Nine quintillion reasons to avoid the costs of investing


Nine quintillion reasons to avoid the costs of investing

The late Jack Bogle, father of index-tracking, proved that performance is radically reduced by running fees

Tim Cohen

There is a theory that human beings are inherently bad at maths. Of course, some are brilliant, and others are pretty useless. Often people feel bad about their mathematical ability, but they may not be as bad as they think – compared to their peers.
But if you were to compare average human decision making prowess when tasked with a linguistic or logical problem, say, compared to a mathematical problem, the average people more often get the mathematical problem wrong. So goes the theory.
The problem is, this is more or less impossible to test, because how do you rate the difficulty of the logical problem compared to the mathematical problem? Yet I suspect the theory is true, and this is why.
Many people know the famous story about the king who considered himself the best chess player in the land and promised any of his subjects that if they could beat him, he would grant them any wish.
A pauper challenged him and won. The pauper demanded a single grain of wheat for the first square on the chessboard, two for the second, four for the third and so on. The king readily agreed because it seemed totally within his means to supply. But when he did the calculation, it turned out he didn’t have enough wheat in his entire kingdom to satisfy the promise.
The question is, how many grains did he need? You guess. You have to be honest with yourself. But go ahead and try.
Did you bet more than or less than a billion? I would suspect that most people would guess around a billion. What about a trillion? Tougher. A quadrillion? My guess is that the vast majority of people would make it under a quadrillion, partly because even the term is virtually unused.
If you did guess that, you would be wrong, because the right answer is way, way higher. A thousand times higher in fact. The correct answer is just more than nine quintillion. That is nine with 18 zeros. The actual number is 9,223,372,036,854,775,807, and it’s a very important number because it’s the maximum value of a long integer in programming on the 64-bit computer.
The reason people have a particular problem with this little example is that they think in a linear way. So much of our world and history depends on divisions that are regular. We are coded in that way, or perhaps it’s ingrained in the way we learn. We are conceptual in respect to politics, for example, and regular in respect to numbers – when, quite often, we should be the opposite. We should measure political effects more rigorously, and think more conceptually about numbers, which are, after all, just another language.
Instead of linearity, the example involves exponentiality. The maths is not that difficult: it is two to the power of 64 plus one.
This is all really just a precursor to paying my respects to the great investor Jack Bogle, who died this month at the age of 89 despite having his first heart attack at the age of 31. Bogle is best known for launching the first index fund. He was labelled “un-American” at the time, but the firm he launched, Vanguard, went on to become the largest asset manager in the world. It currently has just more than $5-trillion under management. Bogle is known for five things; he massively reduced the cost of investing for investors; he enabled people to buy the whole market as opposed to single stocks; he increased the influence of ordinary people over companies; he changed the attitude of investors from being short to long term; and he highlighted the risk of costs. This is a pretty awesome list, and it is the reason why he is considered a great of investing.
But behind all of these things lurks exponentiality. What Bogle discovered was that outperforming the market was possible as an active fund manager, but if you added the cost of doing so, usually you were underperforming. And if you added up the cumulative underperformance, the effect was much larger than people often expect.
At an expense ratio of 1.5%, which is probably close to the average of what South Africans pay, your pension will normally end up about 30% lower just as a result of the expenses you pay. That realisation led Bogle to find ways of eliminating expenses and that led him to index funds.
Still today, Vanguard’s expense ratio is around 0.1%, and its expense ratio on its active funds is 0.2%. Bogle changed the world not only through his famed common sense, but through mathematical imagination, and that is a very rare thing.

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