The Economist's Free Lunch
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In economics and finance, there is no free lunch — every benefit comes with a corresponding cost or risk. The striking exception is diversification: by combining assets whose returns are less than perfectly correlated, an investor can reduce portfolio risk without sacrificing expected return. This principle, formalised by Harry Markowitz in his 1952 paper Portfolio Selection, earned him the Nobel Memorial Prize in Economics in 1990 and remains the foundational insight of modern portfolio theory.
The intuition: if you own only one stock, your return is entirely determined by that stock's performance. If you own a hundred stocks, a single company's disaster affects only 1% of your portfolio. But the risk-reduction benefit of diversification goes deeper than simple averaging — it depends on correlation.
Correlation and Portfolio Variance
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Correlation measures how closely two assets move together. A correlation of +1 means they move in perfect lockstep; 0 means they move independently; -1 means they move in exactly opposite directions.
When combining two assets in a portfolio, the portfolio's risk (variance) is:
σ²(portfolio) = w₁²σ₁² + w₂²σ₂² + 2w₁w₂σ₁σ₂ρ₁₂
where ρ₁₂ is the correlation between assets. When correlation is less than +1, the last term is smaller than it would be if the assets moved together perfectly — portfolio variance is lower than the weighted average of individual variances. This is the mathematical expression of diversification's benefit.
A portfolio of 20 stocks, each with individual standard deviations of 30%, might have a portfolio standard deviation of only 15% if correlations are sufficiently low. The expected return is unchanged; the risk is halved.
Systematic vs Idiosyncratic Risk
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Diversification eliminates idiosyncratic risk — the risk specific to a single company or asset (a CEO scandal, a product failure, an accounting fraud). As the number of uncorrelated holdings increases, company-specific risk approaches zero.
What diversification cannot eliminate is systematic risk (or market risk): the risk that affects all assets simultaneously — recessions, interest rate shocks, global financial crises. In a market crash, correlations between assets tend to increase, precisely when diversification is most needed. This is the "diversification breakdown in crises" phenomenon and is why even well-diversified equity portfolios can lose 40–50% in severe bear markets.
Systematic risk can only be managed through asset class diversification — holding bonds alongside equities, real assets, and other instruments whose systematic risks differ — not through holding many equities.