In finance, more of anything good usually costs you something. A higher expected return usually comes bundled with more risk; lower risk usually comes bundled with a lower expected return. In a 1952 paper called "Portfolio Selection," the economist Harry Markowitz identified a rare exception to that trade-off — one precise enough to be mathematically proven, and important enough to help win him the Nobel Memorial Prize in Economic Sciences decades later, in 1990.
Why mixing imperfectly correlated assets beats picking just the best one
Hold only the single asset with the highest expected return, and your portfolio's risk is simply that asset's own volatility, in full. Add a second asset whose price doesn't move in perfect lockstep with the first — imperfectly correlated with it — and something useful happens: because the two assets' ups and downs don't align exactly, some of that movement partially cancels out when they're combined. The result can be a portfolio whose overall volatility is lower than either asset held alone, while its expected return is still just the weighted average of the two — no worse than what you'd have expected from the individual pieces. That's the free lunch: lower risk, without paying for it in expected return.
Turning that intuition into a precise, optimisable calculation
Markowitz's Modern Portfolio Theory formalised the intuition into something calculable: the "efficient frontier," the set of portfolios that deliver the maximum possible expected return for any given level of risk, or equivalently the minimum possible risk for any given expected return, computed from each asset's expected return, volatility, and how it's correlated with every other asset in the mix. Any portfolio sitting below that frontier is leaving free risk-reduction — or free extra return — on the table, simply by not diversifying as effectively as the math shows is possible.
What we're still unsure about
The model rests on real, imperfect assumptions: that investors can reasonably estimate expected returns, volatilities, and correlations in advance, and that those correlations stay roughly stable over time. In practice, correlations between assets are notoriously unstable, and they tend to spike toward each other — moving together — exactly during market crises, which is precisely when diversification is needed most and precisely when the clean theoretical benefit tends to weaken. That gap between the tidy assumptions of the model and the turbulent behaviour of real markets under stress is a well-documented, still-debated limitation, not one that later refinements have fully closed.
This sits inside Portfolio Theory & Diversification, one of eight topics in Finance, one of five domains in Economics, one of seventeen subjects the app can quiz you on.