**Warren Buffett’s emergence as the world’s richest man illustrates the power of compound interest. Warren neither pays nor makes management charges. The effect is larger than you would believe possible.**

The news that Warren Buffett is now the world’s richest man led to the predictable round of stories about his frugal habits – the cherry Coke, the well-done steaks and the bungalow in Omaha that has been home for 50 years. There is a point here. Like Bill Gates, whom he has toppled from the top spot, Mr Buffett is primarily interested in the business rather than the wealth that results. Money is a means of keeping score rather than an objective in its own right: the fun, Mr Buffett has said, is watching it grow.

Albert Einstein supposedly observed that the most powerful force in the universe is compound interest, and Mr Buffett’s frugality has enabled compound interest to work its magic. During Mr Buffett’s tenure at Berkshire Hathaway, the S&P 500 index has produced an average total return of 10 per cent. That return reinvested over 42 years will multiply your stake 67 times. But if your investments yield twice as much as that – as Mr Buffett’s have done – your wealth increases not by twice 67, but 67 squared, a factor of 4,500. That arithmetic makes Mr Buffett the richest man in the world.

The calculation illustrates a more subtle point. Mr Buffett’s fortune has come not through growing an investment management business, but from his own share in the value of the funds he manages. Suppose he had adopted a more conventional investment management structure, charging the 2 per cent management fee and 20 per cent of performance common in private equity and hedge funds. How much of that $62bn wealth would have been the property of Buffett the manager – Buffett Investment Management – and Buffett the investor – the Buffett Foundation?

The answer is astonishing. At “2 and 20”, the split is $57bn for Buffett Investment Management and $5bn to the Buffett Foundation. The effect of compounding at 14 per cent, rather than at 20 per cent, is to reduce the accumulated pot by over 90 per cent. Of course, it is unlikely that Buffett Investment Management would have reinvested in its own funds sufficiently to have grown $57bn of assets. There would have been bonuses to pay. And the birthday parties! Eat your heart out Steven Schwarzman: Omaha would never have seen anything like it.

You might argue that the seemingly disproportionate share of Buffett Investment Management is reasonable: after all, Buffett Investment Management is very good. So rework the sum on the assumption that Mr Buffett was mediocre and performed in line with the 10 per cent return on the S&P. That would have reduced his wealth to $930m, below cut-off for the Forbes rich list. But only $170m of that more modest sum belongs to investors: Buffett Investment Management would still have the lions’ share, at $760m.

Worse still, suppose Mr Buffett had been no good at all. If returns had averaged 5 per cent a year, then the Buffett Foundation would have a miserly $32m to pass to Bill Gates’ charities. However, inept but thrifty Buffett Investment Management would still have accumulated $82m.

The results of these calculations are as puzzling as they are remarkable. But the difference between compounding before fees and compounding after fees builds up dramatically over a long period. The Einstein quotation is almost certainly apocryphal, but the sentiment has an element of truth.

Ben Franklin discovered electricity, which probably really is the most powerful force in the universe. But he was also impressed by compound interest and left funds to the cities of Boston and Philadelphia to accumulate for a hundred years. Franklin did actually say that the only certain things in life are death and taxes. He might have added another certainty: over a sufficiently long time horizon, your investment manager will become richer than you. The thought was certainly in his mind when he stipulated that no one should be paid for managing his legacies.

Franklin might have warmed to Mr Buffett’s homespun wisdom. The Sage of Omaha has made more money than anyone else without charging management fees. In the long run, the trust of investors and of investee companies may be the most valuable asset of all. And greed may be the enemy of wealth.

Footnote: the maths

There is a good deal of variation in the exact ways rates of return are quoted and fees charged, which can add up to significant amounts over forty-two years. The mathematically simplest and consistent approach is to assume continuous compounding at the specified annual rate, and that is the approach used for the calculations. Hence over forty-two years, 20% p.a growth multiplies wealth by e.exp (0.2 x 42) = e^{8.4}. Continuously charged fees of 2% and 20% imply an analogous return of 14% p.a, implying growth by a factor of e^{(0.14 x 42)}. The difference between these two numbers in the amount which the investment manager would accumulate if all management fees and charges were reinvested in the managers’ own fund. Calculations using spreadsheets, which employ discrete compounding, may generate slightly different results.

Hence the calculated amounts are

Assume $62 bn = iw e^{8.4},

i.e. initial wealth = e^{(ln ($62bn) – 8.4)}.

At 20%, Buffett Foundation receives we^{(0.14 x 42)}

and Buffett Investment Management w(e^{(0.2 x 4.2)} – e^{(0.14 x 42)})

Calculations at other growth rates are identical