Index funds vs active funds: cost and odds

Start with an accounting identity rather than an argument about talent.

Every share of every company is held by somebody. Split the owners into two groups: those holding the whole market in the market's own proportions, and everybody else. The first group earns the market return by construction. Since the two groups together own the market, the second group has to earn the market return too, in aggregate, weighted by the money each participant runs. That holds before costs, in every period, whatever anyone's skill.

Costs then settle the rest. The indexed group pays a small fee and trades rarely. The active group pays research salaries, higher fees and the cost of its own trading. So the active group, weighted by the money each part of it runs, earns the market return minus the larger deduction, and the size of the shortfall is the size of the cost difference. William Sharpe set this out in 1991 in a short paper called The Arithmetic of Active Management. It is arithmetic rather than evidence, so it does not rest on any study, and it holds in rising markets and falling ones.

Three caveats sit alongside it. It constrains the group and says nothing about any individual fund, because inside the active pool one manager's gain is another's loss and winners therefore have to exist. That pool is not only active funds: it also holds pension plans, hedge funds, company treasuries and individuals, so active funds as a class could in principle take from the less skilled parts of it. And the identity is exact only on its own definitions. It wants a passive group holding the whole market in market weights, while real index funds track a slice of it, and the market itself keeps changing as companies list, buy back stock and drop out of indices, which forces even a rule-following holder to trade. Lasse Pedersen set out that objection in a paper called Sharpening the Arithmetic of Active Management. It moves the size of the deduction rather than its direction: the cost gap still has to come out of somebody's return.

A fund's future return is not knowable in advance. Its fee is printed on the page, which is why cost does most of the work in this comparison.

The published number is called the expense ratio in the United States, and the ongoing charges figure or the management expense ratio in other markets. Whatever the label, it is taken as a percentage of assets every year, whether the fund gains or loses. Broad index funds sit at the bottom of the range and active equity funds well above it. Fees on both sides have been falling for years, so treat any particular figure as a snapshot and read the fund's own document rather than a number you remember.

Turnover is the second cost and it sits outside that number, for trackers as much as for stock pickers. Turnover measures how much of the portfolio is bought and sold in a year, and a figure near 100 percent roughly implies an average holding period of about a year. An index fund trades when the index changes and when money moves in or out. A manager with views trades on them, and every trade pays a bid-ask spread and pushes the price a little the wrong way. Those costs come out of the return without ever appearing as a fee.

Turnover has a third effect in a taxable account, and this part is country-specific. In the United States a fund keeps its pass-through tax treatment by distributing its realised net capital gains each year, so a high-turnover fund can hand you a bill in a year you sold nothing. Inside a tax-deferred account that particular problem disappears. Other countries tax funds and their holders on quite different rules, so read the ones that apply to you before carrying this paragraph across a border.

S&P Dow Jones Indices publishes a scorecard comparing active funds against the benchmarks they are measured on. It runs in a number of countries, and the shape is much the same in each, though the American series is the long one and the others are younger. Over one year results scatter and plenty of managers finish ahead. As the window stretches to ten or fifteen years, the share of active funds beating their benchmark falls a long way below half in most categories.

Two adjustments push the picture down rather than up. Funds that do badly get closed or merged, so an average taken across the funds still trading flatters the group, and the honest count includes the ones that vanished. Separately, a fund's shareholders often do worse than the fund itself, because money tends to arrive after the good years and leave after the bad ones.

Persistence is the sharper test, and the one that matters if you intend to pick. Take the funds in the top quarter of one period and ask how many stay there through the next few. The answer, repeatedly, is close to what a coin would give you. Mark Carhart's 1997 study of mutual fund performance found that most of the persistence anyone could see was explained by expenses and by momentum in the underlying stocks rather than by durable skill.

None of that says skill does not exist. It says the spread between good and bad managers is wide, the signal in a past ranking is faint, and cost predicts relative finishing position better than past performance does.

The case for indexing is strongest where costs are lowest and the market is most picked over, which is large-company stocks in developed markets. It softens elsewhere, and a fair comparison says where.

Manager dispersion varies by category. In corners with thinner analyst coverage, less liquidity or awkward benchmarks, the distance between the best and worst managers widens, which gives skill more room to show up and equally more room to do damage. The scorecards still show most funds trailing in many of those categories, so wide dispersion is an opportunity rather than a result.

Some mandates have no sensible index at all, and some investors want a constraint an index cannot express, such as a screen, a risk target or a tax-management overlay. That is a question about what you want owned, not about whether anyone can outguess the market.

Index funds carry their own trade-offs, and saying so is part of being fair. You take the whole of the downside, in full and on schedule, every time. A market-capitalisation weighted index puts the most money into whatever has already grown largest, so concentration arrives quietly. And the word index says nothing about breadth: a one-country or one-industry index fund is exactly as narrow as the index it copies, which is why the index rather than the wrapper is what does your diversification.

One thing travels across all of it. Cost compounds, though how much depends on when the money went in. On a sum left in place for thirty years, a fund netting 7 percent a year finishes about a third ahead of one netting 6 percent. Pay the same money in monthly across those same thirty years instead and the gap is nearer a fifth, because the later deposits are only charged for a few years each. The compound interest calculator will show either shape for any pair of rates, and the guide to index funds and active management works the fee arithmetic through in full.