Primer #11: Thoughts On Execution, Greeks, and Weights
Implementation Unit #5
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The moontower.ai Primer is divided into 2 units: Conceptual and Implementation.
To review, the Conceptual Unit which includes:
The Implementation Unit thus far:
Thoughts On Execution, Greeks, and Weights
Vol Scanner & Bid-Ask Volatilities
Once you have an axe (ie ”I want to sell near-dated XLE calls”) the Vol Scanner tool on Tickers will show you which call options are up the most (or down the least) today, allowing you to zero-in on attractive strikes to sell.
Implied volatility displayed on moontower.ai is derived from mid-market data.
For many symbols, it is unlikely that you will be able to transact mid-market. Your brokerage software should allow you to see the vega of the option. If you need to sell the option 3 cents below mid-market and the vega of the option is $.03 you are facing 1 vol point of slippage. If it costs 1/2 cent in brokerage fees to trade that is an additional .16 vols of slippage (.5 cents / 3 cents).
If your trade thesis is nullified by 1.16 vols of slippage, then the trade isn’t viable.
On Transaction Aggression
Professional option traders use algorithmic order types to send “volatility orders”. This pegs the option price they bid or offer to an underlying price. For example, they may offer the 50-strike call at $2 only if the stock price is $47 or lower. Provided they are not “picked” off due to latency issues, this guarantees a minimum IV they are willing to trade at.
[Perhaps the IV is 22% on the 50 call at $2 with the stock at $47. If the stock is lower, then the implied volatility of the $2 offer is mathematically higher than 22%]
Either way, when trading an option, a stock or any security you face an asymmetry whether you “work the order” by trying to get a mid-market price or simply hit the bid or lift the offer.
This stylized example of the expectancy of passive order vs limit orders demonstrates the logic:
Suppose an option is worth $.45 and a market maker is only willing to trade for $.02 of edge. They make a 2-sided quote $.43 -$.47.
-If you hit the bid, you have lost $.02 in expectancy. But you chose the time to hit it, so that is your maximum loss.
-If you dangle a $.45 offer, you will only get lifted when the option is worth $.47 or more. In other words, your minimum loss is $.02 in expectancy. Because you have allowed the counterparty to choose whether or not to fill you, you have invited adverse selection.
This is not a blanket argument for trading aggressively. If there is a lot of random 2-way flow in a name then passively working an order might allow you to get filled at fair value. That is a liquid market that does not need a market- maker urgently.
Consistently poor execution will ruin any strategy regardless of quality of upstream analysis, especially if you trade frequently.
Using Greeks To Summarize Risk At The Stock & Portfolio Levels
A common way to summarize risk in equities is to “beta weight” your portfolio. Beta normalizes sensitivity with respect to SPX so you can meaningfully sum exposures.
Option greeks are also sensitivities. With minor adjustments we can use their properties to:
summarize risk
specifically target exposures that express our bets
Important properties of the most commonly used option greeks
Delta
Deltas can be summed across a name’s term structure. The net delta represents the change in p/l for a $1 change in the name. In other words, if you owned 1,000 deltas of XYZ, you have the same sensitivity to the underlying as owning 1,000 shares of XYZ. Delta can be positive or negative (short position).
This measure doesn’t lend itself to comparison across names because $1 means something different for a $50 stock versus a $100 stock. And even within a name, owning 1,000 deltas of XYZ is a different level of risk if the stock is $50 vs $100.
It is therefore common to measure dollar delta. The computation is the same as gross market value — delta x share price. Dollar delta will be negative for short positions (ie long puts or short calls or short stock)
P/L = dollar delta * % change in stock
Summing deltas across names
By multiplying dollar deltas by a beta you can beta-weight you can sum positions in a portfolio to answer the question “how many dollar of SPX am I long or short?”
Gamma
Gamma is the change in delta for a $1 change in the stock. They can be summed across the term structure to get a net gamma for a symbol. If your net gamma in XYZ is +500 then:
your position gains 500 deltas (or share equivalents) for a $1 up move
your position loses 500 deltas (or share equivalents) for a $1 down move
Your position moves in the same direction as the stock change. You get longer on rallies and shorter on sell-offs.
If your net gamma is -500
your position gains 500 deltas (or share equivalents) for a $1 down move
your position loses 500 deltas (or share equivalents) for a $1 up move
Your position moves in the opposite direction as the stock change. You get shorter on rallies and longer on sell-offs.
Like delta, gamma is an unnormalized measure — we want to convert gamma to dollar gamma. This answers the question “how many dollar exposure to XYZ do I gain/lose on a 1% move?”
Summing gammas across names
If you are interested in an approximate answer to “what is my dollar gamma with respect to a 1% change in SPY” you must:
Convert each name’s dollar gamma into a SPY equivalent dollar gamma
Simply sum the equivalent dollar gammas
See Moontower On Gamma for formula and derivations
Theta
Theta, or the option decay, can be summed across a name’s term structure as well as across names. It’s the most straightforward.
Vega
Vega is the sensitivity of the position to changes in volatility. Unlike delta and gamma which are sensitive to changes the spot price, vega is sensitive to changes in IV across the curve and technically across every strike.
It’s typical to:
sum vegas by maturity (across strikes)
sum those grouped by vegas by symbol (across the term structure)
multiply the change in volatility for a reference maturity (ie the 90d at-the-money volatility) by the total vega per asset to estimate volatility p/l
It’s a dirty approximation because it collapses the reality. Volatility across maturities and strikes within maturities doesn't actually change uniformly.
Summing Vega Across Names
Practices vary widely concerning summing vega across names. Context matters. You are not running a large volatility book so feel free to ignore this.
While it’s mathematically coherent to sum vegas across maturities, we have seen that unscaled vegas can be misleading because IV does not fluctuate uniformly across the term structure.
Summing vega across a portfolio of names is also mathematically allowable but is misleading because IVs do not fluctuate evenly across names just as they don’t fluctuate evenly across term structures.
A rigorous treatment would first aggregate a scaled vega per name (say, normalized to 90d), then rescale that number based on how volatile the IV is compared to a benchmark volatility market like SPY.
Greeks and Weighting Trades
Greeks are not just handy for measuring risks. Greeks naturally extend themselves to trade weighting.
Once you have made any necessary normalizations for comparison you easily check if your position is neutral to:
delta (ie market direction)
gamma/theta
vega
Of course, your trading decision may be motivated to seek directional, gamma/theta, or vega risk. You will size the trade according to your desired exposure. As volatilities and stock prices move around, your greeks will drift away from your target exposures. Based on your risk tolerance and whether your thesis remains intact you might cut or add to positions.
Appreciating how to normalize the greeks allows you to fine-tune your trade expression. For example, we have seen that buying a calendar spread means you will be long raw vega since the longer-dated option has more volatility sensitivity than a short-dated option. But your scaled vega might be negative with respect to 90d IV.
By constructing a scaled vega neutral trade instead of a raw vega neutral trade (which will almost certainly be short-scaled vega!) you make a purer bet on the slope of the term structure. If your scaled vega exposure is large then you have an implicit bet on the overall level of volatility not just the slope. (We say you are exposed to a parallel shift)
💡 Leg weightings isolate expressions
This concept will be familiar to futures traders who buy and sell calendar spreads in various “beta” ratios to isolate bets on:
Level (1-1 spread)
Slope (ratio spread)
Curvature (butterfly spread or "spread of spreads")