When markets break

On October 19, 1987, the Dow fell twenty-two point six percent in a single day. Under the bell curve that finance had adopted as its model of prices, a move of that size should not happen once in the life of the universe. It happened on a Monday. It has happened, in one form or another, in 1998, in 2008, in March 2020, and in September 2022, and it will happen again.

The three papers in this chapter explain why. The first says that extreme moves are ordinary, and that the model saying otherwise was wrong from the start. The second says that patience is paid, and explains who gets paid for holding what nobody can sell quickly. The third puts the two together and describes the machine that turns a bad month into ruin for anyone who borrowed to invest. I have watched that machine from close by, and the chapter is mostly about staying out of it.

Mandelbrot, 1963

Benoit Mandelbrot was a mathematician at IBM when he took a century of cotton prices and looked at how they moved. What he found was a problem for everyone. The daily changes had far too many extreme days for a bell curve. Moves that the curve called impossible showed up every few years. And the big moves came in clusters. His sentence for it is the most quoted in the paper: large changes tend to be followed by large changes, of either sign.

He proposed a different distribution, one with such fat tails that the usual measure of risk did not even exist. That part of the paper overshot, and the profession later settled on tails that are fat but finite. The destructive half was simply right, and it arrived at the worst possible moment. Finance was about to build its whole edifice on the bell curve. The capital asset pricing model, the option pricing formula, the risk systems that banks use to this day all assume that prices move the way Mandelbrot had just shown they do not. The profession chose the tractable model over the true one, and paid for it roughly once a decade.

In August 2007 the finance chief of a large investment bank explained a bad week by saying its funds had seen moves of twenty-five standard deviations several days in a row. Under the bell curve one such day is not expected in the age of the universe. Several in a row means the model was wrong, and everyone in the room knew it.

The practical rule is short. Any risk model, simulation or borrowing limit you use has to run on fat tails and clustered volatility. The test I apply is to ask the model how often it expects a twenty percent fall in a month, and compare the answer with history. If the model says what already happened several times was nearly impossible, the model is wrong, and I stop using it. The losses that actually end investors live in the region the bell curve declares impossible.

Amihud and Mendelson, 1986

Yakov Amihud and Haim Mendelson asked a question that sounds small. Does it matter, for the return an asset earns, that it is expensive to trade. Their measure of that cost was the bid-ask spread, the gap between what you can sell for and what you have to pay. Their answer changed how institutions build portfolios.

The logic is a page long. Investors care about returns after trading costs. So an asset that costs more to trade must offer a higher return before costs, or nobody would hold it. Then the twist. The cost of trading is paid once, per trade, and an investor who holds for ten years spreads it over ten years. Patient investors therefore find illiquid assets cheap in a way that impatient investors do not, and in equilibrium the patient end up holding them and collecting a premium that the impatient are not able to collect. The relation is concave: it rises fast at first, then flattens. On the New York Stock Exchange from 1961 to 1980, a stock with a spread of one and a half percent earned nearly half a percent a month more than one with a spread of half a percent. Going from a four percent spread to five percent added only nine hundredths.

This paper is the charter of every institution that holds illiquid assets on purpose. The argument for a family with a long horizon is the same one. Impatient money underprices what it cannot sell quickly, and the family that will never need to sell can be paid for owning it.

The fine print matters more than the charter. The premium exists only if it was priced in when you bought, and you check that with the entry yield, never with the label on the asset class. The holding horizon has to be longer than the lockup, measured with the bad years included. And the position has to sit outside every path by which you might be forced to sell. Much of the money that went into private assets over the last twenty years was paid nothing for its patience, because too much money arrived at once and competed the premium away. Illiquidity is compensation for a flexibility you give up. When the compensation is missing, you have given the flexibility away for free.

Brunnermeier and Pedersen, 2009

Markus Brunnermeier and Lasse Pedersen wrote the model of how a market breaks, and the year it was published performed the model in public.

There are two kinds of liquidity. Market liquidity is how easily you can sell an asset. Funding liquidity is how easily you can finance a position: what a lender will advance against it, and on what terms. The paper shows that the two feed each other. Prices fall. Volatility rises. Lenders read the volatility as risk and cut what they will advance. Borrowers must post more collateral or sell. They sell, prices fall further, volatility rises further, and the lenders cut again. The paper calls it a margin spiral. Its worst feature is that margins tighten exactly when financing is most needed, because the same event that produces losses produces the volatility that lenders fear.

Three predictions follow, and all three have been confirmed repeatedly since. Liquidity is fragile: a small shock can dry it up. Liquidity is common: when it goes, it goes in everything at once, and assets that never moved together start to. And money runs to the safest paper and abandons the rest. In the spiral, diversification across assets protects you very little, because the funding of all of them is one channel, and that is the channel that closed.

The cleanest example I know is Britain in September 2022. On September 23 the government announced a budget the market disliked. Over the next three days the yield on thirty-year government bonds rose by one hundred and forty basis points, a move without precedent. British pension funds held those bonds with leverage, through strategies built to match their long liabilities, and the fall in bond prices triggered collateral calls. To meet the calls they sold bonds. The sales pushed prices lower and produced more calls. On September 28 the Bank of England stepped in and bought bonds until the middle of October, to stop the spiral. The pension funds owned the safest asset in the country and nearly went under holding it. The bonds were fine and paid every coupon. What broke was the borrowing behind them: the lenders asked for more collateral in three days than the funds could raise.

That is the lesson for anyone who borrows against a portfolio. The risk of leverage is the stability of its terms under stress, much more than the level of the debt. A loan whose advance rate moves with volatility turns a drawdown into a forced sale. The plan for a crisis is made before it, in the size of the borrowing, the headroom on every covenant, and the reserve that is pledged to no one.

What I do

Every simulation I run on the family’s money uses fat tails, and I check it against the frequency of real crashes before I trust it. Illiquid assets, the land, the buildings, the private funds, are sized so that no scenario I can imagine makes me sell them. I borrow against the portfolio, and I keep the loan small. Small means this: I assume that prices fall hard, that the bank lends me less against what is left, and that both happen on the same day. The loan has to survive that day without my selling anything. And I keep a reserve of cash that no bank has a claim on. It is outside the portfolio, and I do not count it when I look at returns.

I keep a list. Every position that is levered or cannot be sold quickly, the terms it is financed on, what the lender can change without asking me, and the cash it could demand in a bad month. I add up the worst case and compare it with the unpledged reserve. If the first number is bigger than the second, I know that in a bad month I will be selling at the bottom, and I cut the loan until that is no longer true.

Three habits

Check every risk model against the crashes that already happened. Ask it how often it expects a twenty percent fall in a month. If the answer is once in a thousand years, and you can count several in your own lifetime, stop using that model.

Before buying anything you cannot sell quickly, check three things. First, that you are being paid for the wait: the return has to be visibly higher than what a liquid asset of the same risk pays, on the day you buy. Second, that you can afford to wait for as long as the asset can keep you locked in, and then a few bad years more. Third, that no debt, no spending need and no other position could ever force you to sell it early. If any of the three fails, you are giving away your freedom to sell and getting nothing for it.

Keep the spiral ledger. Levered and illiquid positions, financing terms, what the lender can change alone, the cash each could demand in a crisis month, against the reserve pledged to no one. Update it every quarter. The ratio should never reach one.

Gala: markets break, and they break in everything at once. Borrow so that no one can force you to sell on the worst day, and hold what cannot be sold only with money you will never need. Then the crash is a sale, and you are the buyer.