A Cleaner Dashboard: Z-Scores Instead Of Price Changes

Most investors or traders’ dashboards includes a watchlist with the field “percentage price change”. Perhaps you have several fields for this. Daily, weekly, monthly.

Here’s a useful way to filter out the noise and get a nicer view of the market action:

Re-scale all the moves in terms of standard deviations

My preference, although it relies on having options data, is to use implied volatility which is the market’s consensus for what the standard deviation is.

Here’s the formulas:

  • Daily = % change on day * 16/IV from yesterday’s ATM straddle
  • Weekly = % change on week * 7.2 / IV week ago
  • Monthly =% change on month * 3.5 / IV month ago

Implied vols are annualized numbers so the factors (16, 7.2, and 3.5) re-scale the vols for the measurement period.

These are just Z-scores!

Observations

  • If the absolute value of any of these numbers exceeds 1, the asset moved more than 1 implied standard deviation.
  • You can put all the assets on the x-axis of a barchart to see them visually. If you want, you can even subtract 1 from each value to see the excess move above one standard deviation. Or you set your filter at any other level.
  • This is not a tool to find opportunities or anything fancy, it’s literally just a cleaner way to visualize price moves and ignore noise.

I was too lazy to make one for stocks or futures, but the output will look like this (instead of MPG imagine it was “price change”):

If you want to use straddle prices which represent mean absolute deviation or MAD then divide the formulas further by .8.

The reason you use .8 is explained in my post Straddles, Volatility, and Win Rates.

What The Widowmaker Can Teach Us About Trade Prospecting And Fool’s Gold

We’re going to go on a little ride to talk about trade prospecting. We’ll use the natural gas futures and options market to demonstrate how to think about markets and what’s required to actually identify opportunities.
The nat gas market is all the rage these days as we head into the winter of 2021/22.

Let’s start with some background.

The Widowmaker

Enter the famous March/April futures spread in the natural gas market. This was the football famously tossed between John Arnold’s Centaurus and Brian Hunter’s Amaranth. You can get a good recount of the story here as recounted by the excellent @HideNotSlide.

The reason it’s a “widowmaker” is the spread can get nasty. The March future, henceforth known by its future code (H), represents the price of gas by the end of winter when supply has been withdrawn from storage.  April (J) is the price of gas in the much milder “shoulder” month. H futures expire in Feb but are called “March” because they are named by when the gas must be delivered. Same with J. They expire in March, but delivered in April. The H/J spread references the spread or difference between the 2 prices.

If you “buy” the spread, you are buying H and selling J.

  • If the price of the spread is positive, the market is backwardated. H is trading premium to J.
  • If the spread is negative, H<J (ie contango)
On 10/6/2021 the spread settled at +$1.44 because:
  • H future = $5.437
  • J future = $3.997

Introducing Options Into The Mix

There are vanilla options that trade on each month.
So there are options that reference the March future and they expire a day before the future (so in February).
  • H settled $5.437 so the ATM straddle would be approximately the $5.45 strike. Strikes in nat gas are a nickel apart.
  • For April futures the ATM strike is the $4.00 line. You can see the J straddle (ATM C + P) settled around $1.14
Image

Commodities Are Not Like Equities

Every option expiry in equities references the same underlying — the common stock price. If you trade Sep, Oct, Nov, or Dec SPY options they all reference the same underlying price.
The December 100 call cannot be worth less than the November 100 call because of simple arbitrage conditions. Your December options also capture the volatility that occurs in November (in fact if you wanted to bet on the volatility just in December, you would structure a time spread that bought December vol and sold November vol, to strip out all the time before November expiration. The structure of that trade is beyond the scope of this post.)
This doesn’t work in commodities because each month has a different underlyer.
Recall H =$5.437 and J = $3.997
  • The H $5 call is almost .44 ITM
  • The J $5 call is a full dollar OTM

Despite J options having a month longer until expiry, the J $5 call trades waaaay under the H $5 call.

It gets better.

Even if H and J were trading the same price, the H $5 call can trade over the J $5 call. This is where newcomers to commodities from equities find their muscle memory misfires.

The H implied volatility can go so far north of the J vol that it can swamp the 1 month time difference.

As described earlier, in an equity, March and April options would reference the same underlyer so owning April vol exposes you to the March vol.

Not true in NG.

Severing the arbitrage link between spreads

Backwardation
H is trading above J. The spread is backwardated. But H and J are not fungible. They are deliverable at different times. If you need H gas, you need H gas. It’s cold today. You cannot wait for J gas to be delivered. You won’t need it then.
This is generally true in commodities.
There is no arb to a backwardated market.
Contango
A contango market can be bounded by the cost of storage. Be careful though. The steep contangos of oil in Spring 2020 and around the GFC are lessons in “limits to arbitrage”. The cost of storage is effectively infinite if you run out of storage. So contango represents the market “bidding for storage”. You can’t just build new storage overnight. The other major input into contango spreads is the funding cost of holding a commodity either via opportunity cost or interest rates. THE GFC was a credit crunch. Funding was squeezed. That cuts right to the heart of “cost of carry” that contango represents.

So we now understand that H and J can become unhinged from each other. That’s why the spread is a widowmaker. It can be pushed around until convergence happens near the expiry of the near month. That’s when reality’s vote gets counted.

More Complexity: Options On Those Crazy Spreads

You can also trade options directly on the H/J futures spread. Since H/J is considered a calendar spread, the options are cleverly named:
Calendar spread options.
The cool kids refer to them as “CSOs”.
Let’s talk CSOs.
We established that the H/J future spread is $1.44
  • You can buy a call option on that spread. You can buy (or sell) an OTM call, like the H/J $10 call.
  • You can buy an ITM call like the H/J $1 call. That option is 44 cents ITM.
  • You can buy a put on the spread. If you buy the H/J 0 put (pronounced “zero put”), that option is currently OTM. It goes ITM if H collapses relative to J and the spread goes negative (ie contango).
These exist in WTI oil as well. Imagine a fairly typical market regime where oil is in contango. The CL1-CL2 spread might trade -.40. That means the front month is .40 under the second month. CSOs trade on these negative spreads as well! If someone buys the -$1.00 put they are betting the market gets even more steeply contango.
I’ll pause for a moment.

Right now, you playing with an example in your mind. Something like: “so if I buy the -$.25 call, I’m rooting for…ahh, CL1 to narrow against CL2 or even trade premium into backwardation”

Don’t be hard on yourself. This is supposed to hurt. It hurts everyone’s head when they learn it. It’s just a language. The more you do it, the easier it gets and with enough reps you won’t remember what it was like to not be able to understand it natively.

Real-life example

These prices are from 10/6/2021 settlement.
H settled $5.437
The H 15 strike call settled $.42
H/J spread = $1.44
H/J $10 CSO call = $.38
Let’s play market maker.
You make some markets around these values:
  • Suppose you get lifted on the CSO call at $.40 (2 cents of edge or 20 ticks. 1/10 cent is min tick size)
  • Meanwhile the other mm on your desk gets her bid hit on the vanilla H 15 call at $.40 (also 2 cents of edge)

Your desk has legged getting long the H 15 call, and short the H/J 10 call for net zero premium. If we zoomed ahead to expiration what are some p/l scenarios?

  • H expires at $5 and J is trading $4 on the day H expires or “rolls off”. Therefore H/J = $1
    • Both calls expire worthless. P/L = 0
  • H expires $15 and J is trading $4 so H/J is $11.
    • Ouch. Your long call expired worthless and your short H/J $10 call expired at $1.00. You just lost a full $1.00 or 1,000 ticks. That’s a pretty wild scenario. H went from $5.43 to $15 and J…didn’t even move?!

How about another scenario.

  • H goes to $16 and J to $7. So H/J expires at $9.
    •  The $10 CSO call you are short expires OTM and the vanilla H 15 call earned you $1.00. Now you made 1000 ticks.

It quickly becomes clear that vol surfaces for these products are untamed. Option models assume bell-curvish type distributions. They are not well-suited for this task. You really have to reason about these like a puzzle in price space. I won’t really dive into how to manage a book like this because it’s very far out of scope for a post but it’s critical to remember that pricing is just one consideration. Mark-to-market, path, margin play a huge role.

Sucker Bets

The truth is the gas market is very smart. The options are priced in such a way that the path is highly respected. The OTM calls are jacked, because if we see H gas trade $10, the straddle will go nuclear.

Why? Because it has to balance 2 opposing forces.

  1. It’s not clear how high the price can go in a true squeeze or shortage
  2. The MOST likely scenario is the price collapses back to $3 or $4.
Let me repeat how gnarly this is.
The price has an unbounded upside, but it will most likely end up in the $3-$4 range.
Try to think of a strategy to trade that.
Good luck.
  • Wanna trade verticals? You will find they all point right back to the $3 to $4 range.
  • Upside butterflies which are the spread of call spreads (that’s not a typo…that’s what a fly is…a spread of spreads. Prove it to yourself with a pencil and paper) are zeros.
The market places very little probability density at high prices but this is very jarring to people who see the jacked call premiums.
That’s not an opportunity. It’s a sucker bet.

Let me show you what’s going on with the CSOs:

Image

The CSO options tell us that the H/J spread has roughly 3% chance of settling near $2, a 2% chance of ending near $3 and a 0%  chance of settling anywhere higher than that.
And yet the futures spread is trading $1.44 today! And the options fully expect that to collapse.
What is going on?
Look at history. Even in cold winters, the spread almost always settles….at zero! When H expires, it is basically going to be at the same price as J.
Now, I know nothing of gas fundamentals. And none of this is advice. And I’m not currently up on the market, but I am explaining how these prices look so crazy (as in whoa look at all this opportunity) but it’s actually fair.
The market does something brilliant.
It appreciates path while never giving you great odds on making money on the terminal value of the options.

The Wider Lesson

So how do you make money without a differentiated view on fundamentals in such a market?

There are 2 ways and they double as general lessons.

  1. Play bookie

    You have a team that trades flow. You are trading the screens and voice, you’re getting hit on March calls over here, you’re getting lifted on March puts over there, you’re buying CSO puts on that phone, your clerk is hedging futures spreads on the screens. Unfortunately, this is not really a trade. This is a business. It needs software, expertise, relationships. Sorry not widely helpful.

  2. Radiate outwards

    The other way to make money is prospecting elsewhere, with the knowledge that the gas market is smart. It’s the fair market. It’s not the market where you get the edge, it’s the one that tells you what’s fair or expected. So you prospect for other markets or assets that have moved in response to what happened in the gas market, but did so in a naive way. A way that doesn’t appreciate how much reversion the gas market has priced in. Can you find another asset that’s related, but whose participants are using standard assumptions or surfaces? Use the fair market’s intelligence to inform trades in a dumber or less liquid or stale market.

Trading As a Concept

Many people think that trading is about having a view. Trading is really about measuring the odds of certain outcomes based on market prices. Markets imply or try to tell us something about the future. The job is to find markets that say something contrary about the future and take both bets. Arbitrage is an extreme example of this. If one person thinks the USA basketball is 90% to win the gold and another thinks the field is 15% to win the gold you can bet against them both and get paid $105 while knowing you’ll only owe $100. Trading identifying similar examples but of course in reality they are hard to find, more difficult, and require creativity and proper access.To see the present clearly you must be agnostic. You look for contrary propositions. Trading is not about having strong opinions. It’s not thematic. You don’t have some grand view of what the future looks like or the implications of some emerging technology or change in regulations. You just want to find prices that disagree.
Why would you slug it out in smart markets? Use them to find trades in markets that radiate away from them that are not incorporating parameters from the smart market fully. If you can’t get away from fair markets, you are going to need to be absolutely elite.
Battling it out in SPY reminds me of this cartoon:

The solutions in markets are rarely going to be where it’s easy to see because that’s where everyone will be looking.

Happy prospecting.


If you found CSOs interesting recognize there are physical assets that are just like options on a spread.

  • Oil refineries =Heat/Gas crack options
  • Power plants =  Spark spread options
  • Oil storage facility = WTI CSO puts
  • Soybean mill that crushes soy into meal/bean oil

If you had a cap ex program to build one of these assets how would you value it? You’d need to model volatility for the spread between its inputs and outputs!

The owners of these assets understand this. They are the ones selling CSOs! It’s the closest hedge to their business.


I got the data for this post from the CME website’s nat gas settlements page.
The dropdowns on the right of the page should keep you busy.
Image

Teach A Math Idea To Internalize It

My 8-year-old Zak is going to be taking the OLSAT soon. It’s a 64-question test that looks an awful lot like an IQ test. The test (or one of its brethren like the CoGat) is administered to all 3rd graders in CA. If you score in the top 2 or 3% you can be eligible for your local ‘gifted and talented’ program. 20% of the questions are considered “very challenging” and that’s where the separation on the high end happens.

I gave Zak a practice test just to familiarize him with it. He’s never taken a test with a time limit before and never filled out Scantron bubbles. Do not underestimate how confusing those sheets are to kids. It took a while for him to register how it worked because he only saw choices A,B,C,D for each of the 64 questions.

Daddy, the answer to question 1 is ‘cat’ not A,B,C, or D

I know, Zak, it’s just that…you know what bud, how about just circle the right answer on the question for now.

Hopefully, some practice breaks the seal so he isn’t scared when he sits for his first test ever. I think a small amount of prep is helpful even though I get the sense that caring about tests is not in style around here. Call me old-fashioned. I’m not bringing out a whip, but having the option to go to the program seems worth putting in a token effort if you think your kid has a shot.

Anyway, he took one test. Poking around a bit, I think his raw score would land him in the 90th percentile. Not good enough but it was his first shot and if he doesn’t improve much, that’s also totally fine too. Plenty of people are content just flipping burgers (I’m kidding, calm down. Also, get your own kid to stuff your insecurities into). One thing did stand out. He got all the math questions (about 1/3 of the test) correct.

Hmm.

It made me think of how I was a decent math student growing up.

I'm Something of a Scientist Myself | Know Your Meme

Not good enough to compete with peers who did math team in HS, but enough to get through Calc BC. Regretfully, I never took another math class after that. I optimized my college courses for A’s not learning. Short-sighted.

I really felt the pain of that decision when I got hired to trade options and was surrounded by a cohort in which 50% of the trainees had an 800 math SAT. (There were 3 people in our office of about 60 that had an SAT verbal > math. I was one of them.) That inferiority exists even to this day. Until Google Translate can decode academic papers, those things are for lining birdcages.

However…

Every now and then, I’ll come across a math topic that seems useful for making estimates about practical things, so I’ll learn it.

And then I’m reminded I have no math gifts because that learning process is uphill in molasses. When I was young I did lots of practice problems (how else are you supposed to become a doctor and please mom) which got me proficient. Today, it’s a similar process. I just power through it.

But there is a difference in how I power through it.

Instead of practice problems, I watch YouTube until I can write the ELI5 version for others. Everyone has heard that if you want to test your knowledge, teach it to others. In that case, it’s a win-win. We all learn.

So that’s what I did this week. I wrote an ELI5 version of a concept called Jensen’s Inequality.

  • Jensen’s Inequality As An Intuition Tool (10 min read)

    You will learn:

    • Why I found Jensen’s Inequality interesting
    • The conditions and statement of the inequality
    • An example that affects us all
    • Spotting Jensen’s in the wild

    If you struggle to understand it after reading it tell me. I am challenging myself to see if I can relay not just the concept but the significance of it with minimal effort on behalf of the reader. If I can get to the point where I’m “putting in the effort so you don’t have to” then I’ll feel like I’m being useful here.

    If you think you got it, test yourself the way I did. Construct an example. (That’s what I did with the “traffic on the way to Sizzler” example.)

  • If you grok Jensen’s Inequality and want to relate it to portfolio construction Corey is your guy. Before I learned of this concept his tweets would have made no sense to me, but now I at least kinda get it.

Understanding Vega Risk

In a chat with an options novice, they told me they didn’t want to take vol (vega) risk so they only traded short-dated options. This post will explain why that logic doesn’t work.

Here’s the gist:

It’s true that the near-term option’s vega is not large. That is counterbalanced by the fact that near-term implied vols move faster (ie are more volatile) than longer-term vols.

The goal of this post is to:

  • demonstrate that near-term vols are more volatile both intuitively and with napkin math
  • show the practical implications for measuring risk

Near Term Vols Are More Volatile

An Intuitive Understanding

Think of the standard deviation of returns that a stock can realize over the course of a week. If there is a holiday in that week the realized volatility will likely be dampened since there are 4 days of trading instead of 5. If Independence Day falls on Friday, Thursday might see even lower volatility than a typical trading day as fund managers chopper to the Hamptons early. On the other extreme, if a stock misses earnings and drops 25%, then we have a Lenin-esque week where a year happens. The range of realized volatilities is extremely wide. This requires the range of implied volatilities to be similarly wide for a 1-week option. Those large single-day moves are diluted when they are part of a computation for 1-year realized volatility (there are 253 trading days in a year).

This concept is easily shown with a “volatility cone” (credit: OptionsUniversity)

Here we can see the standard deviation of realized volatility itself declines as the sampling period lengthens.

The Napkin Math Understanding

The intuition for why the range of short-dated volatility is wider than long-dated volatility is easy to grasp. To cement the intuition let’s look at a numerical example.

Consider:

A weekly option [5 days til expiry]

Assume the stock’s daily vol is expected to be 1% per day. The fair implied vol can be computed as follows:

IV = sqrt(.01² x 5 days x 52 weeks) = 16.1%1

Remember variances are additive not standard deviations so we must square daily vols before annualizing them. We take a square root of the expression to bring it back into vols or standard deviation terms.

Ok say 1 of those days is an earnings day and is expected to be 3% daily vol.

IV = sqrt([.01² x 4 days + .03² x 1 day] x 52 weeks) = 26%

Look what happened.

The single-day expected vol jumping from 1% to 3% means there is more variance in that single day than the remaining 4 days!

.01² x 4 days < .03²

How did this earnings day affect the fair IV of a longer-dated options?

A 2-week option [10 days til expiry]

 IV =  sqrt([.01² x 9 days + .03² x 1 day] x 26 bi-weeks) = 21.6%

A 1-month option [21 days til expiry]

IV = sqrt([.01² x 21 days + .03² x 1 day] x 12 months) = 19%

The increased vol from a single day is clearly diluted as we extend the time til expiry. When we inserted a single day of 3% vol:

  • The 1-week option vol went from 16% to 26%. 10 vol point increase.
  • The 1-month option went from 16% to 19%. 3 vol point increase.

To understand why this matters look at the effect on P/L:

Remember, the vega of the 1-month straddle is 2x the vega of the 1-week option.

    • The 1-week straddle increased by 10 vol points x the vega.
    • The 1-month straddle increased by 3 vol points x 2 x the vega of the 1-week straddle

      10x > 6x

      The 1-week straddle increased in price 10/6 (ie 66%) more than the 1-month straddle!

      (This is why event pricing is so important. The astute novice’s head will now explode as they realize how this works in reverse. You cannot know what a clean implied vol even is unless you can back out the market’s event pricing)

Practical Implications For Measuring Vega Risk

Comparing Risk

So while a 1- month ATM option has 1/2 the vega of a 4-month option2, if the 1 month IV is twice as volatile it’s the same vega risk in practice. You need to consider both the vega and the vol of vol!

In practice, if I tell you that I’m long 100k vega, that means if volatility increases [decreases] 1 point my position makes [loses] $100k. But this risk doesn’t mean much without context. A 100k vega position means something very different in a 1-week option versus a 1-year option. Looking at a vol cone, we might see that 1-week implied vol has an inter-quartile range of 30 points while 1-year vol might only have a 3 point range. You have 10x the risk if the vega is in the weekly vs the yearly!

Another way of thinking about this is how many contracts you would need to have to hold 100k vega. Since vega scales by sqrt(time) we know that a 1-year option has √52x or 7.2x as much vega. So to have the equivalent amount of vega in a 1-week option as a 1-year option you must be holding 7x as many contracts in the near-dated.

Normalizing Vegas

It’s common for traders and risk managers to normalize vega risk to a specific tenor. The assumption embedded in this summary is that volatility changes are proportional to root(time). So if 1-week volatility increased by 7 points, we expect 1-year vol to increase by 1 point.

This is an example of normalizing risk to a 6-month tenor:

Observations:

  • Your headline raw vega is long, but normalized vega is short
  • Your 2,000 vega in a weekly option is more vol risk than your 10,000 vega in the 6-month
  • You want the belly of the curve to decline faster than the long end. This is a flattening of the curve in a rising vol environment and a steepening in a declining vol environment.
  • If the entire vol curve were to parallel shift lower, you’d lose as you are net-long raw vega.
  • If we choose to normalize to a different tenor than 180 days, we would end up with a different normalized vega. The longer the tenor we choose, the shorter our normalized vega becomes (test for yourself).

Critically, we must remember that this summary of net vega while likely better than a simple sum of raw vega is embedding an assumption of sqrt(time). If you presume that vol changes across the curve move in proportion to 1/sqrt(t), the value of calendar straddle spreads stays constant. At this point, you should be able to test that for yourself using the straddle approximation in the footnotes. This would imply that as long as your total normalized vega is 0, you are truly vega neutral (your p/l is not sensitive to changes in implied vol).

As you might expect, that assumption of sqrt(time) vol changes across the curve is just a useful summary assumption, not gospel. In fact, on any given day you can expect the curve changes would deviate from that model. As we saw above, the bottoms-up approach of adding/subtracting volatility with a calendar has uneven effects that won’t match up to sqrt(time) rule. Your actual p/l attributed to changes in volatility will depend on how the curve shifts and twists. Perhaps the decay rate in a vol cone could provide a basis for a more accurate scaling factor. It does require more work plus scaling to time allows us to normalize across assets and securities more understandably rather than using some empirical or idiosyncratic functions.

Conclusion

Just because the vega of a longer-dated option is larger doesn’t necessarily mean it has more vol risk.

  • We need to consider how wide the vol range is per tenor. We looked at realized vol cones, but implied vol cones can also be used to approximate vol risk.
  • We need to recognize that a steepening or flattening of vol curves means the price of straddle spreads is changing. That means a vega-neutral position can still generate volatility profits and losses.
  • Changing straddle spreads, by definition, means that vol changes are not happening at the simple rate of sqrt(time).
  • Measuring and normalizing vols (or any parameter really) always presents trade-offs between ease, legibility/intuition, and accuracy.

Shorting In The Time Of ShitCos

HTZG, GME, now HWIN.  The more slandered or shorted or ridiculous the name is the more bullish it seems to be for the stock. Just imagine explaining this to an alien.

“I bought a deli for $100mm. It’s an investment.

A deli? Well… it’s a place where people from the surrounding neighborhood go midday for some protein stuffed into wheat…umm, no, not every person in the neighborhood. Just like some of them. Why not everyone? There are other delis I guess. And a McDonald’s. Oh, you have those too? Yea I love the fries myself. Ah, yes back to the deli. Right, so the deli actually has to buy the ingredients. Correct, it doesn’t grow them. Slaves? What? No, no, no. Those people are called “employees”. I have to pay them. And yes, that guy needs to be paid too. IRS. We call him IRS.

Did I mention it has the best dills?”

The entire shorting business model appears to broken. In a period where concentrated shorts are getting lit up, in a period where diamond hands combined with brick brains, shorting just looks like return-free risk. Or at least the style where you try to recruit support after establishing the short.

I think @Mephisto731 is correct. Probably super correct. The best time to sell insurance is after the earthquake blows out your competitors.

You’re sneering. Fine, I’ll play along.

Common Objections To Shorting

It’s common for shorting detractors to mock the strategy as negative EV for 2 reasons. I’m just going to annihilate them now so we can get to a more productive discussion.

  1. Stocks have positive drift (aka “stonks only go up”)

    I get it, you are fighting the most fundamental risk premia. The “equity risk premia”. First of all, that’s debatable. After, all most stocks go to zero. Stock indices have risen over time thanks to rebalancing. But more clinically, the negative drift, can be offset by just offsetting the beta. You can short the target and get long a basket to sterilize the drift. So, in practice, and possibly in theory, this positive drift objection can be put to rest.

  2. Stocks have unbounded upside but limited downside

    This has no bearing on the EV of shorting. Anyone familiar with options understands that individual stocks have positive skew. If a stock is $100 despite everyone knowing that it is bounded by zero and infinity then the odds of it going down are the counterbalance. And the fact that most stocks go to zero is in keeping with that understanding. So, stop citing the unbounded upside as a reason why shorting is negative EV. Remember EV is a sumproduct of terminal prices and probability.

That said, shorting is no stroll in the park. We just don’t need to fabricate objections like the ones above to show that.

The Real Reasons Why Shorting Is Difficult

  • No limit to arbitrage on the short side

    First, think of the long side. I’ll paraphrase Sam Bankman-Fried’s explanation from his recent Odd Lots interview:

If AAPL stock price went to $1 tomorrow, Warren Buffet or whoever would just buy the whole company. It makes billions of dollars in earnings and you could just buy all the earnings for less than the stock price if it got low enough. But on the short side, there is no mechanism to moor the stock to reality (although as we learned from the Archegos saga, a secondary to feed the ducks, has consequences).

This lack of limit to arbitrage doesn’t change the EV of the stock which is already balanced by probabilities, but it does change the path behavior. You need to borrow shares to be short, and any share borrowed means a future buy order. So inflows of cash can cascade into forced covering since the short-seller is effectively levered.

  • The negative gamma effect

    I’ve explained this before with respect to shorting, but I’ll re-hash it simply. When a fund sizes a short it does so as a percentage of its AUM. Say the short is 10% of its AUM. You can think of the AUM as the denominator and the dollar-weighted short as the numerator. This ratio starts at 10/100.

    What happens if the fund wins on the trade because the stock drops 50%?

    Well, now the fund has made 50% on a 10% position, so its new equity is 105. Yet, the size of the short shrank with the stock halved. So now the numerator is 5, not 10 units. So the short is now 5/105 or 4.7%. The fund needs to more than double the size of the short to maintain constant exposure as a percentage of AUM. Both the numerator and denominator moved in a way that reduced the position.

    This looks just like short gamma. You need to sell more as the stock falls!

    When the stock rallies, the size of the short (numerator) increases, while the fund’s equity (denominator) gets hammered. Both forces conspire to force short-covering. Or buying, in a rallying market. Negative gamma. And to think, you often pay to borrow stocks, so you get the indignity of paying theta to play this game.

The Options Approach

Let’s address the ways we can use options to be short.

  • Synthetic shorts

    If you want to implement the short in the most similar way to a short stock position, then you will want to structure a “synthetic short”. Just like a stock position, it has 100 delta and no Greeks except exposure to cost of carry. But you faced that risk from the prime you borrow shares from anyway.  In this case, the borrow cost is embedded in the options but the clearing rate for that cost will be inherited from the arbitrageurs with the best funding rates.

    How to implement a synthetic short

    You buy a put and short a call on the same strike in the same expiry. To prove to yourself that it is the exact same exposure as a short stock position work through this example:

    Stock is $100
    You buy the 1 year 100 put for $10 and sell the 1 year 100 call at $10.

    The stock drops to $80 by expiration. What’s your p/l?
    What if the stock ripped to $120?

The synthetic short will have the same path risks as an actual short so let’s move on to option strategies that mitigate the path risk.

  • Outright puts

    If short-selling seems like it has negative gamma, you could always substitute your trade expression with long options. At least, you get something for the theta.  So while you will be paying to borrow, it might actually be at a better rate than you can borrow from your broker. And the moment you buy the put, the funding rate is capped at the implied cost you traded at. If the borrow gets more expensive from that point forward, your put will actually appreciate in step with its rho.

    The risks of buying puts are familiar. You can be wrong on timing, vol, how far the stock actually falls.  You can get middled. Your thesis can be right but not right enough.

    The benefit is you cannot lose more than the premium (unless you dynamically hedge…but if you are using the puts directionally then you shouldn’t be doing that anyway). This simple fact turns your strong hand into a weak hand. You always reserve the right to roll your puts down as you take profits or up to chase the rising stock. But the basic position, while risky, is path-resistant. And path is why shorting is so hard.

  • Put spreads

    Buying a put vertical (buy 1 put, sell a lower strike put, same expiry) sterilizes many of the Greeks since you buy and sell an option, including some of the borrow costs.  The tighter the strikes the more the bet looks like a pure probability play. If the strikes are wide, your further OTM will not offset the Greeks of the near put as much (if you think about it, an outright put position is the same thing as a put spread where the further OTM strike is the zero strike).

    If the stock has a lot of negative sentiment around it, depending which put spreads you choose, it’s possible you are getting a bargain if the put skew is especially fat.

Options and the “Write Down Your Thoughts” Effect

I’m not shilling for options here. I’m just pointing out that in a market that is scaring vanilla short sellers away, there are trade expressions that allow you to stay in the game at the time when you probably want to the most. Even if you decide not to use options, there is a benefit from walking through the trade construction process — it will tighten up your thinking. It’s like journaling.

Before choosing an option implementation, you should write down your answers. I’d be surprised if the answers to these questions didn’t impact how you might frame a vanilla short.

Let’s walk through questions you must answer before buying a put spread.

  • Edge: if the put spread I’m looking at pays 6-1 what do I think the true odds are? 4-1? 3-1? The amount of edge AND the fact that we are talking about a bet with a sub 25% hit ratio will dictate my risk budget.
  • Risk budget: How much am I willing to lose in premium?
  • Should I spread my risk budget over several months or is there a specific catalyst or expiring lockup that favors concentrating the bet in a single month?
  • Which put spread should I buy? Would I rather buy $1,000,000 worth of the 85%-80% put spread or the 70%-65% if $1,000,000 buys me 2x as many of the further OTM spreads. Or maybe I prefer a higher delta trade, that pays off more often but pays smaller odds. This forces me to think about price targets and the market’s relative implied pricing of those targets. It directs your attention to the meatiness or winginess of your thesis.
  • Does the winginess or meatiness of my thesis correlate to any other forces in the market or is it a purely idiosyncratic idea? For example, if you were interested in owning put spreads on a portion of the ARKK basket, then you could concentrate your put spreads on the subset of the basket that offered the best implied odds. Your thesis wasn’t specific to a single stock but more of a general liquidity trade.
  • How much dry powder do you want in reserve to roll your put spread up when the stock rallies? What thresholds would trigger rollups? Likewise, if the stock sells off, will you roll spreads down? How about down and out into a further calendar month? Will you roll down on a 1-to-1 basis (taking profits) or aggro win-big-or-go-home style where you use 100% of the collected premium to buy a boatload of further OTM put spreads?

Working through these questions refines your thinking and creates a plan for different scenarios. I find that the granularity of options and layers of relative pricing force me to “write down my thoughts” in a way that delta 1 trading can easily gloss over.

Conclusion

Short-selling is hard. Not because it’s negative EV, but because limits to arbitrage and the reality of levered return math create perilous paths. Whether the bruises from the recent mania will usher in a “golden age of short-selling” remains to be seen. But removing an entire direction of returns from your arsenal seems short-sighted. It’s a surrender to the current moment just when you should be thinking hardest about profiting from names that on a long enough time frame will have prices that match their ShitCo status. Options provide a more path-hardy set of trade expressions and may become table stakes for investors (ie hedge funds) whose mandates should not allow them to ignore the short side.


Related:

The difficulty with shorting and inverse positions

Shorting Bimodal Stocks

A Thought Exercise For Outsourcing Liquidity Risk

Understanding Edge

In my indoctrination into trading, the term “edge” was equated to the bookie’s “vig” or a casino’s “house edge”. This makes sense since I started in this business as a market maker. The interview questions I faced were focused on mathematical expectation or expected value. For example, if someone offered you a game that pays you the number that comes up on a single die, what would you pay to play? The weighted average payout of the game is $3.50. So if you can pay $3 to play, you’d make $.50 in theoretical profit. Of course, you could still lose if you roll a 1 or 2, but if you could do this every day, you’d earn 14% ($.50/$3.50) in the long run.

The basic premise of the market-making business is 2-fold: capture edge and manage risk so you can survive to actually see that long run.

  1. The edge comes from identifying the fair price.
  2. The primary risk management levers are diversification and sizing.

If you can price accurately and manage risk competently, you can crystallize the edge as surely as the Wynn prints money.

In this post, I will share:

  • the nature of edge in both trading and investing contexts
  • unbehaved edge in the real world
  • intuitions you can take with you

The Nature Of Edge in Trading And Investing

First, let’s define fair value. I will decompose it into 2 concepts.

  1. Expectation

    This can be a price that is ultimately an arbitrage. The die game from the intro or a casino game can be squeezed into this since the asset’s expectancy can be computed. With a large enough bankroll or sufficiently small bet size, it’s practically impossible to lose in the long run. Cash/futures arbitrage and creating/redeeming ETFs trading away from NAV are market examples.

  2. The liquid price

    In the market maker pasture, I was raised in, we’d call any price that was transparently and liquidly trading “fair value”. If the market for an option was “choice” or “pick’em” with deep-pocketed players on both sides then it was “fair”. We might say “fair value is $5, Goldman Sachs by JP Morgan”. In other words, a GS client was $5 bid and a JP Morgan client was offered at $5, it was trading, and there was enough size available for anyone else to basically participate. It’s a fleeting concept, but useful. We could use that price as a benchmark to compare less liquid derivatives as we looked for relative value.

With the idea of fair value established, we can begin exploring the nature of edge with a familiar toy model — the coin flip.

The Power Of Small Edges

Imagine a coin flip game. Call the toss correctly, make $1, otherwise, lose $1. Let’s pretend you could predict the coin flip with 50.5% accuracy. Sweet.

  • What’s your edge?

The expected value of playing the game is 1% because your payoff is equal to .505 * $1 – .495 *$1

  • What’s the standard deviation?

    From the binomial distribution, we know the standard dev or vol is √(.505 * .495) or 50%

  • What’s your risk/reward (Sharpe ratio)?

    I’m going to use the term “Sharpe ratio” in a specific context, as the ratio of edge to volatility. This is intuitively important since edge doesn’t mean much without a measure of variance. For this single toss, the Sharpe ratio is a measly .02 (1%/50%).

1% edge on this coin flip doesn’t seem like much. The .02 Sharpe ratio is a laughable signal to noise ratio. But as we increase N from 1 flip to many, the binomial distribution can be closely approximated by the familiar Gaussian curve [Taleb, spare my window, I’ll address reality later].

Look closely. The Sharpe ratio increases with N. Specifically, it increases at the rate of √N.

Why? Because the edge or numerator grows linearly with N while the denominator, or vol, only increases at √N. This property of edge is the foundation of trading and gambling. With enough trials, victory is nearly guaranteed. With a 1% edge on a coin flip, you are 90% certain you will be up money after 4,000 trades. So if you have 10 traders making 20 trades each business day, in one month you are more than 90% certain you are winning. In one year, you can’t lose.

Getting A Feel For Edges

Let’s look at the math in reverse. In Excel, we can use Norm.INV() to find what return corresponds to a desired probability for a given EV and vol. Let’s say we want to be 95% certain we make money. In math language, we are interested in the point where the 5th percentile return of the CDF is equal to 0.

We want to ask Excel:

How many trials do I need to have so that my Sharpe ratio sets my 5th-percentile return to zero?

To do this let’s standardize the vol to 1. The equation we need to solve is:

NORM.INV(5%, EV, 1) = 0

To solve for EV we use Excel’s goalseek function. We find EV = 1.645

Since we standardized the vol to 1, then we have discovered that at a Sharpe ratio of 1.645 (again Sharpe is EV/vol), the 5th percentile return is 0. That is the Sharpe ratio we need to be 95% certain we make money.

Remember that having 1% edge on a single coin flip only has a Sharpe of .02

But as we increase N, the Sharpe increases by √N :

SR of 1 trial x N/√N = SRN
.02 x N/√N = 1.645
N = 6,764

If we flip the coin 6,764 times, we are 95% sure we will make money even though we have a tiny edge on a volatile bet.

Let’s recap in English what we did here:

  1. Compute the risk/reward or Sharpe for a single bet
  2. Figured out the risk/reward needed to be 95% certain we will make money on a series of bets
  3. Computed how many times we need to play to achieve that risk/reward

Let’s look at the relationship between a single bet Sharpe to how many trials we need to be 95% certain we win.

  • If we have .02 Sharpe per bet, we need to do 25 trades per day for a year to be 95% certain of making money.
  • If we have .10 Sharpe per bet, then 1 trade per day will help us realize the same risk/reward over the course of a year.

This table highlights another important point: by increasing the Sharpe per bet by an order of magnitude (ie from 1% to 10%) we cut the required number of trials by 2 orders of magnitude (27,055 to 271).

Think about that. The improvement in Sharpe leads to a quadratic reduction in trials needed to maintain the same risk/reward for the series of bets.

Inverting the logic:

If the risk/reward of your bet is halved, you need to bet 4x as many times for the strategy to maintain the same overall risk/reward.

From Trading To Investing

The domain of many individual bets fits more under the umbrella of trading. For investing, we tend to think of the annual Sharpe ratios of investing styles or asset classes. Without looking this up, I’d guess that the SP500 has a long-term Sharpe ratio of about .40. I’m estimating an 8% annual return divided by 20% vol.

We can use the same math we did above to see how many years we’d need to invest to be 95% certain we did not lose money in nominal terms. Turns out the answer is 17 years. The table below finds the number of years for other combinations of expected return and volatility.

Years Required to Be 95% Sure of Profit

The Real World

Bell curves are great to build intuition but they are not reality. We can’t really be 95% sure we’ll make money by holding stocks for a generation because the historically sampled returns and volatilities are just that — sampled. We don’t know what the actual distributions are. Fat tails, skew, other moments I don’t even know about. 

We can use a highly skewed bet to demonstrate how volatility can distort our impression of risk. This renders the Sharpe ratio useless in highly skewed scenarios.

Consider 2 stocks, both are fairly priced at $100. We’ll call them Balanced Corp and Skewed Corp.

Balanced Corp is 50% to go up or down $10.

Skewed Corp has a 90% chance of going up $3.33 and a 10% chance of dropping $30.

Using the bimodal distribution we find that the stocks have the same volatility. However, they would have different straddle prices if there were options listed on them.

(It’s a good exercise for the reader to use what we know about expected value to manually compute the call and put prices).

So here we have 2 stocks with the same true volatility but different straddle prices if we compute them via expected value. Of course, we would not use B-S for a stock that was discontinuous and was going to magically open at one of 2 prices in a year. But this does show how the effect of a strong skew would suppress the value of a straddle for a given level of volatility. 

This is actually more intuitive than it appears. FX carry is a highly skewed trade that might exhibit minimal vol on a daily basis. The volatility imputed by the straddle understates the risk because it derives most of its value from the behavior of daily moves, where the risk of a jump will be better reflected in the cost of OTM options. In the above case, the Balanced Corp 90 put is worthless while the 90 put on Skewed Corp is worth $2 (10% of the time it finishes $20 in-the-money).

So if you use straddle prices to impute volatilities which are then used to calibrate Sharpe ratios, you may be understating the risk of highly skewed assets. Your risk/reward ratio is actually overstated which means it will take far more trials to realize your edge, assuming you actually have any. And remember how diabolical the math is…if your Sharpe ratio is overstated by 2x (let’s say you think it’s .8 and it’s actually .4), then you need 4x the number of trades to maintain the same assumptions about making or losing money. How would you feel if you found at the long-run for your given strategy wasn’t 10 years, but 40?

Takeaways About Edge

Self-aware investors and traders are always questioning their edge. Evaluating a track record or doing post-mortems on your own strategies requires being able to handicap the true distribution of your trades. The more Gaussian they look (for example if you play limit poker instead of no-limit) the easier it is to ascertain the strength of your edge statistically. You can tell the difference between bad run vs a change in the quality of your edge. Some runs would be almost impossible if your edge was real.

Edge is scarce. When we prospect for it, we should expect to mostly find fool’s gold. There are many reasons for this.

On skew

While both high volatility or high skew make it harder to determine if you have an edge statistically, skew is especially tricky. It is hard to see without liquid option surfaces. Here’s an intuitive way to see how skew distorts reality. Imagine finding a video poker machine that didn’t show its payoff table. Under the hood, it gives slightly worse payoffs on a pair of Jacks or better, but offered a billion to one on the Royal Flush. You could play that machine for days or even weeks and never realize you had massively positive EV.

On sample size

  • Having a small edge or number of trials makes it hard to verify an edge. Remember that when evaluating anyone trading highly volatile assets (ie crypto), engaging in highly skewed trades (carry, staking tokens for yield, option selling), or making a few concentrated bets per year (much of discretionary fundamental investors).

  • Remember the phrase “to think in N not T”. If there is a flow that shows up every day for a month do you have a sample of 30 or just 1 bit of behavior spread over 30 days? It’s the philosophical version of how auto-correlation artificially inflates N.

On luck vs skill

  • If you have negative edge, trade less. Short-term variance may turn up a friend named “Luck”. In the long run, she’s lost your number. 

  • In chess, a difference in ELO can be used to handicap a match between 2 players. Chess has no element of randomness. The signal is extremely strong. Backgammon has randomness, so the predictive strength of the ELO spread increases with match length. This comment in a chess forum cements this:

    While Magnus Carlsen would stand virtually no chance against the top chess programs, the Elo rating difference between Extreme Gammon, (the best bot) and the top humans is more like 75 points, so XG would be something like a 2-1 favorite in a 25-point match against the top human player.

The importance of edge

  • When I was a market-maker we were always on the lookout for a new source of edge (perhaps a new name to trade or spotting a new flow to trade against). Edge is pure gold. Its scaling properties are amazing if it’s genuine. We were encouraged to not worry about risk if we could find a legit edge. The firm would find a way to hedge some portion of the risk if the edge was worthwhile, and you could always use sizing to manage the risk. Finding edges was top priority. It’s what you build businesses around.
  • A 1% edge in a stock or ETF is enormous. Imagine buying a stock that was trading “fair” for $50 for $49.50. This is an order of magnitude more edge than HFTs earn. Hold my beer now as we do options. If the fair price for a call or put is $.50 and the bid/ask is $.49-.$51, you are giving up 2% edge every time you hit or lift. Before fees! Option prices themselves are more volatile than the underlying stock so from the market-maker’s perspective the Sharpe of the trade might be pretty small (getting 2% edge on a security that might have a 100% vol for example). But think of the second-order effect…the optical tightness of the market and high volatility of option prices means it can take many trades before the option tourist realizes just how much the deck is stacked against them. For independent market-makers, like I was 10 years ago, the tight markets made our business worse because our risk and capital limits did not allow us to keep pace with the volume scaling required to make up for the smaller edge per trade. But the large market-makers welcomed the increased transparency and liquidity because they could leverage their infrastructure effectively. 

  • If you make a 50/50 bet with a bookie but need to pay them 105 to 100 you are giving up 2.5% per bet (imagine you win one and lose one…you are down 5% after 2 bets). Now think of a vertical spread or risk reversal in the options market. Pay up a nickel on a $2 spread? Might as well have a bookie on speed dial.

Edge in the real world is nebulous

Firms with provable edges don’t try to raise money. If it’s provable it does not need more eyeballs on it. The epistemological status of edges that are trying to raise money is unknown. Many will never get the sample size to prove it. Asset management is the vitamin industry. It sells noise as signal. It sells placebos.  There will always be one edge that never goes out of style — marketing.

True mathematical edge is hard to find.


Related:

  • Nick Maggiulli’s Why You Shouldn’t Pick Individual Stocks: On The Existential Dilemma Of Stock Picking (Link)

  • Moontower Money Wiki: Time And Human Capital (Link)

Interview Questions A Market Maker Gave Me in 1999

SIG is well known for asking probability questions to filter trainees. This is not surprising. They view option theory as a pillar of decision-making in general. Thinking in probabilities takes practice which is why they like to look for talent amongst gamers who make many probabilistic decisions and need to interpret feedback in the context of uncertainty. They require many hours of poker during  “class”. In this 3 month period, junior traders live and breathe options in lovely suburban Philly after apprenticing (“clerking”) on a trading desk for about a year.

Here’s some of the questions I remember from my interviews in 1999.

  1. You flip a single die and will paid $1 times the number that comes up. How much would you pay to play?
    • Suppose I let you take a mulligan on the roll. Now how much would you pay (you are pricing an option now btw)?
  2. My batting avg is higher than yours for the first half of the season. It’s also higher than your for the second half of the season.

    Is it possible your avg for the full season is higher than mine?

    (Hint: Simpsons paradox)

  3. You are mid game that you have a wager on. Opponent offers to double the stakes or you automatically lose. (Like the doubling cube in backgammon)

    What’s the min probability of winning you need to continue playing?

  4. You’re down by 2 with seconds left in regulation basketball game and have a 50/50 chance of winning a game if it goes to overtime. You have a 50% 2-pt shooter and a 33% 3-pt shooter.

    Who do you give the ball to?

    (simple EV question)

  5. You are given $1,000,000 for free but there’s a catch. You must put all of it into play on roulette.

    What do you do?

  6. There’s a 30% chance of raining Saturday. 30% chance of raining Sunday.

    What’s the probability it rains at least one day?

To encourage you to try before looking up the answers, I’ll make it annoying…the answers are somewhere in this thread.

I wrapped that thread with a short post on Trading And Aptitude (Link)

Option Theory As A Pillar Of Decision-Making

  • Understanding Options and Decision-Making (Thread)
    @HideNotSlide

    In an old Barron’s Roundtable, Jeff Yass, the founder of SIG had strong words about how fundamental option theory is to decision making.

    Of course this sounds self-serving, from a guy who understood options as a young teen. But it reminds me of a more famous investor. Warren Buffet. I’ll rely on readers to find it but I remember Munger saying that Buffet was already thinking of options at a precocious age. While Buffet calls derivatives “weapons of mass destruction” his own investing history shows an explicit use of options (his put-selling maneuvers are well-documented…and critically path-resistant since they are not marked-to-market). I’m not a Buffet expert, but his use of “insurance float” sure looks like something that came out of the mind of a derivatives trader.

    • The Moontower Volatility Wiki is growing every week due to submissions from the online vol community. It also includes every post I’ve written on options, many of which try to use options theory to understand markets and think about probabilities.
    • Decision-making is a practice.
      • A pillar of sound decision-making is thinking in probabilities or as Annie Duke’s book is titled, Thinking In Bets. Here’s the notes I took on an interview with her which captures the essence.
      • This weekend I came across a great post by in the same vein by Jonathan Bales The Time I Sold Furbies For Money. I especially liked the bits about Belichick’s non-punt, and poker pro Phil Laak about learning what “5% feels like”. [Phil is a good friend of some friends I made in the options game so it was especially cool to see his thinking turn up in that post].

        I’ve previously commented on the neat analysis Bales himself did on the question of when you should “work for free”. You should follow @BalesFootball if you want to sharpen your “thinking like a gambler” sword.

  • A Personal Take

    I added thoughts on my days at SIG in response to the Yass thread. Here’s the text:

    When I was a Susq I heard Jeff speak a few times. It was always engaging.

    They were savage in my days there but the doubling down on tech and brains thru the years probably makes Jeff the richest dude in the world you never heard of (unless you look at pol donations, then you know). One of the talks was on the primacy of markets (Yass is an extreme libertarian, free-marketer, no fool should be allowed to keep their money type. Appealing views to many traders, esp when they are young). This post was one of his market lessons: Dinosaur Markets.

    One of my interactions with Jeff was a mystery to me:

    I remember when I was a 1st year mm on the Amex and I reported a giant trade that got crossed in AIG on the internal chat. I got a dm. “Pls call”. It was from Jeff. I was never so scared. Was I supposed to break that cross up? I called Jeff from an Amex phone and he just asked me for the trade details. Implied vols, who the broker was, what bank crossed it. I told him and he abruptly hung up. That was it. Still don’t know why of all the trades I’ve ever on reported why that warranted a call.

    Other times I’ve heard Jeff speak was on why the dot com bubble was not an example of market inefficiency and it goes back to understanding option theory and the relationship of volatility to positive skew and what drives volatility. I’ll write about that one sometime.

    He also speaks to every trading class for an hour that goes thru the 3 months of theory and mock trading in Bala Cynwyd. In my class he talked about career risk with NFL coaches affecting decisions (he defended an oft- mocked Barry Switzer decision to not punt)

    I will always be thankful for having worked and learned at SIG. I really didn’t have any business being hired there (2000 was the largest cohort bc $ was raining from the sky. They needed warm bodies to pick it up) and I think I’m proof that traders can be shaped and aren’t born. [By the way, this is very much why I try to teach what I’ve learned. Hopefully people smarter than me can build on it and let me invest in them 🙂 ]

    Incidentally, the head of HR who hired me gave important advice I always remember. When I explained I had a few higher offers she said:

    “You’ll be rich whatever you choose. Decide who you want to work with.”

    She knew SIG held the nuts.

Structuring Directional Option Trades

This post is a response to Twitter buddy @demonetizedblog

Let me take a stab at a “process” answer.

Introduction

For directional trading 90% of the work happens upstream of the option expression.

The option trade construction is the most trivial part of the process. Your fundamental work should inform your opinion of the distribution. This can be compared with the implied distribution from the vol surface.

This mental process is entirely different from vol trading. Remember, you aren’t dynamically hedging. Directional trading and vol trading have totally different starting points.

[At the end of the post you’ll see when the two approaches come to the same conclusion and when they don’t. This can lead to directional traders to trade with vol traders and everyone is happy. It’s still zero-sum. It’s just that the losses can be incurred by whoever provided the liquidity to the dynamic hedger. That entity was not part of the original trade]

Ok, so when it comes to directional trading vs vol trading, you must be clear what game you are playing.

This post is about structuring directional trades.

What’s the distribution?

First, you do a bunch of fundamental voodoo and come up with a distribution of possible stock returns.

[I’ll wait]

Good. We are going to discuss options now. Relax. Take a breath. Don’t worry about fancy words like “moments of a distribution” or kurtosis. You are a fundamental investor. It’s fine to think in prices, percentages, and bets.

Now what?

Let’s establish a focusing principle.

You want the short leg of an options spread to correspond the most likely landing spot of the stock based on your analysis. If those options are the cheapest on the board you might want to consider that the option surface is not presenting you an opportunity. It agrees with you. Don’t rush over that. This is not intuitive. Many fundamental managers buy the strike of where they think the stock is going. Don’t do that. Instead let’s review some basics about distributions. Without real math.

  1. A biotech stock worth $100 might be trading for that price because it’s 90% to be 0 and 10% to be $1000. True bimodal.

    Code-switching this idea into options:

    • The 100 call is worth $90.
    • All the OTM 100 point wide call spreads are worth $10.
    • All the butterflies are zero.

      What are some courses of action here?

      Let’s say you can afford 1 100 strike call. You could have also chosen 9 900/1000 call spreads. Or 3 of the 700 calls. In this case, all the propositions are the same because the options are correctly priced.

      [Prove this to yourself. I’ll wait.]

      Cool. Now you can imagine how if some of the options were priced differently you might be able to find an alluring proposition.

  1. New stock to consider. An insurance company also trading $100. This is not a bimodal stock. Perhaps it looks more like a bell curve with a high peak shifted to the right of the forward price because a pumped up put skew is signaling strongly negative skew.

    Wait. Why does that push the peak to the right?

    Think about it. For that stock to be $100 with a long left tail, it must have a greater than 50% probability of going up. The verticals will show you that. It’s the opposite case of the biotech stock and with much less volatility.

    • If you were super bullish you might want to load up on the depressed slightly OTM calls.
    • If you were bearish but thought the left tail was not as long you might want to buy the .50d/.25 put spread to express the view by exploiting the excess skew you think the market is embedding in the OTM puts.

Just remember, options give a shape to the distribution. Not every $100 stock has the same distribution. Think about where the $100 comes from? What upside force is counterbalancing the downside? The biotech stock has a very long right tail 900% away counterbalancing a large mass of probability that’s only 100% away. The $100 stock price is nothing like the insurance company. Options allow you to express the bet you want to express. The stock price alone is too blunt.

Once you let that simmer you can start to ask yourself useful questions:

  • Would you rather own 1 atm call or more calls for a total of the same premium at a higher strike?
  • Now compare that to call spread candidates. How many call spreads can you buy and at what moneyness?

The nice thing about vertical spreads is they cancel out many of the “greeks” effectively taming your vega and gamma exposures. The bets can be thought of as binaries allowing you to make simple over/under bets. To calibrate your impression of the possible magnitude of a stock move, you consider the moneyness or how far away from stock price the chosen strikes are. The moneyness will depend on your intuition for the volatility of the stock. You will have a sense for which spreads are “close” or “far”. These are technical terms.

And since I mentioned volatility, let’s say a few words on that to help you avoid some landmines.

Is the vol cheap or expensive?

If you are a directional trader you don’t care if the right volatility for an option is 55% or 56%. You aren’t dynamically hedging. But you don’t want to go to the used-car lot without at least checking Carmax online. You can compare the implied vol to the distribution of historical realized to make yourself feel like you did diligence.

Here’s a simple way:

Compare the IV to the stock’s historical vol of a comparable tenor. So if you are considering a 6 month option look at the distribution of 6 month historical vols to see if you are on the high or low side of the range. How? Looking at a vol cone will get you a quick optical answer.

Here’s Colin Bennett’s example (with my highlight) from his book Trading Volatility:

If the recent realized volatility is elevated and you wanted to buy long-dated options it might be a poor time to buy options. You can either wait, trade structures like verticals that have little vega exposure, or even create a directional trade by selling options.

Here’s a few extras to consider when selecting an expiry:

    • The nearer the option tenor, the more event pricing matters. The event’s variance is a larger proportion of the total variance until expiration.
    • Longer dated options have takeover risk. (Cash takeovers mean your LEAP extrinsic goes to zero. Sorry.)
    • Do you plan to roll the exposure to maintain it or is there an expiration to your thesis? The more often you roll the less rebalance timing risk. This has to be weighed against trading costs.

The Real Work Is Not In The Options

When you throw a proper punch the fist is just the delivery method. The point of contact. That’s the option expression. The real work happens from the torque in your hips. That’s the fundamental analysis behind the punch. An advantage of directional trading is you can think in discrete bets once you’ve done your fundamental homework.

Discrete trades let you:

  • Think in terms of how many bets you get paid back vs how much premium you layout and compare that to the probability your fundamental work suggests.
  • You’d like to get to a statement that looks like “I’m willing to risk 1 bet to make 3 because I think the proposition is a 50/50 shot.”
  • This establishes your expectancy and shape of the p/l.
  • Combine that info with your bankroll and now you can size the trade.

Bonus Section: Volatility Traders

I said that directional trading and volatility trading are different games. I’ll briefly talk about that.

First of all, even vol managers sometimes make discrete bets. They will “risk budget” a trade. I’m willing to spend $1mm on 150% calls for winter gas. Or whatever, you get the idea. They might even set up a separate account for tracking and attribution for this.

But really this risk budgeting or discrete framework is different from managing a relative value volatility or market making portfolio. In that environment, you are often responding to values moving around some cross-sectional trading model. You see edge, you pick it up, throw it on the pile and manage the blob. With a decent size book holding thousands of line items you are going to need 3-D goggles to slice and dice the positioning and the risk. You might not even know what you are rooting for sometimes. If you are short SPX correlation and long 200 of the 500 names then you are massively overweight vol in the 200 and you are “synthetically short” vol via the index in the other 300. Hundreds of names x hundreds of strike x hundreds of expiry and you need to bucket and compute quickly and accurately. Totally different animal from directional perspectives.

This does not mean that vol traders and directional traders don’t land on the same conclusions occasionally. A vol manager who finds a name that “screens cheap” might be looking at the same thing a fundamental manager is seeing. The fundamental manager is coming from a different vantage point, but might feel that a stock is hiding some serious upside and the nominal price of the calls are a bargain. In this case, the fundamental manager is going to struggle to find liquidity as the call options might be cheap for a few contracts but once they start calling around the street find that no market maker is willing to join the resting retail offers.

You may be wondering why the screens are so low in the first place? Why are they stale? The market maker’s dashboards are flashing green too. They know those options are cheap. But remember this is a game. They aren’t going to bother lifting the offers for a few contracts. They would rather freeroll on the possibility that some donkey overwriter who systematically sells calls without price sensitivity dangles a mid market offer. Then they’ll lift. (gratuitous “Do You Even Lift Bro?” clip)

So when do vol managers and directional traders trade with each other? All the time. Here’s 2 examples.

  1. Imagine a fundamental trader who is directionally smart but not vol savvy. They might buy calls, and the market makers who have been keeping tabs on this pattern of flow realize its predictive of a price move but has not historically beaten them to implied vol (perhaps it’s one of these dumb accounts that buys the strike of where they think the stock is going. They should probably hire a vol trader, if for nothing else to show them how to do p/l attribution). So the market makers sell the calls and overhedge the delta. Trading 101.
  2. A very common case where directional traders and vol traders are happy to trade is on vertical spreads or ratio spreads. Say a directional hedger buys put spreads. Vol traders can be happy to sell them so they can buy that tail option that the hedger gave them as the lower leg of the spread. A similar example would be a 1 x 2 ratio put spread. Say the stock is $100 and the directional trader buys the 80/75 1 x 2 put spread for a cheap or even zero premium. In their mind, they make make money all the way down to $70. They don’t start to lose money until the stock has dropped more than 30%. The vol trader has a different view. The vol trader cares about path and they know if the stock trades down to $80 quickly and vol explodes, they are going to be long vega and have ammunition to sell into the panicky vol buying. That 1 x 2 put spread is going to mark ruthlessly in the directional traders face. The directional trader didn’t respect path. Option traders are extra wary of path because they are highly leveraged businesses warehousing complex portfolios with non-linearities. There’s no better training for visualizing risk up, down, through time, across correlations, and at different speeds. The trader who honors path will often be the reason that “option that will never hit” is priced so high.

If you liked this post, consider checking out the Moontower Volatility Wiki.

The Moontower Volatility Wiki

Many beginners to options ask me and other professionals what they should read to learn options. I’ve seen this question asked enough times that I built a wiki that I can reference instead of needing to come up with an answer every time.

Voila…The Options Starter Pack (Link)

In the process of curating that I figured why not go the extra step…Introducing the Moontower Volatility Resources wiki (Link)

In addition to Moontower trading content, you will find select options content from the rest of the online vol community.

To maximize how useful this wiki there are a 2 important points.

  1. I will be keeping this wiki updated, but it is not open source. At this time, I think readers are best served knowing I’ve pre-screened submissions.
  2.  If you find a blog, book, video, interview, etc that you feel deserves to be here please submit it. I won’t guarantee I’ll include it but the benefit is we can keep this resource high quality and free of spam.

So there’s a tension involved…one side is that in order for this to be useful it can’t be a free-for-all. If you want a free-for-all there’s Reddit and Twitter and upvoting and ‘like’ buttons. This is not that. This is intended to be a reference with evergreen content subject to my standards. Like any manner of gatekeeping, I will miss things and I might let subpar stuff slide in. Sorry in advance. I’m always open to hearing suggestions/complaints. You’ll need to trust that I’m competent and care.

The other half of this tension is it requires engagement even though it’s not open-source. If you come across a source, a tool, a course or anything that fits neatly with this wiki then please share it.

Finally, here’s the excerpt from About This Wiki:
Option strategies range from directional hedging/speculation to the complexity of index dispersion portfolios and exotic structured product books. You cannot learn to trade options from reading. It is a craft and your understanding of it comes much faster when you have a position. When the feedback of the position comes in the form of mark-to-market p/l you learn what the position is sensitive to. Greeks like delta, gamma, and vega are immediately less abstract.

The good news is I believe any numerate, motivated person can learn options.

The bad news is two-fold:

  1. Experience is expensive.
  2. It is a craft best learned as an apprentice.

#1 is unavoidable. Straight talk — you will lose money learning. Guaranteed. Act accordingly. Don’t sell naked options and make sure worst-case scenarios are tolerable. Bid/asks are expensive. Sure, they might only be a few pennies, but 1 cent on a $1 option is 1% slippage. That’s 10-100x the slippage you pay to trade stock. Vast fortunes have been built on that 1% slippage. It will grind you as surely as a blackjack dealer if you play long enough without an edge.

#2 has better news. The internet in the form of blogs, podcasts, electronic brokerage and social media (esp Twitter) has never made it easier for a voracious learner to educate themselves, find mentors, and have meaningful discussions that would have been impossible even as recently as 2000 when I got into options trading.

I was fortunate to discover options trading right as I graduated college. I joined Susquehanna (SIG) and learned how to think about options, risk, and trading from Jedis. Their curriculum and methods for teaching were so comprehensive, tested, and systematized that it was a massive source of competitive advantage. The cared deeply about cultivating talent. They did not care if you knew what an option or interest rate was when they hired you. They looked for drive and aptitude only since they were secure in their ability to teach everything you needed to start managing a portfolio in as few as 18 months out of college.

I am not a math whiz. I was one of the <5% of hires who got a higher score on verbal than math SAT. Options intimidate many people simply because of the Greek letters and the math behind the models. I get it. I’m intimidated by math whizzes too. I have no more than HS Calc BC math education and a single stats course in undergrad. But the truth is, you don’t need to be able to derive Black-Scholes any more than billiards champ needs to know physics. Don’t get me wrong — the intuition behind the models is critical but the bar to acquire that is much lower than a math degree.

Much of my writing is an attempt to bring the reader to an intuition of the math in the same way that I was taught. I hope it’s even more accessible since my own weakness in math makes it easy to imagine being in the average reader’s shoes.

This wiki sits in that sparse space in-between the basics you might learn from the Series 7 and the nerdom that is derivatives structuring at a French bank. This is that mushy practical area in-between sophisticated retail and professional vanilla options user. It is an area, that will become more popular thanks to the boom in retail option activity and r/WSB. The vig and risk of options is going to weed out many of the new tourists but the few who persevere and have a deeper thirst to learn should find this wiki helpful.

And for the finance professionals who use options directionally but do not “trade volatility”, the resources found here might be just the bridge you need to understand volatility surfaces a bit better. This can improve your trade expressions, risk management, timing and ultimately executions.

If you have feedback, my door is always open.

-Kris