A Short Note on Compounding

Compounding is the most widely understood idea in finance and among the least acted upon. Everyone can do the arithmetic. Very few people arrange their affairs as though they believe the result.

The gap is not mathematical. It is psychological, and it has a specific shape.

The curve is boring for a long time

The problem with compound growth is that almost all of it happens at the end. A process that doubles every seven years spends the first two decades looking unremarkable and the last decade looking extraordinary.

This means that for most of the duration of a compounding process, the evidence available to the participant suggests it is not working very well. The strategy that will eventually produce a large result is, at year five, producing a small one, and it is indistinguishable from a strategy that will never produce anything.

Anyone acting on evidence will abandon it. That is not irrationality; it is the correct response to the information available. The only defence is deciding in advance that the evidence during the flat period will not be treated as informative.

It applies to more than money

The financial case is the one everyone knows, but the structure appears wherever accumulated small advantages persist.

Reputation compounds, because each piece of work is judged partly on the basis of previous work. Knowledge compounds, because understanding one thing makes the next thing faster to learn. Relationships compound, because trust extended and honoured makes further trust cheaper.

In each case the same pattern holds: a long unremarkable period followed by an acceleration that looks, to an outside observer arriving late, like luck.

The negative case is symmetric

Less discussed is that the mechanism runs in both directions. Small recurring costs compound as reliably as small recurring gains.

A fee of one percent, an obligation that consumes a few hours a week, a relationship that requires steady maintenance and returns nothing. Each is individually trivial and easy to justify keeping. Over a long enough period they consume the majority of what the corresponding positive processes generate.

This is the part I find most practically useful. The returns from removing a small recurring drag are identical in structure to the returns from adding a small recurring gain, and removal is usually easier and entirely within one’s control.

What follows

The practical implication is narrow but real: the decisions that matter most are the ones that determine what recurs, and they matter far more than the decisions about any individual instance.

Choosing what to do this week is a small decision. Choosing what you will do every week for ten years is not, and it is usually made carelessly, if it is made at all.