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Tell apart systematic risk and nonsystematic risk

CFA® Level I · Portfolio Construction · Portfolio Risk and Return: Part II · PM.4.b

The idea

Systematic risk is exposure common to the whole market - rates, growth, inflation, policy - and cannot be diversified away because every asset carries some of it. Nonsystematic risk is specific to an individual company or industry and falls rapidly as holdings are added, approaching negligible in a broad portfolio. The pricing consequence is decisive: investors are compensated only for risk they cannot avoid. Bearing nonsystematic risk earns no premium, because anyone could have eliminated it at no cost simply by diversifying.

Formulas

Total risk split into systematic and nonsystematic

variance of a share = β² × σm² + σε²

β
the share's beta
σm²
the variance of the market's return
σε²
the variance of the part of the share's return the market does not explain

The first term is systematic and cannot be diversified away. The second is nonsystematic, and diversification removes it, so only the first is paid for.

A practice question

From the question bank, with the reason each wrong option is wrong.

Which risk can be substantially eliminated by diversification?

  1. Systematic riskWhy not: Affects every security at once, which is exactly why adding more of them does not remove it.
  2. Nonsystematic risk - correct
  3. Inflation riskWhy not: A systematic influence, shared across assets, and not something spreading holdings can diversify away.

Risk comes in two kinds. Systematic risk affects the whole market, such as recessions, interest rate changes or inflation. Nonsystematic risk is specific to one company or industry, such as a factory fire or a lawsuit. Holding many different investments spreads the second kind out, because bad luck at one company is cancelled by good luck at another. Total risk = Systematic risk + Nonsystematic risk. Diversification removes the second part. The first part hits everything at once, so it stays.

A harder one

Two portfolios have the same beta but very different total volatility. What does the CAPM say about their expected returns?

  1. They are the same, since only systematic risk is priced - correct
  2. The more volatile one earns more, since it carries more riskWhy not: Would follow if total risk were priced. Under the model the extra volatility is diversifiable and earns nothing.
  3. The less volatile one earns more, since it is more efficientWhy not: Return per unit of total risk is not what the CAPM prices. With the same beta, both portfolios have the same expected return.

Beta measures how strongly an investment moves with the overall market. The CAPM says: Expected return = Risk-free rate + Beta x Market risk premium. The risk-free rate is the return on a safe investment, and the market risk premium is the extra return investors expect for holding the market. For example, with a risk-free rate of 3% and a premium of 5%, any portfolio with a beta of 1.0 has an expected return of 3% + 1.0 x 5% = 8%, however jumpy it is. The extra volatility of the second portfolio is company-specific and can be diversified away, so it earns nothing.

The hardest tier

An investor holds a single stock with very high total volatility but a beta of 0.6. What expected return does the CAPM assign?

  1. A return between the risk-free rate and the market's, reflecting the 0.6 beta - correct
  2. A return above the market's, because total volatility is very highWhy not: Total volatility is not priced. The market pays only for the systematic part, measured by beta.
  3. A return equal to the risk-free rate, since the stock is undiversifiedWhy not: The risk-free rate corresponds to a beta of zero. This stock has a positive beta and so earns a premium.

The CAPM says expected return depends only on beta, a stock's sensitivity to the overall market, not on total volatility. Expected return = Risk-free rate + Beta x Market risk premium. Example: risk-free rate 3%, market risk premium 5%, beta 0.6. Expected return = 3% + 0.6 x 5% = 6%. The market as a whole would earn 3% + 5% = 8%. The stock's high total volatility is mostly company-specific risk that could be diversified away, so the market does not pay for it. Holding it alone is a portfolio mistake.

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