Portfolio Theory
The one free lunch in finance is diversification — and it has an exact equation. Learn the math that turns a pile of risky bets into a portfolio you can actually defend.
Why a basket of risky assets can be safer than any one of them — the mathematics of diversification. Correlation and covariance, how combining assets bends the risk–return curve, the efficient frontier and the minimum-variance portfolio, the Capital Market Line, and CAPM's beta and Security Market Line.
Pick the single best stock you can and you still have a problem: you’ve bet everything on one company’s luck. Modern Portfolio Theory — the framework Harry Markowitz launched in 1952 and won a Nobel for — proves the almost-suspicious fix: spread money across assets that don’t move in lockstep and you cut risk without cutting expected return. That’s the only free lunch in finance, and it has an exact equation.
We build the machine from the ground up. This course covers:
- Why diversification works — the split between company-specific risk you can wash out and market risk you’re stuck with.
- Correlation and covariance — the engine that makes it tick, and the exact portfolio-volatility formula showing low correlation is the whole game.
- Combining assets — watch the risk–return curve bend inward as you mix holdings.
- The efficient frontier — and its minimum-variance tip, the best return for each level of risk.
- The Capital Market Line — add a risk-free asset to draw the straight line that dominates the curve.
- CAPM — beta, the market risk premium, and the Security Market Line that prices systematic risk.
By the end you won’t just believe diversification helps — you’ll compute exactly how much, and say which portfolios are worth holding and which are dominated.
In this topic
- 1 Why Diversify: The One Free Lunch in Finance Why a basket beats any single stock. Idiosyncratic vs systematic risk, the diversification curve and its undiversifiable floor, and why low correlation is the real lever. 8 min
- 2 Correlation & Covariance: The Math of Moving Together How covariance and correlation measure whether two assets move together — and the two-asset variance formula that turns low correlation into real portfolio risk reduction. 9 min
- 3 Portfolio Risk & Return: Combining Two Assets Mix two assets and the expected return is a clean weighted average — but the risk isn't. See why volatility bows below the naive blend and find the min-variance mix. 9 min
- 4 The Efficient Frontier: Best Return for Every Risk Map every possible portfolio in risk–return space, find the upper-left edge where no mix is wasted, and learn why only the efficient frontier is worth holding. 9 min
- 5 The Capital Market Line: Adding a Risk-Free Asset Add a risk-free asset to the efficient frontier and the best portfolios become a straight line — the Capital Market Line. Tangency portfolio, Sharpe slope, leverage. 9 min
- 6 CAPM: Beta, the Market Premium & the Security Market Line How CAPM prices any asset from its beta. Define beta as a regression slope, plug into the Security Market Line, read alpha off the gap, and meet the critics. 10 min
- 7 Final Exam: The Portfolio Theory Gauntlet A graded, locked capstone exam across all of portfolio theory — diversification, correlation and covariance, portfolio risk and return, the efficient frontier, the Capital Market Line, and CAPM. 15 min
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