A stock’s total risk has two parts. One part moves with the whole market and sits in every asset you could buy. The other is specific to that one company and washes out when you hold many names. The first part is priced. The second is not. That distinction drives most of how portfolios are built.
The decomposition
The market model regresses an asset’s return on the market return: r = α + β·r_market + ε. The slope β measures exposure to market-wide moves. The residual ε captures everything specific to the firm. Taking the variance of both sides gives total variance = β²·(market variance) + (residual variance), the systematic part plus the idiosyncratic part. The R-squared of that regression is the fraction of the asset’s variance that is systematic. A stock with R-squared of 0.30 has 30% of its variance systematic and 70% idiosyncratic. That is a variance share, not a volatility share: 30% of variance is about 55% of standard deviation, so the systematic part looms larger in risk terms than the R-squared suggests.
Systematic risk comes from market structure and general economic conditions and hits all agents, so no asset escapes it. Idiosyncratic risk is inherent to one company or a narrow group, and it shrinks with proper diversification.
Only the systematic part is priced
Under the CAPM, expected return above the risk-free rate is linear in β and nothing else. Idiosyncratic risk earns no premium because a diversified investor can remove it for free, so the market will not pay you to hold it. The model prices only non-diversifiable risk, measured by β. Under the theory, you are compensated for the risk you are forced to bear, not for the risk you chose not to shed. The empirics are messier: Ang, Hodrick, Xing, and Zhang (2006) found stocks with high idiosyncratic volatility earned lower returns, not zero premium, the wrong sign for both CAPM and Merton’s incomplete-diversification prediction, and the puzzle is unresolved.
How fast idiosyncratic risk falls
Adding holdings cuts the name-specific variance quickly, then flattens against the systematic floor. Evans and Archer (1968) ran random portfolios and found that roughly 10 to 15 stocks captured most of the dispersion reduction, with gains tapering sharply after that. Statman (1987) argued the early figure was too low once you account for the cost of diversifying, and put the bar higher, at roughly 30 to 40 stocks. Both results describe the same curve: a steep drop followed by a long flat tail that never reaches zero. The floor is the systematic risk you cannot remove.
This is where the everyday confusion sits. More names cut idiosyncratic risk, not systematic risk. A 200-stock equity fund still falls when the market falls. Count alone does not buy safety.
The split is not fixed
The decomposition assumes correlations between names stay moderate. In a crisis they do not. Idiosyncratic shocks turn systematic as everything sells off together. During 2008, and again in the March 2020 selloff, equity correlations jumped from about 0.35 to over 0.80, and the rise ran across individual stocks, country markets, currencies, and bonds. The diversification that flattened your risk curve in calm markets thins out exactly when the drawdown arrives. Diversification tends to fail in left-tail events because down-market correlations rise. Part of that jump is mechanical, since measured correlation rises with volatility even when the underlying dependence is stable, but the funded-loss effect is real either way. The label on a risk can change: what was diversifiable on Monday can be undiversifiable by Friday.
Try it
Reproduce the Evans-Archer curve in Python (about an hour). Pull daily prices for 60 large-cap US stocks with yfinance over the last five years. For each portfolio size N in {1, 2, 5, 10, 20, 30, 50}, draw many random equal-weighted subsets, compute each subset’s annualized return volatility, and average across draws. Plot mean volatility against N. The curve drops fast then flattens. Overlay the volatility of the S&P 500 (ticker ^GSPC) as a horizontal line: that is the systematic floor the curve approaches but never crosses. To see the crisis caveat, recompute the average pairwise correlation of your 60 stocks in 2008 versus a calm year and watch it climb.
See also
Sources
- Evans and Archer, Diversification and the Reduction of Dispersion (1968) — original 10 to 15 stock result.
- Statman, How Many Stocks Make a Diversified Portfolio? (1987) — revised bar of 30 to 40 stocks.
- Idiosyncratic Risk, Wall Street Prep — definitions and why CAPM prices only systematic risk.
- Going to One: Is Diversification Passé?, FPA Journal — 2008 correlations rising from 0.35 to over 0.80.