Index Funds and the Arithmetic of Costs

Once you know your mix, you have to fill it with something. The choice most people face is between funds run by managers who try to beat the market and index funds that simply own it. It sounds like settling for average. The evidence says the opposite: after costs, owning the whole market has beaten most professionals who try to outguess it, and the reason is arithmetic rather than luck. This chapter explains that arithmetic, what it costs to ignore it, and what an index fund cannot do for you.

The arithmetic that makes indexing work

In 1991 the economist William Sharpe set out an argument short enough to fit on a page. Split everyone who owns US stocks into two groups. Passive investors hold every stock in proportion to its size, so before costs they earn exactly the market's return. Active investors hold whatever is left over, and since the two groups together own the whole market, active investors as a group must also earn the market's return before costs.

Now subtract costs. Passive investors pay very little. Active investors pay more: higher fund fees, the cost of trading, and often more tax from realising gains. So, as a group and after costs, active money must trail passive money. Sharpe's conclusion was that this follows from the definitions and holds in every period, not just on average.

The argument does not say every active fund loses. Some beat the market in any year. It says the average active dollar must lag, and that the size of the lag is about the size of the extra costs.

Can you find the winners in advance?

The obvious reply is to pick the active funds that will be above average. Two lines of evidence make that hard.

Most funds trail their benchmark over long periods. S&P Dow Jones Indices publishes its SPIVA scorecards twice a year, comparing actively managed funds with the indexes they compete against. Edition after edition, a large majority of US stock funds have trailed their benchmark over 10 and 15 year periods, and funds that close or merge, often after poor results, are counted rather than quietly dropped.

Past winners rarely stay winners. Mark Carhart's 1997 study of mutual funds found that most of the persistence in fund returns was explained by their costs and by the kinds of stocks they held, not by managers' skill; the clearest persistence was among the worst funds, which tended to stay bad. S&P's own persistence reports find that few top-ranked funds remain in the top group a few years later.

None of this proves no manager has skill. It says skill is rare, hard to identify ahead of time, and usually charged for in full.

What costs do over a lifetime

Fund costs are quoted as a yearly percentage of your balance, the expense ratio, so a difference of under one percentage point looks trivial. It is taken every year from a growing balance, though, and it compounds against you in the same way returns compound for you.

A saver who starts with $10,000 and adds $500 a month for 30 years, earning 7.0% a year before costs, ends near $648,079 in a fund costing 0.1% a year. In a fund costing 1.0%, the same saver ends near $544,691. The difference, $103,387, went to costs and to the growth those costs would have earned. The expensive fund has to beat the market by almost a full percentage point every year, for 30 years, just to break even with the cheap one.

The expense ratio is not the only cost. Funds that trade heavily pay brokerage costs and bid-ask spreads that do not appear in the expense ratio, and in a taxable account their trading can produce taxable distributions, covered in chapter 3.

The cost you add yourself

The largest cost for many investors is not a fee. It is the gap between what their funds earn and what they earn, caused by buying after markets rise and selling after they fall. Ilia Dichev's 2007 study in the American Economic Review compared the returns of the US stock market with the returns investors actually received once the timing of their money flowing in and out was counted, and found investors' returns were consistently lower, by around a percentage point a year or more depending on the market and period.

Saving $500 a month at 7.0% a year grows to about $584,726 in 30 years. Lose two points a year to selling in slumps and buying back after recoveries, and the same savings grow to about $407,688. An index fund removes the manager's costs; it cannot remove yours. Automatic contributions and a written plan do more for this gap than any fund choice.

What an index fund cannot do

It will not protect you from a crash. A fund that owns the market falls with the market, all the way down. The protection comes from your mix of stocks and bonds, not from the fund.

It will not beat the market. It earns the index's return minus a small cost. That is the point, but it means accepting that someone, somewhere, will always have done better this year.

It owns everything in its index. That includes companies you might not choose. Funds that screen out industries exist, usually at somewhat higher cost and with returns that drift from the broad market.

Market-cap weighting concentrates. Most indexes weight each company by its market value, so the largest companies make up a large share of the fund. In recent years a handful of US companies have made up a big slice of the broad indexes. That is a feature of the market itself, but it is worth knowing what you own.

Choosing an index fund

Index funds that track the same broad market are close substitutes, so choosing among them is mostly about cost and fit.

• What it tracks. A total market index owns large, medium and small companies; an index of the largest 500 owns most of the market's value but not all of it. A total international index covers developed and emerging markets outside the US. A total bond index covers investment-grade US bonds. Read the index name and the number of holdings.
• Expense ratio. It is in the fee table at the front of the prospectus and on the fund's page. Broad index funds from large providers often cost a small fraction of a percent a year.
• Tracking difference. Compare the fund's return with its index over several years. A small, steady gap close to the expense ratio is a sign of good management.
• Where you can buy it. In a workplace plan you choose from the menu offered; look for the index options and their costs. In an IRA or brokerage account almost any fund is available.
• Mutual fund or ETF. The same index is often sold in both wrappers. Chapter 3 explains when the difference matters.