As Robert Arnott was deciding whether to launch his own investment firm, he met with his hero, John Bogle, for dinner. At a steakhouse in downtown Philadelphia in 2001, the founder of indexing powerhouse Vanguard Group spoke with enthusiasm about running his own firm. Bogle, who’s now 82, told Arnott that starting a company could be rewarding once your investing ideas catch fire.

Arnott, 56, says Bogle inspired him to set up Research Affiliates less than a year after that dinner. Arnott then went on to shake the foundation on which the older man built Vanguard: indexing that allocates equities based on market capitalization.

Arnott debuted in 2005 a new type of indexing that uses fundamental measures such as cash flow to pick stocks — a methodology that the father of indexing would later denounce as “witchcraft” in an interview with Morningstar because of its similarity to active management and higher costs. By 2011, the innovator’s brand of stock indexing had produced better returns than Bogle’s.

The PowerShares FTSE RAFI US 1000 Portfolio ETF, which is based on Arnott’s methodology, advanced at an average annual rate of 5.3 percent from its inception on Dec. 19, 2005, through May 9. That beats the flagship Vanguard 500 Index Fund’s 3.2 percent return, according to data compiled by Bloomberg. Armed with those results, Arnott is now planning to stir up the world of bond funds.

As the United States and Europe struggle with record deficits, the money manager is building a new set of bond indexes that shun the world’s most indebted nations and favor developing economies with smaller obligations.

“Fundamental indexing in bonds may very well be bigger than in stocks,” Arnott says. “We’re looking now at how a debt burden affects gross domestic product and capital markets, and it paints a pretty scary picture.”

Economists and money managers — including Clifford Asness, founder of AQR Capital Management, the $38.8 billion hedge fund — have derided Arnott’s indexes.

“Rob’s a good guy. He’s very smart,” says Bogle, who retired as Vanguard’s chairman and chief executive in 1996. “He has beaten the market over the past five years, but one might want to think about what goes into that: risk.”

Eugene Fama, a professor of finance at the University of Chicago’s Booth School of Business who helped develop the efficient market hypothesis, said Arnott’s indexes represent a triumph of marketing rather than an innovation in investing.

In a 2007 interview in the Journal of Indexes, Fama said they simply capture the “value effect” by using measures such as cash flow to select cheaper equities, not unlike what stock pickers do. In an e-mail in April, Fama said of Arnott’s work, “My view hasn’t changed.”

In his office in Newport Beach, Calif., where he keeps a first edition of Adam Smith’s “The Wealth of Nations,” from 1776, Arnott says he enjoys dueling with adversaries.

“I thrive on the controversy,” he says, smiling behind his neatly trimmed goatee. “Intellectual sparring is wonderful fun.”

So is riding motorcycles on California’s coastal highway. Arnott keeps a collection of 20 rare and exotic motorcycles on hoists in his garage. He says his British Vincent Black Shadow was the fastest production motorcycle of its era in the 1940s. His Italian Morbidelli 850 V-8 is one of four prototypes produced for what would have been the world’s most expensive motorcycle.

Arnott started riding motorcycles after high school in Claremont, Calif., when he couldn’t afford a car. Today, he confesses to sometimes exceeding 100 miles an hour on long road trips in Southern California.

“He pushes the envelope a little bit, although no wipeouts,” says Bradford Cornell, a visiting professor at the California Institute of Technology in Pasadena who’s taken excursions with Arnott. “He’s good at it. He brings to motorcycles the same sort of competitive verve he brings to investing.”

Arnott has some of the biggest names in money management on his side in the debate over fundamental indexing. Bill Gross and Mohamed El-Erian, the co-chief investment officers of Pacific Investment Management, are so enamored with Arnott that he’s the only outside fund manager they use.

In 2001, Arnott gave a speech that grabbed the attention of Pimco and produced the most important break of his career. Arnott compared the magic of compound interest to Jesus finding a $1 gold coin on a sidewalk, says John Brynjolfsson, a former Pimco manager who heard the speech. At 5 percent annual interest and over 2,000 years, the gold coin would have grown to the size of Mars’s orbit around the sun, Arnott told the audience.

In 2002, Pimco, whose headquarters is about 2 1 / 2 blocks from Arnott’s office, hired Research Affiliates to start and manage its asset allocation funds.

Pimco is also one of more than 20 firms, including San Francisco-based Charles Schwab, that pay Research Affiliates a licensing fee to use its fundamental indexes. These firms apply Arnott’s strategy to funds with more than $54 billion in assets.

El-Erian says the criticism of Arnott — that he practices active management in the guise of indexing — is beside the point.

“The key issue is, rather than be benchmark-centric, any investment manager should be assessed using three criteria,” says El- Erian, 52. “How have they performed in an absolute sense? How have they done relative to peers? And how have they performed relative to an index?”

By these measures, Arnott is succeeding, with his funds doing well for investors and beating benchmarks, El-Erian says.

Arnott’s next undertaking — fundamental indexes for bonds — is in line with Pimco’s outlook of a prolonged period of subdued returns in developed nations because of record levels of debt. Arnott maintained that view as stimulus measures by the Federal Reserve helped U.S. stocks almost double through early May from a March 2009 low.

To design his new bond indexes, Arnott is collecting and testing data using computer models, going back as far as five decades for the United States and about a quarter of a century for 40 other countries. His aim is to map the relationships between capital market returns and what he calls the “3 D’s”: deficits, debt and demographics.

Arnott says nations with higher levels of debt and aging populations, such as the United States and Japan, will produce lower returns than countries such as China, where debt and deficits are under control.

“The only growth we’ve had in the last decade in the U.S. is deficit spending,” Arnott says, “which is unsustainable as a source of prosperity.”

The full version of this story appears in the July edition of Bloomberg Markets magazine.