Delta approaches one, Gamma will approach zero (decrease). Gamma also approaches zero the deeper an option gets out-of-the-money (OTM) and is at its highest when the underlying is at-the-money (ATM) because price swings ATM have much stronger implications for that option’s intrinsic value.
The last thing I’ll mention about Gamma is what’s known as a Gamma squeeze, which is similar to a short squeeze insofar far as it can put strong upward pressure on price, but it has to do with market makers hedging their risk, not traders covering a borrowed position.
To explain this, let me paint the following picture: An OTM call option will usually gain in value when the underlying asset increases in price, but as that call gets closer to being ATM, it will gain in value at a faster rate. As alluded to, this is because price moves close to an option’s strike price have a more significant impact on that option’s intrinsic value.
If the price of the underlying was repeatedly going above and below the option’s strike price leading into expiration, there’s a good chance that option expires ITM, but there is also a good chance it expires OTM. As a result of those two very real possibilities, the impact tiny price moves have on near- or ATM option values is much greater than the impact moves of the same size have on far OTM options.
So if a market maker sells far OTM call options, the value of those options (the money the market maker is short) increases, which forces them to buy more of the underlying asset as a hedge to stay market neutral. The problem with this approach is when the market makers buy more of the underlying asset to hedge themselves, the value of the option they’re short increases even more, and because the Gamma increases as those calls get closer to being ITM, the option’s value will continue to increase at a faster rate, meaning market makers will have to hedge incrementally more as the underlying moves higher, which can lead to massive spikes in price.
Consider a market maker that sells a bunch of call options on a stock like AMC. When they sell those calls, they are short AMC because they owe the value of those calls, which gain in value as AMC’s price moves close to or deeper ITM because those calls have a higher chance of expiring with intrinsic value. And when price gets closer to being ITM, the Gamma (or the volatility of that option’s Delta) increases, which translates to larger increases in the option’s value. So as the value of those AMC call options the market maker sold increases, they will have to purchase more shares of AMC to balance out all their short AMC exposure, which often leads to the feedback loop of hedging that drives further hedging and rapidly increasing price.
With that exciting concept out of the way, let’s transition to the next greek, Theta.
Theta
Theta is a measure of time decay or an option’s sensitivity to time. In other words, Theta measures the dollar amount an option will lose every day leading up to its expiration. All options that expire OTM expire worthless because of Theta, which eats away at an option’s value every day.
If you have a long-dated option, the effect of Theta will be minimal at first, but it will still decrease your option’s value each day until it eventually reaches expiration. When it comes to a short-dated option, however, Theta will aggressively undermine its value each day, which can easily offset any gains from the underlying moving in your favor. And just to be clear, long-dated options eventually become short-dated options, so Theta will become more and more of a factor for any option as it gets closer to expiration regardless of how mild that Theta decay started. To piggyback off of one of the earlier analogies, it could be helpful to imagine Theta as a car going down a hill and progressively gaining more and more speed. The car might start off slow, but by the time it reaches the bottom of the hill (expiration), the car has never stopped accelerating, so it will be at its highest speed (rate of value decay) at the bottom of that hill.
To calculate Theta’s effect on an option’s value, all you have to do is subtract it from the price of the option. For example, if the value of an option was $2.28 and its Theta was -.02, that option would be $2.26 the next day (all else being equal), $2.24 the day after that, and so on. However, as previously mentioned, Theta isn’t constant. As an option draws closer to its expiration, the rate of Theta will increase, meaning the value of an option will decrease at a faster and faster rate as it approaches expiration. Theta decay may start at -.02 per day but could easily reach -0.25 in the last week, so it can quickly become the most relevant greek in an option’s value.
Theta is perhaps the biggest driver of retail options traders losing money and is certainly one of the main reasons trading options can be so challenging because it forces anyone buying a naked call or put to be right about both direction and timing. Even if you are right about the direction the underlying asset is headed, the time it takes to get there could extend beyond your expiration date or the pace of the move might not offset the value being destroyed by Theta decay.
There are a lot of reasons 90% of investors lose money trading options, but Theta is arguably responsible for the plurality of those losses.
Vega
The next greek is Vega. While Vega is frequently equated to volatility, there is technically a difference. Volatility measures the magnitude of price fluctuations for any given asset, but Vega measures the sensitivity of an option to those fluctuations. More specifically, Vega measures an option’s sensitivity to implied volatility.
In most circumstances, volatility refers to realized volatility or historical volatility. But because historical data is, by definition, backward-looking, realized volatility isn’t a reliable tool for projecting future prices. This is why Vega focuses on the unknown or implied volatility for pricing options. How exactly implied volatility is calculated is beyond the scope of this article, but the shorthand answer is a high-level math equation using the market price of the option, the underlying asset price, the strike price, the time of expiration, and the risk-free rate. Using those inputs, we can conclude the implied volatility of an asset that Vega references.
In terms of the actual mechanics of its implementation, Vega measures the change in an option’s price for every one-point change in implied volatility. So, if the implied volatility of an asset went from 20 to 21.50 (a change of 1.50) and the Vega of that option was .10, you would add $0.15 to the value of your option (+1.5 implied volatility x .10 Vega).
And much like Gamma, the impact of Vega and volatility will be different depending on the specific option. I’ll save you one more car analogy, but know that volatility around an option’s strike price, which also affects an option’s Gamma, will have a greater impact than volatility around prices deep in- or OTM, meaning an option’s Vega (sensitivity to volatility) will also depend on how close the underlying price is to the option’s strike price.
I’ve hammered this point in quite a bit, but I’ll mention it one more time just to be safe. Vega is the highest when the underlying price is near the option’s strike price because any volatility around- or ATM has serious implications for that option’s intrinsic value. Another thing to keep in mind about Vega is it declines as an option approaches expiration. The more time there is to expiration, the more uncertainty and room for volatility there is, and the less time there is before expiration, the less time there is for any volatility to significantly affect the option’s value.
Rho
Alright, let’s get to the last greek, Rho. Rho is often left out of the conversation because its impact on price is relatively minimal compared to the other greeks, but it still plays a role in option pricing, so it’s certainly worth understanding.
Rho is a measure of an option’s sensitivity to changes in interest rates, more specifically, changes in the risk-free interest rate. Interest rates don’t usually change much or that often, which is why Rho’s effect on price is minimal, but they do change and can be much more relevant during times of significant changes in monetary policy.
As an example, if an option has a Rho of 0.25, for every one percentage-point increase in interest rates, the value of that option will increase a quarter of a percent. So, if the price of that option was $5 and interest rates went from 2% to 3%, the value of that option would increase to $5.25.
If you are looking at short-dated options, Rho won’t be much of a factor because interest rates likely won’t change before their expiration. Even if you have longer-dated options, interest rates don’t always move much throughout the year unless there is a significant change in the economy and, as a result, monetary policy, so Rho’s influence can be largely negligible if the Fed holds rates where they are or sticks to its general rule of 25bps per meeting. However, if the Fed is changing interest rates aggressively, Rho will influence option prices significantly more.
In terms of how Rho actually materializes in the options market, calls will have a positive Rho, so as interest rates increase, call options also tend to increase in value (all else being equal). Put options, on the other hand, have a negative Rho, so as interest rates increase, put options tend to decrease in value.
The reason for this is when interest rates rise, it affects the required rate of return that investors demand from holding stocks. This, in turn, will affect the prices of options contracts via Rho. Higher rates make it more expensive to hold certain investments as the opportunity cost of holding the underlying asset increases.
All that being said, you can probably get away with ignoring Rho, but at least now you know why it’s the forgotten stepchild.
Conclusion
With all the greeks now out of the way, I hope the options market and even the market as a whole make a little more sense. While most of the greeks are a tad niche insofar as they find most of their relevance specifically in the options market, things like Delta hedging, Gamma squeezes, option expirations, and sensitivity to implied volatility can significantly influence asset prices and market behavior, so they are not so niche that they should be ignored.
Alpha, Beta, and even Delta are fairly simple metrics every investor can and should use to assess their performance and risk, but developing a basic framework for how the other greeks influence the market or a particular portfolio is also important, as it will add a great deal of context to the mysterious market mechanics operating behind the scenes.
At the very least, just aim to remember what each greek is in reference to:
Alpha: Performance relative to the S&P 500.
Beta: Volatility relative to the S&P 500.
Delta: Sensitivity to price moves.
Gamma: Rate of change in Delta.
Theta: Sensitivity to the passage of time.
Vega: Sensitivity to implied volatility.
Rho: Sensitivity to interest rates.