Robin Powell
By Robin Powell on September 08, 2022

Simple arithmetic that explains the superiority of indexing

As debates go, this one’s always hot, hot, hot: comparing the investment philosophies of active and passive investment management.


More has been written on the active versus passive debate than probably any other issue facing investors. Every day, people come up with different theories as to why one is better than the other.

In fact, the case for investing passively is, ultimately, nothing to do with theory at all. Jack Bogle, the founder of Vanguard and one of the most famous champions of index investing, summed it up as follows:

The index fund relies on a simple arithmetic, a mathematical tautology that could be calculated by a second grader: gross return in the stock market, minus the frictional costs of investing, equals the net return that is shared by all investors as a group.”

That same arithmetic is explained by the Nobel Prize-winning economist William Sharpe (1) in his 1991 paper, The Arithmetic of Active Management. (2) It’s very short and well worth reading, but here, in a nutshell, is what it says:

  1. The investing community is divided into active and passive investors.
  2. Before costs, the return on the average actively managed pound/ euro/ dollar will equal the return on the average passively managed dollar.
  3. After costs, the return on the average actively managed pound/ euro/ dollar will be less than the return on the average passively managed dollar.

Therefore, the average active investor must — no ifs or maybes, must — underperform the average passive investor.

To quote Professor Sharpe: “These assertions will hold for any time period. Moreover, they depend only on the laws of addition, subtraction, multiplication and division. Nothing else is required.”

The investing industry is essentially an intermediator. Fund managers, stockbrokers, consultants and so on all need to pay for the service they provide. Financial mediation is extremely lucrative, yet the industry is clever at disguising the fees and charges investors pay. These costs include not just the annual management charge, but platform charges, for example, custody and administration costs, and the fees entailed with buying and selling stocks. Often the total amount you end up paying is two or three times the figure advertised. 

Few people, even investment professionals, fully appreciate the huge long-term impact of compounded costs on investment returns. But, in the UK, the effect of costs can typically reduce your potential returns by two-thirds.

The reason why investors find this basic arithmetic so hard to grasp is that it seems counter-intuitive. We’re so used to the idea that the more you pay for a particular product or service, the better it is. But with investing, it’s the other way round. The more you pay to invest, the smaller your net returns will be.

The industry doesn’t like to talk about cost, preferring instead to emphasise fund manager “skill”. But, over the long term, the vast majority of fund managers are unable to provide consistent outperformance net of the fees they charge. Time and again, research has shown that the costs are the most reliable predictor of future returns. (3)

Of course, you cannot eradicate costs altogether. There are still fees to pay to invest in index funds, albeit very much smaller than the costs entailed in active investing. Also, for the vast majority of people, it’s well worth paying for a good financial adviser.

But costs are the one thing that you as an investor can control. Keep them to a minimum and you’ll end up with bigger returns than the vast majority of your peers. It’s simple arithmetic.

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Robin Powell is a journalist, author and editor of The Evidence-Based Investor.




Published by Robin Powell September 8, 2022
Robin Powell