Monash University · S1 2026 · FACULTY OF BUSINESS & ECONOMICS

BFC2140 · Corporate Finance

Q: What is the difference between systematic and unsystematic risk?

Unsystematic risk is specific to a firm or industry — a product recall, a lawsuit, a management change — and can be diversified away by holding many different assets, because such shocks tend to offset across a large portfolio. Systematic (market) risk comes from economy-wide factors like interest rates, recessions and inflation that affect nearly all assets at once, so it cannot be diversified away. The key implication is that the market only rewards systematic risk: since unsystematic risk can be eliminated for free through diversification, investors are not paid to bear it.

Q: Why is portfolio standard deviation usually less than the weighted average of the individual standard deviations?

Because of the covariance term in the portfolio variance formula. When two assets are less than perfectly correlated (ρ < 1), their returns do not move in lockstep, so when one is down the other is often less down or up. This offsetting is the diversification benefit: it pulls the portfolio's standard deviation below the simple weighted average of the components' standard deviations. The lower the correlation, the larger the benefit; only at ρ = 1 does the portfolio's risk equal the weighted average.

Q: When do I use the probability approach versus the time-series approach?

Use the probability (forward-looking) approach when the question gives you states of the economy with probabilities and the return in each state — then E(R) = Σ Rᵢpᵢ and Var = Σ pᵢ(Rᵢ − E(R))². Use the time-series (historical) approach when you are given a sample of past returns — then E(R) is the simple average and the sample variance divides by (n − 1). Both estimate the same quantities; the data you are handed tells you which to apply.

Q: How do I tell whether an asset is under- or over-priced with the CAPM?

Compute the CAPM-required return from the asset's beta: R_f + β[E(R_m) − R_f]. Then compare it with the asset's expected return. If the expected return is above the required return, the asset offers more than enough compensation for its systematic risk — it plots above the Security Market Line and is under-priced (a buy). If the expected return is below the required return, it plots below the SML and is over-priced. An asset exactly on the line is fairly priced.

Q: How is risk and return examined in BFC2140?

It is the Week 9 topic and is emphasised on the final (Weeks 5-12). Expect Section B numerical questions computing expected return and standard deviation, two-asset portfolio risk with the covariance term, or a CAPM required return, and Section C reasoning about diversification, the systematic/unsystematic split, and SML mispricing. The chapter also sets up the cost of equity (CAPM) used in the next chapter on the cost of capital.

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Chapter 8 of 11 · BFC2140

Risk and Return

This chapter formalises how investors are rewarded for bearing risk and is the foundation of the cost of equity that follows. It covers the holding-period return; expected return, variance and standard deviation (by both the probability and time-series approaches); two-asset portfolio risk and the covariance term; diversification; the split between systematic and unsystematic risk; and beta and the CAPM/Security Market Line. It is examined as Section B numerical questions (expected return, portfolio standard deviation, CAPM return) and Section C reasoning about diversification and whether an asset is under- or over-priced relative to the SML.

In this chapter

What this chapter covers

01Holding-period return: R = (CF₁ + P₁ − P₀)/P₀
02Expected return, variance and standard deviation by the probability approach
03Expected return, variance and standard deviation by the time-series (historical) approach
04Two-asset portfolio expected return and the variance formula with the covariance term
05Covariance and correlation: cov₁₂ = ρ₁₂σ₁σ₂ and the diversification effect
06Systematic (market) risk versus unsystematic (diversifiable) risk
07Beta as the measure of systematic risk relative to the market
08The CAPM and the Security Market Line: E(Rᵢ) = R_f + βᵢ[E(R_m) − R_f]

Worked example · free

Expected return, standard deviation and CAPM mispricing

Q [7 marks]. An asset's returns depend on the economy: boom (probability 0.3, return 22%), normal (probability 0.5, return 11%) and recession (probability 0.2, return −6%). (a) Find the expected return and standard deviation. (b) Given beta = 1.25, a risk-free rate of 4% and an expected market return of 10%, find the CAPM required return and state whether the asset is under- or over-priced. Give percentages to two decimal places.

2 marksCompute the expected return as the probability-weighted average: E(R) = 0.3(22) + 0.5(11) + 0.2(−6) = 6.6 + 5.5 − 1.2 = 10.90%.
2 marksFind the variance as the probability-weighted squared deviations: Var = 0.3(22 − 10.9)² + 0.5(11 − 10.9)² + 0.2(−6 − 10.9)² = 0.3(123.21) + 0.5(0.01) + 0.2(285.61).
1 markSum and take the square root: Var = 36.96 + 0.005 + 57.12 = 94.09, so standard deviation = √94.09 = 9.70%.
1 markCompute the CAPM required return: E(R) = R_f + β[E(R_m) − R_f] = 4 + 1.25(10 − 4) = 4 + 7.5 = 11.50%.
1 markCompare expected (10.90%) with required (11.50%): the asset's expected return is below what its systematic risk requires, so it plots below the SML and is over-priced.

Expected return = 10.90%, standard deviation = 9.70%; CAPM required return = 11.50%. Because 10.90% < 11.50%, the asset offers too little return for its beta and is over-priced (plots below the Security Market Line).

Sia tip — Keep the two 'risk' measures distinct: standard deviation (9.70% here) is total risk and drives the probability-based answer, while beta (1.25) is systematic risk and drives the CAPM. The mispricing verdict comes only from comparing the asset's expected return to its CAPM-required return — above the SML is under-priced (buy), below is over-priced.

Glossary

Key terms

Holding-period return (HPR): The total return over a period from income and capital gain: R = (CF₁ + P₁ − P₀)/P₀. It combines the dividend/coupon received with the price change, all relative to the price paid.
Expected return and variance: Expected return is the probability-weighted average outcome, E(R) = Σ Rᵢpᵢ (or the simple mean of historical returns). Variance, Σ pᵢ(Rᵢ − E(R))² (or Σ(Rᵢ − E(R))²/(n − 1) for a sample), measures dispersion; its square root is the standard deviation, the usual measure of total risk.
Covariance and correlation: Covariance measures how two assets' returns move together; correlation ρ standardises it to [−1, 1], with cov₁₂ = ρ₁₂σ₁σ₂. The lower the correlation, the greater the risk reduction from combining the assets in a portfolio.
Diversification: Combining imperfectly correlated assets to reduce portfolio risk. Diversification removes unsystematic (firm-specific) risk; the lower the correlations, the more total risk falls — but systematic risk cannot be diversified away.
Systematic vs unsystematic risk: Unsystematic (diversifiable, firm-specific) risk can be eliminated by holding a well-diversified portfolio; systematic (market) risk affects all assets and remains. Only systematic risk is rewarded, because investors can costlessly diversify away the rest.
Beta and the CAPM/SML: Beta measures an asset's systematic risk — its sensitivity to the market. The CAPM prices that risk: E(Rᵢ) = R_f + βᵢ[E(R_m) − R_f]. The Security Market Line plots this relationship; assets above it are under-priced and those below it over-priced.

FAQ

Risk and Return FAQ

What is the difference between systematic and unsystematic risk?

Unsystematic risk is specific to a firm or industry — a product recall, a lawsuit, a management change — and can be diversified away by holding many different assets, because such shocks tend to offset across a large portfolio. Systematic (market) risk comes from economy-wide factors like interest rates, recessions and inflation that affect nearly all assets at once, so it cannot be diversified away. The key implication is that the market only rewards systematic risk: since unsystematic risk can be eliminated for free through diversification, investors are not paid to bear it.

Why is portfolio standard deviation usually less than the weighted average of the individual standard deviations?

Because of the covariance term in the portfolio variance formula. When two assets are less than perfectly correlated (ρ < 1), their returns do not move in lockstep, so when one is down the other is often less down or up. This offsetting is the diversification benefit: it pulls the portfolio's standard deviation below the simple weighted average of the components' standard deviations. The lower the correlation, the larger the benefit; only at ρ = 1 does the portfolio's risk equal the weighted average.

When do I use the probability approach versus the time-series approach?

Use the probability (forward-looking) approach when the question gives you states of the economy with probabilities and the return in each state — then E(R) = Σ Rᵢpᵢ and Var = Σ pᵢ(Rᵢ − E(R))². Use the time-series (historical) approach when you are given a sample of past returns — then E(R) is the simple average and the sample variance divides by (n − 1). Both estimate the same quantities; the data you are handed tells you which to apply.

How do I tell whether an asset is under- or over-priced with the CAPM?

Compute the CAPM-required return from the asset's beta: R_f + β[E(R_m) − R_f]. Then compare it with the asset's expected return. If the expected return is above the required return, the asset offers more than enough compensation for its systematic risk — it plots above the Security Market Line and is under-priced (a buy). If the expected return is below the required return, it plots below the SML and is over-priced. An asset exactly on the line is fairly priced.

How is risk and return examined in BFC2140?

It is the Week 9 topic and is emphasised on the final (Weeks 5-12). Expect Section B numerical questions computing expected return and standard deviation, two-asset portfolio risk with the covariance term, or a CAPM required return, and Section C reasoning about diversification, the systematic/unsystematic split, and SML mispricing. The chapter also sets up the cost of equity (CAPM) used in the next chapter on the cost of capital.

Study strategy

Exam move

Keep total risk (standard deviation) and systematic risk (beta) firmly separate — they answer different questions and feed different formulas. Drill both routes to expected return and variance (probability and time-series), and practise the two-asset variance formula until the covariance term is automatic, since dropping it or mishandling the correlation is the usual error. Be ready to explain diversification in words: it removes unsystematic risk, the benefit grows as correlation falls, and a systematic-risk floor remains. Master the CAPM/SML, and remember the mispricing logic is a comparison of expected versus required return (above the line = under-priced = buy). Finally, see this chapter as the launchpad for the cost of capital: the CAPM you learn here is one of the two ways to estimate the cost of equity in the WACC build that follows.

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