Staring Out The Window

I threw a $500,000 purchase price and a 7% 30-year fixed rate into a mortgage calculator. That’s a payment of $3,327.

Earlier this year, if you secured a mortgage at 3%, you could have bought a home for $790,000 and had the same payment.

Since housing hasn’t dropped 36% this year homes have gotten much more expensive to own. Considering you can buy 1-year t-bills yielding 4% that are state-tax free and nominally risk-free, the investment case for RE is looking pretty poor unless rents skyrocket or real estate craters to bring cap ratios back up.

If the higher rate environment leads to a recession and lay-offs then I’m doubtful that rent increases are going to be the primary normalization pathway. It feels like employment trends will be a clue to how quickly housing will re-price lower (it’s already started of course). The yield curve is inverted, so the bond market is suggesting that the rate hikes in the near term will slow inflation and the economy.

This is all just simple observation. Like looking out the window. And as one does, when they sit at a window, one muses. And muse I shall.

Musing #1: Bid-Ask Widening

A year ago the people that paid ridiculous prices for RE were market orders. “Fill me at any price”. Many of them were immediately in the money (ie they probably could have turned around and sold a month later for more. Maybe not net of transaction costs but you get the idea). This isn’t shocking. When optimism turns to euphoria, the rate of change of the returns themselves can explode into a parabolic curve. Of course, such curves are unsustainable. The smug moment of being in the money is short-lived in the same way that a fund that buys a ton of stock going into the close usually gets a favorable mark on their daily p/l. Their sloppy buys drove the price higher in a short period of time. The real sellers didn’t have time to react before the close. But as soon as they check the comps overnight, you can be sure the supply is coming tomorrow morning.

I think of it like water going down a drain…once most of the water is through the drain the remaining liquid swirls quickly around the drain before you hear that sucking sound. Whoosh. The last bid is filled. With maximum punnage — the liquidity is gone.

In the meantime, many other buyers were priced out. You can think of them as limit bids. It’s an imperfect analogy but it will suffice. As things go south now, some of those bidders might be anchored to their original bids which were “cheaper” than where the home traded. However, if they get filled on the way down, they actually have more negative edge even though they got this theoretical house for a cheaper price than the original buyer. You could belabor this with a stylized model but understanding this concept is a big step towards understanding trading.

Anyway, the old limit bids are probably the new ask and the real bid/ask spread is wide. Prospective buyers are adjusting their bids much lower to keep the monthly payment constant or at least manageable, but sellers who likely have cheap financing from the prior low rate regime do not have to cross the spread. If current prices are 5% off their highs but the new mortgage math means homes they should be 20% lower (similar to the stock market) the current listing prices are the “asks” of a wide market.

Buyers lifting those offers are giving up edge for convenience/immediacy. That’s the usual reason people willfully give up edge for anything. Sellers hitting bids either need to (relocation, getting laid off, divorce, or any other life thing that shuffles liquidity needs) or they think rents aren’t going to increase as part of the normalization process.

Musing #2: Price Can Ruin Any Investment Idea

Always promotional, the real estate industry in an effort to pump bids, always finds an angle. They look at CPI and rates increasing, and peddle “RE is an inflation hedge”.

I mean, sure. But price matters.

By that logic, RE was also an inflation hedge 6 months ago, so are real estate prices supposed to be higher today given the elevated inflation of the past 6 months?

A few weeks ago Tom Morgan published Eight Investing Gems, which was a list of underappreciated, evergreen concepts sourced from investment professionals. I was flattered to be asked and my response fit well here:

Markets are biology, not physics, and that’s important because every good idea can be ruined by price. For example, real estate with a mortgage might be a good inflation hedge, but if history has taught everyone that lesson then it will be less true going forward. In other words, the price today already incorporates that (imagine paying 3x for your current home… how’s that going to work out as an inflation hedge?)

Prices are what matter. Not blanket, lazy sentences like “RE is an inflation hedge”. You’re not trading sentences.

[It’s also not clear that RE is an inflation hedge during periods of inflation]

Musing #3: Bullwhips Everywhere All The Time


The bullwhip effect refers to a scenario in which small changes in demand at the retail end of the supply chain become amplified when moving up the supply chain from the retail end to the manufacturing end.

With Covid closings followed by re-opening, this effect has received lots of attention. It’s not new. The famous beer game lets you play as a retailer, distributor, manufacturer, or wholesaler to make ordering decisions that balance your inventory against your customer’s demand. Orders are a proxy for demand, but the lag times in delivery lead to over and underreaction in ordering decisions.

Bullwhips feel like an apt analogy for the over and under reactions that happen in our largest markets:

  1. The underbuilding of homes since the GFC. Builders’ PTSD and higher lending standards for the past decade have contributed to a housing shortage. In the past, I might have associated building velocity with the credit cycle, but the excess of the mid-aughts seemed to have chastened builders despite the loose monetary conditions of the 2010s.
  2. Energy prices, in the wake of shale’s “growth at all costs”, busted in the mid-2010s. They surged back recently as the reality that fossil fuel transition will take longer than expected has collided with underinvestment in production. Drillers were scolded both from their investors (overproduction) and would-be investors (ESG).

[Just FYI, def not advice:

I sold my energy overweights in the Spring and recently started dollar-cost-averaging back in as I add investment exposure in this pullback. Overall, still overweight cash which I’ve been moving directly into T-bills. I’m in the midst of trying to do a rebalance from RE to equities but need one leg to close first so I don’t get middled. I hate illiquidity. In case curious, my prior energy exposure was XLE in an IRA, but I’m re-entering via deferred WTI futures. Instead of a div yield, you get a theoretical roll return. I am not an especially active trader/investor so I figure I’ll share stuff like this when I’m actually doing something. Again, I’m more weighted in cash than most sane people and don’t consider myself a good investor — I mostly try to avoid disaster. I just want to have my assets match my future liabilities — if I want to get rich, I’ll try a higher signal route of relying on myself not random number generators.]

  • Musing #4: Too Many Assholes Playing A “Loser’s Game”

Read this essay:

Too Many Assholes (7 min read)
by Jared Dillian

Jared is an author. He’s published a couple books, one was fiction. He was an index trader for about a decade before becoming a full-time writer amongst many endeavors. Jared is an exceptional financial writer. I read his professional letter regularly for most of the past decade.

This particular essay starts out:

This will be the only financial essay I write, I promise.

His substack is about culture and life not investing. So when he paused to write a single finance post in this collection, I paid attention. It felt very familiar. It has the same feel as his paid daily writing.

I want to offer a perspective on his writing. When people ask him for a free sample of the paid letter he doesn’t give them out. It’s for the same reason I give when people ask me if they should sub to his letter. The individual letters are not useful if you are looking for a great stock tip or definitive proof that the letter will make you money. So if you ask for a single letter, you miss the point. He’s capturing the broad strokes and he’s repetitive. And this is valuable in its gestalt.

I’ll re-hash my Twitter thread on Jared’s post:

This essay could have been called “play the cards not the man” but Jared is a snappier writer so he cut to the heart. It sounds like a folksy kind of essay but it’s deep. If you can internalize his essay you risk making small mistakes, you’ll almost definitely get the timing wrong, but there will be no catastrophes. Since survival is the goal in what Charley Ellis called the “loser’s game” this essay is an irreverent treatise in financial self-preservation.

Jared brings up contrarianism which by definition is required fo outsized returns. But at the turns in markets, the contrarian instinct is defensive. Yes, it can be expensive mid-trend but I’m not advocating for perma-contrarianism anyway. Sometimes contrarianism is common sense when LPs in private funds are climbing over each other to pay 20x revenue for profitless companies.

Options trading provides a well-balanced education in contrarianism. You spend a lot of time fading “point spreads that went too far” so you learn to deal with the discomfort of positions that are against the crowd. And of course, you do need to manage risk around that carefully (position limits are key because once a price enters la-la land there’s no restraint on it go to la-la-la land). At some point, you are selling because you are approaching “there’s nobody left to buy” territory and that is the exact point in time when it’s hardest to do that.

Playing the hindsight game, in the Spring I sold my energy stocks (a touch early but again it was a small mistake) despite being bullish. The thinking: Everything about oil looks bullish but everyone else sees that too. It’s insane to be bearish. But then you have to switch into the mind of a seller…there is no opening seller. So the price must contain a massive premium in it to attract any sell flows.

And that is enough to pull the trigger to sell for me. Yes, I could be wrong, but the risk/reward said “sell”. No fundamentals. Pure psychology.

[This isn’t any kind of victory lap. I’m losing money because I’m basically a long only investor and my current life is not a trading seat where I have the advantage of being in the mix.]

The question to focus on is “What psychology is in the price?” The price includes all the spreadsheets already. It’s the sum of the emotions and the nerds.

Jared focuses on sentiment. It’s not too useful when the game is played near the 50-yard line. In that zone, I’m perfectly fine to outsource to passive collection of market risk premium. With stocks, you know the proposition — earn 5% over the risk-free rate, give or take 15%, and experience a double-digit peak-to-trough drawdown every other year, and something like a 50% drawdown once a decade. Fat tails. That’s the deal. Over the long-run you’ll make money, but sizing that proposition is a personal matter.

The psychology matters more at the turns. The edges of the field. Marching through the redzone, from the 20-yard line to the goaline, can feel dramatic in compounding space. The 5-yard line to the goaline — this is the blow off top in Doge or the Volkswagon short squeeze in 2008…where the bulk of a total return can come from a short time. This is when things are obviously unstable. Sticking around to find out which down is gonna be the pick-6 is baggie roulette.

You don’t need to be some market genius when things feel crazy. Just realize that the only way the price can make sense is if someone crazier came along. Unless you have a very special edge in that game (I suspect at these critical turns the internal mechanics of liquidity are understood by a handful of insiders/clearing firms/exchanges, perhaps it’s a short squeeze, that connect the trading world to the credit/banking world. If that’s the case, you, sitting at home in your pajamas, are playing no-limit hold’em with a worse than random hand against people who know their cards.)

If you don’t have a hero instinct and just try to get the broader picture roughly right you can avoid the giant mistakes. That’s 95% of the battle. 2021 was stupid euphoria. That was obvious even in real-time. Sure you could have been early to that realization and looked foolish for a while but zoom your perspective out and ask yourself:

“Am I feeling fomo or fear?”

That will tell you what everyone else feels and that tells you what’s in the price. You know what that’s called: empathy. You are putting yourself in the minds of others and therefore the price. It sounds like soyboi shit. But that shit is full is wisdom if you can channel it.

Celibacy Vs Condoms: The Answer To Whether You Should Trade Options

The point of dashboards is to help you make better decisions. Decisions that accord with your objectives.

I’m underwhelmed by the standard of dashboards in the investing world. They are not designed to help you make better decisions. They are designed to make you stick a quarter in a slot machine. The focus is on returns not risks. Returns are less predictable than risk and risk itself doesn’t exactly lay down quietly on the operating table for examination. Jason Zweig called attention to Robinhood’s brazen options GUI near the height of call option yolo’ing:

Robinhood’s emails and other communications were prompting me to trade options, another risky strategy I’d signed up to try. I didn’t trade any, largely because the way Robinhood displays options prices confused me. Other brokers show your potential gain and loss equally prominently. When you look into buying a call option on Robinhood, however, the app shows you a measure called “To break even,” with no indication of potential loss.

Interested in selling the same option? Now Robinhood will show you something called “Chance of profit,” again with no measure of possible loss. But if there is (say) a 65% chance of profit if you sell an option, then there must be a 65% chance of loss if you buy it. By instead highlighting “To break even,” Robinhood draws your attention to how little a stock has to rise for you to begin making money by buying an option—even though you could lose as much as 100% of your investment if the stock goes up less than you anticipated (or goes down).

“Chance of profit,” meanwhile, focuses you on the high likelihood of earning at least a small amount when you sell a call option. If the underlying stock goes up more than you expected, though, that could cost you far more in forgone upside than you earned selling the option. Other major brokers, including ETrade, Fidelity Investments and Charles Schwab, don’t pull this sort of switcheroo. They use the same format whether you want to buy an option or sell it—and they don’t use the term “Chance of Profit.”

“How a brokerage firm displays risk and reward shouldn’t hinge upon whether you’re buying or selling an option,” says Roy Haya, head of options strategies at Fort Point Capital Partners LLC, a San Francisco-based investment firm. “Changing the optics like this could encourage activity on both sides of the same trade, and that seems like a suspect way to entice inexperienced options traders.”

“Each [options-quote] display,” says a Robinhood spokeswoman, “seeks to elevate the information that we have found to be most relevant to a seller or a buyer, who have asymmetric opportunities and risks—certainly not to encourage any particular investment strategy.”

Robinhood’s business relies on churn because active trading in options ensures your customers will either blow up or bleed out. Options trading is high margin for the brokerage. A mirror of what it looks like for the client.

Consider this:

1% slippage in a $50 stock means losing 50 cents on your fill.  Now think of options. If you pay 51 cents for an option worth 50 cents you are incinerating 2% in expectancy. And that’s without fees. The absolute smallness of the numbers is insidious. Optically tight bid-ask spreads lure you into trading more. If the markets were really wide and you had to pay $1.00 for that option worth $.50 you’re almost guaranteed to lose. It’s like borrowing money from the mob. You’d know it’s a bad deal. But when the market is tight, your negative edge is obscured just like it is in blackjack. You actually get to win fairly frequently. And that is the hook. You don’t realize you are playing a losing game.

The danger of options is not unlike the danger of risky sex. It’s exciting. If you sell options irresponsibly your win frequency is still high. It feels niiiice. But if you get burned, the outcomes range from an uncomfortable coyote morning all the way to, well, ending up on whatever the Jerry Springer show of today is disavowing your baby, I mean, account. (I was a 90s teen and my references are frozen in the original Jurassic Park amber).

If you buy options irresponsibly, it’s only a matter of time before you end up with a disease. Hep-B. B for “broke”.

Think Before You Even Get Aroused

When it comes to options, I’m a prude. I preach celibacy. I don’t do it in my personal account (my only account these days). No blanket advice is perfect. But I think it errs in the right direction. There are more people who think they should trade options but shouldn’t than there are people who aren’t trading options who should. I can never keep type I and type II errors straight. Even with this “on-the-nose-for-this-post” graphic:

Taking the other side of your trades is such a consistently good business, I’m picturing every customer opening an options account as Tobias:

From my perspective, I just eased into options as a job. It was simply a subset of trading which is what I more broadly signed up for. I wasn’t inherently interested in options, but as I started learning about them I was as vulnerable to the same nerd snipe that many readers of this blog find themselves mired. I just had the advantage of being on the house side.  So if my plea for celibacy has any hope of working I should at least offer a sound rationale that is more than “you’ll go to [financial] hell”. You need to understand the purpose of options in the first place.

Why Anyone Would Trade An Option?

Let’s address reasons to trade an option.

Directional speculation on the underlying

This is a common and intuitive use of options. You’re bullish so you buy some calls. You’re bearish and sell calls or buy puts. Pretty straightforward. The dominant rationale here is using the options for their “delta” and inherent non-recourse leverage. If this is you then my paternal reminder:

This is really a fundamental trade more so than a trade born of some opinion of the option’s price. In other words, 90% of the work is actually upstream of the options trade. That last 10% involves choosing the exact expiry and strike but if you have an explicit forecast for the stock, a forecast that is presumably fueling the burning desire to go through 2FA into your brokerage account, possibly fill out an “Intent To Trade” compliance form, and then the commitment to follow the thing you bought (and follow it you will — you didn’t trade an option because you’re “in it for the long haul”), then the actual option selection is rather trivial. The best bang for your buck easily falls out from a well-fleshed-out forecast.

If the options part is hard, then it’s inheriting the wishy-washy nature of your upstream fundamental analysis.


Buying an option can act like an insurance policy. Puts can protect a long position, calls can protect a short position. As opposed to a stop order which is exposed to gaps, an option is a “hard” stop. You always maintain the right to exercise at the strike price. This hard optionality is presumably baked into the price because it’s valuable (one of my conjectures is that various flavors of option selling strategies that have rules for covering options when they start hemorrhaging are, at their core, attempting to arbitrage this hard-to-pin-down concept. This starts to rhyme with “vol trading” which we’ll get to because, when you get to the nucleus of the logic, these strategies are premised on the idea that the replication is cheaper than the hard option.)

In any case, when hedging, most people buy options. Like speculation, 90% of the work is done upstream of the option’s decision. The rationale for whether you should hedge versus simply use less leverage or run smaller position sizes is complicated. If your core position is X then is that better or worse than a bigger hedged position? That’s a hard question. Consider the logic I’m recycling from Finance As A Laboratory For Decision-Making:

People understand that even though insurance has negative expectancy it can still improve a portfolio that is focused on compounded returns. It makes no sense to look at the line-item of insurance divorced from the optionality it gives you in the rest of your portfolio.

(I could pull lots of links on this idea, but let’s be brief).

This concept is fractal. Let’s zoom in on the smallest portfolio — a spread. You don’t necessarily care about the p/l of any individual leg of a spread trade but the performance of the spread overall.

Before we consider a spread, let’s just look at the single position. Suppose you buy something for $4 when it’s worth $5 but then sell it for $4.50. You made both a:

  • +$1 expected value trade
  • $.50 EV trade.

If you knew it was worth $5 you negated half a good trade with a bad trade.

In real life, you often might like the price of a spread but it’s hard to tell which leg is the “good side”. That’s one of the reasons you trade the spread. Once you do the spread you don’t care about the individual p/ls.

Another reason you may do a spread is that you might like a trade (ie maybe vol is cheap in X) but can do it bigger if you spread it. This is one of those questions that comes up a lot on real trading desks. Do I like the outright, or do I like the trade better paired against something else (and assuming I can do the trade bigger if I spread it)? Do I like being long z units of X exposure, or do I prefer 5z units of (X-Y)? The answer depends on understanding the distribution of the outright vs the spread and the relative price of each within those distributions.

Again, the decision of whether to mitigate the risk requires more brain damage than actually picking the hedge. You can learn more about the logic of hedging in If You Make Money Every Day, You’re Not Maximizing.

If you are rigorous and clear in your decision to hedge, then once again, most of the work is upstream from the options trade.

Some kinky thing called “vol trading”

“Volatility trading” is another reason to trade options. This is a niche reason because it’s actually the inversion of the first 2 reasons. Those reasons originate from very natural impulses — to speculate or cut risk. Vol trading is the business of supplying liquidity to all those normie investors. It’s a strategy that starts with the idea that the options themselves carry their own reason to be traded — they are mispriced. I use the word strategy as if it’s a form of risk premium like “value stocks”, and maybe that argument can be made, but I think it’s more adaptive to understand it as a subset of trading in general. It’s not an investment strategy, it’s a business (see Trading Vs Investing). 

The semantic distinction between investing strategy and business is useful. You wouldn’t open a restaurant as a side hustle or hobby. Despite the ease of “larping as a vol trader” by picking up some language and opening an IB account, you are not vol trading as an investment strategy. Vol trading is a low-margin business, that requires institutional cost structure and infrastructure. The breadth of diversification and sheer transaction quantity demands economies of scale. Core strategies such as dispersion require those economic synergies making it more efficient as an overlay instead of a clinically administered stand-alone strategy. Knock yourself out with An Example “Options Relative Value Trading Framework”.

For the retail masochists

If you insist you want to “vol trade” from home these interviews are the best guides. I warned you.

Both interviews include Darrin Johnson who is the closest I’ve seen to a person grinding options day-in, day-out who came from a pure retail background. The second interview includes Noel smith, SIG alum, who now backs traders and has seen a gamut of independent traders. I think that episode stands out as the best reality check. It debunks lots of misinformation and frames the entire endeavor of trading brilliantly in the context of “this is a business”. There’s also this one line that reminds us that this is not a good career choice for those who prefer a bit more determinism in their vocation:

You do your best and at some point, you put your finger in the air and if you don’t think that everyone does that at some level you don’t understand how the business works. Everybody has to make some kind of a judgment because if you are only looking at the data you have the same data everybody else has and you have a totally in-consensus opinion. You have to make some judgments.

For the aspiring professional masochists

The 99th percentile vol PM probably makes similar money to the 90th percentile investing PM. The competition to be a top vol trader is likely higher simply because its puzzle-like similarities attract nerds with very specific forms of aptitude. But even worse from a “these are the people you’ll be competing with” point of view is that the specific intellectual nature of the job means it’s fun for them.  The net result when combined with the relative smallness of the market (vol trading is to investing as “math rock” is to music) — more competition per unit of pay. If you want to just make money, almost any other avenue is better if you are in any way ambivalent about the work.1

Addressing covered calls and cash-secured put selling

I claim there are 3 reasons to trade options.

  1. Speculation
  2. Hedging
  3. “Vol trade”

The most popular form of retail option trading doesn’t seem to fit in one of these buckets: covered call selling (and its close cousin cash-secured put selling). What gives?

It actually does fit. It’s hedging.

I know that’s not the intent but if you sell a call against a long position, you are hedging.

Repeated game thinking is a useful lens here and one of the most important mental models you should derive from the world of trading. Here’s the logic: if you sell a 25 delta call against your long, your underlying position gets called away 25% of the time2. In fact, any software that aggregates risk would show your net exposure to the stock dropping to 75% after you sold the call option. Whether you sell 25% of your stock outright or sell a call option that theoretically gets assigned every 4th time you make the trade, your net exposure is the same in the long-run. The option expression changes the shape and timing of the exposure, but it is the same exposure. Any large sample will prove it out.

Now there’s the argument that maybe you get called away less than 25% of the time and therefore that 25 delta call is overpriced. If you want to make that argument, fine. Just own it. You are now making a vol bet.

“Selling calls for income” is in the marketing euphemism hall of fame right next to “re-education camp” and “adult entertainment”. It’s a motte-and-bailey argument where the motte is “cash flow is income”. That’s only superficially similar to the credit you receive for the option. The problem is the bailey — you can’t then conclude that the credit is income. It’s not income. It’s the probability-weighted expectation of the stock being above its strike before expiration.

A stock price itself is the discounted sum of future paths. You simply sold a set of those paths, that appears to be income if the stock does not expire above the strike. If there was an accounting ledger the credit is the option premium, but the debit would be the risk. The risk part is conveniently swept under the rug by assurances that “you’ll be happy if the stock gets there”.

If I benchmark to the counterfactual world where I sold 25% of the stock, then the scenarios where the stock goes up by a lot OR goes down, then the call selling strategy was expensive. Do you see course/book promotor’s sleight of hand?

I don’t want to belabor this anymore. I’ve covered it multiple times:

I’m at the point of invoking Brandolini’s Law and moving on.

Wear a Condom

If you preach celibacy while ostriching any discussion of condoms, you are laying irresponsible odds against pubescent urges. When it comes to options, many of you are insatiably horny. If you insist on using options, take the following concepts to heart:


You are paying for specificity via options because they are priced with a particular vol to a specified expiry. The offsetting benefit is you are highly levered to being right.

From If You Make Money Every Day, You’re Not Maximizing:

The beauty of options is how they allow you to make extremely narrow bets about timing, the size of possible moves, and the shape of a distribution. A stock price is a blunt summary of a proposition, collapsing the expected value of changing distributions into a single number. A boring utility stock might trade for $100. Now imagine a biotech stock that is 90% to be worth 0 and 10% to be worth $1000. Both of these stocks will trade for $100, but the option prices will be vastly different.If you have a differentiated opinion about a catalyst, the most efficient way to express it will be through options. They have the most urgent function to a reaction. If you think a $100 stock can move $10, but the straddle implies $5 you can make 100% on your money in a short window of time. Annualize that!Go a step further. Suppose you have an even finer view — you can handicap the direction. Now you can score a 5 or 10 bagger allocating the same capital to call options only. Conversely, if you do not have a specific view, then options can be an expensive, low-resolution solution. You pay for specificity just like parlay bets. The timing and distance of a stock’s move must collaborate to pay you off.

Since you pay for specificity, you need a well-formed understanding of your edge. If you’re going to trade options directionally I would want to see the specificity in your fundamental analysis that suggests these particular options are the right options to buy or sell.

It’s so easy to lose on timing or changes in vol even if you get the direction right. See:

Destination vs Path

In a previous Money Angle, I pose the following:

If you have a view about the expected return of an asset in 5 years should you care about the path? Depends who you ask. Anyone marked-to-market (HFs, market-makers, futures traders) will say yes especially if they are managing money for others. PE, RE, and bond investors are more likely to say no…I’m biased by my path-or-die experience in trading. Mark-to-market is the goddess of tomorrow, you can’t afford to piss her off.

Options offer you the chance to isolate bets on either path or terminal value if you want.

A few examples:

  • Market prices are clever.  In What The Widowmaker Can Teach Us About Trade Prospecting And Fool’s GoldI show how market prices are clever. They can balance the wagers of path vs terminal value investors simultaneously! The calendar spread options are priced so that the path of the gas price is highly respected, even if there’s strong consensus about the terminal value of the spread (ie the March-April futures spread which is a pure bet on in winter gas being in short supply).

    The OTM calls are jacked, because if we see H gas trade $10, the straddle will go nuclear. Why? Because it has to balance 2 opposing forces:
    1. It’s not clear how high the price can go in a true squeeze or shortage
    2. The MOST likely scenario is the price collapses back to $3 or $4.

Let me repeat how gnarly this is. The price has an unbounded upside, but it will most likely end up in the $3-$4 range. Try to think of a strategy to trade that. Good luck.

      • Wanna trade verticals? You will find they all point right back to the $3 to $4 range.
      • Upside butterflies which are the spread of call spreads (that’s not a typo…that’s what a fly is…a spread of spreads. Prove it to yourself with a pencil and paper) are zeros.

The market places very little probability density at high prices but this is very jarring to people who see the jacked call premiums. That’s not an opportunity. It’s a sucker bet.

  • In options land, many investors like to buy 1×2 ratio spreads because the payoffs look amazing for low-probability events. For example, if a stock is $100 and you can buy the $115 call and sell 2 of the $120 calls for zero premium, you think to yourself:

    a) “If the stock does nothing or goes down I break even”b) “If the stock goes to $120, I make $5” (or $1 if the stock goes to $116)

    c) “I don’t start losing money until the stock goes over $125. That’s 25% away! This is risk-free return”

    Nah dog. That’s first-time-at-the-rodeo thinking.

    The reason the 1×2 is so cheap is the call skew on the $120 strike is pumped up because someone has been buying them like crazy. That’s where the bodies are hidden. The question you need to ask yourself is “conditional on the stock going to $120 did it get there fast and sloppy, or slow and grindy.” If it goes there in a fast way, the market-maker community will be short beaucoup gamma and be scrambling to buy the $120 calls back. You sold some teenies and went to Santorini and are now getting a margin call on the beach because the 120s you’re short are blowing the f out.

    The path-aware trader is plotting how to be long the scenario where your vacation abruptly ends.

  • If path is so important, how can you manage to it?

a) Avoid excessive leverage
b) Pre-determine when you will cut losses (beware this can be a big topic with lots of room for disaster)
c) If you insist on betting on terminal value, do it in fixed premium ways where your max loss is bounded. Now you don’t have to worry about mark-to-market risk.

In There’s Gold In Them Thar Tails: Part 2, I cover the topic of path, how to exploit investors’ lack of appreciation for it, and how Jon Corzine became a symbol for path-blindness.


You probably shouldn’t trade options. But I get it. Everyone gets a little curious.

I hope this post offered some protection.

An Example “Options Relative Value Trading Framework”

Why does vol trading exist?

  • Exists because suppliers and demanders of vol vary along term structure and geography. This can create structural distortions.
  • If you are in the gears, you can understand the players and the rhythm of markets.
  • Total scalability is very limited compared to outright ownership of risky assets. Scalability is in proportion to the total amount of insurance written on the risk assets which is in turn constrained by the credit in the entire system as rationed by the banking system (and manifest through prime brokerage, exchanges, and bilateral credit) since optionality is inherently levered.

Core Competencies

Identifying edge

The Science

Objective: Measure and nowcast what optionality is cheap and expensive globally

    1. Harvest and clean historical and current data (Interest rates, divs, current vols, historical data)
    2. Extract implied parameters: Vol, skew, kurtosis, correlations.
    3. Benchmark fair

The Art

Objective: Portfolio Construction

Trade expressions:

    • relative term structure
    • relative skew
    • relative implied forwards
    • carry (correlation, relative cheapness) vs distribution (percentile analysis)

Risk Management

There is alpha in buying cheap and selling expensive. But in exchange for alpha there is path, self-fulfilling behavior, and adverse selection. The antidote is risk framework designed in anticipation of adverse movements (you don’t want to be full size or worse puking/cutting risk when the trades have their best setups…and the best set-ups happen exactly when others are offsides).

Principles of risk management:

  • The business works so the number 1 rule of the business is: Stay in business. Never jeopardize tomorrow for any perceived edge.
  • The risk framework prioritizes survival and does not contain risk based on historical p/l but constrains position size by shocks. Often pain in a name is a reason to look to enter the trade.
  • Hard risk limits: How much you can lose is determined by position size and aggressive portfolio shocks.
    • Shock examples:
      • bankruptcy for single stock
      • implied parameter shocks
      • extreme time spread shocks for commodities
    • Protocol for position reduction or exclusion
    • Path-awareness: Shocks are not only for p/l tolerance but to estimate what happens to your margin requirement as market risks grow.

Sourcing liquidity

  • Relationships with banks and brokers including electronic connectivity
  • Technology stack to handle effective trade life cycle from execution to clearing, to risk and p/l reporting, to accounting and compliance

Performance attribution

  • TCA of electronic and voice trades
  • Actionable insights based on updated lessons

Horizontal scaling

  • The abstracted framework of doing many positive EV trades and managing the pooled risks is flexible and underpins all alpha trading. Its application inches out from core competency to adjacent classes of securities.
  • Requires new normalizations, data, market structures, understanding new distributions, player landscape

Bet Sizing Is Not Intuitive

Humans are not good bettors.

It takes effort both in study and practice to become more proficient. But like anything hard, most people won’t persevere. Devoting some cycles to improve will arm you with a rare arrow in your quiver as you go through life.

Skilled betting demands 2 pivotal actions:

  1. Identifying attractive propositions

    This can be coded as “positive expected value” or “good risk/reward”. There is no strategy that turns a bad proposition into an attractive one on its own merit (as opposed to something like buying insurance which is a bad deal in isolation but can make sense holistically). For example, there is no roulette betting strategy that magically turns its negative EV trials into a positive EV session.

  2. Effective bet sizing

    Once you are faced with an attractive proposition, how much do you bet? While this is also a big topic we can make a simple assertion — bad bet sizing is enough to ruin a great proposition. This is a deeper point than it appears. By sizing a bet poorly, you can fumble away a certain win. You cannot afford to get bet sizing dramatically wrong.

Of these 2 points, the second one is less appreciated. Bet sizing is not very intuitive.

To show that, we will examine a surprising study.

The Haghani-Dewey Biased Coin Study

In October 2016, Richard Dewey and Victor Haghani (of LTCM infamy) published a study titled:

Observed Betting Patterns on a Biased Coin (Editorial from the Journal of Portfolio Management)

The study is a dazzling illustration of how poor our intuition is for proper bet sizing. The link goes into depth about the study. I will provide a condensed version by weaving my own thoughts with excerpts from the editorial.

The setup

  • 61 individuals start with $25 each. They can play a computer game where they can bet any proportion of their bankroll on a coin. They can choose heads or tails. They are told the coin has a 60% chance of landing heads. The bet pays even money (i.e. if you bet $1, you either win or lose $1). They get 30 minutes to play.
  • The sample was largely composed of college-age students in economics and finance and young professionals at financial firms. We had 14 analyst and associate-level employees of two leading asset management firms.

Your opportunity to play

Before continuing with a description of what an optimal strategy might look like, we ask you to take a few moments to consider what you would do if given the opportunity to play this game. Once you read on, you’ll be afflicted with the curse of knowledge, making it difficult for you to appreciate the perspective of our subjects encountering this game for the first time.

If you want to be more hands-on, play the game here.

Devising A Strategy

  1. The first thing to notice is betting on heads is positive expected value (EV). If X is your wager:

    EV = 60% (x) – 40% (x) = 20% (x)

    You expect to earn 20% per coin flip. 

  2. The next observation is the betting strategy that maximizes your total expected value is to bet 100% of your bankroll on every flip. 

  3. But then you should notice that this also maximizes your chance of going broke. On any single flip, you have a 40% of losing your stake and being unable to continue this favorable game. 

  4. What if you bet 50% of your bankroll on every flip?

    On average you will lose 97% of your wealth (as opposed to nearly 100% chance if you had bet your full bankroll). 97% sounds like a lot! How does that work?

    If you bet 50% of your bankroll on 100 flips you expect 60 heads and 40 tails. 

    If you make 50% on 60 flips, and lose 50% on 40 flips your expected p/l:

1.560 x .5040 = .033

You will be left with 3% of your starting cash! This is because heads followed by tails, or vice versa, results in a 25% loss of your bankroll (1.5 * 0.5 = 0.75).

This is a significant insight on its own. Cutting your bet size dramatically from 100% per toss to 50% per toss left you in a similar position — losing all or nearly all your money.

Optimal Strategy

There’s no need for build-up. There’s a decent chance any reader of this blog has heard of the Kelly Criterion which uses the probabilities and payoffs of various outcomes to compute an “optimal” bet size. In this case, the computation is straightforward — the optimal bet size as a fraction of the bankroll is 20%, matching the edge you get on the bet.

Since the payoff is even money the Kelly formula reduces to 2p -1 where p = probability of winning.

2 x 60% – 1 = 20%

The clever formula developed by Bell Labs researcher John Kelly:

provides an optimal betting strategy for maximizing the rate of growth of wealth in games with favorable odds, a tool that would appear a good fit for this problem. Dr. Kelly’s paper built upon work first done by Daniel Bernoulli, who resolved the St. Petersburg Paradox— a lottery with an infinite expected payout—by introducing a utility function that the lottery player seeks to maximize. Bernoulli’s work catalyzed the development of utility theory and laid the groundwork for many aspects of modern finance and behavioral economics. 

The emphasis refers to the assumption that a gambler has a log utility of wealth function. In English, this means the more money you have the less a marginal dollar is worth to you. Mathematically it also means that the magnitude of pain from losing $1 is greater than magnitude of joy from gaining $1. This matches empirical findings for most people. They are “loss-averse”.

How did the subjects fare in this game?

The paper is blunt:

Our subjects did not do very well. Suboptimal betting came in all shapes and sizes: overbetting, underbetting, erratic betting, and betting on tails were just some of the ways a majority of players squandered their chance to take home $250 for 30 minutes play.

Let’s take a look, shall we?

Bad results and strange behavior

Only 21% of participants reached the maximum payout of $250, well below the 95% that should have reached it given a simple constant percentage betting strategy of anywhere from 10% to 20%

  • 1/3 of the participants finished will less money than the $25 they started with. (28% went bust entirely!)
  • 67% of the participants bet on tails at some point. The authors forgive this somewhat conceding that players might be curious if the tails really are worse, but 48% bet on tails more than 5 times! Many of these bets on tails occurred after streaks of heads suggesting a vulnerability to gambler’s fallacy.
  • Betting patterns and debriefings also found prominent use of martingale strategies (doubling down after a loss).
  • 30% of participants bet their entire bankroll on one flip, raising their risk of ruin from nearly 0% to 40% in a lucrative game!

Just how lucrative is this game?

Having a trading background, I have an intuitive understanding that this is a very profitable game. If you sling option contracts that can have a $2 range over the course of their life and collect a measly penny of edge, you have razor-thin margins. The business requires trading hundreds of thousands of contracts a week to let the law of averages assure you of profits.

A game with a 20% edge is an astounding proposition.

Not only did most of our subjects play poorly, they also failed to appreciate the value of the opportunity to play the game. If we had offered the game with no cap [and] assume that a player with agile fingers can put down a bet every 6 seconds, 300 bets would be allowed in the 30 minutes of play. The expected gain of each flip, betting the Kelly fraction, is 4% [Kris clarification: 20% of bankroll times 20% edge].

The expected value of 300 flips is $25 * (1 + 0.04)300 = $3,220,637!

In fact, they ran simulations for constant bet fractions of 10%, 15%, and 20% (half Kelly, 3/4 Kelly, full Kelly) and found a 95% probability that the subjects would reach the $250 cap!

Instead, just over 20% of the subjects reached the max payout.

Editorialized Observations

  • Considering how lucrative this game was, the performance of the participants is damning. That nearly one-third risked the entire bankroll is anathema to traders who understand that the #1 rule of trading (assuming you have a positive expectancy business) is survival.

  • Only 5 out of the 61 finance-educated participants were familiar with Kelly betting. And 2 out of the 5 didn’t consider using it. A game like this is the context it’s tailor-made for!
  • The authors note that the syllabi of MIT, Columbia, Chicago, Stanford, and Wharton MBA programs do not make any reference to betting or Kelly topics in their intro finance, trading, or asset-pricing courses. 

  • Post-experiment interviews revealed that betting “a constant proportion of wealth” seemed to be a surprisingly unintuitive strategy to participants. 

Given that many of our subjects received formal training in finance, we were surprised that the Kelly criterion was virtually unknown among our subjects, nor were they able to bring other tools (e.g., utility theory) to the problem that would also have led them to a heuristic of constant-proportion betting. 

These results raise important questions. If a high fraction of quantitatively sophisticated, financially trained individuals have so much difficulty in playing a simple game with a biased coin, what should we expect when it comes to the more complex and long-term task of investing one’s savings? Given the propensity of our subjects to bet on tails (with 48% betting on tails on more than five flips), is it any surprise that people will pay for patently useless advice? What do the results suggest about the prospects for reducing wealth inequality or ensuring the stability of our financial system? Our research suggests that there is a significant gap in the education of young finance and economics students when it comes to the practical application of the
concepts of utility and risk-taking.

Our research will be worth many multiples of the $5,574 winnings we paid out to our 61 subjects if it helps encourage educators to fill this void, either through direct instruction or through trial-and-error exercises like our game. As Ed Thorp remarked to us upon reviewing this experiment, “It ought to become part of the basic education of anyone interested in finance or gambling.”

I will add my own concern. It’s not just individual investors we should worry about. Their agents in the form of financial advisors or fund managers, even if they can identify attractive proposition, may undo their efforts by poorly sizing opportunities by either:

  1.  falling far short of maximizing

    Since great opportunities are rare, failing to optimize can be more harmful than our intuition suggests…making $50k in a game you should make $3mm is one of the worst financial errors one could make.

  2. overbetting an edge

    There isn’t a price I’d play $100mm Russian Roulette for

Getting these things correct requires proper training. In Can Your Manager Solve Betting Games With Known Solutions?, I wonder if the average professional manager can solve problems with straightforward solutions. Nevermind the complexity of assessing risk/reward and proper sizing in investing, a domain that epitomizes chaotic, adversarial dynamics.

Nassim Taleb was at least partly referring to the importance of investment sizing when he remarked, “If you gave an investor the next day’s news 24 hours in advance, he would go bust in less than a year.”

Furthermore, effective sizing is not just about analytics but discipline. It takes a team culture of truth-seeking and emotional checks to override the biases that we know about. Just knowing about them isn’t enough. The discouraged authors found:

…that without a Kelly-like framework to rely upon, our subjects exhibited a menu of widely documented behavioral biases such as illusion of control, anchoring, overbetting, sunk-cost bias, and gambler’s fallacy.


Take bet sizing seriously. A bad sizing strategy squanders opportunity. With a little effort, you can get better at maximizing the opportunities you find, rather than needing to keep finding new ones that you risk fumbling.

You need to identify good props and size them well. Both abilities are imperative. It seems most people don’t realize just how critical sizing is.

Now you do.

Finance As A Laboratory For Decision-Making [StockSlam Preview]

With the StockSlam Sessions rapidly approaching, I want to thank Jeff Malec at RCM Alternatives for inviting Tina, Steiner, and me to his show. You can listen to the pod or watch on Youtube. Steiner is an offline guy, so foremost this is a nice introduction to him.

  • The Game of Trading with SIG Alums Kris A, Tina L, & Steiner (Link)

    We have a little saying over here on The Derivative, “The More, The Merrier”, and on this week’s episode of The Derivative, we’re not chatting with one guest, but THREE! Class may no longer be in session, but we are taking a trip down the SIG/Susquehanna memory lane and having our own class reunion with Kris Abdelmessih, Michael Steiner, and Tina Lindstrom.

    If you’re interested in learning how big trading firms find and teach their traders, hold on to your seat because these three give you the answer key! Kris, Tina, and Michael are in session with Jeff and discussing competing with peers, finding an option’s fair value, making markets, and being in the game of trading, educating kids with board games, and of course Steiner’s new trading board game: Stock Slam! Discover how the game works and how you can join up with these three in NYC for a live session in this three-of-a-kind episode

We are doing these sessions because trading is a neat laboratory to learn about decision-making. Weighing risk-reward, thinking adversarially (this thread by @0xDoug is in my hall of fame), resisting confirmation/hindsight biases, using probability, considering counterfactuals, not “resulting”, and much more. So much of my writing focuses on these “meta” topics because trading gave me a better education than school ever did.

If we can help people practice thinking this way, it’s a like growing new brain lobe that’s adaptive for many real-life situations.

The following is adapted from a thread I wrote that demonstrates an idea in a trading context:

People understand that even though insurance has negative expectancy it can still improve a portfolio that is focused on compounded returns. It makes no sense to look at the line-item of insurance divorced from the optionality it gives you in the rest of your portfolio.

(I could pull lots of links on this idea, but let’s be brief).

This concept is fractal. Let’s zoom in on the smallest portfolio — a spread. You don’t necessarily care about the p/l of any individual leg of a spread trade but the performance of the spread overall.

Before we consider a spread, let’s just look at the single position. Suppose you buy something for $4 when it’s worth $5 but then sell it for $4.50. You made both a:

  • +$1 expected value trade
  • -$.50 EV trade.

If you knew it was worth $5 you negated half a good trade with a bad trade.

In real life, you often might like the price of a spread but it’s hard to tell which leg is the “good side”. That’s one of the reasons you trade the spread. Once you do the spread you don’t care about the individual p/ls.

Another reason you may do a spread is that you might like a trade (ie maybe vol is cheap in X) but can do it bigger if you spread it. This is one of those questions that comes up a lot on real trading desks. Do I like the outright, or do I like the trade better paired against something else (and assuming I can do the trade bigger if I spread it)? Do I like being long z units of X exposure, or do I prefer 5z units of (X-Y)? The answer depends on understanding the distribution of the outright vs the spread and the relative price of each within those distributions.

Finally, there’s the general lens of how I approach trading (which I discuss in the RCM interview). Liquid markets tell us a lot about “fair value”. If we take fair value as the consensus “outside view”, then we can examine illiquid markets for pricing discrepancies compared to that outside view. Of course, those markets have their own idiosyncracies, so you need to take an “inside view” and normalize as much as possible to the liquid reference asset. This is a standard way to identify possible opportunities. It’s a mix of art and science. The science is in the measurement but the art is in handicapping how much the differences should matter. This isn’t arbitrage. It’s informed betting. If you need certainty, you will either be too late or the strategy will have the lifespan of a mayfly.

[I actually googled “shortest lifespan” and was met with irony:

We often hear that mayflies, like the whiteflies of the Susquehanna River, have the shortest lifespan of any animal on Earth, just 24 hours for many species.

SIG is named after that river.]

Now let’s broaden the concept to investing. For that, I turn to Byrne Hobart’s paywalled post Assuming Efficient Markets to Exploit Market Inefficiencies:

If there’s an efficient market A and an inefficient one B, A is easier to trade in, but B is probably the one that’s mispriced. So that price inefficiency partly represents a measure of how hard inefficiencies are to exploit! In the case of Druckenmiller’s recession call, he actually made the paradoxical judgment that inefficient market B was priced incorrectly relative to A, but that A was the one to bet on—because the specific inefficiency at hand was that a recession was likely and it wasn’t being accurately reflected by anything.

This raises an important point, because there are two broad ways to look at relative inefficiency. One is to just stick with the relative argument: if stocks are pricing a boom and bonds are pricing a recession, bet that one of these will go away. But that’s a frustrating conclusion to draw, because it basically amounts to saying: The market is telling me something important, and I don’t care what it is. The relative-value bet works equally well regardless of which thesis is right, but it’s still outsourcing a lot of judgment to the market. And annoyingly, once the valuation gap closes, you have two problems: first, you haven’t figured out why the discrepancy existed in the first place, and if there’s an inexplicable 1-standard deviation change in some correlation, there is no law of the universe saying it can’t go to 2 or 3. (There is a weaker law saying it can go to 20, when enough levered participants are betting on it.) The other problem is that real-world theses produce additional ideas; an argument that the economy is going into a recession has second- and third-order consequences, and generates more ideas.

This kind of tradeoff, between a low-risk claim that two views are contradictory and a higher-risk claim that one of them is right, extends far beyond finance.

Through games, direct instruction, and making connections between abstract concepts and examples in the wild, Tina, Steiner and I want to see if we can help others get better. And selfishly, I want to think better, so I’m stoked to be a part of this.

*Applications are closed and invitations already went out but these sessions are an experiment to guide how we test and improve the transfer of knowledge. If you didn’t get accepted it’s because space was extremely limited compared to applicants. This is not meant to be exclusive, we are going to figure out how we can spread what we learn. As Axl once said, we just need a little patience [bandana sway].

Trading Vs Investing

Trading is a business. Like a casino. You spread the risk over a bunch of tables and let the law of averages1 do its magic. Investing, whether it’s a as shareholder, LP, or creditor (ie allocating capital in the primary or secondary markets, but not as a member of management) is something you do in a business. You can invest in a casino. You can invest in a bank. You can invest in a trading business. The point is that investing and trading are actually different.

The distinction seems subtle because the language and mechanics of investing and trading overlap. Traders talk about diversifying as much as investors do. Restaurant owners don’t. Traders and investors both talk about position sizing. Software founders don’t. This makes it easy to confuse trading for investing but the former is a business, not an investment strategy. You would not compare Optiver, Jane Street, or SIG’s returns to a portfolio manager’s. Trading firms think in unit economics just like any business (“how many fractions of a cent of edge do I get per contract?”). The portfolio manager doesn’t have a similar analog. However, if we look at asset management, it collects fees. So if we zoom out, we are at the business-level of abstraction yet again.

There’s an interleaving of concepts that binds notions of “trading” to “investing” in a way that can mislead investors. When they trade are they trading like they are a business, like they are providing a service (temporary liquidity in exchange for a theoretical fee which resolves the desire for a buyer or seller to transact in the absence of a natural counterparty) or are they rebalancing investments? The distinction is one of framing and like all frames, it has a tyrannical grip on one’s downstream decisions. The subtlety can be confusing to new investors who can’t escape terms like “daytrading” or that Robinhood calls itself a “Stock Trading and Investing App”. You wouldn’t take a Porsche off-roading any more than you should confuse these 2 endeavors.

And yet you might for all the superficial similarities I already described. It’s totally understandable. To create the appropriate distance between activities of “trading” and “investing”, I’ll offer 2 thoughts.

  • Time Horizon

In trading, the bets have endpoints. Whether it’s an upcoming catalyst or event, an option expiration, or time to roll a future there is a time when you get to “see the river” to borrow a poker term. Price and reality must converge. Extrinsic values go to zero. Future prices meet spot prices. With equities, the metaphor needs massaging. Perhaps news or earnings is more like the “flop” or the “turn” whereas M&A activity serves as a defacto endpoint.

With investing, the duration of the trades is typically much longer. Stocks are perpetual claims. Perhaps semantically awkward, I prefer to re-brand investing as “re-investing”. This focuses us on a company’s need to compound returns on capital internally. If an oil company sits on massive reserves, but the price of oil shoots to a price that destroys all future demand, the stock would plummet because it no longer has a forthcoming stream of earnings. Yes, its book value would immediately increase, but that is a smaller portion of its discounted perpetuity value.

The “re-investing” frame explains why a market would discount such a one-time windfall. You can even think of a “cheap” stock as a company that the market has decided has a low future return on invested capital. By not increasing their bids, investors are manifesting trader thinking — they are focused on return per trial. Thinking of investments through the lens of how a company re-invests, stretches “repeated game” thinking longitudinally into the future as opposed to traders or casinos who think of edge per trade cross-sectionally.

  • Seeing The Present Clearly

Since the compounded return of an investment depends on how a company re-invests, it requires distant foresight into an inherently complex system. Long-term investing, like long-term weather forecasting has an irreducible bar of uncertainty that sits unpleasantly high off the ground. There’s only so much you can say about a system governed by chaos, biological, and evolutionary forces as opposed to tidy physical properties. Feedback loops are long, causation is opaque, and the signal-to-noise ratios are too low to prove an edge. This leads to a paradox. If a manager’s edge is unprovable, then there’s a chance you can actually access it, you’ll just understand it post-hoc. If the edge was provable, the manager would extract all the excess alpha for themselves by either choosing strategic investors or charging ransom fees.

Trading on the other hand is a provable edge. Because it’s a business. You rake a tournament, take the profits off the table and hunt for new players. Markets might imply or try to tell us something about the future. The business is to find market prices that say something contrary but have visibility to resolving and taking both bets. Arbitrage is an extreme example of this. If one person thinks the USA basketball is 90% to win the gold and another thinks the field is 15% to win the gold you can bet against them both and get paid $105 while knowing you’ll only owe $100.

The business process around this involves measurement, not prediction. There’s no thematic vision of what the world looks like 10, 20, 50 years hence. Instead, you find others who express strong opinions that disagree and build a machine that lets you bet against both of them. You are passionately agnostic. You are in the business of seeing today clearly. Not having visions of the future. That’s your customer’s job. That’s the investor’s job.

A Skinny Bridge

Coming from the trading world, I’ve wrestled with my understanding of investing. I don’t believe in crystal balls. I don’t think any “long term” investor can prove they are special because of the limits of data and sample size. Putting faith in track records feels like betting on coins that just had a long streak. There are a lot of funds out there, it’s inevitable some will have long streaks by chance. Survivorship bias makes the proportion of lucky funds even more visible.

This is a discouraging place to settle. Attempting to invest in a trading business as opposed to doing the trading business, leaves you in the epistemological rut as choosing any business to buy. They are just businesses, to be compared with any other business. In fact, the search is pointless. Most are capacity constrained which means the best ones don’t need your money anyway. Where does that leave me? I don’t trust most people who would take my money to manage it and I don’t have the expertise to invest to the impossible standard of risk-reward that the business of trading anchored me to. And I need to take myself seriously — I just spent this entire essay explaining how it’s a fallacy to compare trading to investing in the first place.

Is there a reconciliation?

I think so. I see a skinny bridge between the business of trading and what it prescribes for investing. It lies in portfolio construction and asset allocation. At one level of abstraction, the investors with their coherent visions of the future are simply tourists in the traders’ casinos. But if we zoom out and aggregate the consensus of competing investors we end up with a total market price. It’s not one market however, it’s many. There are equities, bonds, and commodities. They exist across geography and sovereign systems. These are the legos that can be stacked to construct payoff shapes — carry, insurance, momentum. Those can be described in other language as well — concave/convex, convergent/divergent.

The asset classes themselves contain a risk premium above risk-free rates (by induction — stocks should earn more than t-bills because you need extra compensation to hold something that tanks every now and then). By combining these asset classes under battle-tested principles of risk management, the hope is to capture the weighted average risk premium of your allocation without relying on forecasts. Just like trading businesses. Just like casinos2.

Wrapping Up

Trading and investing are sufficiently different that you should be conscious of what mode you are in when you click a buy or sell button. The awareness will likely lead you to pressing buttons less often, or systematizing when you push the buttons. Unless you’re in it for the thrill, you want to minimize your points of contact with the fee-generating businesses that want you to feel like you are doing a good thing by “investing”. You are doing a good thing when you invest, but be careful — sometimes what looks like investing is trading. And the bar for doing that productively is much higher than they want you to believe.

The Most Underrated Finance YouTube Channel

I feel lucky that Jason Buck reached out to sponsor the letter because I love what he’s doing (Yinh and I were early investors in their latest fund). In addition to managing a fund, Jason is co-host of what I think is the most underrated show on investing YouTube, Pirates of Finance.

In season 3, Jason and Corey Hoffstein changed the format so that there is zero preparation. The conversation is totally off the cuff. And it totally slaps.

It is free, buried booty that our theoretical economist says can’t exist because of efficient markets. But it exists. I’ll prove it by digging up 3 themes from their amazing recent episode Decision-Making Under Uncertainty and mix them with my own thoughts. We’re blending Moontower and Pirate rum up in here today.

Why ETFs Might Be Unsuitable For Some Strategies

ETFs are liquid structures designed to faithfully track NAVs (“net asset values”) because the arbitrage mechanism is outsourced by the issuer to an Authorized Participant. These AP’s are a subset of the market-making community.

The Pirates wonder:

Is the ETF structure, whose allure is transparency, the correct home for opaque, illiquid, or bi-lateral (ie there’s credit risk in the basket) instruments such as inflation swaps? What about semi-liquid holdings like corporate bonds or even TIPs?

The answer to such questions partially rests on the liquidity of the underlying holdings. Consider a question they allude to but I’ll make explicit:

If you hold long option or long convex positions via ETFs (or for that matter directly) will you be able to monetize them when they pay off?

This is a real and highly underrated concern. Bid/ask spreads are positively correlated with volatility. So how useful is it if the paper profit on a convex position can’t be crystallized because the bid-ask is wider than the parted Red Sea?

Suppose you buy a way OTM put option for $1. It explodes to $20 but the bid-ask is now $16-$24. Sure, you can sell it for a 16x return, but when that option was originally valued for $1, the pricing incorporated the idea that in some rare states of the world the option is worth $20. If you can never realize that $20, then you entered into a pretty negative expected value situation when you paid $1 for it in the first place.

Trading is hard enough, you can’t afford to not maximize small edges. In a separate interview Corey talks to option trader Darrin Johnson.

I paraphrase Darrin:

When you sell tails, you need to capture the entire premium. The hit ratio of selling tails is high but when you lose you lose many multiples of the premium. If you fail to collect the full premium, it will not make up for the losing trades. The difficulty of selling tails is even trickier yet.

Darrin explains how betting against longshots leaves you uncertain if you have an edge in the first place. In my words: good luck differentiating between a 50-1 shot vs a 100-1 shot. That’s the difference of 1 probability point but it’s massive in payoff space. [I discuss that idea further in Tails Explained.]

When volatility increases, transaction costs go up for everyone. Since market-makers are part of “everyone” then the cost of their own hedging (ie replication) goes up as well, so they charge wider-bid ask spreads to keep them whole. MMs represent the marginal supply of liquidity so can they pass the transaction costs of their own “COGs” to those demanding liquidity. We know the house wins both ways, but the house edge itself is correlated to what markets are doing. If the house’s margins above their “COGs” expand in times of stress, you need to haircut the expected risk mitigation from defensive positions. That cost will show up when you try to roll or monetize.

There are cases where that bookie’s vig will not be too punitive even in a volatile market. For example, if the option you buy is now so far ITM that it no longer has meaningful extrinsic value, then you can simply trade the underlying to monetize (although re-hedging will put you face-to-face with the market-makers again).

This brings us to the next theme.

Destination vs Path

If you have a view about the expected return of an asset in 5 years should you care about the path? Depends who you ask. Anyone marked-to-market (HFs, market-makers, futures traders) will say yes especially if they are managing money for others. PE, RE, and bond investors are more likely to say no. The Pirates have a nuanced discussion about whether it’s even possible to manage to path versus manage to terminal value.

I’m biased by my path-or-die experience in trading. Mark-to-market is the goddess of tomorrow, you can’t afford to piss her off.

Here are a collection of arguments that I offer her as tribute.

  1. Bond investors who ignore path are fooling themselves.In Why Volatility Still Matters To Buy-And-Hold Investors, I summarize one of Cliff Asness’ pet peeves:

    You may hear some people say they want to buy an individual bond rather than a bond fund. They worry that bond fund prices move around and have no real expiration, so when interest rates rise your losses are somehow more real. But if you buy a bond and hold it to maturity you can put your head in the sand, and never lose.

    This is nonsense.

    You have lost in a real sense since the money you are being returned is worth less in a world in which rates have risen to compensate for inflation. The bond fund is effectively taking your loss today rather than later. If you sell your bond for a loss, you can reinvest at a higher yield going forward. That’s a similar experience to just being in the bond fund. Holding to maturity does not mean you have less risk. It’s an illusion. A real vs nominal illusion.

  2. Using stale marks to “smooth volatility”Having a preference for private assets that are less volatile simply because their marks are stale is like not getting bloodwork because you don’t want to find out your cholesterol and blood sugar are too high.

    The slow-to-mark investments are still volatile. The fundamentals of the private business are correlated with the public market volatility.

    Even if you don’t believe your investment should be marked down, then you should be sad you can’t redeem your private investment at par to rebalance into public stocks after the market drops 20%. Giving up liquidity without a premium because it will behaviorally “save you from yourself” sure feels like you sold the option to rebalance at zero.

    I walk through that argument in How Much Extra Return Should You Demand For Illiquidity? (7 min read)

  3. Market prices are clever. They can balance the wagers of path vs terminal value investors simultaneously!In What The Widowmaker Can Teach Us About Trade Prospecting And Fool’s GoldI show how the calendar spread options are priced so that the path of the gas price is highly respected, even if there’s strong consensus about the terminal value of the spread (ie the March-April futures spread which is a pure bet on in winter gas being in short supply).

    The OTM calls are jacked, because if we see H gas trade $10, the straddle will go nuclear.

    Why? Because it has to balance 2 opposing forces.

    1. It’s not clear how high the price can go in a true squeeze or shortage
    2. The MOST likely scenario is the price collapses back to $3 or $4.

    Try to think of a strategy to trade that. Good luck.

    Let me repeat how gnarly this is: The price has an unbounded upside, but it will most likely end up in the $3-$4 range. The vertical spreads all point right back to that price range.

    The market places very little probability density at high prices but this is very jarring to people who see the jacked call premiums.

    That’s not an opportunity. It’s a sucker bet.

    Another common example:

    In options land, many investors like to buy 1×2 ratio spreads because the payoffs look amazing for low-probability events. For example, if a stock is $100 and you can buy the $115 call and sell 2 of the $120 calls for zero premium, you think to yourself:

    a) “If the stock does nothing or goes down I break even”
    b) “If the stock goes to $120, I make $5” (or $1 if the stock goes to $116)

    c) “I don’t start losing money until the stock goes over $125. That’s 25% away! This is risk-free return”

    Nah dog. That’s first-time-at-the-rodeo thinking.

    The reason the 1×2 is so cheap is the call skew on the $120 strike is pumped up because someone has been buying them like crazy. That’s where the bodies are hidden. The question you need to ask yourself is “conditional on the stock going to $120 did it get there fast and sloppy, or slow and grindy.” If it goes there in a fast way, the market-maker community will be short beaucoup gamma and be scrambling to buy the $120 calls back. You sold some teenies and went to Santorini and are now getting a margin call on the beach because the 120s you’re short are blowing the f out.

    The path-aware trader is plotting how to be long the scenario where your vacation abruptly ends.

  4. If path is so important, how can you manage to it?a) Avoid excessive leverage

    b) Pre-determine when you will cut losses (beware this can be a big topic with lots of room for disaster)

    c) If you insist on betting on terminal value, do it in fixed premium ways where your max loss is bounded. Now you don’t have to worry about mark-to-market risk.

    In There’s Gold In Them Thar Tails: Part 2I cover the topic of path, how to exploit investors’ lack of appreciation for it, and how Jon Corzine became a symbol for path-blindness.

“Long-Short Portfolios All The Way Down”

You’ve heard the expression, “turtles all the way down”.

Corey says “Long/short portfolios all the way down”.

This is an acknowledgment that every trade you make is relative to something else. If you buy a stock denominated in dollars, you are betting that the stock will outperform dollars. It’s a powerful idea. If you want to short XOM but can’t get a borrow, you can buy all the components of XLE except XOM while shorting XLE. Voila, you are now short XOM.

The pirates offer more great examples:

1. Rebalancing

You start with a 60/40 portfolio and stocks go up so the new portfolio is 65/35. You can think of a regular rebalance to get you back to 60/40.

Or you can re-frame the accounting to an algebraic equivalent:

You own a 65/35 portfolio + a long 5% bonds/short 5% stock overlay

It seems like semantics, but just as different words can refer to very similar things, there remains meaning behind the distinctions. And the subtlety here is useful because it forces you to look at the accounting of subsets of a larger position. Corey argues that this lets you think about how things are contributing to your portfolio at any given time or even over time


This lens is the gateway to better p/l attribution. In the 65/35 example, the intuition is fairly basic. Rebalancing trades profit when the market mean reverts and lose money if the market trends. Gamma-scalping works the same way. It’s just rebalancing for option traders. If you trend, your “daytrading p/l” will be negative if it is dominated by gamma scalps and you’ll regret going into work that day (because you will presumably have been hedging your growing delta, for example, you sold the VWAP but the market closed on its daily high.)

I agree with Corey. Seeing the world as long/short portfolios focuses you on the relative nature of every decision! Every time you are long X, you are short [not X]. If you buy a house and it goes up in value along with every other house in your state, when you sell it, did you really make money if the neighboring cost for shelter has appreciated all around you. Start seeing your decisions as long/short portfolios and it has a funny way of focusing you on what you’re specifically rooting for.

2. Corey poses another thought exercise:

Which do you think has a higher tracking error to a passive 60/40?

a) Replacing the passive equity with small-cap value exposure

b) Layering 60% exposure to the SG CTA Index on top

I promise the discussion thread will make you smarter.

I’ll sprinkle in a related idea that comes from options land.

It’s natural for vol traders, especially dispersion traders, to think about positions as a series of long/short portfolios. That’s because all dispersion is “dirty” dispersion. [If you need a refresher see Dispersion Trading For The Uninitiated].

If you sold SPX index vol and only bought vol on value names, your net position is:

  • short growth volatility
  • long value volatility (you are net long, because if you tried to balance your gross index and single name greeks, you’d necessarily have to overweight the value names. This is extra true if you theta-weight the spread since the value names are lower volatility than the growth names.)

If you had this position on before Softbank started buying the hell out of tech calls in the summer of 2020, you got rocked.

But if you put that same position on right before the Covid vaccine was announced, you killed it as value names surged while growth names barely moved relative to their vols.

Index traders are keenly aware of these “synthetic risks” because at some point you’ve been unknowingly exposed to a risk factor that took a bite out of your p/l. That prompts you to slice and dice your risk to further your understanding of positions. Risk management evolves one bruise at a time. The inevitable body shots and jabs hurt, but also teach. You just have to get your overall controls robust enough to survive the haymaker.

[Speaking of teach…did you know that if a stock is halted, you can compute what price the market is implying it will open at? Just compute the price the SPX cash index would need to be at for the futures to be priced fairly to back out the halted stock’s implied price.]

Corey is spot on. It’s long/short portfolios all the way down. This is native vision for derivatives traders.

In closing, know that I’m not just shouting my friends when I say to watch Pirates. That’s seeing causality backwards. Jason is sponsoring Moontower and I met these guys in the first place because I was attracted to how they think (well that’s half of it…there are plenty of brilliant people out there I have zero interest in hanging out with. These are friends that got through the important funnels after I noticed they were smart.) I always learn when I listen to these guys. They’re entertaining and always have good stories.

Actually, you know what? F those guys. Hoggin all the cool in the room.

“The Unplugged Controller”

I’m going to stick with a somewhat irreverent tack for Labor Day with this share.

On Meaningless Careers (7 min read)
by Jack Raines

Jack’s Young Money finance blog is consistently fun to read. A few excerpts from this post:

The abstract:

People love work.

The problem isn’t that the youngest generation hates work; the problem is that many of the jobs offered to the youngest generation aren’t work at all. The spreadsheet-heavy, mid-level-manager-dominated, buzzword-filled roles offered to us are jobs, but they are hardly “work.”

For any gamers out there, one of the oldest tricks in the book is giving your younger sibling an unplugged/disconnected controller, so they feel like they are “playing”, while you are in control the whole time.

Many “jobs” today are simply unplugged controllers. The work would get done, whether or not we take part in the process. We are simply moving numbers, smashing buttons, and staying busy, with no regard for actual productivity.

We never stop to ask “is this job necessary?” Because we are paid increasingly higher and higher salaries for our participation in this ever-growing proliferation of pointless jobs.

Sebastian Junger once said, “Humans don’t mind hardship, in fact they thrive on it; what they mind is not feeling necessary. Modern society has perfected the art of making people not feel necessary.”

The concrete:

Football was overbearing, painful, and straight-up frustrating at times, but from day one on the football team, I felt like my contributions mattered.

Contrast that with my experience working in corporate finance.

The people I worked with and worked for in corporate finance were great. My supervisors were certainly nicer than my coaches (which wasn’t a difficult hurdle to surpass, considering some of my football coaches called me things that cannot be repeated over text). And the work wasn’t hard. It was easy, simple. And anything that I didn’t already know how to do could be learned in a few days.

And the best part? I was paid a living wage for my efforts in this corporate finance job. And yet, I hated it. Actually, hate is much too strong of a word.

The opposite of love isn’t hate, it’s indifference. And I was aggressively indifferent to my work.

If pandemic-induced remote work showed me anything, it showed me how little “work” was necessary to do my job. I legitimately “worked” 5-10 hours per week at times, but I was always pretending to “work”, by either moving my mouse to look active or tinkering with files, models, and decks that didn’t really need tinkering to pass the time.

It was pretty obvious that if I didn’t show up for a day, week, or month, the show would go on. I was playing with an unplugged remote.

I was trading my time for a paycheck, with no regard for the actual work being done.

And I wasn’t alone.

The “prestige lie”:

The paradox of modern work is that the most prestigious jobs often involve the least actual work. If you can grind on tedious tasks longer than anyone else, you can get paid a lot of money. You gain material riches at the loss of your individualistic drive.

To quote David Graeber’s Bullshit Jobs:

Shit jobs tend to be blue collar and pay by the hour, whereas bullshit jobs tend to be white collar and salaried. Those who work shit jobs tend to be the object of indignities; they not only work hard but also are held in low esteem for that very reason. But at least they know they’re doing something useful.

Those who work bullshit jobs are often surrounded by honor and prestige; they are respected as professionals, well paid, and treated as high achievers – as the sort of people who can be justly proud of what they do.

Yet secretly they are aware that they have achieved nothing; they feel they have done nothing to earn the consumer toys with which they fill their lives; they feel it’s all based on a lie – as, indeed, it is.

Of course, this whole thing makes sense. Prestige is the lie we tell ourselves to justify our “bullshit jobs.”

We don’t like the work, and in the back of our heads, it feels like we are selling our souls and our time for a paycheck. If we dwelled on that realization too long, we would probably hop off this treadmill entirely. But prestige is that North Star that continues to pull us forward.

The thing about prestige is that it isn’t real. It’s a vanity metric. Don’t believe me? Then why are half of all middle-management jobs now called “vice president?”


Prestige has mollified our collective work restlessness, our existential angst. Prestige keeps those uncomfortable self-realizations imprisoned in the backs of our minds.

Prestige allows the show to go on.

But if you adjust your values, and if prestige loses its luster, the nothingness of these jobs becomes impossible to ignore.

This all ties back cleanly to my post. The prestige “North Star” is one of many compass headings that can leave you with that “pebble in the shoe” feeling.

I’d imagine Labor Day would be an important day for Graeber. A day to celebrate those shit jobs that pay by the hour. They have no prestige but they are honest.

All of this reminds me of this section from 15 Ideas From Morgan Housel’s Interview with Tim Ferriss:

The optimal amount of bullshit

You had Stephen Pressfield on your show, and he was talking about a time when he lived in a mental institution. He was not a patient himself, but he lived there and he starts talking to all these people. And he made this comment that a lot of the common denominators of these people who lived in a mental institution was they were not crazy, they just could not handle or put up with the bullshit of life. They just couldn’t deal with it. And that was kind of why they ended up in the mental institution. And he said all these people were the smartest, most creative people who he had ever met, but they couldn’t put up, they had no tolerance for the bullshit of the real world. And that to me, just brought this idea that there’s actually an optimal amount of bullshit to deal with in life. If your tolerance for bullshit is zero, you’re not going to make it at all in life…

I listened to that [interview] and it was like, “Oh, see, these people could not function in the real world because they had no tolerance for bullshit.” The second step from that is, there is an optimal amount of bullshit to put up within life. And that was where this article, “The Optimal Amount of Hassle,” came from.

And I remembered I was on a flight many years ago and there was this guy in a pinstripe suit who let everyone know that he was a CEO of some company, and the flight was like two hours delayed, and he completely lost his mind. He was dropping F bombs to the gate agents and just completely making an ass of himself because the flight was delayed. And I remember thinking like, “How could you make it this far in life and have no tolerance for petty annoyance, like a delayed flight?”

And I just think like there’s a big skill in life in terms of just being able to deal with some level of bullshit, and a lot of people don’t have that. There’s another great quote that I love from FDR, who of course was paralyzed and in a wheelchair. And he said, “When you’re in a wheelchair and you want milk but they bring you orange juice instead, you learn to say, ‘That’s all right.’ and just drink it.” And I think that just having the ability to put up with that kind of stuff is, I think, really important and often lost in this age where we want perfection. We want everything to be perfect, and it never is.

[Kris comment: I have a good friend who is insanely smart and well-traveled (top 1% in both categories of everyone I know). His brother is not conventionally successful but I was curious what that brother is like. His brother is also very well-traveled in part to choosing a life in the armed forces. But my friend also described his brother as extremely smart. But…incapable of tolerating the b.s. The military life is simple in the ways he prefers. It has always stayed with me, that my friend quite explicitly described his brother as being unwilling to suffer bullshit. I often feel that “getting ahead” in a conventional sense is really just alpining sedimentary layers of compressed bullshit. When I use the word “integrated” metaphysically, a large portion of that is finding your personal sweet spot on the b.s. continuum.]

Jobs like trading and finance are especially vulnerable to bullshit because we put abstractions like price discovery, efficiency, and liquidity on pedestals. Rightfully so. In Finance Guilt, I defend these ideals. The progress of civilization does depend on them.
The problem is that whenever something is good it’s easy to rationalize its excesses beyond the point of diminishing returns. It’s hard to know when more isn’t better.

You have heard the lament that too many wicked smaht people go into finance when they should go into science. What about the genius trading quants who literally used to build weapons for Russia? I’ll leave this for the utilitarians to sort out. Meanwhile, someone who just learned to spell libertarian is hyperventilating “the market will decide”. As if the market’s outputs themselves weren’t downstream of rules set by politicians horse-trading in “the room where it happens.”

Byrne Hobart’s quote brings object-level framing to an abstract argument:

The defense of 1031 exchanges is that they encourage growth because they keep people spending money on new property developments instead of cashing out and enjoying their gains. Which embeds two assumptions:

  1. It’s generally better to tax consumption than investment, and
  2. Real estate investment is a particularly worthy kind of investment to avoid taxing.

Assumption #1 sounds true, but is circumstantial. Assumption #2, though, is hard to defend. Real estate speculation does produce jobs, but it also produces macroeconomic volatility and sometimes threatens the financial system. From a macroprudential perspective, where the goal is to reduce the odds of financial crises, it might make more sense to have 1031 exchanges for everything but real estate: sell your company, and you can roll the money into starting a new one; sell a mall or skyscraper, and you get taxed. But it’s always fiendishly hard to predict the long-term incentives created by a change in the tax code. Any tax on realizing gains, for example, is implicitly a subsidy on borrowing against appreciated assets instead of realizing those gains. If that’s true, the net effect of eliminating 1031 exchanges would be that real estate portfolios would turn over less often. If we assume that people vary in their ability to make good real estate investments, this would mean that the best such investors wouldn’t make as many discrete investing decisions, which would make prices a bit less efficient. Which might be a reasonable tradeoff: making real estate investing a less tax-optimal choice could be a fair trade in exchange for making real estate prices less reflective of their value. But it’s still a tradeoff, not a straightforward benefit. Quirks in the tax code become load-bearing over time; even if they didn’t make economic sense when they were made, the structure of the economy only makes sense in light of the tax incentives that economic actors have already responded to. If you assume that people are reasonably good at reacting to incentives—or, more plausibly, that over time the people who are good at doing this end up controlling more assets—then any change in those incentives has complicated and unpredictable results.]

Another Kind Of Mean

Let’s use this section to learn a math concept.

We begin with a question:

You drive to the store and back. The store is 50 miles away. You drive 50 mph to the store and 100 mph coming back. What’s your average speed in MPH for the trip?

[Space to think about the problem]




[If you think the answer is 75 there are 2 problems worth pointing out. One of them is you have the wrong answer.]




[The other is that 75 is the obvious gut response, but since I’m asking this question, you should know that’s not the answer. If it’s not the answer that should clue you in to think harder about the question.]




[You’re trying harder, right?]




[Ok, let’s get on with this]

The answer is 66.67 MPH

If you drive 50 MPH to a store 50 miles away, then it took 60 minutes to go one way.

If you drive 100 MPH on the way back you will return home in half the time or 30 minutes.

You drove 100 miles in 1.5 hours or 66.67 MPH

Congratulations, you are on the way to learning about another type of average or mean.

You likely already know about 2 of the other so-called Pythagorean means.

  • Arithmetic mean

    Simple average. Used when trying to find a measure of central tendency in a set of values that are added together.

  • Geometric mean

    The geometric mean or geometric average is a measure of central tendency for a set of values that are multiplied together. One of the most common examples is compounding. Returns and growth rates are just fractions multiplied together. So if you have 10% growth then 25% growth you compute:

    1 x 1.10 x 1.25 = 1.375

    If you computed the arithmetic mean of the growth rates you’d get 17.5% (the average of 10% and 25%).

    The geometric mean however answers the question “what is the average growth rate I would need to multiply each period by to arrive at the final return of 1.375?”

    In this case, there are 2 periods.

    To solve we do the inverse of the multiplication by taking the root of the number of periods or 1.375^1/2 – 1 = 17.26%

    We can check that 17.26% is in fact the CAGR or compound average growth rate:

    1 x 1.1726 * 1.1726 = 1.375

    Have a cigar.

The question about speed at the beginning of the post actually calls for using a 3rd type of mean:

The harmonic mean

The harmonic mean is computed by taking the average of the reciprocals of the values, then taking the reciprocal of that number to return to the original units.

That’s wordy. Better to demonstrate the 2 steps:

  1. “Take the average of the reciprocals”

    Instead of averaging MPH, let’s average hours per mile then convert back to MPH at the end:

    50 MPH = “it takes 1/50 of an hour to go a mile” = 1/50 HPM
    100 MPH = “it takes 1/100 of an hour to go a mile” = 1/100 HPM

    The average of 1/50 HPM and 1/100 HPM = 1.5/100 HPM

  2. “Take the reciprocal of that number to return to the original units”

    Flip 1.5/100 HPM to 100/1.5 MPH. Voila, 66.67 MPH

Ok, right now you are thinking “Wtf, why is there a mean that deals with reciprocals in the first place?”

If you think about it, all means are computed with numbers that are fractions. You just assume the denominator of the numbers you are averaging is 1. That is fine when each number’s contribution to the final weight is equal, but that’s not the case with an MPH problem. You are spending 2x as much time as the lower speed as the higher speed! This pulls the average speed over the whole trip towards the lower speed. So you get a true average speed of 66.67, not the 75 that your gut gave you.

I want to pause here because you are probably a bit annoyed about this discovery. Don’t be. You have already won half the battle by realizing there is this other type of mean with the weird name “harmonic”.

The other half of the battle is knowing when to apply it. This is trickier. It relies on whether you care about the numerator or denominator of any number. And since every number has a numerator or denominator it feels like you might always want to ask if you should be using the harmonic mean.

I’ll give you a hint that will cover most practical cases. If you are presented with a whole number that is a multiple, but the thing you actually care about is a yield or rate then you should use the harmonic mean. That means you convert to the yield or rate first, find the arithmetic average which is muscle memory for you already, and then convert back to the original units.


  • When you compute the average speed for an entire trip you actually want to average hours per mile (a rate) rather than the rate expressed as a multiple (mph) before converting back to mph. Again, this is because your periods of time at each speed are not equal.
  • You can’t average P/E ratios when trying to get the average P/E for an entire portfolio. Why? Because the contribution of high P/E stocks to the average of the entire portfolio P/E is lower than for lower P/E stocks. If you average P/Es, you will systematically overestimate the portfolio’s total P/E! You need to do the math in earnings yield space (ie E/P). @econompic wrote a great post about this and it’s why I went down the harmonic mean rabbit hole in the first place:

    The Case for the Harmonic Mean P/E Calculation (3 min read)

  • Consider this example of when MPG is misleading and you actually want to think of GPM. From Percents Are Tricky:

    Which saves more fuel?

    1. Swapping a 25 mpg car for one that gets 60 mpg
    2. Swapping a 10 mpg car for one that gets 20 mpg

    [Jeopardy music…]

    You know it’s a trap, so the answer must be #2. Here’s why:

    If you travel 1,000 miles:

    1. A 25mpg car uses 40 gallons. The 60 mpg vehicle uses 16.7 gallons.
    2. A 10 mpg car uses 100 gallons. The 20 mpg vehicle uses 50 gallons

    Even though you improved the MPG efficiency of car #1 by more than 100%, we save much more fuel by replacing less efficient cars. Go for the low-hanging fruit. The illusion suggests we should switch ratings from MPG to GPM or to avoid decimals Gallons Per 1,000 Miles.

  • The Tom Brady “deflategate” controversy also created statistical illusions based on what rate they used. You want to spot anomalies by looking at fumbles per play not plays per fumble.

    Why Those Statistics About The Patriots’ Fumbles Are Mostly Junk (14 min read)

The most important takeaway is that whenever you are trying to average a rate, yield, or multiple consider

a) taking the average of the numbers you are presented with


b) doing the same computation with their reciprocals then flipping it back to the original units. That’s all it takes to compute both the arithmetic mean and the harmonic mean.

If you draw the same conclusions about the variable you care about, you’re in the clear.

Just knowing about harmonic means will put you on guard against making poor inferences from data.

For a more comprehensive but still accessible discussion of harmonic means see:

On Average, You’re Using the Wrong Average: Geometric & Harmonic Means in Data Analysis: When the Mean Doesn’t Mean What You Think it Means (20 min read)
by @dnlmc

This post is so good, that I’m not sure if I should have just linked to it and not bothered writing my own. You tell me if I was additive.

The Juicy Stuff Doesn’t Hit The Pit

New Substack recommendation: The Old Rope by @varianceswap

Here’s a fun excerpt from the latest issue:

Real estate in the private market exists in between the two preceding applicable stock market concepts: you want to buy quality, and you want to buy it at the price you’d buy distressed assets at. But you’re okay just buying quality- after all the private market real estate investor needs to find an asset to 1031 exchange within 45 days of a sale. Readily available dirt-cheap bankruptcy-remote leverage from commercial lending operations provides the private real estate investor with a nearly-government-guaranteed reasonable return. Buy quality and stay rich (never pay taxes).

Because private market commercial real estate is private, rarely do these quality assets sell at generous prices to counterparties outside of the “boys’ club” or in-network, off-market participants for whom favors have already been traded, country club memberships have been synched, and alumni events have been planned. This is what I would call the System 1A of real estate investing. This is where common misconceptions occur with real estate: generalist laymen see these slam-dunk transactions and the seemingly risk-free returns generated from them. They observe “dumb people” getting rich not knowing these people are actually repeat-players in a multi-generational game. They play nice with each other to stay in the club and stay rich.

Damn, this brought me back to some of the cronyism in the trading pits. On the NYMEX/COMEX floor brokers were also allowed to be traders. They could trade for their own accounts, but they were not allowed to trade against their own flow. Well, if you can imagine the incentive, you can imagine the outcome.

Here’s the scene: market makers stand in a pit while brokers run their business out of surrounding booths. The booths were the phone banks outside the pit where broker clerks would talk to the “upstairs” customer. If a juicy market order, especially one without a lot of risk or deltas such as a tight vertical spread or butterfly, there was a silent feeding frenzy. Sal couldn’t trade against his own flow, but knew that Tony would get him “next time”. You know, like a running bar tab. Better yet, maybe your sister starts her own brokerage competing (cough) for the same flow.

If a 100 lot of butterflies traded in the pit for a credit (you heard that right…the meat of a butterfly trading over the wings) you can safely deduce that several hundred lots never made it to the pit.

It’s worth reprinting the last line of that excerpt:

They observe “dumb people” getting rich not knowing these people are actually repeat-players in a multi-generational game. They play nice with each other to stay in the club and stay rich.

And if resentment to this old word order wasn’t high enough, we had the experience of watching some of these “dumb” people who owned several, sometimes tens of seats on the exchange, receive nearly $10mm a pop for them when the exchange demutualized.

[Side note: I worked for a SIG at the time who owned a bunch of seats. They made a bonanza buying NYSE seats before the stock exchange went public so they were ready for the same trade ahead of the NYMEX IPO. One of our assistant traders spent most of his time going to the admin office in the building to find the bid/ask on seats and get the color on who was looking to buy or sell. Probably didn’t take much more than regular coffee and donuts to keep in the office clerk’s good graces. On a personal note, I got some shares as part of the seat lease agreements that SIG had to (probably begrudgingly, since prop firms are ruthless maximizers) give to the people whose names were actually on the lease. The IPO priced at $59 bucks but the NMX shares opened on the first day at $120. I sold the opening print along with many other traders. It was a free $25,000 or so. The stock closed at $152 that first day so I left a lot on the table, but even worse was that my mind’s comparison monster left me feeling sour. A lot of folks down there became generationally rich.

And if they were smart, took the money and ran. It was a countdown to the end of floor trading.

[Extra salt in the wound — there was some arrangement where you had to sell your free shares through Merrill (I think) and they charged like a $500 brokerage fee. And yes, this was 2006, not 1966.]

Enough story time. Go read The Old Rope. The second post I’d read is:

Fake Life, True Wealth (2 min read)