Borrowed Water - leverage, margin calls and the growth-optimal bet

A bucket of your own water plus buckets borrowed against it, and the long-run growth curve that rises with the borrowing and then falls. This lesson is why it falls, and what the lender does on the way down.

Education, not financial advice.

Before you start. From A Day That Should Never Have Happened - volatility, the bell curve and fat tails: volatility is how widely returns swing. From Compound Interest, the 8th Wonder: a wild run of returns grows slower than its average suggests, because a 50% fall needs a 100% rise to recover; the shortfall is about half the volatility squared each year (volatility drag). From One Cloud Over Every River - diversification, correlation and Markowitz: a portfolio of many bets swings less than one, unless they all move together.

The idea in 30 seconds

Leverage is controlling more than you own by borrowing; it multiplies every move in the price, up and down, and at L times a fall of 1/L wipes you out.
A margin call is the lender demanding more collateral; with none to give, you sell at the low and the loss becomes permanent even if the price recovers.
Forced sales push prices down and trigger the next borrower’s margin call, which is how one fund’s losses become a Friday of block sales.
Leverage multiplies the average return by L but the volatility drag by L², so long-run growth rises, peaks and then falls.
The peak is the growth-optimal (Kelly) leverage, average return over volatility squared: 1.75 times for 7% and 20%. Nobody knows the inputs, so overbetting is the common mistake.

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