NEW YORK ( TheStreet) -- Wary of falling stock prices, investors have been fleeing to bond funds.Among the popular choices are two solid index funds, Fidelity Spartan U.S. Bond Index ( FBIDX) and Vanguard Total Bond Market Index ( VBTLX). Both track the Barclays Capital U.S. Aggregate bond index, and they have outperformed most competing intermediate-term funds during the past decade. But Robert Arnott, chairman of Research Affiliates, is not impressed with such popular index funds. Like most market benchmarks, the Barclays index is capitalization-weighted, he says. Under that system, bond issuers are weighted according to their total debt. So a struggling borrower with huge amounts of debt will have a bigger weighting than a competitor with little debt and a pristine balance sheet. That is no way to run a bond fund, says Arnott. "A cap-weighted index rewards bad behavior," he says. Arnott has a point. The Barclays index aims to represent the broad U.S. investment-grade market. Because it emphasizes the largest borrowers, the benchmark's heaviest weighting is connected to the biggest debtor of all: Uncle Sam. About 70% of assets in the index are Treasuries and mortgage-related securities that have high ratings because of government backing. The recipe protected investors during the market turmoil of 2008. But now that Standard & Poor's has downgraded the U.S. credit rating, Treasuries could sink, and the Barclays index could take a hit. >> Get your mutual fund news on the go with TheStreet's iPad app. To give investors choices that avoid the problems of cap-weighting, Arnott is developing funds that follow fundamental indices. These give more weight to companies with greater assets and other indicators of performance. "The idea is to weight bonds in proportion to the borrower's capacity to service debt," he says. Arnott's first offering is an exchange-traded fund, the PowerShares Fundamental High Yield Corporate Bond ( PHB), which invests in bonds that are rated below investment grade. The fund weights bond issuers according to a variety of factors, including total sales, profits and stock dividends. Under the fundamental system, companies that have more sales and profits would have heavier weightings than issuers with small sales and scant profits. Arnott argues that his fundamental approach gives more emphasis to higher-quality companies. Over time, that should enable the fund to suffer from fewer defaults and outdo cap-weighted high-yield competitors.