🧮 Математика ризику

In 1994, John Meriwether, formerly a legendary bond trader at Salomon Brothers, founded a hedge fund unlike any before: Long-Term Capital Management. On board were finance academics Myron Scholes and Robert Merton — three years later both received the Nobel Prize for their options pricing theory. The strategy sounded elegant and safe: Convergence Trades. They searched for bond spreads that statistically had to converge again and pocketed the gap.

To turn tiny margins into real returns, LTCM needed leverage. And massive leverage at that. At times the fund operated at 30:1 on its own capital, with the notional of open positions at $1.25 trillion — with a "t", larger than Germany's GDP at the time. For four years LTCM delivered over 40% return per year. Wall Street puzzled over how. Banks fought to be counterparty on every trade.

In August 1998, Russia unexpectedly defaulted on its ruble bonds. What was a footnote in the normal distribution models of Scholes and Merton was, in reality, a wildfire. Panicking investors fled to safe assets — all convergence spreads widened simultaneously instead of converging. The leverage that had been a return machine for four years became a wrecking ball. Within a few weeks, LTCM burned through $4.6 billion. The Fed had to organize a consortium of 14 banks, each contributing around $300 million, just to prevent a systemic collapse.

The mathematics behind the trades was brilliant — but it was based on the assumption that returns are normally distributed. Fat Tails didn't fit the model. And anyone leveraged 30:1 has no buffer when the real world refuses to follow the bell curve.

Barings Bank, founded in 1762, had financed the Napoleonic Wars and enabled the Louisiana Purchase for the United States. 233 years old. Then came Nick Leeson. In 1992, the 25-year-old Briton was sent to Singapore to work as a derivatives trader on the SIMEX. Barings made a mistake that every compliance manual lists as a cardinal sin: Leeson was given both trading AND back-office settlement in one hand. Whoever settles their own trades can also make them disappear.

Officially, Leeson was supposed to arbitrage Nikkei futures between Singapore and Osaka — low risk, but little profit. He soon wanted more. He set up account "88888", ostensibly for booking errors by his clerks, and buried growing losses in it. By 1994 it was already $200 million, by early 1995 around $500 million. In London, Leeson was simultaneously regarded as the wonder boy of the Asian derivatives desk.

On 17 January 1995, the ground shook under Kobe. Leeson held gigantic short straddle positions on the Nikkei — i.e., short volatility. The Nikkei crashed 15%, volatility exploded, and margin calls came in series. Instead of closing, Leeson doubled down on the position hoping for a reversal. It never came.

On 26 February 1995, Barings filed for insolvency. Total losses stood at £827 million — more than the bank's entire equity. ING bought Barings for £1. Leeson fled, was arrested in Frankfurt, served four years in a Singapore prison and afterwards wrote a book.

Jesse Livermore was born in 1877 in Massachusetts, started as an office boy at a brokerage firm at age 14, and made his first own trades at 15 in the so-called Bucket Shops — semi-illegal betting parlors on stock prices. He read ticker tapes like others read novels. By age 30 he had $3 million in assets (roughly $100 million today) and a nickname: Boy Plunger.

Then came the moments that made him immortal. In 1907, during the notorious panic, he earned around $3 million with short positions in a single day — J.P. Morgan personally asked him to stop shorting to prevent Wall Street from collapsing further. In 1929, during the greatest crash of all time, Livermore made an estimated $100 million — he was one of the richest men in America. At a time when others were jumping out of office windows.

And yet: bankrupt four times. In 1915, 1922, 1934, 1940. Each time a comeback, each time with a little less discipline. Livermore was the man who popularized the concept of the trailing stop, who was one of the first to calculate position sizing methodically, and who devoted entire chapters of his book Reminiscences of a Stock Operator to waiting. His most famous quote — "I made my money by sitting, not trading" — became the most cited trader aphorism in history after his death.

In 1940 his third marriage failed. He wrote a farewell letter to his wife — "My life has been a failure" — and shot himself in the cloakroom of the Sherry-Netherland Hotel in New York. The man who had written the rules could not follow his own at the end.