Index funds vs active management

An index is a published list of holdings plus a rule for how much of each to hold. A total market index names every listed company above some size and weights each one by its market value, usually counting only the shares that trade freely. An index fund buys that list in those proportions, or a sample built to behave like it, and does nothing else.

Weighting by market value is the part that makes this cheap. If a holding's price doubles, its weight in the index rises, and its weight in the fund rises by exactly the same amount, because the fund already owns the shares. The weight does not double, since the rest of the index is still sitting in the total, but the fund keeps pace without a single trade. Turnover comes only from index changes, corporate actions and investor flows, so the fund pays very little in spreads and price impact. There is no research department to fund and no analysts to pay, which is why the management fee can sit close to zero.

What a tracker is judged on is tracking. Tracking difference is the gap between the fund's return and the index's over a year. It usually sits below the index by something close to the fund's total costs, though revenue from lending out holdings can offset part of that. Tracking error is how much the gap wobbles from year to year. A well run fund has a small, steady difference rather than a lucky one.

Two things the phrase does not tell you. Index describes the strategy, not the wrapper: the same index is sold as a mutual fund and as an exchange traded fund, and some exchange traded funds are actively managed. And a fund is only as diversified as the index behind it. A tracker of one country's twenty largest companies is a concentrated bet with a low fee, which is a different animal from owning the market.

Start with a definition. Passive investors hold every security in the market in proportion to its size. Everyone else is active.

Now add up the market. Every share is held by somebody. If passive investors hold the market in proportion, then what is left over, all the active holdings taken together, is also the market in proportion. Two portfolios holding the same securities in the same weights earn the same return. So before costs, the average actively managed dollar earns exactly the market return, and so does the average passive dollar.

Costs are the whole of the difference. After fees, spreads and taxes, the average active dollar has to trail the market itself by whatever active management costs, and has to trail the average indexed dollar by the difference between the two bills. William Sharpe set this out in 1991, and the argument has no empirical content at all: it is an accounting identity about a set of dollars over one measurement period. It holds in rising markets and falling ones, in efficient markets and mad ones, and it assumes nothing about whether managers have skill.

Two things it does not say. It does not say nobody beats the market. Before costs somebody has to, because the dollars above the average are matched by the dollars below, which makes active management a zero sum game against the market before costs and a negative sum game after them.

And it is a statement about the average dollar, not the average fund. Company returns are heavily skewed: over long periods a small minority of stocks produce most of the market's total gain. A portfolio of a few dozen names therefore lands below the market more often than above it, even when the picks are made at random. The typical active fund does worse than the average active dollar without anybody doing anything wrong.

A fund fee is charged on the balance, not on the gain. It is taken whether the fund made money or lost it, and it is accrued out of the fund's assets daily rather than billed, so it never appears as a line on a statement. That is the first reason it gets ignored.

The second is arithmetic. If the holdings return $g$ a year and the fund charges $f$, the balance compounds at roughly $1 + g - f$ instead of $1 + g$. Roughly, because the fee is levied on assets rather than on the gain, so the exact factor is $(1 + g)(1 - f)$, a shade lower again. After $n$ years the fee paying balance is about this fraction of what it would otherwise have been:

$$\frac{(1 + g - f)^n}{(1 + g)^n} = \left(\frac{1 + g - f}{1 + g}\right)^n$$

That fraction shrinks geometrically, because every dollar the fee removes also stops earning. At a 7 percent gross return credited yearly, on money invested at the start and left there, one percentage point of annual fee costs this much of the ending balance:

Those shares barely move if you change the gross return, but they do depend on the money being there the whole time. Deposits made later have spent fewer years being charged, so a saver paying in monthly loses a smaller share of the ending balance than the table shows. The first two worked examples below are that case.

Notice what the headline number hides. An expense ratio is quoted against assets, but it is paid out of returns: 1 percent of assets against a 7 percent gross return is about a seventh of the first year's gain, and the share of the final balance it consumes rises with every year you stay invested.

The compound interest calculator at the top of this page is the fastest way to feel it. Enter a horizon you care about, then change nothing but the rate, by one point. The mechanism is the one described in how compound interest works, running in reverse. Inflation does the same thing to the same balance, and the real return calculator handles that half.

The expense ratio is the visible part of a bill with several lines.

• The expense ratio covers management, administration and custody. It accrues daily out of the fund's assets, which is why you never receive an invoice for it.
• Trading costs sit outside it. Commissions, the gap between bid and ask, and the price impact of the fund's own orders are paid by the fund and show up only as a lower return. They scale with turnover, so a fund replacing most of its holdings every year pays them again and again while a tracker barely pays them at all.
• Cash drag is the return given up on the cash a fund holds to meet redemptions, which costs it in rising markets and cushions it in falling ones.
• Taxes, in the United States, are a real cost in a taxable account. A fund that realises gains must distribute them, and holders owe tax that year even if they bought nothing and sold nothing, so turnover creates a tax bill on somebody else's schedule. The exchange traded fund wrapper usually softens this, because redemptions can be met in kind rather than by selling. Inside a tax sheltered account the line stops being an annual cost, though a tax deferred account still taxes the money on the way out, which is why the same fund can cost two different amounts depending on whether it sits in a taxable account or a sheltered one. Other countries tax fund income and gains on their own rules, so how big this line gets depends on where you are.
• Platform, adviser and sales charges stack on top of everything above. A cheap fund on an expensive platform is not a cheap arrangement.

Add them up before comparing anything. The figure that decides your outcome is the total charged against your money each year. The stated fees in that total are published in advance, and the trading and tax costs have to be estimated from turnover, but even an estimate of cost stands on firmer ground than a forecast of return.

In every period some funds beat the market. The question a buyer faces is whether this period's winners are next period's winners.

How that gets measured matters. S&P Dow Jones Indices publishes scorecards comparing active funds with the benchmark for their category, and separately tracks what happens to the leaders. Two corrections do most of the work. Survivorship: funds that perform badly get closed or merged away, so a list of funds that exist today flatters the past, and the studies count the departed. Style: a fund has to be measured against the benchmark for what it actually holds, or a small company fund gets credit for being in small companies rather than for choosing well among them.

What those scorecards keep finding is that most active funds in most categories trail their benchmark over ten and fifteen year windows, and that the top quartile in one period scatters close to randomly across the next. Staying top quartile for several periods running is rare, and in the persistence data those scorecards publish it happens no more often than chance would produce.

There is a statistical reason. A manager's edge, if it exists, is small next to the year to year noise in returns, so separating skill from luck takes decades of data. By then the manager has changed, the strategy has drifted, and the fund is far larger, because money arrives after good performance and size tends to work against the strategies that produced it.

Two related traps. A fund that hugs its benchmark while charging an active fee delivers the index minus a lot. And a three year record is close to no evidence, which is awkward, because three years is what most fact sheets lead with. Turning a start and end value into the annual figure a fact sheet quotes is what the CAGR calculator does.

Indexing is a decision about cost and breadth. It is not a decision about risk.

An index fund falls with its index. Owning the whole market removes the risk of picking the wrong company, which is the point of diversification, and leaves systematic risk, the risk of owning companies at all. That second risk is the one investors expect to be paid for over long stretches, which is an expectation rather than a promise for any particular decade, and pricing it is the subject of risk and return.

Which index you buy matters more than the wrapper you buy it in. A market value weighted national index can carry a large share of its value in a handful of firms and one or two sectors, and that concentration shifts over time without anybody deciding it should. An index of a single country is a bet on that country. A world index is a different exposure at a similar fee.

Prices still have to come from somewhere. Active investors do the work of setting them and indexers ride along. That is a question about the market as a whole, not a reason for any one investor to pay for the work.

Active management still has jobs. Narrow and illiquid corners of the market get thinner coverage. Some mandates cannot be indexed. Tax management, such as tax-loss harvesting under United States rules, happens at the level of your own account rather than inside a fund.

Then there is the part no fund controls. A cheap fund sold in a drawdown can easily return less than an expensive one held through it. Cost and staying invested are things you decide, along with how much goes in and what you hold. The market's return is not one of them. This page is educational material about how the arithmetic works, not financial advice about which fund to hold.