The Leverage Constraint

Are people irrationally afraid of debt, or irrationally fond of it?

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There’s a fascinating Milton Friedman essay on utility functions and risk that starts by noting an apparent paradox: insurance and gambling are both big businesses, sometimes paid for by the same people. There is, of course, a narrow answer about paying to avoid downside surprises and paying for a chance at upside surprises; a casino where you won $1 on almost every roulette spin and periodically lost $50 might not have many customers.1

But it raises a broader point about leverage. On average, we're too tempted by it: it's easy for people to go into debt by spending slightly beyond their means on credit cards, to buy more housing than they need or can afford when mortgages are cheap, or to turn a good company into a bad one by changing nothing but the capital structure.2 On the other hand, many of the anomalies from last week's piece on the capital asset pricing model boil down to "people want to take risk without adding leverage, so they overpay for risky assets," and that explains:

  • Why the lowest-rated investment-grade bonds underperform and the highest-rated junk bonds outperform. An investment-grade portfolio manager could get the same volatility and a better risk-adjusted return by buying A-rated bonds with a bit of leverage rather than focusing on BBB, while a junk bond manager could sell their B-rated bonds and buy BB+-rated ones with a little extra leverage and also pick up some expected returns.

  • Why the smallest and most volatile stocks underperform: you can raise the risk in your portfolio by selling Pfizer and Merck and buying a portfolio of research-phase biotech plays instead, but you can also raise the risk by buying a little more Pfizer and Merck on margin.

  • Why so many retail investors lose all of their money on options: it sounds wildly irresponsible to get exposure to the stock market with 4:1 leverage (and, based on the historical record, that is indeed irresponsible; run that strategy long enough and you will be wiped out; even if you rebalance fast enough to avoid ever literally losing 100% of your money, drawdowns are bad enough that it's net value-destructive even though stocks rise over time). But options traders, especially retail options traders, routinely make trades that imply equivalent leverage.3 Given the transaction costs of trading options, this is a very expensive way to avoid technically borrowing money in order to fund speculation.

The classic illustration of why leverage constraints matter is to consider someone who owns one asset, say, equities, and chooses to diversify into another asset that doesn't perfectly correlate with equities. They can tweak the leverage of the portfolio in such a way that the average volatility is the same as the equities-only portfolio, while making the expected return even higher—even if the asset they're diversifying into actually has a lower expected return than equities. (In fact, this is possible even if the risk-adjusted return for the other asset class is lower.) The diversification of income streams means that the total risk of the portfolio goes down when something new is added to the mix, even if that new thing would be a drag on its own.

One way this gets implemented is through risk parity portfolios, like Bridgewater's All Weather fund. This takes the idea fairly literally, often by selecting a set of assets and then weighting them so they each contribute the same amount of risk to the portfolio. One way to think of this is that it means choosing a mix of securities, and then tweaking the size of each component so that your stock risk is roughly equal to your bond risk which is roughly equal to your commodities risk.

The intuition here is pretty straightforward: bonds go up when rates go down, rates go down when the economy slows down, stocks do badly when the economy slows down, so stocks and bonds move in opposite directions. But when inflation is higher, interest rates don't respond purely to growth, but to price levels and concerns about them (for details, ask anyone who owned bonds in the last few years). But that's also the circumstance under which commodities typically outperform! (For case studies on exceptions, ask anyone who owned commodities in the last few years.)4

There are two investing strategies that take this framework as seriously as possible, and then implement it in two different ways:

  1. "Multimanager/Pod shops" basically staple together a large set of uncorrelated strategies—industry-specific stock selection, betting on changes in indices, volatility trading, crypto, whatever else—impose tight risk rules on every single strategy, and then lever up the result massively, often 6:1 to 10:1 overall. The gross return from any one strategy will be small, but the net return from the mix is more predictable and, with enough leverage, quite high.

  2. Quants will often do this, but at the level of signals rather than portfolios. So a quantitative manager can have a whole menagerie of different predictive models that say something about the returns, volatility, or correlations of different assets under different circumstances. Any one signal will be unprofitable after transaction costs, but they're not trading on just one signal: if it costs 20 basis points to trade in and out of a position in GM, and your model tells you that GM usually rises 10 basis points on Wednesdays, that's not very valuable. But if your model also says that GM rises 10 basis points on days when Ford rose both of the days before, and on days when oil is less volatile than average, and while it's raining in Detroit, then the sum of these signals is enough for a profitable trade.5

Clearly, these investors are not averse to taking on debt. They do have blowups from time to time, in part because of this very diversification. For example, one of the strategies mentioned above was betting on market indices change. This was lucrative for a while, but has gotten crowded and less popular. When a big fund loses money on some trade, they tend to dial back risk for everyone, because they've overestimated how much leverage gets them to their target return. So a random mistake in one strategy means that everyone at the fund running other strategies has to sell some of the things they own and buy back some of what they've sold short—i.e. every strategy they run temporarily works best when run in reverse. And if enough funds run similar enough strategies, the result of that is that every pod shop's risk-adjusted returns look terrible all at once, because every liquidation at Fund A is going to hurt the same positions which are held by Fund B.6

There is another category of investor entirely who finds a way to make effective use of debt: people who get access to borrowing on unusually good terms. Warren Buffett's last few decades of investment results are reasonably impressive on a standalone basis, but blow the competition out of the water thanks to the effects of cheap leverage from insurance. (If you attribute all of Berkshire's float to their equity portfolio, Buffett was almost 200% levered as of year-end 2022. That kind of leverage plus 46% of the entire portfolio in a single tech stock is a pretty risk-tolerant portfolio! Of course, the float gets used for other things, too, and Berkshire has plenty of cash as well.)

So leverage can be useful, but it has to be used carefully. We can really break this into three models: the risk parity/pod shop/quant approach is to accept a fairly commoditized form of leverage that's cheap but that can lead to margin calls—and then structure an entire strategy around the limitations of this leverage. The Buffett strategy is to get even cheaper leverage with fewer restrictions—but to structure an entire business around getting it! And the third alternative is to avoid thinking too hard about leverage, and to cycle back and forth between making bad decisions out of aversion to taking on any debt, or making bad decisions because of a willingness to borrow too much.

Read More in The Diff

The Diff has covered the power and downsides of leverage in a few places:

1. On the other hand, a gambler who tries to play until they've hit some target level of winnings is basically structuring every game to have that payoff function, so maybe not...

2. The example on people's minds at the moment is probably the maker of the Instant Pot ($, WSJ), which was acquired by private equity in 2019 and went bankrupt last month. But suddenly-trendy consumer durables businesses are a graveyard of former high-growth companies that either limp along or die off after their first product is a hit. Sonos, GoPro, and Fitbit all had amazing runs for a while but ultimately fizzled. The trouble with these businesses is that for each new product, they generally buy more inventory than they've ever bought before, but at some point a new product cycle will coincide with market saturation. This isn't just costly; it's a capital-intensive way to fail, because they've spent so much on inventory that they can't move. A natural question is why they don’t just decline to do this; the answer is that if they do, they’re potentially ceding their category to fast-followers. 

3. The details are a topic for another post, but these traders are also paying quite a lot for the leverage they get, on average, since they're also compensating the counterparty of their trade for the fact that the option will be more volatile to the underlying stock, and that its value is partly a function of that same volatility—which is hard to hedge except through more options trading.

4. These kinds of strategies are necessarily backward-looking, but the correlations they find are reasonable; in general, for example, commodities will outperform when inflation is high because commodities are an input into so many of the goods that produce measured inflation. As of yet, there isn't a good systematic way to capture other kinds of inflation, like wage increases or higher markups from big companies that dominate their industries (other than by investing in companies whose products are most appealing to workers with a high marginal propensity to spend, or investing in those dominant companies).

5. Older signals, many of which were profitable on a standalone basis, have a human-readable explanation like this, but as those get arbitraged away the marginal new signal is going to be something very esoteric, where if it has a name and label at all that's going to be a broad descriptor for the side effects of interactions across many other firms' systematic strategies. Depending on the quant, the goal will be either to have a set of discrete strategies that have explanations because those explanations are a way to show why one set of investors is leaving money on the table by trading badly and another is leaving money on the table by not exploiting the trade—or to have a billion or so signals, most of which will never be looked at by a human being from when they're identified to when they stop working.

6. As it turns out, people who work at competing firms and hang out socially after hours while casually batting around pitches can be a source of systemic risk.

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