Product × Finance × AI: Financial Products in the Age of AIPart One · Section Two Risk compensation: the price of bearing risk中文
Chapter 4

DiversificationWhich risks are compensated

Realized return =Time compensation+Risk compensation+Information advantage-Trading costs+LuckPremise: promises kept

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.

1. Why diversification reduces risk

"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.

Stock AStock BHalf-and-half portfolio
1 means perfectly in step, 0 means unrelated, −1 means perfectly opposite
Annual volatility of one stock25%
Annual volatility of the portfolio
Expected return of the portfolioSame as one stock
Example parameters: both stocks have an annualized expected return of 7% and volatility of 25%, simulated monthly over 5 years. The portfolio is rebalanced to half and half each month. On the idea of diversification, see Markowitz (1952).

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.

2. The limits of diversification

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.

Annual volatility of the portfolio
Share of diversifiable risk removed
Floor that cannot be diversified
Example parameters: each stock has an annual volatility of 35%, the average correlation between any two stocks is 0.2, and the portfolio is equally weighted. Portfolio variance is then roughly “average covariance + firm-specific risk ÷ number of stocks”, and the floor is about 15.7%. For empirical estimates of how many stocks are needed for diversification, see Evans and Archer (1968) and Statman (1987).

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.

3. Why only systematic risk is compensated

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.

Illustrative data constructed from the capital asset pricing model (Sharpe 1964): risk-free rate 3%, market risk premium 5%, market annual volatility 18%; each stock’s total volatility combines systematic and firm-specific risk. Empirically the line is flatter than the model predicts; see Black, Jensen and Scholes (1972) and Fama and French (1992).

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.

4. A few stocks created most of the wealth

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.

Returned less than Treasury bills while listed (about 57%)Beat Treasury bills, but added little net wealthCreated all the net wealth (about 4%)

Illustrative, based on Bessembinder (2018): from 1926 to 2016, more than half of US listed stocks returned less over their listed lives than one-month Treasury bills, and all the net wealth the stock market created came from about 4% of stocks. Proportions in the figure are rounded; “catching” a winner only means the portfolio contains at least one big winner.

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.

5. When diversification fails

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.

Annual volatility of one stock35%
Annual volatility of a 30-stock portfolio
Share of risk removed by diversification

Example parameters. Only the correlation changes; the volatility of a single stock stays at 35% (in reality volatility itself also rises in a sell-off). For evidence that correlations rise in falling markets, see Longin and Solnik (2001), who studied correlations between national stock markets.

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.

6. Implications for product design

Diversification is the only almost costless risk-management tool available to ordinary investors, and products should make it the default.

Chapter summary: make diversification the default

Four design requirements, each tied to one mechanism in this chapter.

Firm-specific risk is not compensatedMake diversification the default option

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.

Risk is measured by its contribution to the portfolioShow risk at the portfolio level

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.

A few stocks create most of the wealthDo not encourage bets on a few “star stocks”

Explain that concentrated holdings are more likely to miss the few big winners, not more likely to catch them.

Correlations rise in sell-offsUse sell-off correlations in stress tests

Estimates of portfolio risk must include crisis periods, not just data from calm periods.

References