Desk Puzzle No. 3: The Manager's Half

By EC Assets · Published 1 October 2026 · Updated 1 October 2026

Puzzle No. 3 is below; the solution to Desk Puzzle No. 2 follows it.

Puzzle No. 3: The Manager's Half

A fund earns 10 percent gross, every single year, for twenty years. No volatility at all: the same ten percent, year in, year out. There is nothing to solve about the strategy - this puzzle is entirely about the fee schedule.

The terms are the ordinary ones. Two percent of assets per year as a management fee, and twenty percent of what is left after that as a performance fee, charged annually. You invest 100 and leave it alone for twenty years.

The questions

1. What is your net return per year, and what are you holding after twenty years? What would you have held if the fund charged nothing?

2. Split the total profit between you and the manager. What share did the manager take? Commit to a guess before you compute it.

3. You might reasonably assume that this is a symptom of a mediocre fund, and that a better one would split more kindly. Work out the manager's share for a fund earning 4 percent gross and for one earning 30 percent gross, both over the same twenty years. What does the pattern tell you?

Ground rules

Pure compounding, no tax, no redemptions, fees settled at each year end. The high-water mark never binds, because the fund never has a down year - this puzzle is deliberately the friendliest possible case for the fee schedule. All you need is the ability to raise a number to the twentieth power.

Fair hints

Hedge Fund Fees, Fee Drag, and the Fee drag calculator, which asks what 2 and 20 costs over twenty years as a share of everything the strategy earned. The calculator will confirm your answer to question 2; it will not tell you why question 3 turns out the way it does.

The solution will be published here in next month's note, alongside Puzzle No. 4.

Solution: The Fortieth Strategy

1. Four strategies against forty

With n equally weighted strategies of equal volatility and a common pairwise correlation ρ, the portfolio variance is (σ²/n) × [1 + (n−1)ρ], so the portfolio Sharpe ratio is

SR(n) = S × sqrt( n / (1 + (n−1)ρ) )

At S = 0.40 and ρ = 0.25:

• Fund A, n = 4: 0.40 × sqrt(4 / 1.75) = 0.605
• Fund B, n = 40: 0.40 × sqrt(40 / 10.75) = 0.772

Ten times the strategies bought 28 percent more Sharpe ratio. If you guessed that B would be more than twice A, you were reasoning about the numerator; almost all of the action is in the denominator, and the denominator stops falling.

2. The ceiling

Let n run to infinity. The ratio n / (1 + (n−1)ρ) converges to 1/ρ, so

SR(∞) = S / sqrt(ρ) = 0.40 / 0.50 = 0.80

That is the hard limit. No number of strategies of this quality, at this correlation, ever produces a Sharpe ratio of 0.81.

Thirteen strategies capture ninety percent of everything diversification will ever give you here. Everything from the fourteenth onwards is competing for the last tenth.

3. The fee decides it

B's advantage is 0.772 − 0.605 = 0.167 of a Sharpe ratio. At 10 percent portfolio volatility that is worth

0.167 × 10% = 1.67 percent of return per year

B charges 1.5 percentage points more. A fee of 1.5 points at 10 percent volatility costs 1.5 / 10 = 0.15 of Sharpe ratio, so B's net advantage is 0.017 - seventeen thousandths. Ten times the research budget, ten times the operational surface, and after the fee it is a rounding error.

The second half of the question is the important one. A Sharpe ratio of 1.00 is unreachable at ρ = 0.25, by any number of strategies, because the ceiling is 0.80. Getting there requires the correlation to fall: solving 0.40 × sqrt(40 / (1 + 39ρ)) = 1.00 gives ρ = 0.14.

Count is the lever everyone can pull and nobody should pay for. Correlation is the lever that actually moves the portfolio, and it is the one that is hard, unglamorous and rarely in the pitch book. When a manager sells you breadth, ask what the average pairwise correlation is; the answer prices the pitch.

Further reading: Correlation, Diversification, Risk Parity.