Systematic vs nonsystematic risk and return-generating models

Which part of an asset’s risk does the market pay for?

An asset’s total risk is the variance of its returns. It has two parts, and only one of them is rewarded.

Systematic risk comes from forces that move the whole market: interest rates, recessions, inflation shocks, wars. It touches almost every asset, so holding more assets does not remove it. Nonsystematic risk is specific to one company or industry: a chief executive resigns, a factory floods, a drug trial fails. Holding many assets cancels these events against each other, so it can be diversified away.

Total risk (variance of the asset)systematic plus nonsystematic; add variances, not standard deviations

• Systematic risk Memorize market-wide: interest rates, inflation, recessions, wars
  • Cannot be diversified away also called market or non-diversifiable risk
  • Earns a risk premium Memorize the only risk the market pays for
• Nonsystematic risk Memorize specific to one company or industry: a CEO resigns, a factory floods
  • Diversifiable shrinks toward zero as holdings are added
  • Earns no premium Memorize a diversified buyer outbids anyone who demands one

Why does the market not pay for nonsystematic risk? Because anyone can remove it by holding many assets at little cost. A buyer who demanded a premium for it would be outbid by a diversified buyer who does not need one. Prices settle where only systematic risk earns a premium. This ties back to the first module of this topic: the variance floor of a large portfolio is the average covariance, which is systematic risk.

What is a return-generating model?

A return-generating model estimates an asset’s expected return from a few measurable inputs. The most general form is a multi-factor model : the asset’s expected excess return is the sum of its exposures to a set of factors, each multiplied by that factor’s risk premium. The exposures are factor sensitivity coefficients (also called factor loadings).

$$E(R_i) - R_f = \sum_{j=1}^{k} \beta_{ij}\,E(F_j)$$

Factors can be macroeconomic (growth, inflation, credit spreads), fundamental (earnings growth, book-to-market ratio, size) or statistical (patterns found in the data). Analysts prefer the first two, because a purely statistical factor can be a data-mining accident with no economic reason to be priced.

Two named multi-factor models appear on the exam. The Fama–French model explains returns with three factors: the market, size (small companies against large) and value (high book-to-market against low). The Carhart four-factor model adds momentum, the return of recent winners over recent losers.

The simplest case has one factor. The single-index model uses the market as the only factor. Its everyday version is the market model , a regression of the asset’s realized returns on the market’s.

$$R_i = \alpha_i + \beta_i\,R_m + e_i$$

The intercept α is the return not explained by the market, the slope β is the sensitivity to the market, and e is the firm-specific return, with a mean of zero and no correlation with the market.

Return-generating modelestimates an asset’s expected return from factors

• Single-index model Use it one factor, the market
  • Market model Memorize Ri = αi + βi Rm + ei, estimated by regression on realized returns
• Multi-factor model Use it several factors, each with a sensitivity
  • Macroeconomic factors growth, inflation, interest rates, credit spreads
  • Fundamental factors earnings growth, book-to-market, size
  • Statistical factors found in the data, may have no economic meaning
  • Fama–French and Carhart Use it market, size, value, plus momentum

How much of an asset’s risk is systematic?

Because e is uncorrelated with the market, the variance of the asset splits cleanly into two terms. Systematic variance is beta squared times the market’s variance. Nonsystematic variance is what is left.

$$\sigma_i^2 = \beta_i^2\,\sigma_m^2 + \sigma_e^2$$

The systematic share of the variance is the same number as the R² of the market-model regression.

$$R^2 = \frac{\beta_i^2\,\sigma_m^2}{\sigma_i^2}$$

Move beta, the market’s risk and the stock’s total risk and watch the bar split. Then drag the number of stocks: the nonsystematic band shrinks toward zero while the systematic floor stays. Diversify away the band you are not paid for; keep the floor you are.

Go deeper Why the market model works for every asset, and the CML only for some

The capital market line (CML) describes only efficient, fully diversified portfolios, because it measures risk by total standard deviation. For a well-diversified portfolio the nonsystematic term is close to zero, so σi is about βiσm and the CML reduces to the single-index relationship E(Ri) − Rf = βi[E(Rm) − Rf]. The market model has no such restriction: it applies to any asset, diversified or not, which is why the next lessons use beta rather than standard deviation to price individual assets.

Factor models are also the engine behind many “smart beta” products, which tilt a portfolio toward size, value or momentum.

Exam tip Variances add, standard deviations do not. Square first, subtract, then take the root.