Financial MarketsInvestment

Suspending the laws of arithmetic

By June 6, 2016 No Comments

Simple truths are sometimes the most difficult for people to accept.

A recent article in the The Weekend Australian1 sought to take us to the mythical town of Lake Wobegon, where all the women are strong, all the men are good looking, and all the children are above average.

Speaking to the debate between the investment styles of active management (continuously trying to pick stocks and/or time the market), and passive management (buy every stock in proportion to its market capitalisation, then do nothing), James Kirby reported:

The average active fund manager focused on domestic shares returned 5.6 per cent last year, compared with the benchmark index of 2.8 per cent, according to figures compiled by Mercer. This moves out to 11.4 per cent on a three years compared with the benchmark index of 9 per cent.

The Weekend Australian, May 28-29, 2016 – page 28

Conclusions like this can only be justified by assuming that the laws of arithmetic have been suspended for the convenience of those who choose to pursue careers as active managers – and pay for advertising in the newspaper.

It should be self-evident that

  • any share trade requires both a buyer and a seller, and
  • the buyer and seller can’t both be right

Relative to the market, the winner’s gains must always match the other party’s losses.

Therefore, before costs, the return on the average actively managed dollar will equal the market return. Because collectively, they are the market. Outperformance zero.

This isn’t a theory about market efficiency, it’s arithmetic.

Unfortunately for active managers and their investors,  it’s also before costs: management fees, transaction costs, and taxes.

Or as Nobel laureate William Sharpe2 puts it:

Properly measured, the average actively managed dollar must underperform the average passively managed dollar, net of costs. Empirical analyses that appear to refute this principle are guilty of improper measurement.


This is not to say there are no skilled investment managers – there are. However, given that their outperformance comes at the expense of poor investment managers, you better hope you pick the right one.

Picking stocks is a negative-sum game after costs, so the right questions to ask are:

  • Can I identify skilled manages in advance?
  • Do I have statistically valid evidence of skill, rather than luck?
  • Given the significant impact of taxes, am I looking at after-tax returns?
  • Will their outperformance be sufficient to offset their management fees?
  • Will their outperformance also be sufficient to offset transaction costs and the capital gains tax incurred from buying and selling all the time?

If you’ve answered yes to all of the above, go for it.

If not, we suggest a better way to invest.



  1. “Star stock pickers take on index”, The Weekend Australian, May, 28-29, 2016
  2. “The Arithmetic of “All-In” Investment Expenses” by John Bogle,

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