Science and physics
Leverage
A lever trades distance for force; financial and personal leverage do the same, and every kind multiplies losses as faithfully as gains.
Archimedes, On the Equilibrium of Planes (third century BC); the financial sense came much later.
Archimedes stated the law of the lever in On the Equilibrium of Planes: magnitudes balance at distances from the fulcrum inversely proportional to their weights. The boast that Pappus preserved from him, give me a place to stand and I will move the earth, follows directly. Put the load 0.2 metres from the fulcrum and your hands 2 metres from it and the mechanical advantage is 2 divided by 0.2, which is 10: a 50 kilogram push holds up 500 kilograms. Nothing is free. Your end moves 10 times as far as the load, so the work, force times distance, is the same on both sides. A lever lets a small input applied over a long stroke produce a large output over a short one.
Financial leverage is the same trade with borrowed money as the long arm. Put up $10,000 of your own, borrow $90,000 and buy a $100,000 asset: that is 10x leverage. A 10 percent rise makes the asset worth $110,000, you still owe $90,000, and your $10,000 has become $20,000, a 100 percent gain. A 10 percent fall leaves $90,000, exactly the debt, and your equity is zero. The Financial Crisis Inquiry Commission found that in 2007 the five largest US investment banks ran leverage as high as 40 to 1, so a fall in asset values of less than 3 percent could wipe one out (1 divided by 40 is 2.5 percent). In work, a 'high-leverage activity' has the same shape: a review checklist, a shared library or a well-placed automation where an hour of input moves many hours of output.
The caution is in the arithmetic: leverage amplifies whichever way the asset moves, and the lever does not know which way you wanted. A long arm that lifts a great weight also turns a small slip at the handle into a large motion at the load. High-leverage work cuts both ways too: a bad shared library or a wrong platform default is multiplied across every user, which is why such things deserve a margin of safety and slow, reversible changes. Borrowed money adds an asymmetry the mechanical lever lacks: the lender can demand it back at the worst moment, which is what happened to the banks that could not renew their overnight funding in 2008.
Example
The Financial Crisis Inquiry Commission's report of January 2011 found that, as of 2007, the five major US investment banks (Bear Stearns, Goldman Sachs, Lehman Brothers, Merrill Lynch and Morgan Stanley) were operating with leverage ratios as high as 40 to 1: for every $40 in assets there was $1 of capital to cover losses, so a drop of less than 3 percent in asset values could wipe out a firm. Much of the borrowing was overnight and had to be renewed every day. At the end of 2007 Bear Stearns had $11.8 billion in equity and $383.6 billion in liabilities, and was borrowing as much as $70 billion a night; the Commission likened it to a small business with $50,000 in equity borrowing $1.6 million, with $296,750 of it due each day.
Where it applies
Before taking on leverage of any kind (margin, a large dependency, a central shared service), compute the move that wipes you out: 1 divided by the leverage ratio. In engineering, find the places where one change multiplies, such as a linter rule, a base image or a prompt template every agent inherits, and treat edits there as high-stakes with a margin of safety around them.
Think about it
Where in your life or codebase is a small input multiplied many times over, and have you checked what a small mistake there would cost?
Applied it to something real? Log it.
Test yourselfWith 10x leverage, what happens to your equity on a 10 percent fall in the asset, and why?
It goes to zero. $10,000 of equity plus $90,000 borrowed buys $100,000; a 10 percent fall leaves $90,000, exactly the debt. Leverage multiplies losses the same way it multiplies gains.
Related models
- Margin of safetyLeave a wide gap between what you expect to need and what you build or pay, so that your errors and bad luck do not sink you.
- Asymmetric betsTake bets where the most you can lose is small and known and the most you can win is large, even if you expect to lose most of them.
- Bottlenecks and the theory of constraintsA system's throughput is set by one constraint; improving anything else is wasted effort until that constraint is fixed.
- CompoundingReturns earned on past returns: a steady rate applied to a growing base turns small repeated gains into large ones, mostly at the end.
Sources and further reading
- Chris Rorres (New York University), Archimedes: The Law of the Lever (On the Equilibrium of Planes, Propositions 6 and 7)
- Chris Rorres (New York University), Archimedes: The Lever, introduction (Pappus of Alexandria, Collection, Book VIII)
- Financial Crisis Inquiry Commission, Conclusions of the Financial Crisis Inquiry Commission (January 2011), pages xix to xx