# Where are the customers yachts?: the power of compounding

**Where are the customers yachts** is the title of an investment book I bought 20+ years ago: an old book even though , but still relevant today.

John Kay has been one of my favourite writers on economics for many years. His articles, in the FT, tend to be ‘just right’ for me: hard, but not too hard, and with effort what he is saying can normally be grasped. Occasionally, his articles are too hard for me, at least to read during the pressure of the working year, and my habit for many years is to cut and keep such articles, for reading when there is more time, such as whilst on holiday.

I had faithfully kept since March 2008 the article which is pdfed below. Whilst I ‘sort of’ understood what John was getting it, and ‘knew’ the answer he came to was right- that the winner in the way management and performance fees are charged is the investment house, I wanted to try to prove the maths.

Starting with the 67 squared comment, here John is comparing 1.1^42 with 1.2^42. The latter can be rearranged to be (1.1 * 1.2/1.1)^42, and further rearranged to be 1.1^42* (1.2/1.1)^42. The fraction (1.2/1.1) is approximately 1.1, so the calculation becomes approximately (1.1^42)^2: QED.

For the 42 year compounding problem, I chose to build a spreadsheet to compute the returns over 42 years, so I could flex it in the way John does for different investment performances. Whilst John’s calculations (in the PDF, but not into FT article) use continuous compounding, my spreadsheet was somewhat less sophisticated, compounding annually. However, as he says, it doesn’t make much difference to the answers. For interest, at 20%, John’s 5/57 split equates to my 6/56; at 10%, 170/760 is 181/749, and at 5%, the calculations are the same.

What I most like about John’s article is his one sentence summary: **over a sufficiently long time horizon, your investment manager will become richer than you.**