Portfolio theory
Why is a holding worth judging only by what it does to everything else you own?
12 of 12 chapters published
Chapters
Beginner
- What a portfolio is, mathematicallyA list of weights that sum to one. That definition sounds like bookkeeping and is the whole argument of the subject — because it makes every holding a statement about every other holding rather than a judgement on its own.
- Expected return and varianceA portfolio's expected return is the weighted average of its holdings'. Its risk is not the weighted average of theirs — and that single asymmetry is where everything else in the subject comes from.
- Covariance, and where diversification comes fromChapter 2's cross term, taken seriously. It explains why adding holdings reduces risk, why the reduction stops, and exactly where it stops — which turns out to depend on one number that nobody controls.
Intermediate
- Two assets, then manyVary one weight and the portfolio traces a curve. The curve bends left, which produces the result that persuades people: adding a riskier asset to a safe portfolio can raise its return and lower its risk at the same time.
- The efficient frontierMost portfolios are beaten on both axes by some other portfolio. The ones that are not form a boundary — and the useful thing about the boundary is not where it is but how little we can trust our estimate of it.
- The capital market lineAdd one riskless asset and the curved frontier is replaced by a straight line that beats it almost everywhere. The consequence is startling: every investor should hold the same risky portfolio, and differ only in how much of it.
- CAPM and betaIf everybody follows chapter 6, the tangency portfolio must be the market itself. That one step turns a theory of how to choose into a theory of what returns have to be — and it predicts that only shared risk is ever paid for.
Advanced
- What beta is notBeta is a covariance, scaled. It is not volatility, not the chance of losing money, and not a property of a company — and when the prediction it makes is tested against Indian index data, the line comes out flatter than the model requires.
- Sharpe, Sortino and the ratios that get misquotedThe ratio is the slope of chapter 6's line, which is why maximising it is the whole of portfolio choice. It is also misquoted in four specific ways, and Sharpe's own paper identifies most of them.
- Factors and the evidenceCAPM says nothing but beta is priced. Characteristics that should not matter do. But the premia fell sharply after they were published — and a century of the original authors' own data is where that is easiest to see.
- The arithmetic and cost of rebalancingWeights drift, so a portfolio left alone becomes a different portfolio. Fixing that is a risk-control decision — and simulation says it costs return rather than adding it, which is the opposite of how it is usually sold.
- What the theory gets wrongThe last chapter of the subject. Six failures, sorted by how much damage each does — and an account of what survives all of them, which turns out to be most of what an individual actually needs.