Trick question. The real answer is "it depends".
You hold both of these in your head. Almost nobody notices they point in opposite directions.
The quiet one who compounds a modest return for decades crushes the flashy one who has a single 20x year and then blows up. Less drama, more terminal wealth. You've seen it a hundred times.
The raw talent with one truly rare skill and obvious flaws beats the safe pick who's "good at everything, great at nothing." When it hits, it pays for everything. The best teams do this on purpose.
One says minimise variance. The other says maximise variance. Both are right. So one of them must be wrong, or there's a deeper rule that makes both true at once.
Take the exact same set of results. Feed them through three different aggregation functions and you get three different answers about how much variance you want. The function decides, not your gut.
Each result builds on the last. One terrible result doesn't subtract, it multiplies everything down. Your brand. Your reputation. Long-run wealth.
You take lots of shots and keep the single best. The flops get discarded. Creative testing. The big brand film. Hiring a rare specialist.
Hundreds of tiny results pile into one total. No single one makes or breaks you. Always-on lead gen. The pipeline that keeps the lights on.
Below is a single variance dial. Drag it from calm to chaos. All three functions read the same dial, and the live numbers under each chart show exactly what variance does to the result.
One dial moved σ. The Compounder's geometric mean fell below its arithmetic mean and the gap (the volatility drag) widened. The Swing's expected best climbed. The Drip's total barely flinched. Same variance, three different signs on the derivative. That is the whole idea.
Each machine is just a different way of collapsing many outcomes into one number. Change the function and the relationship between variance and value flips. Here are all three, with the single result that drives each.
Outcomes multiply across periods. By the AM-GM inequality the compound (geometric) rate is always at most the average (arithmetic) rate, and the gap grows with variance:
Every unit of variance you add is subtracted straight off your growth rate. Two portfolios with the same mean return but different σ finish miles apart. Minimise σ.
Only the best draw survives. For a sample with normal tails the expected best climbs with the spread and the number of attempts (extreme value theory):
The mean barely appears. The ceiling is dragged up by σ and by \(n\). Fatter tails, more shots. The floor never enters the formula. Maximise σ.
Outcomes sum. The wobble in the average shrinks with volume, the law of large numbers at work:
Quadruple the volume and you halve the relative noise. Variance neither helps nor hurts the total, so don't optimise for it. Raise μ.
Why one great year doesn't save the Compounder. Variance bites asymmetrically here because losses multiply. A 20x year followed by an 80% drawdown lands you at 20 × 0.2 = 4x, not 19.2x. The same fat tail that builds the peak in The Swing quietly drains the product in The Compounder. Identical statistics, opposite sign.
The opening case for The Compounder. One investor has a single blowout year, then sits frozen. The other compounds a steady return every year. Drag both sliders and watch how soon, and how violently, boring overtakes brilliant. The vertical axis is logarithmic, so each gridline is a multiple of the one below it.
Read each situation. Pick the aggregation function before you decide whether to minimise or maximise variance. That order is the entire skill.
Every one is the same mistake: importing a variance preference from a system with one aggregation function into a system with a different one. Tap a card to flip it.
Ask it before every decision involving uncertainty. The CFO who wants the Super Bowl ad de-risked and the agency that wants to take the swing aren't arguing about creativity. They're implicitly assuming different aggregation functions, and neither of them knows it. Name the function out loud and the disagreement usually resolves in minutes.
\(\prod(1+r_t)\). Minimise variance at acceptable mean. Your brand is this. Protect the floor, be boring for years.
\(\max(X_i)\). Maximise variance at acceptable floor. Many attempts, kill losers fast, fund the one hit.
\(\sum X_i\). Optimise the mean, ignore variance. Let the law of large numbers do the work.
A brand is built in drops and lost in buckets. That one line is the Compounder in full. A thousand tiny consistent moments compound it up. One catastrophic moment multiplies it down. Which is exactly why you run wild, fat-tailed creative tests inside it, but never run the brand itself like a creative test.