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.

Certain topics re-infect popular social media discourse like an engineered cold virus. Like when the NY Times is having a slow week and drops the “Couple Can’t Make Ends Meet in NYC on $500k a Year”

This is not a fresh take. Sorry to be crass, but NYC is a beacon for dreamers around the world who want to partake in a life tournament. It is entirely indifferent to your needs.

Plus, $500k is not what it was. Also not news.

[The number of millionaires in the US has doubled twice in 20 years. For the investment-brains Rule of 72’ing that in their heads, it’s 7% growth in millionaires per year.

Also when you break out their expenses, it always includes “private school”, “max 401k contribution”, and a parade of “needs” that insult normal people’s definition of “ends meeting”. The headline should say “I make $500k and don’t feel rich”. And for that our nice couple that got As in school should be banished with their expectations to either 1992 or literally any place that is NOT the final table at the Main Event. Sorry, but aliens only need apply. ]

The fintwit version of “discourse that doesn’t die even though everything we know about the situation is evergreen” is whether one should use a stop-loss.

I’ve watched this conversation come and go so many times. I can no longer restrain the impulse to do that thing that nuisance colleagues do in meetings… raise my hand to hear my own voice.

[You know as soon as that hand goes up you’re just “omg please kill me what set of life decisions brought me to this moment in the universe where I have to hear this pick-me baby perform this routine in a conference room in front of a weary audience of which 2 are muted on a zoom call with their camera off in their car on the way to Starbucks for the will to finish Wednesday” ]

With that pep rally…

let’s talk stop-losses

First, the obvious:

A stop-loss is a risk management tool, not an alpha tool.

The purpose and effect are to change the shape of your P&L so you can endure.

The cost of a stop-loss, aside from slippage and transaction fees, is sometimes cutting eventual winners.

Euan Sinclair gives this a proper treatment with math.*

The tribal intuition is closely related to the idea behind a one-touch option.

Remember this from Sunday?

You can also analogize to options trading.

Gamma hedging is not an edge. It’s a hedge. It reduces position size. It’s a cost.

[See a misconception about harvesting volatility]

Stop-losses, like gamma hedging, are a kind of passive flow — they’re independent of signal and discernment.

They’re forced in the sense that the time of trade chooses you, not the other way around.

If you chose the time because you thought you had an edge, you’d evaluate it based on alpha criteria. But since it’s risk management, you benchmark it against other ways to manage risk — like starting with smaller size.

If you place a resting bid or offer and it gets filled, you’re probably losing to that trade. It’s a stale order.

But — if you’ve decided that the sum of losses from stops is less than the counterfactual of trading smaller from the start, then it’s accretive.

My gut is that most people have no idea whether that’s true for their strategy.
Which is just a sub-instance of a bigger issue: they don’t fully understand their edge.

Not a damning criticism — the admonition is a matter of degree. Having an edge is hard enough. Appreciating all the contours of that edge is even harder.

If it were easy, professionals wouldn’t blow up. But they do.

Even market-makers, whose businesses hinge on understanding risk and tradeoffs, sometimes blow out. They weren’t clueless, but every serious professional still has open questions about their strategies that bump up against the types of tradeoffs we examine when constructing risk rules.

The best firms are probably closest to the efficient frontier of those tradeoffs.
Clueless tourists are far below it — and often don’t even see the problem.

For the narrow audience of vol traders, I think the traditional stop-loss framework makes little sense.

I explained why in this 5-minute clip from The Trade Busters.

To wrap up…

I’m not a directional trader, so maybe this doesn’t mean much, but I’ve never placed a hard stop order in my life.

If I want something with a stop-like profile, I use options. Otherwise, I size the risk appropriately at the start (imperfect, but I prefer this to overbetting and then using a negative expectancy maneuver more frequently as a risk management tool. If you have been on an options desk you know that traders are obsessed with “how do I hedge less?”).

If the risk grows, which happens because vol is not constant — then I check:

Is the risk bigger than what’s allowed?

If so, reduce the position.

Follow the risk protocol.

It’s not about price levels.

It’s not about P&L memory.

It’s a binary: Is the risk too big or not?

I go deeper on that in this short clip.

I’ll leave it there. I’m done with this topic. Conceptually it’s not hard. It’s a trade-off and the details of that trade-off matter with their relevance varying with the strategy.

[Trend-following is a good example of a strategy that strongly lends itself to stops. It’s built into the premise. It’s managers understand exactly what the trade-offs are in quasi-replicating an option that samples vol over longer periods because they know more frequent sampling understates vol in the presence of auto-correlation.]

If someone is religious about the utility of stops in some general sense without parsing the properties of the underlying risk, I’m suspicious that they are parroting some guru. Or trying to make their NYC rent by selling investment tips.

Eh, who are we kidding… these YouTubers are always telling you to smash the subscribe button from a subdivision in South Florida.

*Euan discusses stop-losses in chapter 9 of Positional Option Trading. This is just a blurb but the chapter is more technical:

• stops are complicated:
  • Many trades that would have been winners will have been stopped out, so it is not as simple as assuming that you are just cutting off the left tail of the distribution. You would need to know how many trades would cluster at the stop threshold [This is a question of path].
  • Simple simulations show that the expected value of a strategy will fall if you use a stop, although you shed the large losers.
  • Trailing stops cost even more than a fixed stop because they are always in play, as opposed to a fixed stop which gets further away.
  • Stops don’t just stop losses. They drastically change the shape of the return distribution and can lower the average return. Adding stops won’t transform a losing strategy into a winning strategy. The only reason that we would add a stop is that we prefer the shape of the stopped distribution.
    • Stops make more sense if we are trading momentum and less sense if we are trading mean reversion. [Kris: note that much of option trading is mean reversion on some meta-level]
    • A position should be exited when we are wrong. Sometimes this will coincide with losing money. In this case, a stop is harmless. But sometimes losing money corresponds to situations for which we have more edge. Here, a stop is actively damaging and contrary to the idea behind the strategy. [Kris: Fully agree and why I believe in risk rules that are independent of P/L for option trading and more thoughtful of ex-ante risk shocks]

2 weeks ago I shared this tweet:

By saying I’d buy that proposition I’m saying “I’d buy that vol”

Andy, responded with a joke about what’s the “one touch” option worth, which I asked him to delete because I really would have liked a fool to sell me that proposition and Andy’s comment gives away the sauce.

[X’s killer app would be to escrow bets, but that’s another convo altogether]

I’d be a size buyer of a 50% probability that we get back to the highs before the end of the year.

It’s not bullishness. It’s vol trading. If you could buy that probability for 50% you could arb it vs the value of a one-touch call that pays off “if the stock ever touches or exceeds the strike price before expiry’.

That call will trade for a higher implied probability than 50%.

I’ve alluded to the rule of thumb before, but a one-touch probability is approximately twice the delta. At the time Andy tweeted, the highs would have corresponded to the 10% out-of-the-money call strike.

If we double the delta of that call, we estimate the one touch probability. Given SPX vol, I knew immediately that a 10% OTM call expiring on Dec 31 has a higher delta than 25% so the one-touch probability would certainly be at least 50% bid.

So as a matter of education there’s multiple lessons in this simple exchange.

Estimating the one-touch probability

Using our rule of thumb, we just need to estimate the delta.

@quantian’s got that trader reflex — do the napkin math:

What did he do in steps:

1. Used VIX as a proxy for implied vol which is annualized
2. Scaled it to 9 months using √time or √.75… 25% * √.75 ~21.7%
3. 10% / 21.7% ~ .46 sigma
4. 1- normdist(.46) ~ .35 probability [assumes probability ~ delta]
5. Double the probability —> 70% chance of one-touch

😈Possible enhancements to the estimate if you are a masochist:

• With VIX at 25 I’d expect the term structure to be inverted so 9 month vol is lower. This would lead you to be more conservative on your delta. Sigma is directly proportional to our vol estimate so if we use 75% of the vol our sigma increases by 1/3 (since we dropped lowered the vol by 1/4). Normdist is not a linear function so still use the calculator and that pushes the delta down to .27 or 54% probability.
• The delta depends on the the moneyness of the forward price not the spot price and since interest is greater than dividends for SPY the delta is a touch higher.
• We’ll assume the positive skew embedded in Black-Scholes lognormality assumption offsets negative call skew. In sum I’d sell quantian’s delta of .35 and buy a delta of .27 so let’s call the fair delta .31 and the probability of the one-touch as 62%. I love getting even money odds when I should be laying 5-3.

Someone else knows their options btw:

My response to quantian showed another way to conservatively estimate that the probability was higher than 50%

Intuition for why one-touch probability is 2x the probability of expiring ITM

I’ve discussed the shortcut before in crossing over zero. But I sketched an intuitive example using a trader’s favorite binkie — the binomial tree.

The image is self-contained explanation and follows from a simple assumption of a stock 50/50 to go up or down $1.

Starting from $100 and traveling 5 periods what’s the probability of the stock expiring $99 vs the probability of it “touching” less than $99?

Learn more:

Estimating the probability of a stock expiring above or below a strike from the delta works for relatively low vol or short dated option. The below post explains the real meaning of delta and why/how that estimate can break down:

Lessons from the .50 delta option

 

Trader Math

I’ve included the one-touch probability in the wiki-style collection:

Math Shortcuts Traders Know By Heart

The “weekend effect” in options refers to the tendency of implied vol to increase on Mondays.

Why does it happen?

First, perplexity.ai provides not only a decent start. In fact point #5 is quite impressive and clue-y.

The trading implication, point #6, is somewhere in between incomplete if you know what you’re talking about to dangerous if you are a novice reader. I’ll address later in the post.

Perplexity does admirably but it doesn’t get to the core.

My condensed summary:

The weekend effect is a mathematical artifact that presents itself as “implied vol increases on Monday”.

Why?

Empirically, from Friday’s close until Monday’s open, options typically do not decay as much as the model’s theta would predict.

Therefore, to fit the the Monday a.m. option price, the implied vol must necessarily be higher than it was on Friday.

This post will explain why this is a mathematical artifact as opposed to a real change in the IV.

If the upward change in IV is an artifact, then does that suggest that an unchanged IV means vol is actually down?

Yep. Sure does.

Right now this tweet is a puzzler:

I’m going to explain it in detail.

And for your part, you’ll walk away understanding weekend theta and volatility time in a new way.

This post is going to get you over the line by zooming in on weekends in a basic way.

However, you could reconstruct all the ideas if you deeply understand this benchmark post:

⌛Understanding Variance Time

In that post, we start high and you can use it pinpoint how to think about weekends.

In this treatment, we zoom in on a weekend and you could use that to scaffold your own construction of the high-level post.

 

Day counts

Conventional option models such as Black Scholes accept a days to expiry parameter. This input is represented as a fraction of a year.

When you encounter an option calculator in the wild, this fact is abstracted away. A calculator usually asks for a trade date and expiry date. If the trade date is March 1, 2025 and expiry is June 1, 2025 there is 92 DTE.

The model, if it uses a 365-day tenor, will convert 92 DTE to 92/365 = .252 years. This is known as a calendar day model.

You can have models that specify other tenors. A common variation is the business day model. It will have a 251-day tenor because it starts with 365 days but subtracts weekends and holidays (don’t forget Juneteenth).

From March 1 to June 1 there are 63 business days. DTE for that model is 63/251 = .251

There is slighty more DTE in the calendar day model than the business day model. Therefore, for a given option price, the calendar day model will have a slightly lower implied vol than the business day model. After all, both models are looking at the same option price but the first model thinks there’s more time to expiry.

On January 1, there is 1 year to expiry (365/365 or 251/251) for both models. But as soon as the clock starts ticking, the DTE between the 2 models diverges. The divergence depends on the ratio of business to non-business days until expiry.

How much time has elapsed?

Armed with this knowledge, let’s measure how much time has elapsed from Friday’s close to Monday’s close.

1. Calendar day model

3 days have elapsed.

Friday pm to Saturday pm, Saturday pm to Sunday pm, Sunday pm to Monday pm

Using the calendar day tenor, 3/365 or .82% of a year has elapsed.

2. Business day model

1 day has elapsed.

From Friday pm until Monday pm is just 1 business day.

Using the business day tenor, 1/251 or .40% or half as much time as the calendar day model!

Therefore from Friday’s close to Monday’s close, relative to a business day model, a calendar day IV will need to be ratcheted higher.

Relativity

What’s more “correct”, a calendar day model or business day model?

Wrong question.

There is no “correct”.

Consider what we know.

• Most conventional models use a 365-day tenor. The VIX calculation, the representation IV most broadly tracked, uses a 365-day tenor.
• Market observers are so used to seeing IV increase on Monday that they give it the name “weekend effect”

I’ll let you think about it. Based on the comparison with a 251-day model can you explain the effect?

 

Ok.

Here’s the logic…relative to a 251-day model, a conventional calendar day model must see its IV increase on Mondays. If this is a recurring trend, we should deduce that the market’s consensus is not decaying the options as much as the 365-day model predicts. The market’s pricing behavior strongly suggests that it believes time passes more slowly over a weekend.

I used the 251-day model to be extreme. The 251-day model assumes time doesn’t pass at all over a weekend. Time did not tick until Monday transpired. From Friday to Monday’s close it thinks 1/2 as much time to expiry elapsed.

It’s not that the market uses a different model. The market is not a monolithic entity with one model setting option prices. Consensus does. And the sum of everyone’s opinion suggests that time passes more slowly over a weekend than calendar models predict.

You can also appreciate this by inversion.

If you use a business-day model the weekend effect is inverted…IV looks like it falls on Mondays!

It makes sense.

The 251-day model thinks no theta happens on the weekend days, so the fact that option prices are lower on Monday am than Friday pm makes their model think that IV must have fallen.

It seems like we have a 2-sided market.

A Saturday is neither a full trading day or a zero. It’s worth something between 0 and 1 day.

Split the difference

What if I say that weekends and holidays are half days? Said otherwise, variance time passes 1/2 as fast.

If we continue to denominate our basic unit, a full trading day, as 1.0 and weekend days or holidays as .5 we get the following tenor:

251 x 1.0 + 114 * .5 = 308

We have a 308-day model that decays days at different rates.

When a Tuesday rolls off the calendar 1/308 or .3% of a year elpased.

When a Sunday peels off, .5/308 or .15% of year elapsed.

Turns out if you use a calendar like this, weekend effects are dampened. Which means your model is decaying time closer to the market’s consensus. The IVs in your model need less adjustment to match the market.

Overnight

We need to talk about one more topic before I can explain the tweet above.

It starts with a question.

In a calendar day model, how much time has elapsed from say Thursday’s close until Friday’s open? In “wall” or clock time it’s 4pm est to 9:30am est or 17.5 hours.

But if time passes slower on a weekend, it’s reasonable to assume time passes slower overnight if we start getting to the hour level. After all, I don’t think 17.5/24 or 73% of an option’s daily decay occurs just as the market opens.

If we define 1 day as close-to-close then we need to defined close-to-open as some proportion of 1 and 73% sounds way too high.

The US is the last market to open after Asia and Europe so it’s reasonable to assume that the overnight includes more than zero volatility (in the spirit of “if a tree falls in a forest”, even if the US was the first to open the overnight would be worth more than 0. The world happens when the market is closed. At the very least BTC volatility could be used as a ruler to measure with).

You could do a big study where you measure the ratio of close-to-open variance to close-to-close variance but for the purpose of this post I’ll use .25. It’s in the right ballpark.

Back to our question: how much time has elapsed from say Thursday’s close until Friday’s open?

.25

How much time elapses from Friday’s close to Monday’s open?

Friday PM to Sunday PM = 2

Sunday PM to Monday AM = .25

2.25 days elapse from Friday PM to Monday AM in our calendar day model.

How about in a 308-day model?

Friday PM to Saturday PM = .5

Saturday PM to Sunday PM = .5

Sunday PM to Monday AM = .25

1.25 days elapse from Friday PM to Monday AM in our 308-day model.

Explaining the tweet

Translating:

1. On the floor I used a 365-day calendar model.
2. On Monday, the market seemed to only decay the options by 2/3 of what my model theta expected.
3. If I divide 1/3 the model’s theta for the weekend by the option vega that translates cents to vol points. Raising the vol in my model by that many vol points usually fit the market.
4. I would think of that as my benchmark for “vol is unchanged”. Differences in IV from that benchmark would be interpreted as “change in vol”

Measuring vol in this way means “vol does not structurally go up on Mondays” which makes sense. It probably doesn’t. It only looks like it does if your measuring stick assumes time passes as quickly on non-market days as business days.

Again, from Friday PM to Monday AM:

🕛Calendar day model: 2.25/365 or .6% of a year elapses

🕛Blended 308-day model: 1.25/308 or .4% of year elapses

The blended model says time passes at 2/3 the rate of the calendar day model.

Hence adding back 1/3 of the theta in vol points seems to line up well with assumptions of overnight .25 and weekend days being .5 each (inclusive of the overnight, just as 1 business day is inclusive of .25 overnight).

[Weekend is .5 weight but made up of weekend day .25 and overnight .25. You could argue weekend overnights are worth less because foreign markets are also closed, but since .5 seems to align with how much I’d have to adjust vols it’s a fine assumption even if I’m attributing the overnight and weekend day incorrectly. Hand-waving the deomposition would be a problem if I had to price an option on a Saturday.]

Bringing it altogether in an illustration

The percent of theta added back is in the ballpark of 1/3 depending on DTE but if you look at the error in vol points, it’s quite small (10% of 10 cents theta is a penny…for an option with 8 cents of vega this is .12 of a vol point).

Wrapping up

I’ll leave you with an assortment of considerations:

• If you are comparing IVs on assets with the same schedule the biases “cancel out”. Who cares if you are looking at relative vols and everything is biased high or low proportionally? This is the case for many option users. In other words, for almost everyone you can ignore this knowledge.
• (But moontower is written for an audience over a wide range so many of you will care and then there’s all the readers who just like weird technical stuff. And vol-time relativity is as worthy a nerd-snipe as anything else yea?)
• If you trade options on different expiry calendars (for example a USO option vs a oil futures option) then these differences will distort the IV spreads you’re observing.
• The distortions are amplified as event vols are incorporated into differing expiry calendars or am vs pm expirations.
• This matters far more for nearer dated options (ie < 1 month).
• Notice how I measured days from PM to PM. This is an artifact of working backwards from the expiration time which is typically after the close. But the more granular you get, the more the meaning of “when does this option actually expire?” matter. Can you contrary exercise? Does your broker have an earlier or later cutoff than other brokers. If AAPL pins on expiration but the index futures dive on geopolitical news after the close, then you would abandon any long calls on the pinned strike, exercise puts…or if you are short options on the strike expect to be stuffed with APPL shares by your counterparty. In other words, there is optionality after 4pm est.
• Spicier take: Trump having an interest in the assets open all weekend has implications for how fast time passes over the weekend. If weekends have more volatility, you’ll notice it in more decay transpiring from Friday to Monday. Unlike that last perplexity.ai bulletpoint’s assumption, this is not free money. The weekend gaps are larger (ie Friday pm to Monday am variance as a percent of Friday pm to Monday pm variance increases).

At the close of Friday, I was looking at far OTM gold put spreads.

With GLD at $275, the April 251/249 put spread is similar to a binary bet that GLD expires below $250 at expiry or about a 10% sell-off.*

You get 39-1 odds.

This is using market-based pricing, net of skew.

At-the-money vol is 16%.

Turns out 39-1 is about the right odds if we use 16% as a standard deviation. When I say “about right” I simply mean the gold left tail is basically conforming to an out-of-the-box Black Scholes distribution. I don’t mean B-S is “right” just that the put spread odds conform to what the B-S would say.

I wouldn’t expect that for SPX puts, but gold downside doesn’t have that much skew or tail fatness.

See the table mapping ATM vol relationship to the likelihood of ~10% selloff in a Black-Scholes world:

But a lesson that is far more important jumps out:

Implied volatility—the second moment of the return distribution—has almost no direct connection to the probability of catastrophic price moves!

Look how likely a 1-month 10% selloff is as a function of implied vol. If vol is 15% instead of 12% such a sell-off is 4x as likely and if it’s 18% instead of 12% it’s 10x as likely.

Just think of VIX…it can easily be 12 or 18, right? But what you should really take away from that is that volatility tells us very little about the tails.

Option Pricing on the Wing

A few things option traders learn early about pricing tails:

1. At-the-money volatility tells you nothing about the true probability of large moves.

2. Tail risks are not just “scaled-up” versions of small market moves.

3. Historical data is almost useless for extreme events because of sample size is too small to build robust probability estimates.

Instead, traders price tails based on…other tails.

Not backtests.

I invite you to keep your eyes open for sales pitches that pretend they know the likelihood of extreme moves and how they claim to know it. And if the sample sizes weren’t small enough, marketers might try to condition the probabilities — “when the market does X the probability of an extreme event does Y” which reduces the sample sizes even more. Godspeed with analysis that looks like that.

Inferring tail behavior from the meat of a distribution is so sensitive to small changes in volatility — so sensitive that it’s a clue that they’re not strongly related. I’m not making a math argument (I’m sure many readers could say what I’m saying formally). It’s a common sense observation that falls out of the volatility itself being volatile and sensitive to sampling.

The true odds of extreme moves are unknowable but there’s no reason to think they move increase an order of magnitude when VIX goes from 12 to 18, or for that matter, get cut by an order of magnitude when VIX falls from 18 to 12.

*The concept explained in a deeper understanding of vertical spreads