[...] Ellis observes, the true cost is even higher. Because indexing consistently delivers the market return at no more than the market level of risk," he writes, "the informed realist's definition of the fee for active management is the incremental fee as a percentage of incremental returns after adjusting for risk. Suppose a fund produces a net annual return that is 0.5 percent higher than the return of its benchmark index. The reality here is that when we poor sheep buy a managed fund, we're buying an investment lottery ticket. [...] your lottery ticket has what statistical types call an "intrinsic value" of 50 cents. With a 33 percent chance of adding 0.95 percent to what your money would earn in an index fund, the intrinsic value of your "ticket" is 0.32 percent, annualized (.33 times .95). [...] your management lottery ticket will cost 1.03 percent more than a low-cost exchange-traded index fund. The expense ratio average for this group of managed funds is 1.07 percent, and a low-cost exchange-traded index fund costs 0.04 percent.