Martingale Beliefs

Plus! Martingale Beliefs; Diff Jobs; Country Equity; Costs and Benefits; Continuation Funds; Deepfaking the Dead and the Last Generation of Celebrities; Mature Financial Systems

Byrne Hobart Byrne Hobart

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The Diff May 6th 2024
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Martingale Beliefs

Martingale betting is a popular and effective way to lose all of your money. It goes like this: bet $1 on some game where your odds are 50/50 minus whatever the casino takes. If you win, go home. If you lose, double your bet. Repeat this long enough and you’re guaranteed to make a dollar eventually—unless, of course, you run out of money. Which is inevitable because bankrolls aren't infinite, and because you’ll need to dig deeper into your pockets the longer you have bad luck. But in all probability, losing will be preceded by a very long winning streak in which you train yourself to see all drawdowns as temporary, and eventual profits as a guarantee.

Martingales are very obviously a bad idea, albeit a tempting one if you don't think through to the logical conclusion (or don't just take the first-principles view that if your expected value is negative on any given bet, there is no betting strategy that is superior to the others). Regardless, it's a useful pattern to look for, not just because the risk of ruin shows up in so many other places, but because the mid-Martingale psychology is so toxic.

There are many live examples, in finance and in other places.

On the fundamental side, consider a case where there's a complicated stock with many moving pieces (maybe a Liberty company, maybe a business with messy corporate governance, maybe a company that's threatened by a new competitor—the details change, but the general pattern fits). Let's say that this company is mature enough to generate some free cash flow, and that it periodically buys back stock.

An interesting feature of companies that buy back stock regularly is that their expected return rises when the stock declines. Suppose a company trades at 10x free cash flow and uses half of its cash flow to buy back shares. That's a 5% decline in shares each year, so if the business is static, cash flow per share rises 5.3% compounded (i.e. 1/.095). If the stock drops 20%, and the company is still buying back at the same pace, the free cash flow yield is now 12.5%, and that rises at 6.7%. So in a simplistic model where long-term returns converge on yield plus growth, its expected return has risen from 15.3% to 19.2%. Wonderful! Time to buy more!

This general approach does work—it's adding a little extra explication to the general concept of buying low and selling high, or of having a value tilt in your factor exposures. But do this religiously, and it becomes a Martingale bet as soon as you add in some uncertainty. That’s ultimately because there are two kinds of cheap stocks: the kind that get cheap for a while and then snap back to normal, and the kind that look cheap all the way down. Consider Jim Chanos: he’s talked about shorting Eastman Kodak at a single-digit earnings multiple, and adding to the short at a similar multiple of 90% lower earnings. A value investor who is mechanically buying larger stakes in companies as their market price drifts further from that investor's assessment of their intrinsic value will end up with a portfolio dominated by mistakes.

This gets especially bad when companies make the object-level prudent decision to appeal to their investor base. As the investor base consists of more and more people who are confident in the core business, their incentive is to double down on it, even if the short sellers' view is that this business is challenged and that's why the stock is a good short. So you can have cases where a stock trades at $5, could liquidate and return $6, but is going to keep reinvesting in the business because their shareholders think it's really worth $10.

Buying a stock and adding to the position all the way to zero is at the far end of the long-term investing spectrum, but the same Martingale-style returns show up at the opposite end, in market-making. The most naive possible market-making strategy is to look at the midpoint of the bid/ask spread and quote a slightly narrower spread. So if someone can sell shares for $9.95 or buy them for $10.05, you quote $9.96/$10.04. Most of the time, this works just fine! Orders will be roughly 50/50 buys and sells, and the market-maker is earning eight cents on a round-trip. There's some risk, sure, but if the stock doesn't fluctuate much, that risk is not especially damaging. There might be a few unlucky draws—if orders happen at random, a little over 3% of the time you'll get five buys or five sells in a row. But on average, with random orders, it's a wash over time.

The catch is, of course, that the stock doesn't stay still. If the midprice is $10.00, on average the stock will be at around $10.00, but sometimes a big buyer or seller will show up, and for the duration of their activity they'll be pushing the stock in whatever direction they're trading. Meanwhile, the market-maker has been helpfully providing competitively-priced liquidity. This strategy entails accumulating large positions at exactly the wrong prices—if you're always the high bidder, then when the stock moves from $10 to $9 you have a large long position with an average price of about $9.50, while a buyer pushing it to $11 means you've shorted a lot at $10.50. This is a small loss for a longer-term, more fundamentals-oriented strategy, but market-makers have an extraordinarily high ratio of dollar volume traded to capital. They really aren't in the business of taking large directional risks, and an implementation of this strategy that got acceptable returns on capital in a stable market environment would be wiped out in a large market move.[1]

This applies beyond business and finance. There's also a set of Martingale Beliefs, or, more strictly, Martingale strategies for coming up with things to believe. Natural contrarians are indispensable for advancing our ideas by instinctively shooting down the bad ones, but they're always running a risk: what if they succeed in persuading everyone that they're right? The last few decades have been net amazing for libertarians on social issues—things like cannabis legalization and gay marriage were hypotheticals in the 90s, then snuck into the Overton Window, and, in many places, are now the law of the land. It's a huge political victory. But from there, what's a contrarian to do? What often happens is that some people moderate for the reason that other people drift into extermism—the midpoint changes and their views don't. But the other option is to just stay equally disagreeable, and to find a new cause with a 90% unfavorable rating. (This, of course, drives the former-radicals-turned-satisfied-moderates absolutely crazy. "No, I'm not one of those 'if the grade school student consents to buying Fentanyl' types.")

But all of these have a deep commonality: they're all a form of liquidity provision, the means by which resources get transferred to people with better information and analytical abilities. This is literally true in the case of the bad market-maker, who is essentially subsidizing informed traders by letting them take a larger position at a better price. The company that keeps pandering to the desires of shareholders who don't understand how the business is impaired is also giving short sellers more time to refine their thesis, and more opportunities to bet against the stock. And contrarians add liquidity to the market for ideas. It's costly, and usually not worth the cost, to advocate heterodox ideas in public. But sometimes the Overton Window has moved slowly because a given idea has been beyond consideration—even as facts on the ground have made it a better idea. So the contrarians are engaged in a negative expected value pursuit for them, but it's good for the rest of us that they periodically insist on re-raising important questions.

  1. This doesn't mean that market-making is an inherently blowup-prone strategy. Anyone can think through this thought experiment, though some DeFi liquidity providers don't. In fact, the skewness of returns from a naive market-making strategy, and the fact that more advanced strategies start with that approach and then elaborate with different ways to manage risk, means that long-lived market-making firms are actually a great repository of unwritten wisdom about risk-management. Not that they're talking; every mistake they avoid that a competitor doesn't is a contribution to their future market share. ↩︎

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Elsewhere

Country Equity

A finance thought experiment, adjacent to "what if we could buy stock in each other?" is "what if we could buy stock in a country?" This is a very old idea; Genoa was issuing bonds that paid interest based on tax receipts during the Renaissance. (Yes, it's a bet on taxes rather than GDP. But GDP is better thought of as a proxy for the taxable piece of the economy than the economy itself; if I cook dinner for my family instead of buying takeout, GDP goes down but the economic impact is potentially positive.)

Sri Lanka is considering issuing GDP-linked bonds to restructure its current debts ($, FT). There's an incentive alignment here, which is best understood by thinking of the debt trap that would otherwise ensue. Sri Lanka is a small, impoverished country with a persistent current account deficit. A lender would need to be paid a substantial sum to take credit risk, but at a rate high enough to compensate for that risk, there might not be ways for the country to spend money in order to produce a return sufficient to service the debt. Whereas if it's GDP-linked, then this is closer to an equity investment: if the country gets its economic act together, investors prosper; if they don't, a lender wasn't going to collect much, either.

Costs and Benefits

Microsoft CEO Satya Nadella has sent a company-wide memo on the importance of security. This is obviously something Microsoft needs to care about, but perhaps its importance is cyclical—something similar happened two decades ago in response to a similar spate of security problems. The key point is in the closing paragraph: "If you’re faced with the tradeoff between security and another priority, your answer is clear: Do security." (Emphasis in original.)

Sometimes memos like this can be dismissed as fluff—what CEO would, after a series of breaches, send out an email saying that security is their #3 priority after next quarter's revenue growth and next quarter's EBITDA margin? Still, they do matter, because large organizations are sufficiently unwieldy that a top-down directive like this is the only way to force a shift in priorities. There's always a near-term speed/security tradeoff, and it's easier to get people at all levels of the org chart to accept delays if there's a top-down mandate explicitly tolerating them. In the long run, speed and security are less of a tradeoff: at least in the next few quarters, Microsoft's pace of shipping would be higher if they'd counterfactually spent a bit more time locking down what they already had.

Disclosure: Long MSFT.

Continuation Funds

One of the reasons there's a relative shortage of small, high-quality companies in public markets is that the good ones often get bought by private equity firms. In recent years, these companies have stayed private for longer through continuation funds—when a PE firm reaches the end of its life, the manager will sometimes raise a separate vehicle to acquire a portfolio company that they believe will be more valuable in an IPO if that IPO takes place a little further in the future. Now, venture funds are experimenting with this, and with other ways to give investors liquidity ($, FT). It's a paradox that even when the tech industry is changing fast, the companies that push it forward take longer to incubate before they're ready for public markets. But an unavoidable consequence of the growth of VC as an asset class is that quality companies can delay an IPO more or less indefinitely, and now the venture industry is adapting to the consequences of its own size by giving those companies a way to stay private even longer.

Deepfaking the Dead and the Last Generation of Celebrities

Political groups in India are using deepfaked videos of dead politicians (these all appear to be disclosed). This is on the same spectrum as a political party doing the entirely normal thing of pointing to the legacy of a now-deceased politician whose name they know still resonates with voters.

But it's also an instance of changes in media distribution making it harder for new mass-market celebrities to break through. There are still plenty of famous people out there, but they're increasingly famous to a small subset of the population (the list of most-followed TikTok accounts has a huge number of people who are, objectively, some of the best-known on earth, and whom I've never heard of). Algorithmic content distribution means that these people find their audience, and that the people who aren't naturally part of their audience will never encounter them. Meanwhile, better cosmetics, healthcare, and digital touch-ups meant that actors and musicians could stay active for longer. And now, even if they're physically incapable of delivering a live show or a great stump speech because they're deceased, they're still digitally capable of this. The celebrities who broke through when media was less fragmented have a name recognition advantage over new ones, even if the new ones are, technically, still alive.

Mature Financial Systems

A new study reveals that more than 90% of stablecoin transactions are from speculators and hedgers, rather than people who are trying to buy goods and services directly. Ironically, this means that the stablecoin world is actually much less financialized than the fiat economy: global OTC FX turnover was $7.5tr per day as of the last BIS triennial survey, or $2.7 quadrillion annually. That means that the comparable stat for fiat is roughly 96%. In any financial system, as the system grows, the non-end-user pieces grow faster: as transaction costs drop, they stop affecting consumer purchases much because the prices for those purchases are constrained by other costs (like the wholesale cost of whatever's being sold, the overhead required to sell it, fixed costs the seller needs to pay regardless of what's sold, etc.). But in hedging transactions, the transaction cost is the cost, so every basis point of transaction cost drops enables more hedging and more speculation. For its size, the crypto economy has more purely-financial transactions ($, Diff) than other systems, which can and does crowd out real-world economic activity. But that's also partly because it can take advantage of the technological and social infrastructure created by the legacy system. Crypto didn't need to invent the concepts of margin loans, shadow banking, statistical arbitrage, or financial-instruments-as-gambling. All crypto had to do was re-implement them.