Diversification & CorrelationStart here

The only free lunch in finance — served daily, portioned by correlation, and withdrawn without notice in a crisis.

Why it works: the math of not putting eggs together

Combine two assets and the portfolio's return is the weighted average — but its risk is not. Unless the assets move in lockstep, some of their wiggles cancel:

Everything hangs on ρ, the correlation: at ρ = 1 nothing cancels; at ρ = 0 risk shrinks meaningfully; at ρ < 0 one asset actively offsets the other. Same expected return, less risk — Markowitz's "free lunch", and the only one on the menu.

How many holdings is "diversified"?

• Idiosyncratic risk (one company's troubles) diversifies away fast: ~20–30 reasonably different stocks capture most of the effect — the classic result behind index investing.
• Systematic risk (the market itself) never diversifies away by adding more of the same market — the floor in the chart. Crossing asset classes, not adding tickers, is what lowers the floor.
• Diversification across time (regular saving), across factors, and across currencies each attack different layers — the savings-plan calculator quietly assumes the first.

The efficient frontier

• Plot every possible mix: the upper-left boundary — most return per unit of risk — is the efficient frontier. Portfolios below it waste risk.
• The famous surprise sits at the bend: adding some stocks to an all-bond portfolio historically lowered risk while raising return — correlation math beating intuition.
• In practice the frontier is estimated from noisy history and shifts constantly — treat it as a way of thinking (risk is bought, return is paid for it) rather than an optimiser's gospel. "Estimation error maximisation" is what practitioners call naive mean-variance optimisation.

How much to bet: the Kelly criterion

Diversification answers "across what"; Kelly answers "how much". Given an edge and the odds, one stake size maximises long-run growth — and stakes beyond it reduce long-run wealth even though expected profit keeps rising.

When diversification fails: crisis correlation

• Correlations rise toward 1 in crises — the empirical regularity behind "the only thing that goes up in a crash is correlation". Diversification is weakest exactly when needed most.
• Why: in stress, everything is priced by the same variables — liquidity, margin calls (see margin & collateral), risk limits — not by fundamentals. Forced sellers sell what they can, not what they should.
• 2022 as the modern case: stocks −18%, long bonds −25% — the 60/40's worst year in decades, because inflation repriced both through one discount rate. The stock-bond correlation is regime-dependent: negative in demand-shock decades, positive in inflation-shock ones.
• What still worked historically in the worst moments: cash, short government paper, and genuinely uncorrelated cash-flow sources (cat bonds pay on hurricanes, not on the Fed) — each with its own cost of carry.

Practitioner rules

• Count exposures, not line items: forty tech stocks are one position wearing forty tickers. Diversification is measured in independent risk drivers.
• Stress-test the correlation assumption: re-run any allocation with all pairwise ρ at 0.8 — if the result is unacceptable, the portfolio relies on peacetime staying peaceful.
• Rebalancing is the enforcement arm: without it, winners concentrate the portfolio back into one bet; with it, you systematically sell high and buy low (see the glossary's rebalancing entry).