Desk Puzzle No. 1: The Coin-Flip Fund

By EC Assets · Published 14 August 2026

A fund manager offers you the following deal, and he is completely honest about it.

Each year, a fair coin is flipped. Heads, the fund returns +30 percent for the year. Tails, it returns −25 percent. The flips are independent, the odds never change, there are no fees, and you can stay invested as long as you like.

The questions

1. What is the fund's expected return per year?

2. An investor puts in 100 and holds for 40 years, reinvesting everything. What happens to the typical investor? More precisely: what is the probability that she is above water, at more than her original 100, after 40 years? Before computing anything, commit to a guess: is it above or below 50 percent?

3. A second investor splits her money half into the fund, half into cash earning nothing, and rebalances back to half and half at the end of every year. The fund is unchanged, the cash earns zero, and yet something fundamental is now different about her long-run outcome. What, and why?

Ground rules

Pen and paper are enough for all three parts; a coin is optional. There is nothing hidden in the wording: the coin is fair, the returns are exactly as stated, and question 2 is not a trick about the word "typical". If your answers to questions 1 and 2 feel like they contradict each other, you are close.

The solution note will be published on this page in mid-September.

Fair hints

If you want to check your instincts against the underlying concepts, these are the honest places to look: Rebalancing, the Kelly Criterion, Volatility Targeting, and the Drawdown Recovery calculator, which contains the asymmetry at the heart of the matter.