I just want to say that you people are sick. This is the most viral tweet I can remember sending in recent times.

Because I happened to be helping the 3rd grader with improper fractions recently I saw 1.25 as 5/4 which is immediately recognizable as a square root of 25/16.

Sprinkle in some trader math that condemns you to see the sqrt(251) as 16 and you get an even more compact version:

Step by step:

The real masochism in that thread happens further below…

People will message me with charts like this to ask my opinion of a pairs trade:

This is not a pair anyone sent me but the form is the same.

I guess-and-tested a few pairs whose daily return correlation is at least as high as some pairs I’ve been sent. In this case, I picked 2 homebuilders whose correlation over the last 500 calendar days turned out to be .90

[I used the hedge ratio tool from last Thursday to find this pair]

I respond to these messages with a few things that come to mind but I’ll flesh the responses out more in this post. Think of it as a map of data and interpretation pitfalls. There are bits in here for both novices and pros that’ll stimulate a “I never thought of that before”.

The charts above aren’t worthless but they’re very faint beeps on a metal detector during a beach stroll.

Let’s see why…

 

Thoughts as they come to me when I look at the chart…

👁️The first thing my eyeballs say to my brain when looking at a vol spread chart is “why not a ratio chart?”. Over the period, the mean vol spread of LEN to DHI is +.83 and the vol level is about 40%

If vols doubled and the vol spread had the same average I’d be surprised, so a vol ratio strips out the level-dependant assumption that is silently suggested in a spread chart.

The nature of the relationship is of practical importance because it affects how you weight a pair. Any weighting scheme has trade-offs and matching the trade-offs to the bet you are expressing is, well, advisable.

I won’t rehash weighting here but both of these links go into it:

• Weighting An Options Pair Trade (moontower)
• To dollar-weight or share-weight a dislocation in a highly correlated pair? (moontower notes from Financial Hacking)

In this case, the spread and ratio seem good enough proxies for one another. A scatterplot rather than a time series would provide a more granular look but given the 30d maturity and no earnings extractions the extra granularity would probably cause us to overemphasize extremes that would probably be smoothed by arduous surface cleaning.

🔁Possible spot/vol artifacts

If LEN price drops relative to DHI I expect its vol will expand more than DHI. To the extent that a widening vol spread simply reflects recent price action we may deem the vol aberration “more justified” or “not an opportunity”.

Whether a widening vol spread being explained by a sell-off is meaningful or not is unavoidably context-dependent. If LEN falls relatively after earnings, I’d expect its vol spread to narrow from a wider reading that we likely sampled before earnings. But this is just an example of “news flash: lazy low-resolution charts are too underpowered for a trading thesis”.

That said, I do believe the idea of spot/vol mattering in terms of how much weight we’d give an aberration even qualitatively is at least relevant enough to pivot data in a few ways to understand the shape (or lack thereof) of a relationship.

Let’s play “charts plus thoughts”:

• We see a hint of vol/spot effects in the downward-sloping trendline. As LEN price increases relative to DHI its vol premium falls. But the r-square is trash. Weak relationship.
• This isn’t saying that spot-vol relationship in the stocks vs their vols is weak just that the vol ratio to price ratio relationship is weak. Remember these stocks’ returns are .90 corr. When LEN goes down, it’s vol expands but DHI usually goes down when LEN goes down (and its vol will likely be expanding as well in that case).
• My background is in commodities where the spot/vol correlations in general are higher than they are in single stocks (but not as strong as equity indices which I’ll address a bit more below). Here’s just LEN IV vs spot

  

  The grey trend line shows a weak relationship between spot and vol in terms of slope and a correlation that would be around .55-.60…but then I drew those red dashed lines because the story is really:

  LEN is been like a 30% vol stock give or take 5 clicks in a price range of about $165 give or take 30% (ie an annual st dev). It sold off recently with the rest of the world and vol went up to 40% or about 1/3, as the stock stepped from one economic platform down to another.

  As a matter of generalizable perspective:

  All of this feels interesting from the altitude of an investor’s vantage point, but beneath the level of signal from a trading pov. The distinction is useful for any type of money decision — am I getting trader or investor resolution? Is the option trade I’m doing matched to a trader’s dashboard or an investor’s?

   

The vol ratio vs price ratio chart showed a weak relationship. Not unexpected. LEN vols and price ratios are correlated. So instead let’s scatterplot the 1-month change in vol spread (our first chart said it’s a reasonable stand-in for ratio) vs the 1-month relative performance of LEN vs DHI directly. This is not about levels but about motion.

Honey badger, I mean the vol spread, don’t care. For a pair of 30% IV names that are 90 corr, 5%-10% relative performance is significant (can you use the risk-remaining lesson in last Thursday’s post to show that? The learning sticks if you apply it.)

And yet the scatter doesn’t validate the IV spread caring that much.

Let’s do a final chart before chatting.

We saw above that there’s a faint vol ratio to spot ratio relationship in the pair. As LEN goes up relative to DHI its vol ratio declines a touch but there’s a useless amount of noise from our distance.

Straddles are another way to look at vols and spot prices in a combined way. The approximation for a straddle price depends on vol, spot price, and DTE. DTE is constant. If spot and vol were negatively correlated with a -1 beta you’d expect straddle prices to stay constant over many price levels. If vol has a less than a -1 beta to spot then as price increases straddles increase and vice versa. Over large moves I always expect this to be the case.

For smaller moves, the constant straddle might hold as it often does in something like crude oil, a market where traders have a history of speaking in terms of straddles (or “breakevens” in case you ever wondered about Ari’s twitter name) instead of vol. In that market, discussing vol without price level is like owning one shoe.

For single stocks, this effect is going to be less pronounced. I expect straddle prices to rise with price as the spot effect in the straddle formula overwhelms the declining vol. Voila…the LEN – DHI straddle spread vs price ratio. Upward sloping af.

[Additional thought on this chart:

It likes like there are 2 channels which lovingly accommodate the trendline’s horny advance. I didn’t bother, but when you see things like that, it’s usually a clue to color code your dots by date. I don’t mean to abuse the metaphor but there are probably a couple periods of note here.]

🚧Detour on spot-vol correlation in single stocks

The spot-vol correlation in single stocks will vary by sector. The correlation looks fairly small in these homebuilders. We saw that directly in the spot/vol charts, the change in vol ratio vs change in spot ratio, the change in the vol spread vs change in relative performance, and in the strong positive relationship between straddle spread and price ratio suggesting straddles don’t stay constant but are driven by price more than vol.

One reason I could imagine homebuilders in particular having a muted spot vol relationship is they benefit demand side from lower mortgage rates. I’ll put my finger in the air and say they act like a levered 60/40 portfolio. They are diversified if stocks and bonds are anti-correlated.

[In fact, one way to potentially think of their vols is possibly from the quanto lens that one might think of pricing EWJ vol by considering the individual vols of Nikkei vs Yen. The options on EWJ relative to the legs imply a correlation between Japanese equities and FX — which is substantial in an export-led economy.]

Even though spot/vol corrs vary by sector, overall the skew and spot/vol correlations will be smaller than equity indices. Consider 2 reasons that derive from logic not vol surface data which only reflect the logic:

✔️Stock returns are positively skewed

Most companies go bankrupt. A few drive the total return of the indices. Black-scholes’ positive skew lognormal distribution is not a horrible description of companies…pump up the vol and it says, the median return is negative but there’s a long right tail. See Is There Actually An Equity Premium Puzzle?

✔️Average single stock skew must be less than index skew

An equity index is a portfolio of stocks. The vol of a portfolio depends on the vol is positively related to the vol of its constituents and their cross-correlation. If the correlation falls, all else equal, the portfolio vol falls.

Index downside skew must account for both pathways of vols increasing:

1. The average stock in the basket’s vol increasing
2. The cross-correlation of the stocks in the basket increasing

Most stocks share a systemic, undiversifiable risk — the possibility of the economy as a whole slowing down. This shared risk gets priced in index skew as an extra kicker over single stock skew because as correlation goes up, index vol increases faster than the increase in single stock vols.

Recast as a trading statement:

If you could sell all the single stock skew at the same level you could buy the index skew you’d be getting “correlation going to 1” for free.

 

What the vol spread chart hides

In traditional investing, we look at charts that prices travelling from the lower left to the upper right. We can’t feel the drawdowns along the green path it draws. Our eyes focus on the endpoints. Looks easy. All the suffering that you are getting paid for is eradicated, nothing but an expectation of profit for showing up remains.

This turns out to be (has been?) a salutory illusion. The chart makes it easy to buy while hiding the source of edge — a time horizon to not care about the dips. The time series of a mean-reverting vol spread does the same thing.

Let’s break down its lies.

🔮Snooping ahead

The mean and standard deviation are known for the sample period only after the sample period is over. If we transport ourselves to a place on the graph where it’s “obvious” to sell we are doing so with the benefit of hindsight. At the time of the trade, we didn’t know we were “there” on the finished chart. This insidious self-deception happens easily when we look at charts, don’t bring it with you when you move towards actually trading.

🧩Implied vol is only part of the puzzle.

The actual p/l of an option trade done to capture a vol discrepancy is a combination of:

1. vega p/l or change in implied
2. your realized p/l or what I call the “tug of war between your gamma and theta”. For a 1-month option the tug-of-war is going to have a large influence on your results but the chart’s thesis was IV driven.

    

If the market were strong-form efficient all the money you’d make on mean reversion of the IV spread would be lost on your realized vol p/l if the IV spreads perfectly predicted subsequent stock movements! I’m not saying that they do, I am saying that any focus purely on the IV spread only studying half the p/l drivers.

Discrepancies result from flow. Updating fair value based on flow is an inexact science, but to assume that the full amount of discrepancy is edge is the same as saying the flow has zero information.

🍦Vanillas are the real exotics

Vanilla options are messy. How?

1. This time series is a constant maturity vol. To replicate it, you’d need to rebalance the options of the 2 expires bracketing 1-month on each trading day.
2. As the spot prices of the pair move around, your moneyness and greeks change knocking your initial weighting off balance. Contrast this with a variance swap where holding time constant, your gamma is constant over the range of strike prices. The pricing is exotic but the experience is familiar because it ties mechanically back to a familiar calculation — the standard deviation of close-to-close returns. Vanilla pricing is familiar but the experience is exotic.
3. You were trying to capture a vol discrepancy which means you probably want to delta-hedge to isolate the edge.

    

🩺Clinical vs practical

Maintaining a desired exposure in vanilla options requires rebalancing both the options and deltas. To do this faithfully every day as a taker would cost more than any perceived edge is paying.

This means in practice you must be willing to warehouse and tolerate noise. This means you must trade smaller for a given amount of edge if you want to maintain the same risk/reward of the clinically hedged expression.

In the real world, this type of trading is the domain of entities that can sell on the offer and buy on the bid, allowing them to leg the hard leg for edge (the liquidity of which will also be the limiting reagent on the trade).

If you are not a market-maker, trade the leg you have more conviction in or use the history to enter/exit the leg that fits into your overall portfolio more synergistically.

 

Last word

These charts should be thought of as indicators as opposed to backtests. The allure of these charts is they hint “backtest”. By peeling back their insidious, white lies, we can approach them with the right humility —they are clues. The opening statement in a trial, not the final verdict.

 

Stay groovy

☮️

I fired up Corey Hoffstein’s goated Flirting With Models podcast to hear Scott Phillips discuss “ugly” edges in crypto. This episode came highly recommended in my corner of twitter. It does not disappoint.

But I want to zoom in on one part. Scott says:

If you did what I do perfectly, you’d be up well over Sharpe two, and probably with size. But the way that I do it, our four-year Sharpe is 1.7 with retail-level costs. So cross-sectional momentum is a little bit better than that, but you don’t have the really nice positive skew of trend. And cross-sectional carry is about a Sharpe 1.7 as well, and slightly orthogonal. So you blend the three of them together, and then you’re at Sharpe two easily — and without even good execution…The math holds. Returns scale with the square root of independent bets.

Scott misspeaks here (easy to do in a conversation) but what Scott means is volatility scales with the square root of independent bets (returns scale linearly). This concept underpins one of my most important posts — Understanding Edge. It is the basis of all trading businesses without exception. It’s Day 1 learning at a prop shop. Munger has that “Take a simple idea and take it seriously” advice…This is THE idea Jeff Yass took seriously.

I’m repetitive on log and compounding math for 2 reasons that extend beyond the shock factor of the “lilypads in a pond” puzzle:

a) Investing is a serially repeated game so compound returns are our primary concern

b) Option theory sits atop logreturn math which is just continuous compounding (in fact e, the Euler constant of 2.718, is your growth of $1 if you continuously compound at 100% rate for 1 unit of time. See Using Log Returns And Volatility To Normalize Strike Distances)

We’ve confronted this math many times from different angles:

• The Volatility Drain
• Path: How Compounding Alters Return Distributions
• Examples Of Comparing Interest Rates With Different Compounding Intervals
• Well What Did You “Expect”?
• Geometric vs Arithmetic Mean In The Wild
• Understanding Log Returns
• I Felt Bad For Picking My 3rd Grader Off
• Getting Comfortable With Log Charts
• you can ONLY eat risk-adjusted returns
• Growth rate = 70% * (doublings/years)

Compounding is a multiplicative process that describes how returns scale across time. “Volatility drain” reminds us that volatility’s interaction with growth is embedded in that process.

We already understand how compounding scales across time as a function of volatility.

But volatility itself has scaling properties.

That’s what Scott means when he says (or meant to say) it grows by the square root of independent bets. Regular readers have seen me scale a daily return to an annual return by √251 or ~16 many times. But I don’t always remember to say that this assumes no correlation between daily vols (mapping to the “independent bets” language).

In multiple posts, we have seen that volatility is understated in the presence of autocorrelation:

• Thinking in N not T
• Volatility Depends On The Resolution
• the option market’s point spread (part 2)

Autocorrelation affects how we scale vol through time per asset.

This is only half the volatility scaling story. It’s one vector.

The second vector is how we scale vol across our portfolio.

This depends not on autocorrelation, but on pair-wise correlation.

Independent bets are simply bets that have no (ie zero) correlation with one another.

It is why you can blend several strategies and end up with a composite Sharpe greater than any of the components.

Let’s look closer.

Let’s consider an equal-weighted portfolio of ETFs:

• IBIT (BTC)
• GLD (gold)
• HYG (high yield credit)
• IEF (10-year notes)
• QQQ (Nasdaq stocks)

Method:

1. I used the hedge ratio tool to fetch the correlation of daily returns for each of the 10 possible pairs (5 choose 2) for the past 16 months.
2. I chose a reasonable vol for each name and then backed out an expected return by assuming the Sharpe Ratio of each asset is .40. I’m ignoring RFR in SR — I’m just using expected return / vol.
3. I convert the correlation table into a covariance table to do the matrix multiplication for computing portfolio vol. I explain the math in writing, video, and in a spreadsheet I’ve shared before:
   1. ✍🏽Computing portfolio vol (moontower)
   2. 🔻 Portfolio Vol Spreadsheet (download)
   3. 🎥Portfolio Vol Explainer (Moontower YouTube)

 

Here’s my work for the equal-weighted portfolio:

What to take note of:

• If we compute the portfolio vol in the “stressed” condition where all the pair-wise correlations are 1.0, then the portfolio vol is equal to the weighted average vol of the components. In this case, the portfolio vol is 20%. There’s no diversification benefit to the portfolio vol or SR!
• When we use the actual correlations the portfolio vol drops to 12.5%. Since the expected return is unchanged the SR improves from .4 to .64. Massive diversification benefit.
• The ratio of the portfolio variance to average weighted stock variance is the average weighted pair-wise correlation. The average weighted stock variance is the same as the portfolio variance if all the correlations are 1.0
  • For the option fans: this math is exactly how implied correlation is backed out of the index option market. The ratio of index variance to weighted average stock in the basket’s variance is the implied correlation! The cheaper index vols are relative to stock vols, the more implied diversification benefit there is in the index. This concept sits at the heart of dispersion trading.

A portfolio that equal weights IBIT and IEF sounds a bit comical. Let’s re-do the analysis with an inverse vol-weighted portfolio:

Now IEF has 10x the weight IBIT does. If you multiply each component’s weight by its vol you’ll notice they each have equal risk contribution.

The normal portfolio has a Sharpe of .68 but if all corrs go to 1.0 the SR drops to .40 and the portfolio vol goes from 6% to 10%.

Even if the math isn’t interesting, the principle should be seared into your risk brain. Adding zero or negative correlation assets to a portfolio can improve its risk/reward even if the asset’s individual SR is inferior to the average component. An asset’s stand-alone properties are not as important as how it contributes to the risk/reward of your portfolio just as how an asset’s arithmetic return does not mean much if don’t consider its vol. After all, we care about compounded returns.

These dual concepts, timer-series volatility (influenced by auto-correlation) and cross-sectional volatility (influenced by pair-wise correlation of components) give a fuller picture of how returns AND volatility accumulate through time. You care how both the numerator (return) and denominator (risk) scale.

Application to allocators

Professional allocators recognize that much of the low-hanging fruit of long-term results is sound portfolio construction. Basic hygiene in how you stack investments by understanding their properties in various states of the world is something you have more control over because volatility and correlation are more stable than expected return predictions. Simple optimizers are incredibly sensitive to expected returns — which is a bit self-defeating when you realize this is the metric we know the least about.

To add a bit of practical color. I have a good friend — a physics academic turned investor — who was CIO for the family office of one of the partners of [insert the best quant firm you’ve heard of and it’s probably the one]. He admit something he found embarrassing — a shockingly small number of ideas underpinned the family office’s approach and none of them is a secret. The scaling property of portfolios is one of them. If they sourced 16 investments that generated a high-quality portfolio, in order to double the shape they needed 4x as many additions to that portfolio of similar quality (which was already high) to double the portfolio Sharpe. Pretty much impossible when all the investments are LP stakes in quant funds (due diligence alone is too labor intensive, never mind finding that many great managers).

[I’ll get around to toying with this tool a bit more to tinker my way to seeing how the scaling works — for example going from a 3 stock to 12 stock portfolio where I add names with equal SR but different correlations. I’m down to the wire on writing this post as it is.]

Application to traders

The last part of this video shows how the interaction of return and volatility can inform how you think about sizing risk.

If you prefer text, the heart of the material is captured here:

Understanding Daily vs. Annual Sharpe — and Sizing Risk with Intent

Let’s start with something simple but important.

🗓 Daily SPX Returns

The S&P 500 has a daily mean drift of about 3 basis points, with a standard deviation of about 100 basis points in normal conditions. That gives you a:

Daily Sharpe ≈ 0.03

(This ignores the risk-free rate, which is roughly 1.5 bps/day.)

---

📆 Annual SPX Returns

Now zoom out.

The S&P’s annual return is roughly 8%, with an annualized volatility of 16%. That gives:

Annual Sharpe = 8 / 16 = 0.50

Here’s the interesting part:

Annual Sharpe (~0.50) ≈ 16× Daily Sharpe (0.03)

Why? Because volatility annualizes by the square root of time:

√251 ≈ 15.8, or roughly 16

---

🎯 Sharpe Ratio Benchmarks

Let’s anchor a few examples to make this more intuitive:

• SPX benchmark: 3 bps return / 100 bps vol → Sharpe 0.03
• Sharpe 16 strategy: 1% return/day, 1% vol/day → Sharpe 1.0 daily
• Sharpe 2 strategy (annual) =
  → Daily Sharpe ≈ 2 / 16 = 0.125

So:

A Sharpe 2 strategy means your daily standard deviation is ~8× your expected return.

That 8-to-1 ratio is a helpful sanity check.

---

💰 Backing Into Risk Limits

Let’s say you want to size your book around a Sharpe 2 strategy. Here’s one framing:

• Daily P&L target: $1,000
• Daily volatility: $8,000
  → Daily Sharpe = 0.125
  → Annual Sharpe = 2.0

Now annualize:

• Yearly expectancy: $1,000 × 251 ≈ $251,000
• Annual volatility: $8,000 × √251 ≈ $126,744

What does this imply for annual ranges?

• A +1 SD year: $124,256 – $377,743
• A +2 SD year: ~0 – $500k
• You’re brushing against zero at 2 SDs

---

📐 How to Use This for Book Sizing

You don’t just ask how much do I expect to make?

You ask:

• What kind of daily swings are consistent with my goals and risk tolerance?
• Can I size positions and set Greek tolerances so that my volatility lands near ~8× my expectancy (for a Sharpe 2 strategy)?
• Do I have enough emotional and capital runway to survive the downside scenarios?

Via prompting ChatGPT:

Helper Notes

I replaced my IBIT shares into long calls when BTC vol got crushed this week while selling my VIX futures which held up quite well on the equity rally, a possibility I suggested when I explained that the elevated but also flat term structure of VIX suggested vol was here to stay in 2025. From vol speed round:

As I was looking at IBIT I thought I’d share a habit I picked up from distant past of ETF arbitrage — estimating the prem/discount baked into the ETF price I’m about to trade:

1. Go to the IShares web page to grab 3 values (highlighted)

2. Enter them in my spreadsheet to compute the ratio of NAV to BTC price. The cells with the box around them are via the previous close values. I then apply the fair ratio to the live BTC price compute IBIT’s live premium or discount.

Net of last week’s April expiry the flurry of trading from the last few weeks has left me net long delta. That’s not accidental. I had plenty of room to be a buyer on balance in the turmoil since cutting lots of portfolio delta heading into the election.

[If interested…I rebalanced much of stock delta into t-bills bills then re-deployed into bonds, TIPs and silver in late January.]

Coming out of the April expiry last week, my position gained ES futures, VIX futures, IBIT, with my only outright option position being some May AAPL put spreads.

Back in November I published this video which show how I look at the risk of our household portfolio.

But in the flurry of trading while I’m mentally separating what I’m doing for edge and my total portfolio, I do have some delta bias under the hood to effectively dollar cost average since I de-risked in October.

But I want to keep close tabs on how much I’m adding which means summing positions in a vol or even better beta-aware fashion. NVDA is far more volatile than SPY so just as traders combine all their deltas into SPX or some other benchmark terms I like to also normalize back to SPY equivalent risk.

This is a doorway into hedge ratios and beta-weighting. Beta-weighting is not just vol weighting but includes correlation.

I’ve written extensively about how to do this in:

🔗From CAPM To Hedging (17 min read)

That post steps through derivations and the basics of correlation math but in my personal portfolio spreadsheet I needed to make a little widget where I could just put 2 symbols and get a hedge ratio.

We actually have a calculator in the app but you need to supply the inputs.

However I realized with Excel’s built-in =stockhistory I could not only get the inputs, but easily plot time series and scatterplots to understand the shape of the “idio” risk and variation in the beta over time.

🚀We are going to add this functionality to the moontower.ai app. We already have the data, just need to extend the UI.

In the recent month, I wanted to understand how many SPX delta equivalent I had in VIX futures. I used VXX as a proxy put it into Excel and voila got some idea of how much “less” long SPX I am with the VIX futures incorporated.

So….

I made a video walking through the Excel tool. It’s some of the most practical traders-use-this-everyday-type knowledge. We skip the derivations and jump to how do I actually use this data to size hedge ratios or estimate my book’s beta.

I hope you find it as useful as I think it is. (If not, I’ve got more work to do on the explanation side so let me know!)

Paid subs get the spreadsheet. If you have the stockhistory function in Excel this will work seamlessly for you. It’s addicting to toggle thru pairs so fair warning!

The spreadsheet link below has 2 bonus items not shown in the video:

1) A widget for spitting out the hedge ratio not just running data

2) A little position radar template on a separate tab to keep your gameplan organized

Before getting to the sheet, tomorrow night is Ricki Heicklen’s Trade Gala party in SF. I mean yesterday we learned that Jane Street made $20B in 2024 which doubled what they made in 2023 which shattered their record from the prior year. I think they are the most profitable firm in the world per employee (they have about 3k employees).

I think it was Morgan Housel who once wrote that very few orgs in the world could say their edge is just flat out “we’re smarter than you”. There’s usually some other sauce. He gave the example of RenTec. Jane Street is another that can boast the same. This is a cool opportunity to see how that crowd thinks.

This is a special moontower invite that Ricki sent me. She’s repeatedly acknowledged that anyone she meets that comes out of this community is a breath of fresh air which she poses as a compliment. I’m not one to insult a compliment but it’s a testament to y’all. I don’t control how you act.

Anyway the party starts at 8pm and runs thru 6am…well I’ll let you click on this yourself. This is actually a custom invite for Moontower readers:

Trade Gala Party

A quick description..Trade Gala is a limited-access costume party with markets, a puzzlehunt, and demo-ing a new trading game.

If you want to attend the trading BootCamp the rest of the weekend sign up below. It’s truly ridiculous. If you are a novice it will open your mind to what trading looks like thru the eyes of sharps. It is hard to come by this in the level of detail you’ll see here.

If you are a pro, well, you might want to know you might notice some things that you are up against. There’s a lot to learn for everyone.

trading.camp

It’s view only but you can save a copy for yourself and do what you like from there.

1. When you click the link it the link will open in your browser.
2. Download a Copy. (see pic)

A reminder in the spirit of being attuned to seemingly far-fetched risks:

If short selling were restricted in any way, the value of puts relative to calls on the same strike increases in a put-call parity framework.

Another way to say this is being long stock is more valuable since only long sellers can sell. If puts increase relative to calls on the same strike, as they do when borrow costs increase, that is like a synthetic future on the stock trading at a discount to the stock price.

Similarly, being short futures vs being long index or SPY expresses the same bet. If futures start trading at a sustained discount to the cash index value it could also reflect an implied probability of short-selling restrictions being imposed.

If futures are trading at full carry and you think such a ban is possible it’s an asymmetric bet to put on conversions (ie short futures, long stock or for options short combos long stock).

Broadly speaking, the derivatives market becomes the underlying market. When the underlying market becomes encumbered do to technical frictions, derivatives are no longer just “derivatives”. The arbitrage mechanism is severed. The derivatives market becomes the home for price discovery.

I’ve seen this happen throughout my career. Just a few examples in addition to hard or impossible to borrow/short situations:

1. HYG becoming a liquid referendum on illiquid high-yield bond market
2. Cotton option synthetics continuing to trade even when the underlying futures are locked limit up (my trading claim to fame is selling the all-time nominal high in cotton in late 2011…it was an option synthetic around $2.25)
3. When a stock is halted, the premium or discount to any ETFs holding that stock computed using the halted stock’s “last” price before the halt implies the price the stock will open when it resumes trading. These situations were common during the dot-com heydey when stocks would be halted intra-day on pending news announcements.

🔗Related

📽️Teaching Options Basics With Live Data (Moontower YouTube)

📔Synthetics: Alternate Realities (Market Jiujitisu)

In Sunday’s surfing volatility, I recapped my IBIT (the spot BTC ETF) options trading for the 10 days preceding the March 14th expiry.

That post steps through the conceptual steps and flow of trading “surfing” volatility. I mentioned that trade went about as well as it could have since the stock pinned my short. But that’s reporting results. Evaluating the trade requires decomposing the “vol p/l” because that was the intent of the trade.

Just to recap, Sunday I wrote:

On March 4th, I initially paid 61 vol for the April 38 puts and sold them at 63 at the Mar14 expiry, while the Mar14 48 puts I had sold at 64.5 vol saw their IV get crushed as they pinned near my short strike. The stock was $48.50 when I put the trades on and was trading $48.14 at expiry.

The ratio trade collected $0.67 [I wrote .65 in the last email but as I did the autopsy it was actually $.67] on the small leg upfront. As the fronts expired worthless, I closed out the larger short leg at $0.40 per contract, yielding a total profit of $1.47.

When I break down the attribution, I see a small win on IV (although the vega isn’t as meaningful as the gamma/theta battle on options of these tenor), a giant win on realized, a small loss on delta, and then the positive luck on path which is the short expiring at the strike.

I promised to publish the actual attribution.

From that point of view you will see how I got lucky. But you’ll also see inherent noise in evaluation.

There’s big lessons in this.

We will work through this in 3 steps.

1. Actual performance
2. Benchmarked performance
3. Why they differ and what that reveals about vol trading

Onwards…

Actual Performance

This is the most straightforward part of the analysis. It’s simple. But it also teaches us nothing. Unfortunately, this is where most people stop so learning takes longer (if it ever happens at all).

On March 4th, with IBIT at $48.50, I traded a calendar ratio spread:

• sold 1 March12 48 put @1.79
• bought 2 April 38 puts @.56

I net collected $.67 per 1 lot “on the small side” (language for ratios trades can be weird).

On March14th expiry, IBIT closed $48.14:

• The March puts expire worthless
• I liquidate the April puts at .40 (they have expanded in vol by about 2 points since I purchased them but the vega was small)

P/L per 1×2:

+$1.79 on the March put

– $.16 x 2 April puts = -$.32

Total profit = $1.47 per 1 lot on the small side or $147

[If I traded 10 lots on the small side, ie a 10×20, the profit is $1,470. A 100×200 lot ratio would be $14,700 and so on.]

Summarizing*:

Hooray, right?

Not so fast. This is just “resulting”. Trading is too noisy to learn from that.

Let’s go deeper.

 

*I actually did another trade which made the performance even better but adding another trade at a different date complicates the coming analysis which I want to keep approachable. I’ll mention it at the end. It’s more interesting as a matter of “vol surfing” rather than direct attribution but it also highlights just how dynamic option trading is.

Benchmarked performance

This table shows where the stock was when I first did the trade, the change in stock prices during the holding period, and there the stock was at expiration when the trades were closed.

To annualize a daily move into a volatility you can multiply by 16. Notice how large the daily moves have been since I sold the options. 4 out of 8 days the moves were greater than 1 st dev with 1 exceeding 2 st devs (st devs as implied by the March IV).

Once we have 5 returns we compute a 5-day realized vol. The closing IV is always less than the RV (although intraday the IVs did whip around a lot). Negative VRP!

This table shows the total greeks as if the position is short 100 March puts and long 200 April puts:

Things to note:

• The position is short gamma. Even though its long 2x as many April options as it is short March options. That’s because the shorts are closer to expiry and closer to the stock price than the April 38 puts.
• The closer the stock is to $48 and the less time to expiry there is, the larger the short gamma position, and the larger the theta collection.
• At expiration, the stock expires above the strike. Going into the expiration I’m short gamma so above the strike my position becomes short as my March puts “go away”. My greeks at the end of the day, reflect my April puts — now I’m short delta, long gamma and vega, paying theta.

Estimating p/l attributable to greeks

✔️Realized p/l = gamma p/l + theta p/l

where gamma p/l = .5 x gamma x (change in stock price)²

✔️Vega p/l = vega x change in IV

Over the life of the trade, the position wins to April vega p/l but those gains are swamped by the sheer size of the gamma/theta tug-of-war.

If I hedge daily…

I’m losing that battle.

The negative gamma p/l dominates the daily decay because the moves are larger than what’s implied in the vol (which determines how much theta I collect — in this case, I’m “not collecting enough” to compensate for the short gamma).

To evaluate a vol trade you need a benchmark just like if you buy a stock you might benchmark the decision in comparison to how the SPX or QQQ did over the holding period. Since this is a relatively short-dated trade, benchmarking to “how did my position behave assuming I hedged my deltas daily” is a solid idea.

Here’s how that looks:

The trade won small to vega, lost big to realized, but the attribution decomposition overestimates the loss because the gamma profile wasn’t as short on the large down move because of vanna.

💡Vanna is a second-order greek we are not attributing. It can intuitively be understood in words: “when the stock was at the bottom it was far away from the March shorts and closer to the April longs and therefore lost a lot of short gamma on the move”. The gamma p/l estimate assumed constant gamma across the move. You can imagine how if we computed gamma p/l over every $.50 interval it would progressively decline as the stock kept approaching our long options. The assumption of constant gamma therefore overestimated the loss in this case and that overestimate is accounted for as positive “unexplained p/l”.

Back to the attribution. Here’s a visual of the hedged p/l vs the stock price (left panel) and p/l vs move (right panel).

The 100×200 lot ratio spread, delta hedged daily (assuming no slippage) lost about $1,000 or a dime in option terms.

$1,000 = $.10 x 100 contracts x 100 multiplier

If this trade was done with 1×2 contracts only it would have lost $10 (ie a dime on a 1 lot).

In sum, benchmarking the decision to do the trade to “what if I hedged it daily” the trade is a small loser even though the realized vol over the holding period was much higher than the IV sold.

The 2 primary forces that kept the theoretical loss in check were:

1. When the stock was most volatile (on the down move) my gamma became much less short. This is why I wanted the downside. I expected BTC vol to outperform the skew as I expected the down move to be “destabilizing” (just as it has been in other risk assets recently…I would expect the opposite for something like gold).
2. The stock expired at the short strike. I’ve discussed this before but it’s the roulette aspect of these dirty vanilla options. See Short Where She Lands, Long Where She Ain’t

Actual vs Benchmarked Performance: Why they differ and what we can learn from that

Recall, my actual performance was making $147 per one lot vs a “hedge daily” benchmark of losing $10.

What the hell is going on here?

Remember last week’s post a misconception about harvesting volatility?

I wrote:

By hedging your delta at various time intervals or as your position size breaches a threshold, you are first and foremost reducing market exposure risk. You do this because you don’t want directional p/l variance to swamp the vol-driven reason for doing the trade. A byproduct of this is your hedges “sample the vol”. If you hedge on the close every day and the market always comes back to unchanged after having large intraday ranges, you will sample a zero volatility. If you hedged intra-day you will sample a much higher volatility.

There’s no escaping the reality — every option trader experiences their own realized vol regardless of what the close-to-close volatility says unless they hedge close-to-close. If you benchmark realized volatility as close-to-close, you could think of your sampling as ‘volatility tracking error’ even though there is no “single volatility”.

Your hedges might sample the vol, but the intent is to cut risk, ie manage position size. You can appreciate this by considering the opposite extreme — you do option trades for volatility driven reasons but you never hedge.

What happens?

You are still trading vol. The expirations are the moments when you “sample” vol. The realized vol you experience is point-to-point volatility over longer stretches of time. It’s just hedging on a long interval.

I didn’t plan it this way. That post came out Thursday morning. I didn’t know how my Friday expiry position was gonna turn out. But the difference between my actual p/l and the theoretical p/l if I hedged daily is a perfect example of that quote.

I did not do any delta-hedging. I was prepared to own the shares if IBIT closed below the strike and sized the trade, which was driven by a vol axe, to be ok with an unhedged outcome. If you recall this video, I showed exactly how I studied what a disastrous result could look like:

Still, why was my actual performance much better than the delta-hedged counterfactual?

By not hedging I only sampled the vol in 2 places. I sold the near-dated 48 strike puts with 10 DTE when the stock was $48.50.

At expiry, the stock was $48.14.

Despite all the whipsawing, the 10-day point-to-point return was a measly -.75% and I was short 65% vol. I won to being an ostrich.

Of course, this is luck and not a strategy. If I bought the options and didn’t hedge I wouldn’t have “sampled the high volatility” and would have gotten slammed.

You can’t know the path.

The benchmarked “delta-hedged” performance of the position is a better measuring stick of a vol trade than looking at what happens if you do nothing since part of the reason for trading the vol was a comparison of the implied vol to the daily realized vol. You can’t pretend the daily realized vol doesn’t matter when you do an autopsy.

You may not agree that “daily delta hedged theoretical performance” is the right benchmark for what you are doing, but just “resulting” is active self-deception. If you trade over longer time scales the vega attribution will gain relative importance. You might even benchmark realized vol using weekly sampling. If you trade dailies, you can probably just compare straddle prices to dollar moves and ignore IV measures altogether. Whether it’s report cards or stopwatches, students and athletes don’t get better without measuring. The same is true for traders.

A humble bit of advice: to get better, construct benchmarks in light of the metrics that drive your trading decisions.

Wrapping up

My actual performance was much better than a more platonic version of how I should have done. I’ll take it. The opposite happens too. Vanilla options are filthy. If you love being fooled by randomness and like to brightside your results, options will give you all the rope your heart desires.

I recommend assassinating your ego and looking at the chalk outline. The IBIT autopsy report:

• Sold an IV that turned out to be too low (bad)
• Owned a downside put ratio (good risk management and judgment about how vol would react on a large risk-off)
• Got lucky on pinning the short

Final note

I mentioned that I did another trade in the fracas that I didn’t include in the attribution because it was done on a different day.

Let’s talk about that one.

Near the depths of the sell-off with vol ripping, I launched another clip of puts. This time the March14 43 strike at $.77 with the stock around $45 (they were about 85% IV) or about 20 vols richer than my April puts.

Here’s the scenario. I’m getting worked because I’m long delta as my short $48 puts are now $3 ITM but I’m long 2x as many April puts which are picking up greeks as my March puts are losing vega and gamma.

In other words, I got bullets. This is not an accident. This is in the DNA of how I trade (the readers who’ve spent a lot of time trading beside me are laughing right now because they know exactly how I’m thinking…pit trader to the f’n bone).

Now I can sell when they’re really coming for it. Those teeny puts’ value don’t come from some actuarial place. It’s from the dynamic understanding of how things trade when shtf. I didn’t buy the ratio to go to the grave with it but so I can paint. IBIT is down nearly 10% and vol is singing. So I monetize some of these extra options that have greeks. But instead of selling the April puts I sell the March 43 puts because that’s what the market is paying up for.

To be clear, this is risky. I’m taking calendar spread risk. I’m also not hedging. My risk is capped of course, if IBIT goes to zero I ride the long shares down to $38 but then the pain is over.

However, if IBIT rips back up to $55 all I’ve done is collect premiums. The p/l will be positive but the autopsy will say “this man left a lot on the table by being short vols that turned out to be a buy”. Let’s not sugarcoat short gamma.

As it turned out, those $.77 options expired worthless so the entire series of trades amount to $224 per contract of profit ($147 for the first package + $77 for the additional puts) per 1 lot.

[Again, just basic option accounting — if you sold 100×200 ratio then sold an additional 100 puts then you are net flat option units. The p/l at expiration is $22,400.]

All of that said — the second batch of sales also fail an honest attribution lens. The 5-day rv that prevailed after selling 85% vol was 100.6%.

[I’m reminded of the wild Oct 2009 nat gas options. There was no IV level that ever traded that was above the realized vol. Vol got over 100% and it wasn’t enough. But that lasted much longer than this boondoggle.]

On a point-to-point basis, it is a 7.2% move in 4 days or ~57% vol move.

[7.2% * sqrt(251/4) = 57.3% ]

Note that the up and down is worse than if the stock went up 2% per day for 4 days. Even though that move would have been further, in a delta-hedged strategy it’s more benign. The whippiness is like a treacherous course through the mountains that would otherwise seem short if you measure by “how the crow flies”.

Options are fascinating because they must balance both path and destination. 2 investors can trade with each other, one based on path and one based on destination and both win. At the macro level, the participant who gave liquidity to the delta-hedger lost. Just imagine buying the 43 call for 50% vol and the stock goes up 2% per day for 4 days. The call seller who hedges daily and the call buyer who goes on vacation both win. The trader who sold the hedger shares all the way up holds the bag. Of course, we’re anthropomorphizing a system here but you get the idea.]

To repeat what I said earlier, this second trade is more interesting as a matter of “vol surfing” rather than direct attribution. It highlights just how dynamic option trading is. It’s a 3D boardgame that slides along a time dimension. I’ve alluded to a lot of this conceptually in my writing over the years but with the moontower.ai visor on I’m getting my sea legs back bit by bit which means I can get more concrete.

If you are reading this as an options novice with a process for using options already, I’m not advising or encouraging you to invite this kind of brain damage into your life. The tools are useful for much simpler options applications because they are, say it with me, always about vol (with an exception for vertical spreads but our Payoff Visualizer has you covered for that anyway).

Let’s leave it there.

I bought December COIN straddles yesterday, so instead I’m going to discuss:

1. Premise
2. Expression & Execution
3. Management plan
4. Miscellaneous aspects

[Normally, Thursday posts are paywalled but in honor of the upcoming Spring Break this one’s on the house. I’ll make it up to you paid subs I promise.]

Premise

Most people use options for directional reasons. A relatively small number of people use them because they have a view on vol. As I like to say, “Most investors have a view on a stock and assume the options are fair. Option traders have a view on the vol and assume the stock price is fair.”

Moontower.ai is built to help both.

If you are directional, then it allows you to marry your directional bias to the right option expression OR show you that the options are not a strong expression, suggesting you should just trade the underlying.

If you are the vol trader, the tools follow a funnel progression to lead you to possible vol trade candidates.

Today’s trade is an example of one from the vol trader lens. I bought COIN vol but have no view on the stock.

The progression:

First, the crypto sector has low implied vol compared to its own history while many other asset classes do not. So crypto is also low on a relative basis.

Zooming in on crypto only:

What’s interesting to me is that COIN is in a low vol percentile but also has a flat term structure. The steepness or ratio of 6m to 1m IV is flat. Usually, when vols get low, the term structure is ascending as you see in BTC for example. 6-month constant maturity IBIT vols are trading at a 1.16 ratio to the 1 month, which amounts to over 7 vol clicks. Looking at chain data (not constant maturity interpolation) it’s even steeper.

You can see the IVs on the left column with the implied forward vols in the matrix reflecting steep ascension in the term structure.

In COIN, we see the flatter term structure (although a touch steeper and noiser in chain data bc of earnings months)

I’m not interested in a relative value trade here but I’ll circle back to that a bit later. I’m just pointing out that the flattish term structure in COIN is unusual when vols are low and something like BTC term structure is more expected.

Let’s focus on COIN by itself.

We know it’s in a low IV percentile, but there’s no notion of its VRP in that metric. How is the IV priced relative to how it moves? That’s the second step in the funnel.

COIN like IBIT and NVDA have negative VRPs…they are moving much more than their implied vols (the ratio of IV/RV -1 is negative). However, we are coming out of an especially high vol period, those names have a realized vol that is in the 75th percentile so the market’s implied pricing says RV will relax. We can see that in the fact that the average VRP is negative across this watchlist. But these names are heavily discounted even beyond that.

So far, I’m thinking COIN is still cheap, but it’s not a smoking gun. Realized clearly has room to fall and that chart doesn’t give me a sense of how much.

Another view:

This is again using interpolated IV. It is very much on the low end of the range for 6-month vol. Admittedly, 180d realized is a very slow-moving metric and since it’s an overlapping time series (each day is the trailing 180), it’s low sample size. I like this chart mostly for the IV aspect, which gives us a sense of range and in this case certainly shows the low IV percentile.

Let’s look at the vol cone:

This chart shows you the distribution of realized vols sampled from daily readings at various lookbacks over the past 3 years. Again, the long lookbacks by their nature are low sample size since so much of their daily readings are overlapping. We superimpose the IV term structure through the cone.

That deferred IV is as low as the lowest reading of long-term realized vols. To be clear, we have certainly had 1 and 2 month periods where the realized has been lower than the mid 60s IV priced into the deferred vol, but they happen less than 25% of the time.

If you scroll through charts in this way, you typically don’t see vols that look low from all these lenses. This sticks out. That comment has a relative spirit behind it so it’s a nice segue back to a comparison with IBIT.

The December COIN IV is being priced at about 66 vol. Look at that IV compared with it’s 10d and 20d rolling RV history below. It looks quite cheap given the upside skew to the realized vol.

I also included IBIT’s realized vol. Knowing that the COIN Dec vol is about a 10 vol premium to IBIT Dec vol. It’s a small premium compared to how much COIN moves compared to IBIT:

If you think IBIT vols are cheap, or even just fair, then COIN looks really cheap.

I don’t like the pair trade as there’s enough idiosyncratic risk in the relationship given how volatile the correlation is underneath the hood. This is also evident when, instead of looking at vol from daily returns, we peek at point-to-point total returns since January 2024 when IBIT was listed…COIN is up around 35% or close to half as much as IBIT is up, despite having a typical beta greater than 1 and being more volatile.

[“Idio” or what I was taught as “risk remaining” is how much of the vol in COIN is unexplained by IBIT. The formula is sqrt(1-R²). For more on that, see From CAPM To Hedging]

At this point, I like the COIN vol on its own. Now what?

Expression & Execution

The thrust of the trade:

Implied vol is cheap, I can “lock it in” further out in the term structure. There’s margin of safety in that it’s carrying well currently and the level is cheap enough that I’d expect it to carry well in most scenarios.

I think a fair vol would be somewhere around 72% based on median historical realized for the past 2 years (if I go back to 2022 the IV was much higher, but I prefer to be conservative…it’s stabilized since that crazy year). This also aligns with median realized vol using 30d lookbacks. I chose 30 to balance sample size a bit better but also because looking at longer periods makes the IV look even cheaper, and again, trying to be conservative. Low 70s is congruent with COIN having no VRP to median vol levels (although that hides lumpiness in the sense that the median realized includes earnings moves).

I have no major view on skew or direction and I want maximum exposure to vega and gamma. I’ll buy the 0 delta straddle.

It’s a bit hard to see (try right-click “open image in new tab”) but I’ll point out noteworthy items on the December chain.

Stock price ~ $193.82

The first thing I do is check the implied interest rate. The 200 strike is where the call and put are almost equal so that’s the closest price to the synthetic future.

synthetic = call – put = $44.40 – $44.25 = $.15

implied synthetic future = strike + synthetic = $200.15

Since there are no dividends, the implied rate can be quickly estimated by:

($200.15 / $193.82) – 1 = 3.266%

Annualized:

3.266% * (365 / 268 DTE) = 4.45%

In line with the yield curve suggesting no hard-to-borrow issues, implied divs, or other carry “gotchas” which will taint IVs.

The 0 delta straddle, according to IB, is the 230 strike. The call is .52 delta, the put is .48, so the straddle delta is really .04

[If you are surprised that the .50d strike is $40 or about 20% OTM then review Lessons from the .50 Delta option]

Because the put is in-the-money and markets are nominally wide I want to compute what straddle price corresponds to mid-market for the call IV. When looking at a vol surface, OTM options are a more reliable estimate of implied vol relative to the ITM options, which will be wider because of extra delta risk market makers must cushion their quotes for. Plus, OTM options are naturally more liquid.

Mid-market on the call is 66.9% vol. A bit higher than the tools suggested which could be some lag or bid/ask sampling artifact. Vols in December are unchanged but overall vols were firmer today as COIN was down 5% or more than 1 st dev.

Fixed strike vol changes:

 

The Dec 230 straddle assuming 66.9% vol, the 4.45% rate we determined from the market itself, and a spot price of $192.82 using a European calculator, is worth $96.60

Mid-market on the straddle, which includes the noisy ITM put market,t was $96.93

I went through the hassle of computing the rate because I really want to know the implied vol I’m buying and you can’t just map the mid-market price back to mid call IV. You need a rate to use the calculator. This might not be obvious until you actually try to trade and then ask yourself what vol did I just trade? Whether you figure it with a calculator or using put-call parity in your head, you’ll realize you need to know the cost of carry.

So I want to buy the call’s mid-market vol of 66.9%

But I expect to pay slippage. 1/2 a vol point on such a vol level seems completely reasonable. The straddle vega is $1.28. Half a vol point is $.64

At 66.9% vol the straddle is worth $96.60

If I pay up 1/2 a vol point or $97.24 I am paying 67.4% vol.

I bid $97.25 to tip my local market maker. It’s a small trade, 5 contracts, or about $48k of option premium.

I got filled on 1 lot quickly.

And within 90 seconds…the balance.

I felt good I didn’t get hit on the whole 5 lots immediately. Old habits die hard.

If I think a fair vol is 72% that’s about 4.5 vol points or $5.75 in option terms. $2,875 in premium terms. Like I said, it’s a small trade. I have dry powder if it gets cheaper which is my preference right now, but I wanted a taste.

(I generally avoid single stocks so this was out of character…ETFs and commodities just feel way more familiar and I can situate that risk into my broader portfolio naturally. But this one was compelling enough to dabble in and document for an audience.)

Management plan

Managing the trade is in some ways the easiest part of the process. As I explain in this clip, I have a “day zero” mentality. I don’t care where I got in and what my p/l is. If the same reasoning process that led me into it, tells me to get out of it…either the vol appreciates too much or the rest of the “blob” gets cheap relatively then I’ll kick it out.

As far as isolating the vol, the trade size is well below my risk threshold so I’m willing to tolerate a fair bit of noise in “what vol I sample” so I may check on it once a week to trade some delta (the max delta of the structure is equivalent to 500 shares so we’re talking about odd lots most of the time).

Realistically, I probably won’t do anything unless it’s made enough of a move to make it worth trading 100 shares or heck, even more realistically, I might only trade the shares if my delta is short and I want to flatten (I’m underweight risk assets in general).

I hope it makes sense that my hedging strategy, or lack there,f has no bearing on the vol trade aspect of this. It only creates “tracking error” vs some platonic benchmark like “what if I hedged daily?”.

[I talk about this more in a misconception about harvesting volatility]

I’ll share how it’s going intermittently, and I’ll track any actions to do an autopsy when the trade is off the books.

Miscellaneous aspects

A smattering of thoughts in no particular order.

straddle vs vol thinking

As I discussed this in the Discord, a member said the straddle sounded expensive compared to the stock price.

This is a natural reaction. Option prices are highly unintuitive as you go out in time. They are priced based on some concept of integral or area under the curve of how much money you can make from flipping stock as it takes a jagged path from here to some distance that is probably not as far as the straddle price. Our mind sees the net distance but overlooks the nooks and crannies in the shoreline.

It’s almost like you unfolded a cube, looked at the sum of the perimeters and thought “that looks way longer than sum of the edges, sold!”

Not intuitive.

Conversely, thinking in terms of vol for straddles that have just a week or two to go is not necessary if you can reason about how much the stock can move. A common demonstration of this point is earnings. We think of the straddle, not the vol. The vol is irrelevant to our intuition because the realized vol vs theta battle will dominate the p/l decomposition not the change in IV. Short-dated options are all about dollar gamma and what gets realized. After all, we all know IV will fall after earnings but the only relevant question is “how much is this sucker gonna move?”

This dichotomy, the “particle/wave” of options — “is it a straddle or is it vol?” is not something you find in the textbook. It’s just where the gambling instincts bleed into the theory of replication.

[I feel a bit deficient saying so considering how long I’ve thought and dealt with this stuff, but at the end of the da,y I’m just like ‘sometimes these concepts resist easy sorting at the practical level so let go and live with some paradox’. Options trading is moving pictures, not photographs. I’m sure there’s mathematics that reconciles it all, but it’s not the language of thought for most of us.]

I do wonder if deferred vol cheapness might be structural because of some “price stickiness”. The straddle just appears too fat compared to the stock price. Another reason could be some collective market brain grokking the idea that if you sample vol over longer periods than daily it tends to be lower, so a seller, less exposed to gamma risk, can be a bit more aggressive. But if this were a universal idea, I’d expect to see instances of ascending vol term structures.

takeover risk

One of the major gotchas in single stock vol is the risk of a cash takeover which assasinsates extrinsic option premium. I don’t see that as a material risk given exchanges like ICE and CME are only about twice the size of COIN.

In a stock takeover where the acquisition shares are swapped for shares of the acquirer, options on the acquired shares will reference the acquiring company in the correct proportion. Larger companies are typically less volatile/more diversified so while not as disastrous for a long option holder as cash, vol still gets crushed in the target name.

COIN itself is in talks to buy Derebit which has the largest market share for crypto options.

 

That seems like a good place to close. I’ll follow up when I adjust the position.