you can ONLY eat risk-adjusted returns

Last month my friend Khe published a letter pointing to Money With Katie’s adjustment to the 4% rule for avoiding “lifestyle creep”. The 4% thing is a rule-of-thumb for spending so you don’t outlive your assets in retirement.

My Rule for Avoiding Lifestyle Creep: Don’t Live Beyond Your Assets (2 min read)

Katie’s adjustment is a simple formula that marries both assets and income to come up with a spending rule that balances the desire to spend more as you make more while still saving enough for your future.

The formula = (4% of net worth + post-tax income) / 2

I think of rule-of-thumb like this as an API to a complex code base known as “retirement finance”. Nobel Prize winner William Sharpe said knowing how much to save and spend for retirement is “the nastiest, hardest problem” in finance.

That 4% rule abstracts away the interaction between investment returns, inflation rates, longevity, and taxes because, well because, we can’t let ourselves be paralyzed by this problem before brushing our teeth every morning.

But that 4% rule and any other “rule” is obviously a guideline sitting on assumptions with generation long lookback windows. And as we learned in Sunday’s letter, we don’t have a lot of samples of generation-sized windows to generate any confidence-inspiring inferences.

The entire output of the personal finance industry on the topic of investment history is a streetlight problem. But forgivable. Remember “hardest, nastiest problem” and we still gotta find the toothpaste.

Despite a career in options trading, replete with greek letters and complex financial instruments, I find myself in total agreement with Corey Hoffstein’s recent podcast guest Victor Haghani who despite being a super-quant (sometimes super means flying to close to the sun as he was also a partner in LTCM) admit that when he left high finance he realized he didn’t know how to invest.

From Last of the Tactical Allocators:

After LTCM, I woke up, and it wasn’t a dream — I realized that I needed to focus on managing my family savings. Up until that time, I had worked at an investment bank that took a lot of my compensation and put it into the stock of the company, Solomon. At LTCM, it was pretty natural to invest a lot of my savings in our fund that we managed.

It was a shocking realization to see that I had been working in finance for about 17 years, alongside some really brilliant minds — practitioners and academics — yet I had never really thought much about investing for myself. All of my focus had been on research, to begin with, and then proprietary trading.

[Kris: I wrote a post my own wake-up call: My Investing Shame Is Your Gain]

My situation was typical: you come out of college, go to Wall Street, and get trained in everything related to Wall Street. Unless you’re going into private wealth, which Solomon didn’t even have at the time, you don’t get trained at all in personal finance. So, there I was, looking around to see what my friends and respected colleagues were doing. Everyone was following the Yale Endowment Model that David Swensen had made so popular. Yale’s returns were incredibly attractive.

I knew people in private equity, hedge funds, venture capital, and distressed investments, so I started investing as though I were a one-man Yale Endowment. Meanwhile, I was on sabbatical from working, spending time with my young kids. After four or five years, I had this realization that what I was doing made no sense — from a life perspective or a risk-and-fee-paying perspective.

The final straw was when I sat down with my accountant, David, to review my tax return for one of those years. I asked him, David, why am I paying all this tax? I haven’t had that much income this year. He explained, Well, you have this income here as short-term capital gains, and you have these expenses over here that you can’t deduct because they’re miscellaneous itemized deductions.

It was like an epiphany: Geez, what am I doing? I realized I had to go back to basics.

A category of basics that I think are fundamental to investing is what I broadly call return math. It matters because investing is really a nesting of many re-investments. And compounding is the realm of multiplication. While it’s true that multiplication is just addition on ‘roids, a failure to understand it can mean the difference between the prefix “ste-” or “hemor-”.

We’ll go to Victor for some education.

Eating risk-adjusted returns

Corey, playing devil’s advocate, confronts Victor with a common charge leveled against quants:

“you can’t eat sharp ratios”

Victor: Risk-adjusted returns are the ultimate thing that we care about I think investors should be trying to maximize risk-adjusted returns. And what is a risk-adjusted return? Well, a risk-adjusted return is the return that you expect to get or that you did get minus a cost for risk. And the cost for risk comes from the fact that typically we have a decreasing marginal utility of wealth or consumption that makes us risk-averse.

We could write down a formula in an idealized world for what risk-adjusted return is, but let’s just think about what it is qualitatively. I mean qualitatively what it is is that I come to you and you have your optimal portfolio of equities and safe assets and whatever, and I say to you all right, that’s it, I’m going to take away that portfolio from you and I’m going to give you in its place a 100% safe portfolio. But you can’t have the portfolio that you have right now that has all these risky assets in it. What is the lowest return that you would accept on a totally safe portfolio so that you would be not happier or less happy than you were with this risky portfolio that had this positive extra expected return?

Well, when you answer that question you’ve just answered the question of what is the risk-adjusted return on your portfolio. The risk-adjusted return could also be termed the certainty equivalent return of your portfolio. It’s basically what would be the 100% safe annuity that you could turn your wealth into without taking any more market risk. That is what you eat. That’s what you’re going to spend on your food. That’s the only thing that you have to eat — that’s the annuitized risk-adjusted stream of consumption that your wealth will support. And so that is what you eat with the appropriate inflation adjustment.

[Kris: There’s a question bandied around Twitter every now and then cutting to the heart of this — what would the TIPs yield need to be for you to plow all your savings into it and not concern yourself with investing anymore? In this interview, Corey and Victor frequently speak in terms of real returns and what sticks out to me is how much higher people think equity real returns are above TIPs but in reality that number over long periods is ~ 3% give or take 2%, maybe 3%. If the TIPs yield were 4% you could really live by the 4% rule without worrying. Except for taxes of course. But if we are going to talk about taxes, that’s the muscle movement that makes any realistic form of alpha look like 10lb dumbbell curls as far as impact. Reclassifying your entire income to a friendlier tax code is a better use of time than trying to outsmart markets. Unless your answer to a calendar with no meetings is afternoon delight with the solar credits section of the IRS code.]

Sharp ratio is not what you eat. Sharp ratio is we’re looking for portfolios that have the highest sharp ratio, but we’re not trying to maximize the sharp ratio of our portfolios. We’re trying to maximize the risk-adjusted return of our portfolio, and there’s going to be all kinds of cases where you’re going to prefer a lower sharp ratio portfolio to a higher one depending on what your constraints are and other things. But it’s the risk-adjusted return that you’re eating. You’re not eating the sharp ratio, and nobody’s claiming that you’re eating sharp ratio.

[Kris: In this next part, Victor doesn’t use the words “arithmetic” and “geometric”. That’s ok. He’s a gentleman, you buy someone a drink before you go there.]

What you’re not eating is you’re not eating expected return. If you start eating expected return, bad things happen. Let’s take a toy example where somebody tries to eat their expected return. Say you have your wealth, you’re retiring, and you look at your portfolio. You construct this portfolio, and you believe that this portfolio has a 5% real return after cost of living adjustments. So, you got this portfolio. The only problem is that you had to build this portfolio with a bunch of risky things, unfortunately, because maybe you were a pharmaceutical person. So, you’ve built it with different pharmaceutical companies, and this is a pretty risky portfolio, but it has a 5% average annual real return.

And let’s just say the volatility of this thing is much higher than the market volatility, that it’s got 30% annual volatility. You got $10 million, and you say, “Oh, well, the expected annual return of this portfolio is $500,000 a year. I’m going to spend $400,000 a year adjusted for inflation for the rest of my life, and I should be fine because my portfolio has a 5% average annual return. So, I’m just going to spend $400,000 — you know, that’s the 4% rule — I’m going to spend $400,000 adjusted for cost of living for the rest of my life, and everything should be fine.”

What’s your most likely amount of wealth in 25 years? Your most likely amount of wealth in 25 years is zero. You’re going to be wiped out. Why are you going to be wiped out? Because the up 30, down 30 is killing you. The first year you went up 35%, so you went up to $13.5 million. You spent $400,000. Beautiful. It’s all great. But the next year you went down 25%. You went down to 30%, but there’s the 5% expected return. The next year you go down 25%. Uh-oh. Now after you spent the $400,000, you have less wealth than you started off with. It’s volatility drag, and that volatility drag means that your median portfolio has gone to zero before 25 years. Once it starts going down, it really starts going down fast.

That’s what happens when you eat expected return. So, you have to eat risk-adjusted return. If you eat your expected return, it doesn’t end well. Maybe that’s where we get all these missing billionaires from — they were eating expected return. People get rich, and they think the expected returns are high, and then they try to eat a fraction of the expected return, but they’re not eating risk-adjusted return.


I will leave you related ideas to chew on.

Dr. Philip Maymin was recently interviewed on the CFA Institute podcast. You might recognize his name because he’s the author of book I constantly recommend, Financial Hacking.

About Philip:

Dr. Philip Maymin is Portfolio Manager and Director of Asset Allocation Strategies at Janus Henderson. He is also the Endowed Schramm Chair of Analytics and the MSBA Program Director at Fairfield Dolan, the CTO for Swipe.bet, and an instructor at Analytics.Bet.

In the past, he has been a portfolio manager at Long-Term Capital Management, Ellington Management Group, and his own hedge fund. He was Assistant Professor of Finance and Risk Engineering at the NYU School of Engineering, as well as an analytics consultant with several NBA teams and the Chief Analytics Officer for Vantage Sports.

Maymin co-founded the journals Algorithmic Finance and the Journal of Sports Analytics. Additionally, he was a policy scholar for a free market think tank, a Justice of the Peace, a Congressional candidate, and an award-winning journalist.

I recommend listening to it for several threads.

There’s a lot about AI. He’s very much in the weeds, so much so that it’s the topic of his next book.

Next, there’s some nice reinforcement of some of Victor’s ideas (maybe not an accident, Maymin was also at LTCM). Both Victor and Philip talk about dynamic vs static allocations. Victor’s firm helps you dynamically size your portfolio according to your risk own risk function as well as expected return (I call it “Kelly aware”). Phillip emphasizes tail risk management (not in a financial product sense necessarily, he’s speaking generally) because like many things in life, it’s a few moments that have most of the impact or if Wu-Tang Financial went quant — ”power law rules everything around me”.

For Maymin, the focus should be on risk management since the forces of competition make it hard to win big on alpha (alpha being defined as capturing excessive return without paying the risk cost) but those same forces do not keep not inhibit you from avoiding disaster which is a nice asymmetry for the individual.

That conclusion flows easily from his articulation of efficient markets hypothesis. His coverage of that idea, what it actually means, and its copious shortcomings are the best I’ve heard. I also remember him covering it in his book to a poetic degree and extending well beyond markets iirc.

Postscripts

  • Philip suggests de-risking during higher vol periods because if you don’t then those periods will be a much higher proportion of your performance than the length of time that coincided with those periods which is another way of saying that a fixed position size is bigger part of a risk budget when times are volatile. That’s fairly obvious but the open question I have is whether higher volatility periods also coincide with higher returns. I presume they do in arithmetic terms but not geometric which is what matters so my unverified take is you want to be smaller when vol is high even if the expected returns are higher. My own investing process doesn’t switch gears hard with the vol level so this is an area I need to do some work on.
  • I thought about including ideas from Mason Malmuth’s book Gambling Theory and Other Topics, because it emphasize that the most important concept in gambling is to follow a “non-self-weighting” strategy. Which is another way to say “vary your size with the edge”. Such an observation would be banal to this audience but he points to several common strategies that are counterexamples that people generally approve of. He’s a pretty incendiary character, arguing against diversification (he admits this is the largest area of pushback he receives) and claiming that “money management” is a stupid if not moot topic. He also gives the example of nuclear MAD as a self-weighting strategy and the brevity of the Gettysburg address as a non-self-weighting strategy. I gotta admit, reading it again 25 years later, I feel the dude’s a bit of crank. It was required reading at SIG but that must be in spite of the diversification thing. Jeff Yass has repeatedly emphasized that diversification is a free lunch.

Inoculate yourself against “persuasive” charts

The original moontower blog is https://moontowermeta.com/. The “meta” is an important word. Important enough that Facebook stole my language and turned it into their ticker. F’n Zuck. Leave some for the little people bruh.

The reason I used “meta” (besides the fact that moontower.com wasn’t available) was because a lot of things I think about are fairly meta. Knowledge is the object but how we acquire knowledge is the meta. Trading is a very meta discipline because games with counterparties require a solid “theory of mind”.

In the spirit of meta, I really enjoyed a recent post by Robot James titled:

Valuation Timing with Excel (6 min read)

It’s meta because it’s really about arming yourself with data analysis to confront a narrative or chart. It’s worth stepping through the article together to appreciate just how many meta-nuggets it contains.

First, we start with an object-level observation that you’ve likely encountered. I’ll quote freely from the post but all bold is mine:

You may have seen a lot of charts like this recently:

The conclusions people tend to draw from this chart are:

  • there is an obvious and strong relationship between valuation and expected future returns (cheap = good, expensive = bad)
  • valuation estimates are currently historically high; therefore, expected returns of the S&P 500 are historically low.

We should always be wary of drawing strong conclusions from stuff people share on the internet or in sell-side research.

There are a few reasons to be skeptical of the strong conclusions people tend to make on seeing this:

  • the chart might just be wrong (people screw up financial data analysis all the time)
  • 10 years is a really long time horizon
  • all of the 10-year total returns are actually positive
  • why are there so many points? How many 10-year periods has the index even existed for?!

The good news is that, with a few simple skills, we don’t have to believe what randos on the internet say.

Even if we can’t write code, we can use Microsoft Excel and free online tools to investigate these things ourselves.

James shows how simple it is to grab the data that would feed such a chart so we can manipulate it ourselves. One of the first manipulations is addressing the fact that such a chart is really derived from an extremely small sample size because each data point is highly overlapping to the others. A rolling 10-year return is comprised of 120 months so each new “sample” overlaps with the prior one by 119/120.

James starts the exploration by looking at monthly returns (instead of 10-year returns) vs CAPE.

Let’s turn back to James for interpretation.

Unsurprisingly, that looks like a big blob. (Anything with monthly returns on the y-axis will look like a big blob.)

[Kris: that bold statement is a useful bit of knowledge that comes from looking at financial data frequently]

What does James do next?

We can look at longer non-overlapping periods. Let’s keep with the 10-year forward window and look at decades.

The problem is that we now only have 15 observations! Ten years is a long time, and we simply don’t have that many unique non-overlapping ten-year periods. And we certainly don’t have many unique non-overlapping ten-year periods that are similar to the current market structure and competitive environment.

[Kris: that bold bit is an evergreen problem in finance because investing is biology not physics. Markets learn so output become inputs. What does that mean? Markets are more likely to fall AFTER everyone starts believing they can only go up. The “only goes up” is the output or observation that then becomes an input into how much risk investors take. There is always some price that peers back at history and says “not this time”.]

So James slices the data another way.

Plot the valuation metric itself…

whenever we see an effect, we should ask what other than our pet theory might be causing that effect to appear. In particular a lot has changed over that time period. The market looks nothing like what it did in 1900 today.

And, indeed, if we plot a time series of our valuation metric, it looks kinda drifty.

It’s not really reasonable, I don’t think, to assume that CAPE 20 would “mean” the same thing in 2024 as it did in 1900.

He tries another manipulation:

One cheap and dirty way we can make that metric a bit less drifty and more comparable over time is to standardize it by its values over a recent rolling window.

For example, here I’ve standardized it as a 10yr rolling score. (Not necessarily cos I think that’s the right thing to do – I just want to make a point).

Now it looks a lot more stationary. It stays in the same range. It doesn’t drift off. This is unsurprising cos we forced it to look like that.

[Kris: the bold is another lit bit of fingertip knowledge that you acquire from frequent contact with data.]

Yet, another manipulation:

Now, we can plot our next year’s returns vs this standardized z-score.

If we still see an effect when we do this, it would make us more confident in the valuation effect. If we don’t, it won’t destroy our confidence because we’ve made some pretty arbitrary and dubious scaling choices here.

Indeed, at least with this scaling choice, we don’t see the effect we are looking for.

That’s ok. That’s the nature of work like this. We’re just exploring, trying to break things. We try to look at things from as many different angles as we can and see how much of the limited evidence lines up.

[Kris: I just want to pause for beauty as my wife likes to say. James is spoon-feeding serum against chart crimes and charlatans who read “How To Lie With Statistics” as a manual].

James’ Conclusion

I think the evidence (and economic sense) supports the idea that high valuations are correlated with lower expected returns. But it’s nowhere near as clear-cut as the initial scatterplot suggests. We simply don’t have enough data, and the market is constantly changing underneath us, making it hard for us to draw strong inferences.

My conclusion

This points to an uncomfortable reality. If a data analysis was conclusive then everyone would do the thing prescribed until the data exhaust from the behavior was no longer conclusive. This is deeply reminiscent of what I call the Paradox of Provable Alpha.

Notice what James did.

He recognized that the data proves nothing but it’s simply too underpowered to accept or reject any claims. His prior barely gets updated: “I think the evidence (and economic sense) supports the idea that high valuations are correlated with lower expected returns.”

He goes to bed at night with judgment as his best guess much like a farmer’s almanac will do better at predicting the weather in a month vs some meteorological model.

 

Thanks again to Robot James for the heavy lifting on the original article. I was just narrating alongside it to highlight what stood out to me and how it related to other topics we discuss here.

seat arbitrage

If a tree falls in a forest, does it have a delta impact?

I didn’t feel like writing so you get the answer I’d give over a beer in Roppongi if you gave me a few minutes to collect my thoughts (and if I drank).

Dark arts. Microstructure. Options.

Enjoy…

 

Another story with some powerful lessons…

Let’s start with one of the best stories I got to be a part of at SIG.

Tina recounted it on Twitter, I’ll offer more color below.

Tina:

Ok, seat arb story. One day, ICE announced that they wanted to buy the NYBOT. Jeff Yass runs into me when he came into the NY office one day when this started, and asked if we should be buying these seats for edge – ICE stock in exchange for seat. I was Head of the NYBOT for SIG at the time with traders in coffee, sugar, cocoa, as well the Russell 1k,2k,3k.

I had talked to many traders beforehand and overwhelmingly, they were against the buyout. So I told Jeff, no it won’t pass and and we would lose buying these seats. Then I dug around more and realized that the vast majority of people against the buyout were leasing the seats and that owners with votes were for.

Called Jeff back and told him I changed my mind. Jeff green lights it. This became such a fun crazy time because, I would be trading during the day, watching ICE stock, watching the seat tape -seat prices on the ticker on the boards, and then when the seat offered were at a sufficient discount, I would stop trading, send my clerk to run to the membership office and bring me docs to sign. The edge from these seats became more than the edge from trading so I would literally stop trading during the day at times to do this. Of course then I had to call Jeff’s right hand man Shawn, and then the COO to free cash up.

We had to put all these seats under individual traders, since technically the traders were the members. So myself, Kris Abdelmessih, etc had many many seats in our names which was also funny. The seats were maybe $650k and I bought maybe 30-40 for SIG.

In the meantime, the CME was also bidding for the NYMEX which was in the same building btw as the NYBOT. Somehow the head of energy for SIG was out for a bit and so I was the most senior in the building. I saw Jeff during that time and he said “ I really really want to buy some NYMEX seats”.

So one day, this guy I knew who owned a clearing company is alone w me at the elevator and asked if I would buy his seat. Jeff had given me a $10m top when the seat was maybe worth $10.8m. Think the displayed market for seats was $8.5 at $9.3m or something. Guy is like, “I will sell you my seat for $8.8m. “

I call Bala [Cynwyd], get his admin, he’s in a meeting but I tell her I needed him. Jeff picks me up, approves it, tells me to call the COO to free margin up and wire the money. Was pretty exhilarating that one trade to get so much edge I must say. The best part was also that, SIG got awarded the CME specialist post on the NYSE so we were the only ones who could sell CME short, setting up for a real arbitrage.

All of this happened when I was pretty young, so you can imagine this was all super cool, the trust Jeff had in me to manage so much of his money. I am forever grateful for the opportunity.

Pretty neat.

I’ll add a bit more.

The head of energy on the NYMEX oversaw nat gas trading as well as me (I oversaw oil trading). Before we came to the NYMEX, he was also my boss on the NYSE. I remember being at the NYSE member meeting when then CEO John Thain (after the Grasso departure) started explaining what would become Reg NMS!

SIG also bought NYSE seats before it went public. By the time, the NYMEX and NYBOT were ready to demutualize they understood this particular style of special sit quite well.

Aside on the NYMEX deal

Before the NYMEX was acquired, it was member-owned. The member owned a “seat” which gave them voting rights as a matter of exchange governance plus the right to trade on the floor.

The CME offered buy the NYMEX in stock. A member would receive some amount of CME shares for each seat they owned. To value a seat you had 2 primary inputs:

  1. The amount of CME shares you get x the price of the shares during some fixing window (I don’t remember the details)
  2. The value of the permit which allowed you to trade on the floor

The permit could be valued by a simple DCF based on how much you could lease a seat to a trader or broker on a monthly basis. Forecasting lease rates could be tricky since the life of the trading floor was already in question.

In fact, this is why lessees were so against the deal. They owned no equity in the deal and their livelihood was at risk if the floor’s days are numbered. The seat owners had their golden ticket. In the time leading up to the sale, seats more than 10x’d in value with many seat owners buying even more. That deal spawned lot of generationally rich Sal’s from Staten Island.

The trading permit however was a small portion of the overall seat value so the DCF exercise was fairly inconsequential. The main risk was the CME’s stock price but as you saw from Tina’s story — there was a lot of edge. If CME stock had 30% vol, with the trading permit, you were basically buying the shares at a 1 standard deviation discount (and that’s if you had to hold for a year). With SIG able to short CME to it was a good trade to plow size into.

I know 9 figs sounds quaint, but it was a lot of dough in a pre-GFC, pre-Fartcoin world

 

Being Nimble

You could relate this story back to my video above. There was some opacity to the market because the seat bid/offer prices were maintained by a small group of office workers employed by NYMEX. Our trading assistant would frequently go up to the membership office bearing coffee or treats to chat them up for color on who’s been poking around the order book. Know the chokepoints.

It reminds me of someone who knows their local RE duplex/multi-family market cold. Occasionally a listing comes up and they will know the exact block and layout so they immediately notice that while it says 3 bedroom, it’s really a 4 with a minor change plus it’s on a side of the street worth a 5% bump. Call the broker, offer 50k thru ask if they take the listing down immediately (and this is in the subset of cases where you didn’t get the look before it hit MLS).

Usually this type of fingertip knowledge in dark corners doesn’t scale, but the seat arb was a rare exception. A bunch of jabronis just made their grandkids rich out of the blue and didn’t want to gamble on the closing of the last 20%. Edge.

I think my favorite part of the story though was the moment. We were all in our 20s and Jeff trusted us. SIG was very entrepreneurial. I got to be a member of every exchange in NY except the NYFE in under a decade. You have enough social aptitude plus lots of training in how to think about risk…“go break into that pit”.

Trading firms, at least ones with a floor heritage, have a fairly flat org structure which is strongly on display in Tina’s story. Empowering employees and limiting bureaucracy seems to be a real edge but requires the right culture and alignment. I recently highlighted the flat structure of Valve, but like SIG they don’t answer to any outside investors.

Going from this real-life example up to the level of lesson, this is SIG’s Todd Simkin explaining the advantage in his interview with Ted Seides.

Ted: Over the 30 plus years you’ve been at SIG, you’ve seen in the hedge fund world this growth of multi-manager platforms. How do you view yourselves competitively to some of the bigger people that you see in the markets?

Todd: We have been in the fortunate position of having the most patient capital of all. One of the challenges with hedge funds is their need to frequently manage not just quarterly reports but monthly, weekly, or even daily reports. They must demonstrate adherence to their outlined strategy and deliver consistent returns.

In contrast, our investors are the principals of the firm.

They understand the risks we take, including outsized risks, and they are the ones driving these decisions. If I decide to put on a $100 million insurance risk tied to the winner of the Super Bowl, I’m not worried about explaining losses to a multitude of stakeholders. Instead, I have a single conversation with the relevant decision-maker, outlining the edge I perceive and the terms of the deal. Their involvement includes monitoring the situation, such as checking the health of the quarterback throughout the season.

This patient approach has enabled us to stay in and grow businesses during downturns while shutting down exposures when needed. Unlike others who must adhere to predefined strategies, such as maintaining a certain percentage of long-short equity exposure, we can dynamically allocate capital.

We benefit from the large capital base while retaining the flexibility and focus of having a small number of decision-makers. These decision-makers avoid imposing artificial rules that might constrain our strategies, a common issue when managing external money.

 

Ted: When it comes to trading, even though long-duration capital is an advantage, your focus often remains on relatively shorter time frames. What sets the traders at SIG apart that allows you to stay successful in an extremely competitive market?

Todd: I think there are a few things.

One is that we focus a lot on the decision process—the information available, how we used that information, and then what trade we made—all of that way before we discuss the results. I think a lot of other people have that upside down. They say, “How did you do? If you made money, great, keep doing what you’re doing. If you lost money, that means that you took too much risk, and that’s a bad thing.”

Whereas our traders are focused on the decision process and the expected value first, and because of that, we don’t do things that I’ve seen some of our competitors do that we would think would bleed away some of those profits.

For example, say you do all your work, there’s no selection bias, there’s no reason to think that you’ve gained new information by being able to enter a trade and you get to buy an asset for $10 that you think is worth $20. Seems great, and then somebody comes along and they say they’ll buy it back from you for $19.

Do you want to sell it?

A lot of people at that point would say, “Well, that’s great. I bought it for $10. I sell it at $19. I make $9. I put it in my pocket, and I go away pretty happy, and I sleep well tonight. Nothing bad can happen tomorrow with my position. I’m out of it, and I’ve just made my money.”

And we say, “No.” If anything, if we’re able to buy more at $19 and we still think it’s worth $20, then we would. The fact that we got to buy it for $10 is great, sort of confirmed now by the fact that someone’s willing to pay $19, but that doesn’t mean we want to sell it and lock in this profit just because you have an opportunity to close a position.

That is part of the culture of the firm. We’re not going to give something up just to feel better in our small individual portfolio, which is part of this much, much bigger firm-wide portfolio. If the whole firm had the opportunity to do that and gave up 10% of our profits every time we had a profit-making opportunity, that would be really costly. Somebody else is on the other side of that trade picking up all that extra money that we’d be giving away.

[Kris: That’s exactly the NYMEX/CME example!]

So part of the culture of the firm is one in which we are finding edges wherever we can find them but then capturing all of it by either holding to maturity or holding to expiration or closing at an appropriate rate when we have either new information or where the markets have changed.

Path, VIX, & Hit Rates vs Expectancy

The CBOE’s VIX index interpolates 30-day implied volatility based on options struck on the SPX index.

A VIX future settlement price is based on the prevailing VIX index at the future expiry date. It’s a bit of a confusing concept. A future that expires to a VIX index level that looks ahead 30 days.

There are ETFs and ETNs that reference VIX futures (VIXY, VXX). They also come in levered and inverse forms (UVXY, SVXY).

Despite the abstract nature of trading “a level of volatility”, these are popular products. There is 2-way interest in them. SPX returns are inversely correlated to implied volatility making long VIX positions a natural hedge. At the same time, the upward-sloping term structure of SPX implied volatility means implied volatility in the future trades at a premium to volatility today. Many traders will short VIX futures and ETFs to capture the downward drift they expect if the market remains calm as the futures will “roll down” to converge with spot VIX by expiration.

Quant finance geeks about these volatility term premiums. Term structures recognize that volatility is mean-reverting. Historically, SPX realized volatility bounces around 15% give or take a couple percent over long periods. Implied volatility typically trades at a risk premium. The premium also bounces around but 16% IV on a 15% realized vol (ie 1% premium) is in the right ballpark.

The averages mask the distribution. VIX is bounded by zero. It’s rare for it to get to about half its average. It’s rare to double but less rare than halving from 15%. But it’s even possible to triple or quadruple (Covid and Aug 5th 2024 for recent examples). It’s also more common for VIX to go to 12 than 18, at least in recent years.

This low-res farmers almanac description paints a picture of a lognormally distributed index. VIX futures will drift lower frequently but occasionally spike and sometimes those spikes are very high (and fast).

It’s natural for us to think in terms of averages. This habit persists despite witnessing price moves that would be impossible if normal curves were in charge (and despite the warnings from cranky Lebanese deadlifters). The nasty side effect of Gaussian-brain is when it creates the illusion that something is massively mispriced when prices are just properly reflecting a skewed or fat-tailed distribution.

In the 2 min read, The Benefit Of Betting Culture, you can see how the price of a futures-style bet vs an over-under style focuses your attention on the distinction between probability and expectancy. This is the heart of the matter. Investors confuse hit ratios with expectancy constantly.

I field emails and calls too often that are basically retail traders saying “I was doing great selling options for 6 months then I lost it all in month 7”. The reasons for these mini-blow-ups vary from oversizing because they’ve been winning to naive pricing but the universal mistake is in the epistemology.

Some traders are executing without understanding the nature of the proposition. It’s not that selling options is a mistake (there’s a price for everything). It’s that you shouldn’t be surprised by the shape of the payoff. Roughly speaking, if I sell a 10-delta option every month and I win 6 months in a row, I haven’t learned anything about whether my strategy has an edge. I should expect to win most of the time. That says nothing about the expectancy. The person is thinking in terms of 50/50 averages, ie win or lose. But the proposition if it’s fair is more like win $1 9 times and lose $9 one time. If you have an edge, then you either win more often for the same payouts or the payouts are not as far apart but the hit ratio is the same. But most retail traders don’t have large enough sample sizes to infer anything from such skewed results. The track record is nothing but a statistically underpowered study.

Unlike rolling dice or flipping coins, it’s hard to learn anything about the distribution of prices from direct experience. Historicals help but you only have to look at acute incidents in markets over the past 5 years alone to appreciate the challenge of calibrating what’s improbable.

But we can strengthen our conceptual understanding to hopefully be a little less blind to hit rate vs expectancy (or median vs mean) illusions. Option surfaces themselves are great teachers in this regard. In a deeper understanding of vertical spreads, we’ve seen how call and put spreads are a rich source of information about a distribution.

In the remainder of this discussion, we’ll get some mileage towards internalizing the difference between hit rate and expectancy from a non-technical discussion about the price of a VIX future.


Pricing a VIX future (via arbitrage)

If you are a professional trader who just heard me say “price a VIX future” and “non-technical” in the same sentence, you feel like you’re at a Houdini act…” How’s this mf gonna pull this off?”

[cracks knuckles, bends neck side-to-side, deep breath]

Ok, a little background for the uninitiated.

The VIX complex of futures, ETFs, vanilla options and VIX options is one of the more technical areas of options trading. There are arbitrage triangles between these things.

They’re not exactly clean though.

Replicating a variance swap also isn’t clean (not every strike exists and even for the ones that do transacting entire strips is not economical). Neither is dispersion. Neither is isolating forward vol.

But all of these things lend themselves to a fair value that can be F9’d in Excel if you ingest the real-time bid/asks for the building blocks. Every large vol desk has a group that computes a fair value for VIX futures that is derived from SPX options and VIX options. You can trade around that fair value by being better bid on the building blocks that are relatively cheap and vice versa. Manage the residual risks and over time you make money.

I’ve never worked out a model for VIX futures fair value myself as I’ve never traded the SPX complex. But we can still step through it conceptually.

Imagine you are short 100,000 shares of VXX at $16.

*VXX references VIX futures. Just to avoid computing position ratios let’s just pretend VXX and the VIX futures trade for the same price.

You are short 100,000 vega because your position vega by definition is “change in p/l per 1 point change in volatility”.

If vol (ie the VIX future) drops by 1 point, you will make $100,000.

Arbitrage pricing comes from replication. If I can construct a portfolio with a cash flow of 0 in every state of the world, then I have a risk free position (and if I get paid to hold that portfolio I have an arbitrage profit).

To offset my VIX futures risk, I must therefore buy 100,000 vega via SPX options.

[This is conceptual, so we are hand-waving important details like what strikes, expires, weights and managing the deltas.]

At this point we are vega-neutral. Long SPX options, short VXX.

What happens if vol suddenly doubles?

You’re going to make a lot of money.

Why?

Because you lose linearly on your VXX short (-$1.6mm or 16 vol points on 100k shares) but you win more on your SPX option longs.

The reason: you are long not just ATM options but OTM options too. OTM options pick up more vega has vol increases. It’s like being long “vol gamma” (it’s literally called volga). Remember how a long gamma position gets longer delta as a stock goes up and shorter delta as a stock goes down. Well, this is the same effect but for vega via vol.

💡See Finding Vol Convexity for a full explanation.

The fact that you make money because your are long “vol of vol” means you aren’t quite replicating the VIX future though. That’s a problem.

[There’s a cost to being long “vol of vol” so we can deduce that vol never changed and expiration arrives that this so-called hedged position would have lost. There has to be a flip-side to the fact that if vol makes a large move that portfolio wins.]

Conveniently there is an instrument that’s a pure expression of “vol of vol”. You guessed it — VIX options.

The conceptual algebra:

VIX future = SPX options – VIX options

In our example, you can short VIX future, buy SPX options, and then sell VIX options to neutralize this long volga exposure.

This identity is loaded with insight.

  • If I’m long VIX futures and short SPX options, I’m synthetically shorting “vol of vol”.
  • If I’m short VIX futures and long SPX option, I’m synthetically long “vol of vol”.
  • If I’m short VIX futures and long VIX options, I’m short vol but long vol of vol which is similar to be being short SPX straddle but long strangles.

You can envision how looking at the VIX complex you can see which leg stands out as cheap or expensive relative to the others. Layer in implied correlation which relates index vols to single stock vols and suddenly you’re Neo in the matrix.

A day in the life of a vol arb desk is market-making all the flows with an axe. Based on the price of the various parameters like vol, skew, convexity, term structure and correlation you might be:

  • Selling VXX
  • Buying 1-month VIX calls
  • Selling 1-month single stock OTM calls
  • Buying weekly SPX calls
  • Selling SPX 6-month straddles
  • Buying 9-month single stock downside puts

Like a chess player chunking their position, you look at this and think:

“I’m short SPX call spreads and vol near-dated, long upside implied correlation near dated, long a 6 month/9month time spread with a dispersion kicker.

I’m long gamma, short vega, long tons of volga, paying theta”

[Note: the greeks will vary based on the ratio of position sizes. If you’re playing along at home you can try to map the positions to the first line of the summary. And for the greeks you can try to imagine what position sizes are required to make the sign of the greeks make sense]

You do this not because these positions are inherently right or line up with some macro view. You do this because the prices are “right”.

You take what the market gives you. Everyone who’s out there trading on their opinions is moving the price of these parameters around. You are agnostic. Pick up the edge, manage the risk.

All you care about is others having strong enough opinions to move prices around and that you can find contradictions in the matrix.

To quote the closing line in Pacino’s speech in Any Given Sunday:

“That’s football folks. That’s all it is.”

Pricing a VIX future (like an option)

The fact that a VIX instrument has a fair value in a similar manner to how an ETF has a NAV has always kept me away from it. Just like I wouldn’t trade an ETF if I didn’t know its premium/discount. If a box has a dozen donuts I don’t want to buy it for a price that implies a baker’s dozen. Negative edge.

That said, lots of people trade VIX products with a belief that they have an edge based on a relative value lens rather than an arbitrage framework. I’m guessing this leads them to selling VIX futures (which is probably the right side from the arbitrage perspective as well.)

[I’ve often thought that if I were to build a VIX or SPX suite in moontower.ai I’d want to “do it right” which is to use the arbitrage lens rather than extending the in-place moontower analytics to VIX as if it applied. I’ll leave it to you to decide if other platforms do it right or if they’re like children playing house pretending to be grown ups. By the way I have similar opinions about 0DTE. I’d use a totally different framework than the one we currently use in moontower.ai to deploy a 0DTE suite.]

Since a proper VIX complex treatment is prohibitively scarce for retail, it’s additive to think about another way to price VIX. I think it’s intuitive to consider VIX itself an option.

(Again, we’ll stay conceptual. Working out the details is out of scope for this post).

I got the idea for “vix as an option” while answering a reader who emailed me. I’ll share my response so as to not expose the question explicitly.

I wrote (this is edited and expanded):

How do you model option prices and even the underlying price itself if it’s a future that is trading for $1 that will likely expire at 0 but can surge to $10 sometime before that? It’s basically a bubble pricing problem because all known bubbles start to have that distribution and even tech stocks themselves in 1999 were pure extrinsic values themselves. It’s also the distribution that governs the H/J nat gas futures spread.

First let’s discuss pricing an option on this asset. Like what’s a reasonable vol for the $10 call?

I understand your temptation to think strike vol is “what IV will be when it gets there” but this like saying life expectancy is 85 if you survive the first year of life. The option needs to balance the price of many states of the world not just the conditional case. In other words, it’s more like what is your life expectancy at conception.

[For the technical, non-metaphor version see the “local vol” discussion in Chapter 7: Skew Trading of Colin Bennett’s Trading Volatility. The book is a free pdf.]

Another approach might be bootstrapping a discrete model. For example, you could use the price of vertical spreads to compute the implied distribution. Then you can those probabilities as your p and then fit various levels of vol to the call options in various states to see which vols are reasonable. I’d guess you’d end up with something that made the market look pretty rational. Like that call option might have a 10% chance of being 200 vol contributing 20 vol points to its IV and the remaining vol points are some sumproduct of the non spike scenarios.

One thing that a bit hairy is implied probabilities are “terminal” probabilities.

It’s easy to understand the distinction when you think of VIX. You have a 9m future that’s trading 18 but will probably expire at 12 or 13. But if I told you it’s 75% to touch 30 during its life how does that effect your intuition of value?

If you use VIX call spreads to assess the probability you miss this because they will assign very little probability to touching 30.

Instead you can use the deltas (delta x 2 is a useful guess for a one touch probability). The one-touch probability is much higher because it respects path.

 

That was the end of my response. But a skeleton for pricing VIX as an option is there.

Think of the lognormal distribution (bounded by zero, positive skew, fatter right tail). As you increase volatility, the distribution “squishes” to the left.

wikipedia commons

A look at March 2025 VIX Implied Distribution from the futures options

Here’s a condensed view of the Mar2025 options chain using mid-market for calls and puts.

Things to note:

The extreme IV skew

  • The 20% OTM call (~21 strike) is 3x the price of the 20% OTM put (~14 strike)
  • The delta of that 21 call is 2x the delta of the 14 put

The distribution

Remember:

the price of a put [call] spread divided by the distance between the strikes estimates the probability that the underlying expires below [above] the midpoint of the strikes.

By looking at the spread of adjacent spreads (ie the butterfly) we estimate the probability density at the midpoint. If we do this across strike we have the implied PDF.

[It’s a bit noisy because of market widths and strike distances not being uniform but I normalized in a reasonable way for these artifacts]

Even though the future is 17.35, the put spreads are expensive and the call spreads are very cheap telling us that March VIX is most likely to expire between 12 and 14.

If you are betting on roll down, it’s already priced in. The 16/14 put spread is $1.03 but the most it can be worth is $2. So despite the fact that the future is 17.35, you get slightly less than even money on the future expiring below 15. In other words, the future falling 14% is already baked in as the median outcome.

Implied distributions like this tell you the market expects the price to fall but it must still balance the chance that in the meantime it can double, triple, or more. It’s the kind of distribution you expect in bubble names where “the market can remain irrational longer than you can remain solvent” but everyone knows the asset is eventually going to be much lower.

Next time VIX spikes watch what happens. The VIX vols will pop, but the put skew will get smashed. The net effect is the put spreads get very expensive because VIX looks like a rubberband to investors…the higher it rips the more distance it has to snap back down which it eventually does. On a VIX rip everyone wants to buy put spreads to have a rick-contained way to capture that reversion, but the surface is too smart for that. You might end up with a VIX future at 25 and all spreads say…”meh, it’s going back to 15”. The contrarian bet would be to bet that it it’s NOT going back home. The options market will give you that bet all day. for good reason. But the trade you want to do is priced like a Chiefs point spread. Sure you’ll probably win, but the risk/reward a priori not a “excess return”. It’s consensus so you’re flipping coins for fair.

This is how the SLV surface repriced in 2021 when the WSB apes tried to squeeze it higher GME style. I was a very active silver options trader then and just found myself frustrated about how smart the surface was in adjusting. Speaking of GME, this type of extreme lognormal distribution took hold when Kitty roared. The cheap call spread beg you to buy them because nobody thinks GME is actually going to expire higher even though it might touch a high price. That it will touch a price is basked into the expensive calls outright and their deltas.

Look at the VIX chain again. The 30 call has a .24 delta. This implies that there’s a 48% chance that VIX will touch 30 at some point before expiry. With such a framework, you can start to see how the VIX future option vols and therefore deltas inform what the price of VIX futures should be. You might draw opinions about a VIX call being expensive relative to VIX itself (notice this is exactly equivalent to saying the implied volatility is expensive).

To be honest, this is all dancing around the fact that just pricing the VIX futures, SPX option, VIX option triangle is the final boss. But the point of this is to give you exercise in noticing that the fact that a VIX future is probably going from 18 to 13 doesn’t mean selling it is necessarily edge. There can be a better leg out there but focusing on “what will probably happen” is a form of probability myopia that distracts from expectancy thinking.

[The difference between positive expectancy and probability is the fertile soil of investing charlatanism. If you were to start a scam strategy from scratch you’d start with trades that have a high hit rate and just hope you collect enough profits before you see the whole distribution. Ideally with someone else’s money.]

We’ll leave it there.


Related reading:

What Equity Option Traders Can Learn From Commodity Options

Bubbles: Knowing You’re In One Is Not Even Half The Battle

laying in the weeds

Friends,

Within a week of the furious post-election rally I went to Twitter:

What is the most asymmetric way to bet on deflation? Is there an option on this that’s left for dead?

There’s conventional choices like bond calls but i want to hear what ya got…also not a short run expression…something long dated that gives time to see the possibility of deflation looking out the Overton window.

Also I know you think it’s impossible. I don’t care about “think” though.

I want to know where deflation is “offered at impossible“.

Deflation doesn’t have to be likely for a bet on it to be profitable. And it’s certainly nowhere near impossible — this is a rich country with wealth concentration (rich people have low MPC), declining birth rate, and an NVDA market cap says robots will have lots more high paying jobs, and an incoming government promises lower spending (although this doesn’t translate to a smaller deficit if the tax receipts fall by even more).

There were plenty of responses.

(Unsurprisingly and for good reason, the most common answer was calls on treasuries or nitroglycerine like 30 year zeros.)

After I posed the question, I thought I’d follow up with a meta-trading lesson that governed how I thought about execution as a discretionary trader. It’s more relevant for professional trading where slippage is a larger concern but I expect anyone can at least benefit from hearing about it.

Laying in the weeds

Right now the market optimism thermometer is Sahara hot.

I charted SPX earnings using data from Gurufocus:

SPX earnings are up 48% in 5 years from 9/19 to 9/24 or ~8% per year

SPX total return over that period is 110% or 16% per year so multiple expansion has been riding shotgun 1-for-1 with earnings.

And now for 2025, forward earnings expectations are expected to grow 16% after being fairly flat from late 2021 until late 2023. Forward p/e has actually dipped despite SPX at all-time highs because of the animal spirits baked into the denominator.

I’m just using this as an example of divining sentiment. You could use option surfaces, COT reports, the “is my aunt or Uber driver talking about investments” indicator to get a pulse. (See Staring At The Window for an example of thumb-in-the-air vibe detection).

Your vibe detector gives a little elbow nudge, “hey knuckle-dragger, pay attention for a sec, it would make sense that some state of the future is being heavily discounted or left for dead.”

And so you start thinking along the lines of the tweet I opened with. What’s hated? What’s offered at zero? What’s being extrapolated to where only disappointment is possible?

[The most popular post I’ve written is once again relevant: Why Investing Feels Like Astrology]

If you are in a professional seat, you have time. You’re not gonna top-tick it anyway. Relish the complacency. The FOMO. It’s the yang to the yin and why you are able to get the other side. You should toe in and hope to lose while your position is small, because every bad mark is spring-loading energy for Newton’s 3rd Law,

You don’t go lifting and hitting. You don’t aggress. You lay in the weeds. Your waiting for flow that opposes your idea.

But you also want to understand “why”.

You wonder, is there some dumb structured product flow out there whose greeks need to be recycled into listed and happen to match what I’m looking for?

Is the driver of that flow some easy-to-package message about how inflation is here to stay so convince the clients to basically sell the deflation option for free.

Classic Wall St momo herding. Package a trend as a cornerstone allocation. Commodity futures for the long run right? (Nobody talked about roll return in 2004 and it’s all anyone talked about a decade later).

Ride the narrative to sell product because the narrative “makes sense”.

While the vampires seduce the consultants and investment committees you search the conference room trash bin for glossy marketing literature. What product are they hawking now? It probably spits off a ton of greeks that are hated, contrarian, and most importantly — cheap.

So you lay in the weeds with your little axe to own that which nobody wants. You get edge on the price because it was “sold”, you didn’t have to cross the market. As a discretionary trader looking for long shots you generally don’t wanna go around overpaying for lotto tickets. Instead you wait for handsome Oxford grads with accents to convince everyone that the lotto ticket is worthless. The prepared responder vs the enthusiastic aggressor.

And the really fun thing about greeks is now someone has the other side. You don’t just want your low probability idea play out — you want someone in pain on the receiving end. It might not be your direct counterparty but it could be a part of the ecosystem that is implicitly short that option whose clamoring exacerbates the problem. When unexpected things happen, something somewhere breaks.

(I may be showing a bit too much of my commodity roots but my model for those markets is — boring, business as usual until a cowboy shows up. It’s a zero-sum game so the other big players who’ve been around for while see the cowboy pyramiding and winning. And so the funds lock arms — time to run the new guy in. Oh the margin requirements changed overnight, never saw that coming did ya cowboy.)

When the crowded side starts to realize that what was 95% true is only 90% true. They sold something at 5% that’s now worth 10%.

Then you get a little mutual reinforcement…narrative can follow price too. As they need to cover the Overton window is also moving against them. It’s invisible but visceral at the same time.

I know I want the “long where it ain’t” option. The option with volga. Because that “it’ll never get there option”, the one nobody wanted, is now the one you can’t touch and that feeds on itself.

One last thing…

Noticed this yesterday:

Better than T-bills but gotta pay state tax.

[Heard those rates have actually come down too! The crypto peeps tell me the cash/futures arb is insane right now so this is presumably a trickle down to any levered long on BTC, although I’m not sure how fat the margin requirement is on the short IBIT put would be if you were just long the synthetic future.]

Even simple SPY cash/futures arbs are fat.

I’ll re-tell some market history that I remember hearing. Hedge funds did well avoiding the dot-com crash. If you weren’t mandated to be long stocks at extreme valuation you could hide out in 5%+ treasuries. Today with P/Es where they are, the forward implied returns on stocks look pretty awful compared the risk/reward of these simple arbs.

I get the excitement. Deregulation, lower taxes, AI, all that. But I also remember the fiber bubble of the late 90s. The longs weren’t wrong — laying cable across the ocean was gonna change the world. But the competition was fierce and changing the world didn’t mean “earn a return”. shale changed the world. And we got a bunch of consumer surplus because it’s a COMMODITY. AI is amazingly useful. But what if it’s a commodity. My guess based on auction-clearing prices being set by the most optimistic bid —OpenAI, Anthropic, and a host of big companies are in a money-incineration competition. But we’re all gonna be better off for it. No reason to double down on the benefits in your portfolio where the eventuality of the benefit is least reliable.

Personal portfolio thoughts

My equity allocation is on the low end of the range I manage in it as I’ve been trimming in the 2nd half of 2024. Also poking around for asymmetric bets of the wide strangle variety. Basically replacing some length with soft upside deltas as blow-off top insurance plus some downside bullets.

One thing I find tricky is that I suspect that we are going to stay in a low correlation regime absent a large sell-off as I suspect the incoming administration will create all kinds of upside and downside headline risk for single names. But implied correlations are already low which means single-stock vols are relatively high. So this particular view is baked into market already. Means if I’m buying it’s with one hand not two.

In alignment with the trimming, my cash position is on the high end. Speaking of cash, some personal convo on real estate…

One of the reasons we are holding extra cash is we have been house-hunting more actively instead of just passively browsing. Our lease ends in August at which point it will have been 5 years. The landlords have indicated they might want their house back although we are still crossing fingers that they won’t.

Cash is a valuable option when buying a home. Especially here in the Bay Area. In fact the option is probably quantifiable. When we sold our house in 2020, the winning bid was 10% higher than the cash bid behind it and well-thru our asking price. Why?

Because the buyers were contingent on selling their home and they were getting a mortgage so they knew they had no chance if they didn’t dangle a sum that enticed us to accept the risk of their offer vs a clean cash offer.

When we bid (we have bid 3x this past year) we offer all cash and quick close times.

[This also helped us win the house in TX against 4 other bidders…which we ended up flipping a year later. See Reasoning Through a Housing Trade Out Loud]

We are never the best bid, but the cash offer is useful because it gets us a callback and into a situation where we have more info than the initial approach which is our objective. So we can probe.

Sellers don’t like closing uncertainty. They are wary of bidders drawing them into a contract with contingencies then trying to re-trade. In fact, you have no chance of buying here if you don’t waive inspection contingencies. Bring your contractor friend to check it out before you bid.

I guess this cash thing is becoming more common too. In the past year, we’ve given cash to 2 separate family members in other regions so they could win their bids. They financed after closing to pay us back.

[Random: the family we sold our TX house to financed the property with a loan against their stock portfolio. Morgan Stanley sent an appraiser!]

Anyway, back to our recent bids this year. We whiffed on all of them. And that’s fine — that’s a feature of our strategy. Mostly. Missing on the last one hurt. In hindsight, I still can’t tell what the right play was. I’ll walk you through it.

We made a cash offer about 2% higher than the asking price which seemed a touch low. We asked for a 3 day inspection period. At this point the game is hang around long enough to find out if the house is attainable at a price we are comfortable with and then sharpen our pencils if we get to the next round.

There were 7 offers. Ours was middle of the pack but attractive enough from a “they will probably close point of view” so we were one of 5 offers that received a counter.

They asked for another 3% and to waive the inspection period. That morning we brought our contractor and architect friends to see if we could do what we wanted to the house. They gave the green light.

(Having another 9 months on our lease, this was a great opportunity to scoop a smaller house put another 50% into it over the course of a year and end up what we want for an all-in price that we are comfortable with — I’ve been looking long enough to know those stars rarely align which is why this was the first house I started to feel excited about)

We accepted the counteroffer requirements.

That night Yinh and I were going out on a dinner date. I was excited that it could be a celebratory one.

I was wrong.

We were outbid by another 1.5% and they weren’t going to do more rounds. The final bid was also cash.

We understood our choices when presented with the counteroffer:

  1. Accept
  2. Counter with lower offer than what they ask for
  3. Be aggressive and counter even higher

The winners chose option 3.

The tricky thing about the final price is it reminds me of the paradox from The Most Underappreciated Aspect of Trading:

When you look at a price, you wish you could have traded it as counterparty to the aggressing order.

Now for the anti-climax.

It’s a fake idea because had you been on the price, the price would have been different. You would have affected it. This idea is like a painting to be viewed from afar. It’s not of any practical value, um, other than the fact that it holds the deepest insight in all of trading.

Knowing the final price, gun to my head, I would pay it. But if I tried to pay that in real-time I probably wouldn’t have gotten filled and instead hit our top (at this point we are 8% through the asking price which is close to but probably still a touch short of what the highest price I could have imagined the house going for).

Pretty unsatisfying.

If I knew we could rent forever I’d just do that. I have no interest in signing up for renovations, $12k/yr home insurance bills, maintenance (or the cost of outsourcing it), and the forgone returns on the cost premium of buying vs renting.

But renting is roulette in many ways. We won to it for the past 5 years but we know we got lucky so it’s hard to get to down about the recent miss.

And yet…

I become more Georgist by the day.

random oil option features

A moontower.ai user asked about oil volatility and correlation in the context of WTI and Brent crude. I did the editorial equivalent of showing him a cool scar:

Let me take these in turn.

USO is relatively illiquid these days relative to the futures options. It used to be more liquid. I spent the better part of a decade relative value trading it vs the futures options including doing create/redeems (I was constantly at OCC position limits — which have a horrible one-size-fits-all application).

Long-dated USO options are very interesting instruments because they are effectively long-dated options on a rolling CL1 contract. This is very different from say a 12-month futures option that references a less volatile CL12 contract.

This difference is why you can relative value trade it, but it’s a complicated model (actually I think a good interview question for a trader or quant is to come up with a model for this conceptually). It’s nice that it offers you an option chain on CL1 while the futures options don’t.

As far as Brent or for that matter heating oil and rbob which you didn’t ask about, the correlations to WTI change periodically when the fundamental details become bottlenecks in their respective markets. Refineries can’t just easily switch their slate between product grades so you can get over/under supply idiosyncracies. There’s an active “arb option” market which is options struck on the spread between WTI and Brent.

Further complicating matters is that Brent and WTI futures and futures options for a given month do not have the same expiries so when you do relative vol trades between them you end up with these residual calendar risks (brent options expiring a week earlier than WTI!)

There was a period of time where this is all I traded so to download all there is to say on this is impossible. You can make a career out of doing nothing else. If you like bloodshot eyes and your hair to be drained of youthful pigment of course.

2 key concepts for traders

This past Wednesday I did an AMA with Kris Longmore’s RobotWealth community. Kris’ work and general way of being is a personal inspiration. I’m a big fan.

(His bootcamp is my #1 recommended course for retail trading because it’s grounded in both the practicality of trading but also in the conceptual — what is edge, where to find it and why it might exist)

This is all to say it was quite an honor to nerd out on his channel 🤓

​📽️Watch the replay of our conversation here.

Just a sampling of topics we discussed:

  • Some differences between professional and retail trading
  • How a retail trading operation can be set up to align with your life
  • Good options trades and where to find them
  • How important is modeling time decay?
  • How important is backtesting for options strategies?

2 ideas that received some extra emphasis:

1) Traders are searching for contradiction not prediction

This is a callback to Measurement Not Prediction which explains why trading rests on “seeing the present clearly” as opposed to playing Nostradamus. The distinction might sound abstract or subtle. This section of a thread I wrote this week is a concrete example:

2) On timing vol

The topic of timing vol came up. And I shared something I suspect people might find surprising.

I had no edge in timing vol. In fact, I don’t think most professional vol traders have any edge in this. In other words, their edge doesn’t look anything like “vol in general is cheap here, let’s load up”. I almost always regret drawing lines in the sand about getting net long or short a bunch of vega. Did I tend to be leaning long vol when it was cheap and vice versa? Sure, but I was usually long or short for a considerable amount of time before it bottomed or peaked too, because markets love to stretch like they’re double-jointed ballerinas before reverting.

After getting humbled by a timing opinion gone awry, I always centered myself by going to back to basics. What does that mean?

The most basic decision in a trader’s arsenal, their reliable fastball so-to-speak is some version of:

“I’m buying this for X, because that is Y bid”

“I’m buying 1-month APPL straddles for X vol, because 3-month QQQ puts are Y bid”.

When you get away from decisions that take that grammatical form you are in the realm of “I’m buying this because the line went down”.

When you feel enough pain to accept that you did something wrong you will usually find this subtle switch in decision logic is the source. It stings the ego because re-focusing on the basics is admitting that you haven’t transcended the grind to become some market maven who just knows when something is about to turn.

(I think all traders subconsciously expect that their 10,000 or even 20,000 hours of practice will unlock that ability. These back-to-basic moments, if you are lucky enough to overcome your pride and negative p/l, to rediscover are humble reminders that markets are learning just like you are so the value of the 10,000 hours isn’t exerted on your ability to beat them, but instead on the practice of process so you have a chance of keeping up. There’s no “best”, only “next”.)

Guest Post: Market Impact and Strategic Execution

Quant @imotw2 published Market Impact and Strategic Execution as an article on X.

With permission, I’m cross-posting it here. It turns execution inutition into market quantitative models. I’ll let the quants debate the models — my interest is in how well this post explains the actual dynamics of accessing liquidity, minimizing slippage, and leaking information with trade/bid/offer behavior.

Enjoy! 


The dirty secret of market impact? It’s messier than anyone admits. This article challenges conventional models by looking at how information actually flows through markets. Here’s the real problem: impact hits differently when you’re getting in versus getting out of positions – a fundamental asymmetry that most models miss entirely. Add in the fact that every major player’s algos are scrapping for the same liquidity, and traditional execution models fall apart.

By diving into the weeds of price formation and what drives liquidity providers, we crack open why impact behaves this way. The result? A framework that bridges pure theory and trading reality, giving you both the mathematical firepower and street-smart tools to optimize execution in markets.

1. Introduction

It’s the ultimate catch-22: you’re playing both sides of the impact game whether you like it or not. Every time you trade, you’re leaving footprints in the market while simultaneously trying to read everyone else’s tracks. Consider a large institutional trader executing a significant position. Each clip they trade isn’t just soaking up liquidity – it’s sending smoke signals to every shop watching the tape. The market sniffs out these patterns and adapts, forcing the trader to navigate the mess they’ve created for themselves. Talk about trading against your own shadow..

Impact also isn’t just about what you’re doing now – it’s about what the market thinks you’ll do next. Planning to unwind a monster position? Just prepping for it changes how you trade today.

You’re not the only one playing this game. Every decent-sized player is running their own book, trying to figure out your next move while hiding their own. Your optimal execution strategy? It depends on guessing their guesses about your guesses. Welcome to the hall of mirrors that is modern market microstructure.

2. Foundations of Impact

2.1 Beyond the Square Root Law

Everyone knows the square root law of impact – trade twice the size, eat about 1.4 times the slippage. But that’s not the whole story, actually its not even close. Markets aren’t this clean. Impact comes from a brawl between volatility feeding on itself, how fast the market digests your trades, and dealers trying to figure out if you know something they don’t. This changes how we need to think about moving size in markets.

At the heart of our framework lies the recognition that trading activity both responds to and generates volatility. Consider a large institutional trader executing a significant position. Their trading consumes liquidity and reveals information, and also increases local volatility, that same volatility changes how the market reacts to their next trade. It’s like throwing stones in a pond where each splash affects how the next one ripples. Classic impact models completely miss this self-reinforcing cycle

Sure, cramming all this into one model is like trying to catch lightning in a bottle. But we’ve built something that tries to capture what we see in live markets.


This model implements the volatility feedback term:

But we have to acknowledge some limitations. Trading isn’t as clean as the math suggests. That linear relationship between impact and vol feedback? Markets are messier than that. And β and γ(t)? They jump around – and good luck predicting when they’ll shift. And the volume-volatility interaction f(v)? Probably more complicated than we’re letting on. Plus, markets don’t slide smoothly between states – they snap.

So why bother with this framework? Because it gives us something concrete to work with. It nails the basic idea that impact and vol are stuck in this toxic relationship, and it actually works well in normal markets – which is most of the time. Run this during the 70-80% of trading days when markets behave, and you’ll get solid signals.

No model’s perfect. This one’s useful not because it nails every market move, but because it gives us a solid framework for thinking about how our trading pushes markets around and how markets push back. Use it to shape your execution strategy, but keep your eyes open – markets have a way of humbling anyone who thinks they’ve got them figured out

2.2 Ready, Set, Go!

Impact hits the market in three waves, and each one in its own way. Even in those first few milliseconds, when you’d think simple orderbook mechanics would rule everything, volatility’s already messing with you. Start working a big order, and the vol spike from your first fills immediately changes how the market handles your next batch.

Then things get interesting. Market makers aren’t just looking at your flow anymore – they’re betting on where vol’s heading because of it. You need to get your trade done, but you’re walking on eggshells trying not to kick off a vol spiral that’ll jack up your costs.

Here’s how it plays out in real time: You start hitting bids with size. Not only does price take a hit, but vol spikes. The market makers see this and think, ‘Great, vol’s about to rip – better back off these quotes.’ Now you’re stuck paying up even more for your next fills. Classic feedback loop that can turn a tough trade into a nightmare.

Long-term is where it gets really twisted. Trades that set off these vol feedback bombs? They tend to leave permanent marks on price. Why? Because the market’s reading these vol spikes as smoke signals – where there’s smoke, there must be fire. Throws the whole temporary versus permanent impact debate out the window. Instead, think of it like this: the bigger the vol feedback, the more likely the market thinks you know something they don’t. Price discovery through chaos, basically.

Our framework also reveals the strategic behavior of market makers and other liquidity providers. Their quote adjustment process now explicitly incorporates volatility feedback through a response function:

That λ(σ,t) term? That’s market makers getting twitchy when vol spikes. They’re playing a delicate game – dodge getting picked off versus making bank on those juicy vol-driven dislocations.

This flips everything we thought we knew about smart execution. You might actually want to take a bigger hit upfront if it keeps vol from spinning out of control. Sometimes you’ve got to pay the toll to avoid the avalanche.

We tested it briefly across equities, futures, and crypto. The model crushes it, especially during those nasty regime shifts when traditional models fall flat on their face. It nails the vol feedback effects, giving you a much better read on your true execution costs and how to optimize around them.

Bottom line? Impact isn’t just some tax you pay to trade. Every move you make reshapes the book for your next play. Once you start thinking about impact this way, whole new strategies open up. You’re not just minimizing cost anymore – you’re actively managing how your trades shape the market you’re trading in.

3. Information Theory of Execution

3.1 Order Flow Toxicity and Adverse Selection

The elephant in the room: toxic flow. Your algo’s (seeminly) crushing it, getting fills left and right – but is that actually good news? Could be perfect timing, or could be you’re getting picked off on stale quotes. Classic execution dilemma: go aggressive and risk getting fleeced, or sit back and watch alpha decay while everyone figures out what you’re up to.

We’re looking at how trades cluster in time and how order flow ripples across related products. Because let’s face it, when someone’s running a smart toxic arb, they’re hitting everything in the complex.

Here’s the math behind the magic – for a given order flow sequence, we compute the toxicity score T as:

Where V_i(t) represents the normalized volume in bucket i, C(t,i) captures the temporal correlation structure, S(t,i) measures cross-sectional spread dynamics and ω are weights that reflect market conditions.

This metric provides a measure of order flow toxicity that can be used to adjust execution algorithms’ aggression levels and venue selection strategies.

3.2 Learning and Adaptation

Modern execution algos are constantly learning – but there’s a catch. How do you know when the market’s actually changed versus when it’s just noise? Every trader’s been burned by overreacting to a head fake.

We tackled this by measuring what signals actually matter for execution. Forget trying to predict where prices are headed or cooking up the perfect schedule. Instead, we built a framework that attempts to cut through the noise to find what really drives execution quality.

Our framework splits market signals into three components:

  1. Structural information about liquidity conditions and market dynamics
  2. Temporary effects from specific order flow patterns
  3. Noise terms that should not influence execution decisions

For each signal, we measure how much juice (information ratio) it’s got like so:

where I(S; O) represents the mutual information between the signal and execution outcomes, and H(S) is the entropy of the signal. This tells us how much actual information we’re getting about execution outcomes versus how noisy the signal is. Translation? We can spot real market changes worth adapting to and ignore the head fakes that would otherwise trip us up.

3.3 High-Frequency Market Making and Latency Arbitrage

Evolving market structure has introduced a new layer in the interaction between execution algorithms and high-frequency traders. Your execution algo sees a fat stack of liquidity on the book – but good luck actually hitting it. Modern markets aren’t your grandfather’s NYSE floor where a handshake meant something. That liquidity? It in a way both exists and doesn’t exist until you try to trade it.

Imagine this: you spot 100,000 shares posted at the offer. Traditional models would tell you to size your child orders assuming that liquidity is actually there. Rookie mistake. Those quotes vanish faster than you can even start thinking about your next move. Market makers are running smart playbooks, adjusting their quotes every microsecond based on everything from correlated ETF moves to the temperature in New Jersey. Yeah, seriously.

What you see isn’t what you get. The odds of filling against posted liquidity aren’t just about time priority. This isn’t even academic hair-splitting – it changes how we need to think about modeling impact and designing execution strategies.

The displayed liquidity in the order book represents a conditional commitment that is fundamentally probabilistic in nature. This probability structure manifests through several key mechanisms:

Firstly, quotes don’t just sit there waiting to be hit. They dance. And not randomly – they move in patterns. When a big order hits, market makers don’t just pull their quotes at the affected price – they scatter like cockroaches under a kitchen light, repricing their entire book before you can blink. Why? Because they’re not idiots – they know one big trade usually means more are coming.

Secondly, What looks like a simple limit order is actually a war zone. That 100k share quote? It’s really multiple market makers playing chicken with each other, each one’s algo trying to figure out if the others know something they don’t. Meanwhile, every other trader with a similar strategy is trying to get to the same party.

Finally, there’s the speed game. By the time your order hits the exchange, that juicy quote you saw might be ancient history. We’re talking microseconds here, but that’s an eternity. Between your network latency, the exchange’s matching engine having its morning coffee, and Jump Crypto cooking you with their radio towers – well, good luck. Even if you’re fast, queue position is usually everything. Being second in line might as well be last when the music stops. The order book isn’t a menu, and if you’re modeling it that way, you’re bringing a knife to a gunfight.

We find that the likelihood of a quote remaining available for execution follows a more complex distribution than previously recognized:

Where λ(t,s) represents the base cancellation intensity that varies with both time and market state, τ(v,σ) captures the reaction time that varies with volume and volatility, and f(OFI, IMB) adjusts for order flow imbalance and book pressure. This creates an effective liquidity profile that differs markedly from the observed order book, forcing execution algorithms to operate in a probabilistic framework.

In English? The faster you need to trade, the bigger your order, or the more the market’s moving – the more likely that liquidity is gonna vanish before you get there. And if the order flow’s getting lopsided or the book’s getting thin? Forget about it.

The implications of this extend beyond simple quote availability. Market makers aren’t just watching your stock. They’re watching everything. Hit them too hard in SPY? Watch their quotes disappear in IWM before you can even think about going there. These guys are hunting for any sign that you’re about to unload size.

The presence of latency arbitrage opportunities introduces systematic biases in observed market impact that must be considered. Every microsecond of delay between exchanges is a gold mine for the right setup. While you’re still seeing stale quotes in Jersey City, someone’s already cleaned up in Mahwah. The really fun part? This isn’t just noise – it creates predictable patterns in how markets react and impact spreads. Those theoretical arb profits (αcross)? They’re like a fingerprint showing exactly how quotes are gonna move and where the impact’s gonna hit first.

Market manipulation remains a massive concern in markets, especially in crypto where it’s not just an edge case – it’s a daily reality you need to deal with. Quote stuffing, layering, and other manipulation schemes regularly distort impact measurements. By tracking specific order book patterns – quote stuffing intensity, layer depth stability, and price oscillations – we can build real-time manipulation indicators. This lets execution algorithms adapt dynamically, threading the needle between adverse selection and efficient trading paths.

Speed management is make-or-break in this environment. Every algo faces a core tradeoff: execute faster to dodge adverse selection, or slower to minimize information leakage. It’s an optimization problem where the sweet spot shifts constantly with market conditions, participant behavior, and execution objectives.

The data shows static speed strategies consistently underperform. Effective execution requires continuous adaptation based on market toxicity metrics, participant patterns, and market state. But nailing this in practice? That’s where things get interesting.

Implementation demands extreme precision at the infrastructure level. Microsecond-level clock sync isn’t a nice-to-have – it’s essential. One timing slip and your execution quality falls off a cliff. Network stacks need to handle the market data and order flow and how they interact, seamlessly. Risk controls need to maintain deterministic latency while actually protecting you. Memory management has to deliver rock-solid performance at the microsecond level.

4. Advanced Impact Modeling

4.1 Cross-Asset Impact Propagation

Trading ETFs or index futures? Your impact bleeds everywhere, and not in the neat way most risk models predict. Markets are connected through a nasty web that shift based on regime and time. Worse still, these relationships aren’t symmetric – the way impact flows from futures to stocks isn’t the same as stocks to futures, and good luck if volatility is spiking.

Here’s how we try to model this mess:

Where:

  • K_ij(t) represents the kernel function capturing lead-lag relationships (how moves in one market spill into another over time)
  • α_i(t) models time-varying direct impact sensitivity (how much bang for your buck you get in each market)
  • β_ij(S(t)) are state-dependent coupling coefficients (how strongly markets are linked, which changes with market conditions)
  • S(t) encodes market state including volatility regimes, basis levels, and order book conditions
  • φ(L_i, L_j, t) captures non-linear liquidity interaction effects (how liquidity dynamics in one market screw with impact in another)

The coupling coefficients β_ij(S(t)) follow a regime-switching process:

Where R(t) indicates the market regime based on a multivariate state classification incorporating relative volatility levels, basis spread dynamics, order book imbalances, trading volume ratios and market stress indicators.

The liquidity interaction term φ(L_i, L_j, t) models how the availability and cost of liquidity in one market affects impact propagation in related markets, which essentially ties it all together:

This captures several features absent from traditional correlation-based approaches

  1. Temporal lead-lag relationships through the integral terms
  2. State-dependent coupling strength
  3. Non-linear feedback effects
  4. Regime-switching behavior
  5. Cross-market liquidity interactions

If you’re trading across multiple markets, you need a model that deals with reality, not just correlation matrices and linear spillovers. This framework gives you the tools to handle the mess.

4.2 Queue Position Game Theory

The management of queue position in modern markets creates a game-theoretic problem. When placing passive orders, traders have to consider their position within the queue and the information content of their queue placement decisions. Every time you join a queue, you’re not just picking a spot in line, you’re sending signals to every other algo watching the tape. And trust me, they’re all watching.

Think your queue position is worth what your transaction cost model says? Think again. That premium spot at the top of the book might be fool’s gold when everyone’s running the same playbook. Or it could be pure alpha when the market’s choppy and other players are gun-shy.

You’ve got to price in the option value of that queue spot, factor in what your queue placement tells the market about your book, and figure out what everyone else’s queue dancing means.

5. Implementation

5.1 Engineering in High-Frequency

Developing excecution algorithms in the context of latency creates significant engineering challenges, that if you get wrong, will crushingly affect trading performance. First up: timestamp management. Sounds boring, right? It is, but it could the difference between making money and getting run over.

Here’s the thing about timestamps in modern markets – they’re a mess. That pristine timestamp you think you have? It’s about as accurate as a sundial here in Norway. When you’re building impact-aware algos, you need to know exactly when things happen, but that’s harder than it looks. Here’s what you’re really dealing with:

Where:

  • Δ_netword_send represents outbound network latency including TCP/IP stack and route-specific jitter. Hope you like randomness.
  • Δ_exchange captures exchange gateway processing time and order validation delays. Different by exchange, time of day, etc.
  • Δ_matching accounts for matching engine queueing and processing time. Where your order sits in the queue. Spoiler: not first.
  • Δ_network_recieve represents inbound network latency and potential packet loss recovery (So fun, said no one ever).
  • Δ_market_data includes feed handler latency and order book reconstruction time
  • Sum of epsilon sub i represents a composite error term incorporating:
  • Systematic variations in processing times
  • Random jitter components because why not
  • Regime-dependent uncertainty factors

This model creates option-like properties in order management. For example, the uncertainty in matching engine response times during high-volatility periods effectively grants a free option to other market participants, who can react to price movements before our timestamp uncertainty is resolved.

5.2 Risk Management Under Impact Constraints

Here’s where VaR gets interesting – and by interesting, I mean breaks down completely. You can’t just run standard VaR when your exit price depends on how fast you’re trying to get out. It’s a nasty circular problem: your risk depends on your liquidation strategy, but your strategy depends on your risk limits. Fun times…

We develop a modified risk framework that tries to account for these dependencies:

where E[I(Q, t) | Q, M] represents the expected impact given position Q and market conditions M. This allows for more realistic risk assessment and better integration of risk constraints into execution algorithms. Now your risk numbers might actually mean something.

6. So What? And Where Next?

We’ve built something that tries to bridge the gap between ivory tower theory and reality. By thinking about execution through the lens of information theory, we’re getting at how markets work.

Here’s the big takeaway, TL;DR if you will: stop thinking about impact as just a cost to minimize. It’s actually telling you something about how the market reads your flow and how other players are positioning against you. Once you get that, everything about execution strategy starts looking different.

It’s about making money and, more importantly, not losing it when things get ugly.

“A sale is made on EVERY call”

On Thursday I published a post called laying in the weeds, an expression I used regularly. Whether it was getting ready to pounce on an offer that accumulates suddenly, sniping with electronic eyes while streaming, or just keeping your mouth shut while others leak info, the lingo fits. It’s ultimately about execution — how do I get the price and size I want?

We can use that background to riff about execution which is easy but dangerous to develop lazy habits about (like laying in the weeds this is more of a professional topic because of the imperative to reduce slippage)

Here’s a common scenario in the voice option market.

Assumptions:

  • An option is worth $.90
  • A broker is bidding $.92 for 10,000 lots
  • You and 3 additional market makers are offering at $.94. You know this because the broker, who we will assume is honest, relayed the full picture.

The case of simple 2 choice scenario tree

  1. You hit the bid and get all 10,000. Expected profit = $.02 x 100 x 10,000 = $20,000
  2. Nobody breaks rank, the offer is lifted with 4 market makers getting equal allocation. Expected profit = $.04 x 100 x 2,500 = $10,000

Seems like you should hit the bid. Except for that, if you do, next time all the offers are more aggressive. Tit-for-tat mutually assured destruction.

You get an interesting result if you unravel the game theory. Assuming none of the market makers are particularly axed in the option, and they all have a similar hurdle rate on how much capital they are willing to deploy for some amount of risk/reward you end up with a stable equilibrium that looks similar to what pre-communicated collusion would have resulted in.

[Aside from the dinosaur era: The way to get a lightly capitalized newcomer to your options pit to give up and go home is demoralizing attrition — trade everything for fair until they go away. I even remember days as a clerk on the specialist post where the boss would tell me to offer something so cheap on our exchange to embarrass a specialist on another exchange who ripped off the buyer at a higher price. The away specialist could lift our lower offer and lock-in a profit but they wouldn’t want to because by forcing the print they would make the customer feel bad about their fill. And if they did lock in the profit by trading with us, we were more than happy to incinerate money to make the customer think twice about routing around us in the future. I can remember the boss, crossed arms, still as Vader: “Keep offering. Filled? Reload.”]

More than 2 choices

Realistically, there are many scenarios. The option could have traded $.92 or $.93 with similar splits even if the first trader who hits the bid thinks she is getting the full bid size, but the broker being a diplomat who needs to deal with each of the market-makers daily decides to split it 4 ways anyway at the lower price. This result is common and explains why it doesn’t make sense to break price. They are unlikely to get the benefit unless they clarify with the broker that they are only going to hit the bid if they get full size (the broker weighs whether they should box the other 3 out and consequently piss them off).

How this plays out depends on your business relationship to the broker both in terms of how much you pay them and how useful you are in making fast, tight markets. When I was a local on the NYMEX I didn’t trade huge size but I was super-responsive so I could get those 25 and 50 lot berries. Those tight markets were also useful to the brokers who could use them “cuff” a related market or fish for business. At the fund, my value in the ecosystem was size, so I had leverage in setting the price of a larger order (maybe I could convince the broker to make the splits 4k, 4k, 1k, and 1k where I’m one of the larger allocations) but didn’t get the small layup orders.

We can get bogged down in scenarios forever, but the point is that this little game is being played all day. In the voice market and the electronic algo logic of sophisticated market-makers. If I divide all my profits by how many contracts I traded I end up somewhere in the penny ballpark. That’s the margin. That’s the difference between tossing coins for fair and a highly profitable business. It also means, that without a lot of reps it’s hard to tell if you have an edge.

Let’s do another example of cat-and-mouse.

An option is quoted $.21-$.23

You think it’s worth $.25

What do you do?

The correct answer is “it depends”. The first step to building a model for solving this execution problem is to identify the dependencies.

A few off the top of my head:

  • If I lift, I make $.02 of edge on Y volume
  • If I join the $.21 bid, what’s the probability I get hit (therefore making $.04) and how much volume would I get? Handicapping this depends on if the matching engine is time priority or pro-rata as well as if there is any priority that derives from my designation (customer, pro customer, professional, and more)
  • If I bid $.22 and get hit I make $.03. But would that bid cause someone else to lift $.23s? I need some map of what other market observers think an option is worth.

Broadly, I need some priors about the distribution of what others think this option is worth based on existing bids/offers, the trades that have happened, and trades that have not happened (ie bids/offers that have been displayed but nobody cared on).

You could start with a simple equation.

P(getting hit) * volume when I get hit * edge to the bid_price= volume when I lift * edge to the ask_price

You can solve for P(getting hit) to find a breakeven for how often you’d need to get hit to compensate you for not lifting.

While this is stylized and simple it’s not an attempt to point to some abstract HFT optimization problem. It’s a reminder that reflecting on your execution techniques sharpens your thinking about trading, conditional edge, adverse selection. It’s less important for retail or if you don’t transact often, but for professionals and asset managers it is justifiably top-of-mind.

“A sale is made on EVERY call”

Remember Ben Affleck in Boiler Room:

And there is no such thing as a no-sale call. A sale is made on every call you make. Either you sell the client some stock or he sells you a reason he can’t. Either way a sale is made, the only question is who is gonna close? You or him?

Every time you trade with a broker someone gets the best of it. If you consistently get allocations for 60 contracts when you should have gotten 70 you are destroying 14% of your annual profit. Specialists and DMMs had rules about allocation quantities but there were also unwritten rules. You were expected to fight for even a single contract that you are “entitled” to and advocate forcefully for your interests constantly. The pugilism was built right into the training and culture. The stories of ruthlessness were culturally rewarded. As a junior trader, sticking it to a competitor or getting into a nose-to-nose screaming battle with a broker just to define boundaries was a way to earn stripes.

[This is not my native personality but you adopt what it takes. After all, the only point of this job is to make as much money as possible. Sure, the cost likely bore itself as chronic anxiety about work but only the most well-matched people get the luxury of getting paid and being comfortable. I don’t miss all the daily haggling but I did take it seriously since it was one of the most impactful contributions to profit for the reasons above.

One story I had brought to my attention in the past year — a PM who ran one of the large banks deriv desks reminisced about the AMEX when we were in the same pit. He’s a bit younger than me and apparently I made a big scene sticking up for him to a broker who tried to bully him in the pit. Nice to hear even though I don’t remember the exact incident. I do have a vague memory of lots of battles in that pit because it was a large crowd in a very liquid name.]

Final thoughts on this theme: if you manage a business that’s a game of inches, it’s good to periodically check-in and ask “are we clawing for those inches?

Is everyone at the point-of-sale aware of what needs to be done or are we getting sloppy? Are we leaking info? Are we too nice? Would it pay to be squeakier? Are we paying the brokers we want to be paying? Are we paying the brokers the right amount?

Evergreen:

Tax-Loss Harvesting On Levered Long/Short

Real estate people understand the value of accounting losses in service of deferring taxes while an asset’s returns compound.

In the institutional investing world many investors such as endowments are tax-exempt.

Retail investors in public stocks have less places to hide outside of tax-advantaged accounts which are hard to jam lots of assets into in the first place.

The rise of ETFs have come with some relief on the tax side as you decide when to pay taxes because you decide when to sell even as the holdings are rebalanced. Mutual funds can leave you footing a prorated portion of the pool’s taxes regardless of how long you’ve been an investor.

While the ETF advantage is real it’s relatively minor compared to the ability to tax-loss harvest. By owning the individual components of a stock index you can sell losers, rebalance into peer stocks, and accumulate short-term losses to offset long-term capital gains on the subset of names that moon.

I say minor because of the “brain damage” (more effort, slippage, tracking error although if it’s random only matters if you’re managing money for others) and higher management fees associated with TLH. See Alpha Architect’s The Costs and Benefits of Tax-Loss-Harvesting (TLH) Versus an ETF.

Another restraint on TLH enthusiasm is limitation on writing off losses greater than $3,000 per year. Losses are more valuable in an NPV sense if you can use them to offset significant capital gains when diversifying out of a large gain in a concentrated position. With markets where they are, especially the Mag 7 and BTC, this is common high-class problem.

Still, the fintech world with the rise of robo-advisors and software is enabling both retail and advisors to “direct index” making TLH both easier and less costly.

Getting a sense of proportion

Let’s do some simplistic hand-wavey math to get a sense of proportion for how TLH might work if you were simply long a $1mm basket of stocks.

Assuming individual stocks were i.i.d. (“independent and identically distributed”) with expected mean monthly return of 0 and standard deviation of 10% (10% *√12 ~ 35% annual estimate of single stock volatility) then conditional on a stock being down its expected loss is 6.75%

This is symmetrical. Given that a stock is up the average expected return is +6.75%. We are just using arithmetic returns.

In mathematical expectation you expect the portfolio p/l to be 0, with half the stocks up and half down. Thinking about the portfolio as 2 halves, you expect $500k to earn 6.75% or $33,750 and $500k to lose $33,750.

Now suppose you rebalance the losers into a Wario basket of names that have the same exact characteristics as the ones we sold. You have now crystallized $33,750 of short-term tax losses but our exposure is the same. You have gained an asset to offset future tax liabilities.

Just staying simplistic, if all the stocks proceed to go up by 5% over the next 365 days and you sell on day 366 to get LTCG treatment (assume 23.8% — which is just Federal!) then what is your after tax return?

Winning stocks:

$533,750 * 1.05 = $559,728.75 or $59,728.75 total profit on a basis of $500k

Losing Stocks:

$466,250 * 1.05 = $489,562.50 or $23,312.50 profit on a basis of $466,250

resulting in:

+$83,041.25 LTCG (5% on $1mm exposure)

-$33,750 short term losses

= taxable gain of $49,291.25

tax bill = 23.8% x $49,291.25 = $11,731.32

After cutting the check what do you have in your account?

$1,049,291.25 – $11,731.32 = $1,037,559.93 or a 3.75% after-tax return.

 

💡The tax benefit

You’ll notice that if you bought $1mm of an ETF that went up 5% in a year and sold on day 366 your $50,000 profit less 23.8% taxes would net you about the same after-tax return.

So where’s the benefit?

It’s in the optionality of this pool of short term losses that you have control over. You could just let this $1,050,000 portfolio grow and keep the short-term losses as an asset in your back pocket to use against future tax liabilities, some of which are going to be taxed higher than LTCG rate. Alternatively if you need to divest a large chunk of a profitable position to raise cash, you’ll have a large pool of losses to offset the gain.

The real value of TLH emerges when:

  • Offsetting Higher Tax-Rate Gains
    • Short-term capital gains (STCG) or ordinary income are taxed at higher rates than LTCG. If your harvested losses offset STCG or ordinary income, you reduce your taxes significantly.
  • Perpetual Deferral
    • Step-Up in Basis
      • If you hold the portfolio until death, the heirs may receive a step-up in basis, erasing deferred taxes entirely.
    • Charitable Contributions:
      • Gains on low-basis positions can be avoided by donating appreciated securities to charity.

This toy example is compelling enough to realize it’s important. But there’s also another flavor of TLH on the scene with the potential to generate significant short-term accounting losses while the overall value of the portfolio grows.

TLH on levered long-short portfolios held in a separately managed account (SMA)

Using portfolio margin and a quant framework (this can range fairly basic to factor-intensive), an investor can run the same beta they desired in a typical long-only ETF but generate significant short-term losses by using their stocks as collateral to overlay a long-short portfolio.

This is typically done with an advisor who will in turn be using a sub-advisor whose infrastructure allows them to scale portfolio adjustments across thousands of custom custom portfolios held in SMAs.

I’ve heard some claims of how much more impactful this can be but again it’s critical to sanity check with actual numbers to make sure the sense of proportion is reasonable. From there you start layering common caveats which are easier to handicap in terms of bps per year.

In this case, the sanity checks called for simulation.

A little foreshadowing — if you are in a high tax bracket or trying to work out of a concentrated position with a low cost basis you are going to want to see this.

You get the simulation code, you can run it in your browser and it will even download the full output. I’ll show you a few manipulations for the output so you can get a strong grasp on the mechanics. This is one of those concepts that you can’t unsee once you see it. Multiple bulbs going on at the same time.

(It’s also quite depressing so much time is spent on taxes and the ROI on that time is validated by the math. Both taxes and the time spent on their minimization is deadweight loss. I like markets, I hate structuring and law and tax and basically all the crap that’s probably higher yield to understand. And just going through this exercise depressed me even further because it confirmed how important it is.)

Onwards…

This Jupyter notebook can be run directly in the Google Colab environment.

🔗TLH.ipynb

Open the link and press “play”.

The output will:

Return a summary in the browser of the simulation results

download a CSV to your browser

 

Stepping through the tax-loss harvesting (TLH) simulation

This simulation models a tax-loss harvesting strategy applied to a hypothetical stock portfolio over a 12-month period. The objective is to demonstrate how TLH can potentially reduce taxes by systematically harvesting losses on individual stocks while maintaining the portfolio’s market exposure.

Key Steps and Mechanics of the Simulation

  1. Portfolio Setup: $1mm long equity portfolio
    • The portfolio consists of two parts:
      • Long Positions: $1,300,000 allocated across 100 individual stocks.
      • Short Positions: $300,000 allocated across another 100 individual stocks.
    • Each stock in the long portfolio has a starting price of $100 and is equally weighted. Each stock in the short portfolio also has a starting price of $100 and is equally weighted.
  2. Return Simulation:
    • Every month, the returns for each stock are randomly and independently generated based on a normal distribution with:
      • Mean Return: .80% per month (approximately 10% annualized compound return).
      • Volatility: 10% per month
  3. Monthly Rebalancing for Tax-Loss Harvesting:
    • Harvesting Criteria: At the end of each month, the simulation checks each position to see if it meets the tax-loss harvesting criteria.
    • Long Positions: If the price of a long stock falls below its cost basis ($100), the position is “harvested.”
      • Harvesting Process:
        • The position is closed, and the realized loss is calculated based on the difference between the cost basis and the current price.
        • This loss is recorded as a crystallized loss, and the realized loss amount is added to the cumulative short-term losses for the portfolio.
        • A new stock is bought in its place with a fresh cost basis of $100 using the harvested amount. Since the original position suffered a loss, the proceeds will be less than $13,000 ($100 * 130) worth of shares. Since the new stock is also $100, the share quantity must be less than 130.
    • Short Positions: If the price of a short stock rises above its cost basis ($100), the position is similarly harvested.
      • Harvesting Process:
        • The position is closed, realizing a loss based on the difference between the cost basis and the current price.
        • This loss is recorded as a crystallized loss, and the amount is added to the cumulative short-term losses.
        • A short position in a new name is established to match the notional amount of the covered position. A fresh cost basis of $100, but the short share quantity will necessarily be less than 30 shares.
    • No Harvest for Profitable Positions: Positions that remain above (long) or below (short) their cost basis are not harvested and continue with their updated prices and fixed share quantities into the next month.
  4. Tracking Results:
    • For each month, the simulation tracks:
      • Monthly Short-Term Losses: The sum of all realized losses from harvested positions within the month.
      • Cumulative Short-Term Losses: The running total of all realized losses harvested up to that point in the year.
      • Monthly Tax Benefit: Calculated as the monthly short-term losses multiplied by a specified long capital gains tax rate (assumed to be 23.8%) since that’s what they will be used to offset.
      • Cumulative Tax Benefit: The running total of tax savings from all harvested short-term losses over the year.
  5. Assumptions:
    • Consistent Cost Basis: Each new position, whether long or short, always has a fresh cost basis of $100, regardless of the prior stock’s price at liquidation.
    • Monthly Frequency: The portfolio is evaluated and rebalanced for TLH at the end of each month, meaning opportunities to harvest losses are considered 12 times over the year.
    • Independent Stock Movements: Each stock’s returns are generated independently of others, with no correlation among stock prices.
    • Equal Allocation and Reinvestment: Both the long and short portfolios are equally allocated across the stocks, and any harvested amount is fully reinvested into a new position with the same initial investment amount.
    • Static Portfolio Size: The portfolio maintains 100 long and 100 short positions, with new stocks replacing harvested ones to keep the portfolio composition stable.
  6. Output:
    • At the end of the simulation, the following information is displayed:
      • Detailed Monthly Summary Table: Includes individual stock performance, crystallized losses, and other details for each stock every month.
      • Month-End Summary: Shows monthly and cumulative short-term losses and tax benefits. This provides insights into how the strategy’s tax benefits accumulate over the year.
      • Overall Portfolio Statistics: Total portfolio gain/loss, gross return, accumulated short-term losses, and the final tax benefit as a percentage of the initial portfolio value.

Summary

I address a few of the real-world considerations further below.

But to put the value of this concisely:

Making a $100k capital gain on an investment is not as useful as making $300k with $200k of short-term losses even though the net is the same.

[Notice how you might not have enough capital gains to take advantage of all these short-term losses. Which is why a strategy like this is especially useful for investors sitting on concentrated profits — they can work out out of it much with smaller tax impact. Holdings can be used to collateralize shorts with portfolio margin!]

Real World Considerations

  • In practice, a TLH strategy would seek to rebalance into names with similar characteristics (whether by factor, sector etc) to avoid wash-sale rules. In the simulation each stock has the same vol but this proxies using equal-vol weighting in the real world.
  • There is a cost of leverage although it is partially offset by the short-stock rebate on shorts.
  • Note that as the market rises, the number of positions that are underwater declines. Names you recently rebalanced into will have a better chance to experience loss to harvest than a name that you have been holding for years of a bull market. However the levered version of TLH which includes shorts and longs offers far more opportunity to harvest than a long only portfolio which might have very few losers after several years.
    • As time passes the surface area for loss harvesting stabilizes towards something of a steady state.
  • The strategy is meant to maintain a 100% long exposure (130 long vs 30 short) so if volatility increases it is still bad news. But the tax loss harvesting portion can actually benefit from higher volatility so there’s a natural buffer.
  • Monthly turnover means slippage costs. Those will increase with volatility.

Wrapping up

I leave it to you to decide how interesting this all might be.

(I find it compelling but still taking it apart.)

I’m not a tax expert. I’m not a simulation expert. Hell, it was a long battle with ChatGPT to get that code to a place that felt right. (It was about 50 iterations of “run code”, “pivot table the CSV data”, “see if the lifecycle of trade/rebalance/accounting made sense”, “tell ChatGPT how the desired behavior of the code diverged from the actual behavior”, “repeat”).

Example of stitched together images of pivot tables to investigate:

  • This one allowed me to see crystallized losses by month. You can see how they decline over time. That’s because as the market rises the further stocks are above their cost basis which means less opportunity for harvesting. This would be much more pronounced if there you did not employ shorting.

This table lets you see price paths

 

Position and portfolio values over time

I hope some of you will get your hands dirty with this as well. I want to know what I’m missing or flat-out misunderstanding. Even placing sane error bars around the real-world considerations would be helpful.