Correlations go to One, in Good Ways and Bad

Plus! Network Effects, Rebalancing, Leapfrogging, Getting Funding, Diff Jobs

Correlations go to One, in Good Ways and Bad

One fun way to conceptualize finance is that it's a form of time-travel. A mortgage is just a way to collect some of the next thirty years of your income, bundle it up, and use it to buy a house today. The price of a risky biotech stock is the blended result of two futures, the common one where they fail and the rare one where they succeed. This is quite socially useful; the present expected value of X happening in the future can be transported to the present, where it can fund investments that make X more likely to happen.

But finance enables time travel in another generally darker way. A good rule of thumb in a crisis is "all correlations go to 1." Normally there's some variance between different sectors, industries, and specific stocks; a bad day for healthcare might be a good day for energy, or a rough day in equities can be offset by a good day in corporate bonds or commodities. But during the worst days, almost everything falls apart. When the worst versions of the future happen, they happen all at once.

You can think of this as an indicator of panic selling; if investments in dollar stores, cigarettes, and defense stocks are underperforming at the same time that homebuilders, software companies, and airlines are, it may be a sign that investors aren't thinking clearly. But another way to look at it is to flip things around: a bear market in every asset class is just a wild bull market in the universal denominator, the dollar.1

What about inflation? There are two ways to look at that. One is to say that while there's inflation almost ($, Economist) everywhere right now, the dollar is doing fine relative to other currencies. "Fine" actually understates it: the DXY index is at levels last seen in August 2002, after a big bull market in dollars. The last time the dollar was this high before that was the summer of 1986, before I was born. Even when the proximate cause of investor worries is a decline in the purchasing power of the dollar, sufficiently worried investors will often pile into dollars.

Understanding what fundamentally drives this correlations-to-1 behavior is straightforward:

  1. Look at a set of asset classes (stocks, bonds, real estate, whatever) or a set of specific assets within classes—or even signals like value and momentum.
  2. Measure their historical correlations.
  3. Find a set of assets whose historical correlations are low enough that buying them together maximizes risk-adjusted return—if bonds and stocks both produce positive returns over time, but tend to move in opposite directions, then a bonds-plus-stocks portfolio looks better than just one or the other.
  4. Add leverage until the expected return of this portfolio matches that of some benchmark asset class—equity-like returns with less-than-equity volatility is a compelling offering.

In the short term, this works wonderfully and seems like a prudent form of diversification. It's the same kind of thing a company might do if it found that most of its customers were in one high-growth industry, and sought out other customers in a more stable one—the combination of these two would provide enough revenue growth and stability to justify faster expansion.

It tends to go wrong gradually at first, and then suddenly. The gradual part comes from the fact that many financial actors are engaged in exactly this kind of calculation, and are constantly rebalancing their portfolios. The rebalancing effect means that if one part of the strategy lags, they move more money into it. And this means the strategy's risk-adjusted return goes up—if there's a population of investors who will systematically buy some category of stocks whenever it declines, that category's drawdowns won't be so fierce. And this kind of behavior slightly improves the measured anticorrelations, too; when asset A goes down, and the response is to sell asset B and buy more of A, the combination of that buying and selling means that A and B get more anticorrelated. So these portfolios tend to look better as they get more popular. But the aggregate flows and rebalancing flows have another pernicious effect: they increase risk-adjusted returns by reducing expected returns and reducing expected risk faster. In other words, the numbers can look great, but only if leverage goes up.

At the time, this can feel intoxicating, because what it looks like—which is accurate, to an extent—is that the strategy has identified a systematic way to outperform, and that other investors are slowly catching up. When deviations from the trend snap back faster and faster, it provides lots of confirmation that the trend is real.

If there's a big enough exogenous shock, the model can break down: levered investors selling to rebalance can cause enough declines in the other assets they own that other investors in these assets also have to sell, and this can deliver some wonky results. The "quant quake" of August 2007 is a great example: losses from subprime investments led some equity investors to reduce exposure, and that led to margin calls for other equity investors. As it turned out, many of the most levered investors were trading using the same signals, so they were trading exactly the same stocks. Since these were market-neutral investors, the net impact on share prices was modest; the S&P dropped 8.5% from its intraday peak on August 9th through its low on the 16th, but the index ended the month with 1% of where it started. But under the surface, every stock that screened well on momentum was collapsing, and the ones that did poorly on that factor were rising; statistically cheap stocks went down, and statistically expensive ones went up. As Goldman's then-CFO put it, "We were seeing things that were 25-standard deviation moves, several days in a row... There have been issues in some of the other quantitative spaces. But nothing like what we saw last week." (That quote is from this excellent piece.)

Crucially, this kind of loss can only happen if it happens to many funds at once. Which doesn't do much for investor psychology: when you're panicked, you're more likely to call the smartest people you know and ask them what they're seeing. The more specialized you are, the more you fine-tune this judgment of "smart" based on someone's skill at doing things you're also good at. So when there's a levered quant blowup, quants all discover that other smart people blew up, too. This applies to very smart people indeed; The Man Who Solved the Market says that Medallion lost 20% in a few days.2

One element of market cycles is that new asset classes emerge, they get popular because they're uncorrelated to everything else, and when that's a driver of their popularity, they suddenly end up correlated again. This has been part of the story with crypto, for example: it's true that some cryptoassets are designed to retain their value in times of high inflation, but if the marginal trader of that asset is a diversified investor with leverage, then a bad CPI print that pushes stock prices down can lead to crypto positions getting liquidated, too. In the modern financial system, it's basically a coming-of-age ritual for a previously-uncorrelated asset to suddenly get correlated with the broader market again.

Even though the thought of correlations going to 1 gives risk managers nightmares, there's another version of that story that's fairly positive. I've written before about how improbable startups can be modeled as a series of low-probability events, and that part of their success consists of making the joint probability of all of them working out higher than the naïve result you'd get from multiplying the odds together.

It's important to consider that from any perspective sufficiently far back in the past, newly-successful industries today are the result of a series of absurdly improbable events that all worked out in exactly the right way. From the perspective of 1990, the crazy things that had to go right for Google to work at its current scale would have included:

These are the obstacles that have to be surmounted before you even get to the point of asking whether there's a viable business model, not to mention figuring out which company will win it.

Modern supply chains are a similar chain of improbabilities, all of which generally get managed to the point that errors are relatively rare and complex goods with inputs from multiple companies in multiple countries get to store shelves on time.

Two-sided networks are a fun example of how companies push through the veil of improbability, by figuring out which problems are fundamentally hard, and which ones can be solved more easily. This is what lots of two-sided networks do. It's hard to get a critical mass of Airbnb guests without a critical mass of hosts, and vice-versa, but one of those problems turned out to be harder than the other—and in a competitive market, the only thing that matters is solving the hardest necessary problem before competitors do.

All this ends up meaning that markets, both in the economic sense and the financial one, are machines for producing valuable information about how the probabilities of different events are connected. Bubbles and megaprojects do this by solving multiple dependencies for one outcome in parallel, which raises the odds that it will be achieved even if the process entails a lot of waste. Financial markets do it by showing that over the long term, there is no free lunch: strategies that get better risk-adjusted returns through diversification will only work that way if someone monopolizes them, but the fact that this diversification is achieved by measuring historical returns means that they're always in the process of commoditization.

Inverse correlations tend to go away when people rely on them. And close-to-perfect correlations are never quite as good as they look; modern supply chains are still impressive, but they've struggled to cope with supply disruptions and demand shifts as a consequence of the pandemic, and their future steady-state probably involves more redundant production, more backup inventory, and consequently lower earnings. The two most dangerous correlation coefficients in the world are "approximately one" and "approximately negative one." But both of them are always lurking around successful industry and financial models.

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Network Effects, Pt. 1

The Washington Post has an interesting look at YouTube's strategy for poaching streamers from TikTok, where the focus is not on absolute popularity but on collaboration. One of the factors media companies have to worry about is the burnout rate, and that's an especially acute problem for solo streamers because they can almost always work more hours to earn more money. It's easier to pace yourself in other kinds of media production, where a whole film crew needs to be working for a scene to get shot. So retention will be a big problem over time. Collaborators may stick around longer, both because of their social ties to their collaborators and because of peer pressure from the same.

This may be less visible to newer media companies, partly because their earliest winners will have some benefits from early adoption, and won't need to work quite as hard for a given level of fame and income, and partly because they simply haven't been around long enough for their stars to get tired and quit. (If people start to burn out after five years, for example, TikTok won't see any of this because the app didn't take off in the US until mid-2018.) Media is a two-sided network between audiences and creators, and running such a network means finding which side is harder to maintain and then identifying every little trick to keep them around longer.

Network Effects, Pt. 2

Dozens of cities and small towns are paying tech workers to relocate ($, WSJ). For workers, choosing where to live is either a case where there are a handful of viable but incommensurable options (near family versus in the biggest economic cluster for that industry), or, if they're fully remote and indifferent to big city amenities, effectively infinite options. When there are lots of options that all have pluses and minuses, effective search adds a lot of value. So this is somewhat like a decentralized version of the online travel agency business, where cities bid money upfront partly to highlight the qualitative perks of choosing them over other comparable places.


Some industries have an exciting bull case, where they're well-positioned to profit from some general improvement in the human condition. For others, it's a bit more depressing. Private equity fits partly into the latter category, where one of the reasons to be optimistic about the industry is pessimism about defined-benefit pension plans, which, in the US, generally commit to return targets that are hard to achieve in any other asset class. And private equity investments aren't marked-to-market as regularly as public ones, meaning their perceived volatility is lower. So it's striking that CalPERS, the 11th largest public pension fund globally, has sold $6bn of private equity assets at a 10% markdown from their most recent valuation. The goal is not, however, to move out of private equity. Instead, it's partly a way to move into direct investments into private equity deals and direct loans. These are even harder to accurately mark to market. Of course, there may be better opportunities participating in individual deals rather than funds, but the favorable accounting treatment helps.


A common pattern in international development is that countries that prosper later can skip some investment-intensive phases that other countries went through. The classic example is going straight to cell phones without having to build out much land line infrastructure. An interesting case study in this is happening in Japan, where office work has been slow to digitize compared to other rich countries. Covid led to a rise in telecommuting, which seems to be sticking around: "Pre-pandemic, just 9% of the Japanese workforce had ever teleworked, compared with 32% in the United States and 22% in Germany... Nearly a third of jobs in Japan were done remotely during the first COVID-19 wave in spring 2020, the Japan Productivity Center says, even though the government never imposed strict stay-at-home orders. The rate has since fallen to 20%..." And that has some notable second-order effects: it means that more workers can move to extremely cheap places instead of a handful of expensive cities. It also means that hybrid companies have to move more of their work away from paper and in-person meetings; it just takes one remote worker to make the old system nonviable.

Getting Funding

A big element of China's financial system is "local government funding vehicles," which are partly-off-the-books financial entities that borrow to fund local infrastructure. They're like a much wilder version of the quasi-public/quasi-private status of Fannie Mae and Freddie Mac in the US before the financial crisis.3 These vehicles used to raise money from banks, but are increasingly raising funds from individual investors at higher interest rates ($, FT). Investors know that these are financially shaky entities, but also know that a default is politically costly—and gets costlier still if it hits lots of individual investors, instead of being contained by a bank that can be bailed out by the government. This isn't a sustainable setup, but it's hard to imagine an easy exit. (One option I've talked about before ($) is for the central government to assume these debts in return for structural reforms that put the local governments on sounder footing. One benefit here is that there's a global shortage of RMB-denominated debt, and creating more of it brings China closer to reserve currency status. Whether or not they'd like that status is a different question.)

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  1. Even here, there are distinctions and degrees. A prudent bull-market-in-dollars operator is someone who sees the dollar as, per Warren Buffett, the universal call option with no expiration date. If assets are getting more volatile, this call option is more valuable; there are chances to scoop up desirable stocks and companies on the cheap. The grimmer version of a bull market in dollars is when you're googling to find out what the average ATM's withdrawal limit is, and figuring out how many you could get to in a day. (It's uncomfortable to read about the financial crisis and realize that the best-informed people were often the ones thinking these kinds of thoughts in September 2008.)

  2. Which raises the question: can you hedge this kind of risk? Possibly! If these strategies are lowering volatility for some set of assets, that will make out-of-the-money options cheaper, so betting on tail risk is a possibility. On the other hand, those same factors mean that those options are cheaper-for-a-reason: the asset prices are less likely to swing wildly before the blowup. Buying tail risk protection is expensive, and creates a drag on performance. And it's tough to tell investors "Don't worry about how we persistently underperform our direct competitors. It's just because we lack confidence in our models and believe that our strategy will inevitably deliver calamitous results!" This is an especially hard sell for the more sophisticated investors; systematically buying when something drops and systematically selling when it rises is, for interesting reasons too complex to go into just now, equivalent to selling options. So a strategy that does this and hedges with options is actually executing a complicated volatility spread trade in an incredibly over-engineered way. More on this in a future post.

    In a deeper sense, levered strategies that try to minimize volatility by selecting positions with low correlations are already trying to hedge against a narrower form of this kind of risk, by betting that some trades will do well when others do worse.

  3. And it should be noted that Fannie Mae was privatized as an accounting gimmick to reduce perceived public debt, but bailing out Fannie and Freddie ended up costing a peak of $191bn, an amount roughly half the size of the (nominal) federal debt at the time of the privatization. So, not an ideal precedent by any means, though the $191bn did get paid back and then some.