INVESTORS collectively spend around $100 billion a year trying to beat the stock market. That’s the finding of a rigorous effort to measure the total costs of Americans’ efforts to surpass the returns they would have received by simply holding a stock index fund. The huge price tag helps explain why beating a buy-and-hold strategy is so difficult.

The study, “The Cost of Active Investing,” began circulating earlier this year as an academic working paper. Its author is Kenneth R. French, a finance professor at Dartmouth; he is known for his collaboration with Eugene F. Fama, a finance professor at the University of Chicago, in creating the Fama-French model that is widely used to calculate risk-adjusted performance.

In his new study, Professor French tried to make his estimate of investment costs as comprehensive as possible. He took into account the fees and expenses of domestic equity mutual funds (both open- and closed-end, including exchange-traded funds), the investment management costs paid by institutions (both public and private), the fees paid to hedge funds, and the transactions costs paid by all traders (including commissions and bid-asked spreads). If a fund or institution was only partly allocated to the domestic equity market, he counted only that portion in computing its investment costs.

Professor French then deducted what domestic equity investors collectively would have paid if they instead had simply bought and held an index fund benchmarked to the overall stock market, like the Vanguard Total Stock Market Index fund, whose retail version currently has an annual expense ratio of 0.15 percent.