Risk compensation is not paid in proportion to the size of the risk. The risk of a stock can be split into two parts: firm-specific risk, which belongs to that company alone, and systematic risk, which the whole market bears together. Firm-specific risk can be removed through diversification at almost no cost, so the market does not pay for it; only systematic risk, which cannot be diversified away, earns compensation. Holding a few stocks in concentration means bearing more risk without earning a higher expected return.
"Don't put all your eggs in one basket" is an old saying, but why it holds was not explained clearly until 1952. In "Portfolio Selection", Markowitz showed that the risk of a portfolio depends not only on how volatile each asset is, but also on how closely the assets move together. As long as two assets do not rise and fall in perfect step, one may rise when the other falls, and the volatility of the portfolio will be lower than the average of their individual volatilities. The lower the correlation, the stronger the effect of diversification.
Half in each of two stocks
The two stocks have the same expected return and volatility. Adjust how closely they move together (the correlation coefficient) and see how volatile a half-and-half portfolio is.
For this work Markowitz shared the 1990 Nobel Memorial Prize in Economic Sciences with Sharpe and Miller. The key point of the discovery is that reducing risk does not necessarily mean giving up return; it only requires combining assets.
As more and more stocks are added to a portfolio, its volatility keeps falling, but it never reaches zero. The reason is that the risk of a stock has two components: firm-specific risk, which belongs to that company alone, such as a failed product or the departure of a senior executive; and systematic risk, which all companies face together, such as a recession or a rise in interest rates. The more stocks one holds, the more the firm-specific risks offset one another; systematic risk, however, cannot be removed no matter how many stocks one holds.
As you hold more stocks, how far does risk fall?
Drag to change the number of stocks held. Grey is firm-specific risk that can be diversified away; green is systematic risk that cannot be diversified away however many stocks you hold.
Evans and Archer estimated in 1968 that holding about 10 randomly chosen stocks removes most firm-specific risk; Statman, applying a stricter standard in 1987, concluded that at least 30 to 40 are needed.
Since firm-specific risk can be removed through diversification at almost no cost, the market does not pay for it. In 1964 Sharpe formalized this reasoning as the capital asset pricing model: if investors all hold diversified portfolios, the risk a stock poses to them is only the part it adds to the portfolio, that is, the degree to which it moves with the market as a whole, usually measured by "beta". Expected return therefore depends only on beta, not on the total volatility of the stock itself.
Compensation follows systematic risk, not total risk
Twelve example stocks. Arranged by total volatility, their expected returns look scattered; arranged by beta (how much they move with the market), they fall on a straight line. Tap any stock to see how its risk is made up.
Tap any stock.
This means that a highly volatile stock whose movements bear little relation to the market does not have a higher expected return than a less volatile stock that closely follows the market's swings. Bearing firm-specific risk is bearing risk that goes uncompensated.
Empirical studies have found that the actual relationship is flatter than the model predicts. Black, Jensen and Scholes found in 1972 that high-beta stocks did not earn as much extra return as the model predicted; Fama and French found further in 1992 that from 1963 to 1990 there was almost no relationship between beta and average return. This suggests that there is more than one kind of systematic risk and that a single market beta is not enough to explain differences in returns. That is precisely the starting point of factor research.
The case for diversification goes beyond reducing volatility. In 2018 Bessembinder studied every US listed common stock from 1926 to 2016 and found that more than half of them returned less over their listed lives than one-month Treasury bills; all the net wealth the US stock market created over those ninety years came from only about 4% of stocks.
Out of a hundred stocks, which ones created the wealth?
Illustrative, based on US listed stocks as a whole from 1926 to 2016: each dot represents 1% of stocks. Pick a few at random to hold in concentration and see whether you catch one of the few big winners.
This means that an investor who holds only a few stocks is likely to miss these very few big winners and may end up doing worse than a bank deposit. Yet in practice most individual investors hold only a few stocks. Goetzmann and Kumar's 2008 study of US individual investor accounts showed that under-diversification is widespread, and that investors who trade more often and prefer more volatile stocks are the least diversified.
Diversification relies on assets not moving in perfect step. In a sharp market fall, however, correlations between assets often rise suddenly, and assets that are normally unrelated begin to fall together. Studying national stock markets in 2001, Longin and Solnik found that correlations rise markedly when markets fall, but not when they rise. Diversification works in ordinary times, and its effect is reduced precisely when it is needed most.
In a sell-off, assets fall together
The same 30-stock portfolio. Example: suppose the correlation between stocks is 0.25 in calm markets and rises to 0.7 in a sharp fall. Switch the market state and see how much of the benefit of diversification remains.
This echoes the fat-tailed nature of risk: extreme falls are more common than expected, and diversification is weaker during extreme falls. Estimating portfolio risk only from calm periods systematically underestimates the true risk.
Diversification is the only almost costless risk-management tool available to ordinary investors, and products should make it the default.
A new user’s first portfolio is diversified by default; when holdings are concentrated, state clearly how much uncompensated firm-specific risk is being borne.
When assessing a trade, look at how much systematic risk it adds to the whole portfolio, not just at the volatility of the stock itself.
Explain that concentrated holdings are more likely to miss the few big winners, not more likely to catch them.
Estimates of portfolio risk must include crisis periods, not just data from calm periods.