The book describes Bouchaud tail-chiseling approach as portfolio construction focused on minimizing joint severe losses for a target return rather than relying only on ordinary covariance.

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Jean-Philippe Bouchot and some colleagues at Capital Fund Management were running two hedge funds with combined capital of $725 million as of the end of 2003. The funds engage in statistical arbitrage. They use mathematical models and computer horsepower to find what they think is incorrect pricing in the market, or other unstable patterns on which they can bet. The individual bets are small, but it is, for them, a game of large numbers Many small profits can mount In 2002, their biggest fund, Ventus reported a stock market gain of 28.1%, this in a year when the market overall had fallen by a third. But it is also a game of chance. In 2003, they were less lucky with gains of just 3.32%. Their other fund, Discus, in the futures market, reported a 14.1% profit that year. With statistical arbitrage, there are ups and downs. Bouchot says with a shrug. Their strategy is part multifractal, part many other things.

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Good diversification would mean some stocks zig when others zag. But Bouchot's method takes it as given that prices exhibit long-term dependence, have fat tails, and scale by a power law. He focuses then only on the odds for a crash, sharp, catastrophic price drops. After all, it is not small declines that wipe an investor out. It is the crashes. So their scaling formula minimizes the odds of too many of the assets in a portfolio crashing at the same time. They use that to draw a generalized efficiency frontier analogous to Markowitz's original portfolio technique to help pick a portfolio that maximizes returns for a given amount of crash protection. As the paper put it, the frequency of very large, unpleasant losses is minimized for a certain level of return. Thus, it is not just the stock picking that is important, but also the risk protection. For the latter, Usho says, Multifractal thinking is most useful. Fractals in finance have followed a winding path.