Gerry O’Reilly wasn’t fazed by Brexit.

On the Friday morning after the U.K. voted to leave the European Union, the manager of the world’s biggest mutual fund was on the trading floor in Malvern, Pa., watching numbers flickering on the four screens in front of him. Stocks were down 8 percent in Europe and 3 percent in the U.S. O’Reilly didn’t appear stressed. “For what we do, it’s not a huge deal,” he says.

That’s because O’Reilly’s job at Vanguard Group is to embrace the market, not avoid volatility. Every trading day, he makes sure the $450 billion Vanguard Total Stock Market Index Fund matches the performance of its 3,600-stock benchmark. That means owning stocks whether they’re plunging, surging, or unchanged.

O’Reilly manages a lot of money. In addition to running the biggest mutual fund, he oversees the third-largest exchange-traded fund and 16 other funds. Total assets for which he’s responsible: $800 billion.

Investors, driven by evidence that even the best active managers have trouble beating the market, have flocked to index funds like O’Reilly’s. As a result, Vanguard, the index investing pioneer, is now the world’s largest mutual fund manager, with more than $3 trillion in assets. Index funds are often called “passive investments,” yet there’s nothing particularly passive about what O’Reilly and his Vanguard colleagues do all day.

Joe Brennan, the head of the firm’s equity index group, likens managing an index fund to a game of darts -- one in which both the player and the target are constantly moving. Money rolls into Vanguard’s funds almost every day, and that cash has to be put to work. The funds must match hundreds of small shifts in their underlying indexes, caused by corporate actions such as acquisitions and share issuances. “We have to deliver perfection every day,” Brennan says. “Sometimes you have to deliver perfection-plus.”

In theory, the best an index fund can do is the return of the benchmark minus the fund’s fees. In reality, a fund faces additional costs from trading and transactions that can widen the gap between the returns of a fund and those of its benchmark. Success or failure is measured in tiny increments. “A basis point to us is a huge deal,” O’Reilly says.

The best index fund managers find small ways to wring out additional gains while tracking a benchmark. For the past five years, the Vanguard Total Stock Market fund has lagged its index by an annual average of only 1 basis point, or 0.01 percent, even as it charges an expense ratio of 0.04 percent in its institutional share class.

How does the fund pick up the extra return? It makes some money by lending shares to short sellers. Last year it made about $95 million, or 2 basis points, from that. The rest comes from smart trading.

Vanguard’s traders continually walk a tightrope. On the one hand, they want to match their indexes as closely as possible. On the other, they want to buy and sell at the best prices while not letting other market participants take advantage of their need to stay fully invested. And even as it tries to be smart about where and when it trades, Vanguard’s equity team doesn’t want to get too smart. “We don’t want to take arbitrary risk,” says Ryan Ludt, co-head of U.S. equity trading. “My job is not to try to time the market to outperform.”

Vanguard has invested heavily in technology. Algorithms help managers figure out where to buy and sell while minimizing market impact. Risk software makes sure the portfolio stays close to the index. Because of these technologies, Brennan says, “we probably have the most assets per head of any asset manager in the world.” (The key determinant of staffing, he says, is the number of portfolios, not the assets in them.)

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