Returns Math

ROI, IRR, MOIC, CAGR, time-weighted return, and the difference between a realised and an unrealised gain.

ROI, IRR, MOIC and the vocabulary of a real result

Lessons

ROI, and the one thing it leaves out — Return on investment is the simplest measure there is, and it is silent about time. Two investments with the same ROI can be wildly different propositions. (9 min)
IRR: the measure that knows about time, and what it assumes — IRR is the rate at which every cash flow discounts back to zero. It is the right tool for irregular timings, and it systematically flatters anything held briefly. (14 min)
MOIC: the multiple, and why it ignores time on purpose — The multiple answers one question exactly - how many times your money came back - and refuses to answer any other. Its blindness to time is a feature and a trap. (10 min)
CAGR: the smoothed rate, and the path it deletes — Compound annual growth rate is the straight line drawn between two points. Two investments with identical CAGRs can be completely different experiences to live through. (11 min)
Time-weighted and money-weighted: two true answers — One measures the decisions about what to hold; the other measures what actually happened to your money, including when you added it. They can disagree enormously. (13 min)
Realised and unrealised: a mark is not money — An unrealised gain is somebody's opinion of what an asset would fetch. A realised one is what it did fetch. The distance between them is where a great many returns go to die. (10 min)