Mean-Variance Optimization
Markowitz 1952 in modern form — what variance and covariance actually do to a portfolio
In March 1952 a 25-year-old graduate student named Harry Markowitz published a fourteen-page paper titled simply 'Portfolio Selection' in the Journal of Finance. Before that paper, an investor who wanted to maximize return at acceptable risk would mostly pick the stocks they liked best, in proportion to how much they liked them. After the paper, that approach was visibly incomplete.
Markowitz's central observation was that two assets with identical individual risk and return characteristics can produce dramatically different portfolio behavior depending on how they move together — and that ignoring how assets move together left enormous risk reduction on the table for free. Two stocks at 20% individual volatility, blended 50/50 with zero correlation between their returns, produce a portfolio with volatility of about 14.1% — a 29% reduction in risk with no sacrifice of expected return.
The math is unforgiving in both directions: that same 50/50 blend with correlation of +1.0 stays at 20% volatility, and a +0.5 correlation lands at about 17.
3%.
That is the opening. Finishing a lesson is where it stops being interesting and starts being useful: the full lesson runs to 8 sections and ends with 6 practice questions. A free account is what opens the rest, and the other 255 lessons in the Academy with it. No card.
What this lesson covers
- 1Variance and covariance — the two ingredients
- 2Why this is more than a math curiosity
- 3Two-Asset Frontier Builder
- 4Mean-variance optimization in matrix form
- 5How portfolio volatility changes with correlation — same two assets
- 6The N-asset diversification limit — why owning more than ~30 stocks does not help much
- 7Where to see this on the platform
- 8Summary