What does it mean to beat the market?

Beating the market means earning a higher return than a fair benchmark — usually a broad index — over the same period, after all costs. It sounds simple, but a fair comparison needs care, and most informal claims of beating the market do not survive it. Over long periods, most professional fund managers do not beat their benchmarks after costs.

What a fair comparison requires

The difference between the portfolio's return and the benchmark's is the active return:

\text{Active return} = R_p - R_b

For it to mean anything, the comparison needs:

The right benchmark, matching the portfolio's mix of assets and regions. A portfolio with 30% cash is not measured against a pure stock index, nor a European stock portfolio against the S&P 500.
The same period. Start and end dates matter a lot; choosing them afterwards can produce almost any result.
Returns after all costs, including trading fees and taxes.
The right return measure. The time-weighted return removes the effect of deposits and withdrawals, which the benchmark does not have.
Total return on both sides, with dividends included.

A simple illustration

A portfolio of European and US stocks shows a return of 14% for the year, while the MSCI World returned 12%. On the surface, it beat the market by two points. But the 14% is the portfolio's money-weighted return, flattered by a large deposit made just before a rally. Its time-weighted return — the performance of the holdings themselves — was 11%:

\text{Active return} = 11\% - 12\% = -1\%

Measured properly, the holdings lagged the index by a point.

Luck or skill

Even a correctly measured outperformance can be luck. With a tracking error of around 5% a year, the uncertainty of the average yearly active return after $n$ years is:

\text{Standard error} = \frac{\text{Tracking error}}{\sqrt{n}}

After nine years that is still about 1.7 points: an average outperformance of two points a year is barely distinguishable from chance.

What the evidence shows

Long-running studies such as the SPIVA reports, which compare actively managed funds with their benchmarks, consistently find that a large majority of active funds lag their index over ten years or more, mainly because of their costs.

For private investors, the practical question is often simpler: after all the effort, did the portfolio do better than a single low-cost index fund would have? If not, that index fund is the benchmark worth adopting.

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