Unsystematic Risk

Unsystematic risk is the portion of the risk of a security that arises from factors particular to its issuer or industry, and not from movements in the market as a whole. It is also called specific risk, idiosyncratic risk or diversifiable risk. A product recall, a lawsuit, the loss of a major customer, a strike or the departure of a chief executive are typical sources. Such events affect one company or a small group and are largely unrelated to what happens to others.

The concept is defined in contrast to systematic risk, which stems from economy-wide influences such as interest rates, inflation and recessions and affects nearly all securities. The distinction is central to portfolio theory, because unsystematic risk can be largely eliminated through diversification while systematic risk cannot.

Under a single-index model, the variance of a security's return splits into a market-related part and a specific part:

• $\sigma_i^2$ is the total variance of the return on security $i$.
• $\beta_i$ is the security's beta, its sensitivity to the market.
• $\sigma_m^2$ is the variance of the market return.
• $\sigma_{\varepsilon}^2$ is the variance of the residual, the unsystematic part.

Suppose a share has total volatility of 30 percent a year and a beta of 1.2, and the market has volatility of 15 percent. The systematic volatility is $1.2 \times 15 = 18$ percent, a variance of 324. Total variance is $30^2 = 900$. Unsystematic variance is $900 - 324 = 576$, which is a volatility of 24 percent. Specific factors account for $576 / 900 = 64$ percent of the share's variance. For a typical individual share, most of the risk is unsystematic.

Specific events at different companies are largely independent, so in a portfolio they tend to offset one another. If $N$ shares are held in equal amounts and their specific risks are uncorrelated, the unsystematic volatility of the portfolio is:

With specific volatility of 24 percent per share, a portfolio of 25 shares has unsystematic volatility of $24 / \sqrt{25} = 4.8$ percent, and a portfolio of 100 shares has 2.4 percent. The systematic part is unaffected by the number of holdings. As a portfolio grows, its total risk falls toward the level set by the market.

Early studies suggested that 20 to 30 shares removed most specific risk. Later research found that the volatility of individual shares relative to the market rose during the late twentieth century, implying that more holdings were needed for the same effect. Holdings must also be spread across industries, since companies in the same industry share risks. A broad exchange-traded fund removes almost all of it at low cost.

In the capital asset pricing model, investors are compensated only for risk they cannot avoid. Since unsystematic risk can be diversified away at little cost, the market offers no risk premium for bearing it. An investor who holds a concentrated position takes on extra risk without a corresponding increase in expected return. This conclusion is one of the main practical lessons of modern portfolio theory.

The evidence is not entirely tidy. A 2006 study by Andrew Ang and co-authors found that shares with high idiosyncratic volatility had earned unusually low subsequent returns, a result that standard theory does not predict and that is known as the idiosyncratic volatility puzzle.

Unsystematic risk is unrewarded on average, but it is where security selection takes place. A manager seeking alpha deliberately holds specific risk in companies expected to do better than the market prices imply. The skill of the manager lies in whether that specific risk pays off.

Market-neutral strategies isolate it. In pairs trading and statistical arbitrage, long and short positions are balanced so that market exposure cancels, leaving a portfolio whose results depend almost entirely on company-specific returns. A factor model is used to separate the specific component from exposures to the market, industries and investment styles.

Specific risk also shows up in options. Implied volatility on an individual share is usually higher than on an index, because the index benefits from diversification among its members, and the gap is the basis of dispersion trading. Scheduled events such as earnings announcements concentrate specific risk into known dates.

The boundary between the two kinds of risk depends on the model used. Risk that looks specific under a one-factor market model may be explained by industry or style factors in a richer model. Diversification also relies on specific risks being independent, which can fail. In a crisis, correlation between shares rises and events at one firm, such as a bank failure, can spread to others, turning what appeared to be specific risk into systemic stress. Finally, investors such as founders and employees often cannot diversify their holdings, and for them specific risk is a real cost.