Caveats of Adding and Comparing Greeks: When Net Greeks Lie

Wide Spreads on ITM Options in Illiquid Markets

If you use Greeks when trading options, you might add them together to find the net Greeks of your portfolio. Or you might compare the Greeks of different contracts when deciding which option to trade.

But netting and comparing Greeks can be misleading and inaccurate. Sometimes the error is small and negligible, but sometimes it’s large enough to make you enter trades you didn’t actually intend to take.

This post summarizes when it does and does not make sense to add or compare Greeks. There are many other caveats when using Greeks, but we’ll ignore those nuances and focus only on one thing: making sure we are comparing apples to apples.

✅ Do add and compare Delta and Gamma for the same underlying

Let’s start with the most obvious case. Delta and Gamma tell you how much an option’s price or its Delta changes for a $1 move in the underlying.

If the options share the same underlying, you can safely add and compare these Greeks. Summing the Deltas or Gammas of your positions tells you how much your portfolio’s value or Delta will change for a $1 move in the underlying, and comparing them between contracts can help you choose the exposure you want.

❌ Do not compare Gamma between different underlyings

Gamma measures how much an option’s Delta changes for a $1 move in the underlying. But a $1 move does not mean the same thing for every asset. When the underlying price itself is lower, a $1 move changes its moneyness and Delta more significantly than it does for a higher-priced underlying.

Because of this, options on lower-priced underlyings tend to have higher Gamma values. Unlike Delta, which has a defined range between 0 and 1, Gamma does not have a well-defined upper bound.

A good example is SPX vs XSP. They track the same index, but SPX trades at roughly 10 times the level of XSP. As a result, SPX contracts have about 10× the Gamma of the corresponding XSP contracts.

For this reason, comparing Gamma between contracts on different underlyings can be misleading.

✅ Do net and compare Theta across underlyings

Theta (as well as Rho, but who cares?) is the most flexible Greek when it comes to netting and comparing. Because time passes at the same rate for every option, Theta is naturally comparable across contracts and underlyings. Your net Theta for a given underlying tells you how much those options are expected to gain or lose in value each day from time decay.

You can also add up the Theta of all positions in your portfolio to estimate how your portfolio’s value changes over time. For this reason, Theta is one of the few Greeks that can usually be safely netted and compared across the entire portfolio.

⚠️ Be careful when adding and comparing Vega

Option contracts on the same underlying with the same expiry can have dramatically different IVs because the market usually prices downside protection higher than upside potential. This is known as volatility skew. Let’s assume you have an OTM put with a 40% IV and an OTM call with a 25% IV. While the Vega of each contract correctly tells you how much its price changes for a 1% change in IV, their implied volatilities do not move in lockstep. The put’s IV might drop to 38% while the call’s drops to 24%, so your portfolio’s value changed by roughly 2 × the put’s Vega plus 1 × the call’s Vega. Your net Vega would have been misleading, because you cannot expect the IVs to move by the same amount.

Similarly, different expiries can have very different implied volatilities even for the same strike. Major announcements like earnings often cause expiries before the event to have lower IV than expiries on or after the event. The further you go beyond the event, the less impact it has, so IV generally declines for later expiries. Even on broad market indices and ETFs, jump risk tends to push short-dated IV higher, and macro announcements can also impact implied volatility. This is known as term structure, and like skew, it means the Vega of different contracts is not always comparable.

When thinking about net Vega, you should be more deliberate about what would cause IV to change and how that event would affect the IV of each contract in your position. Only if you can reasonably expect them to move by a similar amount can you use your net Vega as a rough estimate of how your portfolio might change.

Conclusion

Greeks are useful tools for understanding how option prices respond to changes in different factors such as the underlying price, volatility, and time. Traders often add Greeks across positions or compare them between contracts to better understand their exposures.

But this only works when the comparison makes sense. If the contracts differ in ways that change how the Greek behaves, simply adding or comparing the numbers can give a misleading picture of your risk.

Making sure you’re comparing apples to apples helps ensure that the Greeks you rely on actually reflect the exposure you’re trying to measure.