Vanguard is losing its crown as the king of low-cost index investing. Fidelity recently launched two index mutual funds with zero expense ratios, undercutting fees on even the cheapest Vanguard mutual fund: the Vanguard 500 Index Fund Admiral Shares, with an expense ratio of 0.04%.

Another battle is taking shape over investment minimums, and Vanguard is losing on that front, too. Fidelity now offers 18 index mutual funds with zero minimum investments, and they all have lower expense ratios than nearly identical Vanguard funds, many of which have $10,000 minimums.