FNCE20005 · Corporate Financial Decision Making
Risk and the CAPM
Every valuation in this subject discounts risky cash flows, and the discount rate has to compensate for risk. This chapter builds the machinery to set it. Start with one asset: the expected return is the probability-weighted average outcome, and variance and its square root, the standard deviation, measure total risk. Combine assets into a portfolio and return is a clean weighted average, but risk is not — the portfolio variance adds a covariance cross-term, and the lower the correlation, the more risk cancels out. Keep adding imperfectly-correlated stocks and the firm-specific (unsystematic) risk washes away, leaving only systematic, market-wide risk — the only risk investors are paid to bear, because anything you can diversify away for free earns no premium. That surviving risk is measured by beta, the slope of a stock regressed on the market. The pay-off is the CAPM: ke = Rf + β[E(RM) − Rf], the cost of equity you feed straight into WACC next chapter, read geometrically off the security market line.
What this chapter covers
- 011 Expected return, variance and standard deviation of one asset
- 022 Covariance and correlation — how two assets move together
- 033 Portfolio return (weighted average) and portfolio risk (the covariance term)
- 044 Diversification — systematic vs unsystematic risk
- 055 Beta as the surviving, priced risk measure
- 066 The CAPM, the cost of equity, and the security market line (SML)
- 077 Worked example — cost of equity via CAPM
Worked example: cost of equity via CAPM, from a regression beta
- +1Identify the three CAPM inputs: Rf = 2.75%, β = 1.25, MRP = 5.76%. (If handed E(RM) instead of the premium, subtract Rf first.)
- +1Stock's risk premium: β × MRP = 1.25 × 5.76% = 7.20% — the extra return for above-average systematic risk.
- +1Add the risk-free baseline: ke = Rf + β·MRP = 2.75% + 7.20% = 9.95%.
- +1Sense-check on the SML: β > 1, so ke must exceed the market return E(RM) = 2.75% + 5.76% = 8.51%. Indeed 9.95% > 8.51% — consistent.
Key terms
- Expected return and variance
- E[R] = Σ piRi is the probability-weighted average outcome; variance σ² = Σ pi(Ri − E[R])² measures dispersion, and its square root (standard deviation) is the everyday measure of total risk in the same percentage units as the return.
- Covariance and correlation
- Covariance σAB is the expected product of two assets' deviations; correlation ρ = σAB/(σAσB) rescales it to between −1 and +1. The lower the correlation, the more diversification reduces portfolio risk.
- Systematic vs unsystematic risk
- Unsystematic (firm-specific) risk can be diversified away and earns no return; systematic (market-wide) risk cannot be diversified away and is the only risk priced. Total risk = systematic + unsystematic.
- Beta
- A stock's sensitivity to market movements — its dose of systematic risk — estimated as the slope when its returns are regressed on the market's. β = 1 is average risk, β > 1 amplifies the market, β < 1 dampens it. Beta, not SD, is what gets priced.
- CAPM / security market line
- The capital asset pricing model: ke = Rf + β[E(RM) − Rf]. Plotted against beta it is the security market line (intercept Rf, slope the market risk premium); every fairly-priced asset sits on it.
Risk and the CAPM FAQ
Why is beta, not standard deviation, used in CAPM?
Because only non-diversifiable (systematic) risk earns a return. A stock can have a huge SD from firm-specific noise yet a small beta, so the market pays little for it. Investors can shed firm-specific risk for free by diversifying, so a competitive market commands no premium for bearing it. CAPM rewards the contribution to a diversified portfolio's risk — beta — not standalone SD. Plugging total SD into a required-return equation is the most-baited trap in this topic.
Why isn't portfolio risk just the weighted average of the SDs?
Because risk is not linear. Portfolio return is a clean weighted average, but portfolio variance adds a covariance cross-term: σp² = wA²σA² + wB²σB² + 2wAwBρσAσB. When ρ < 1 that cross-term is smaller than under lockstep, so the portfolio SD lands below the weighted-average SD. Averaging the SDs directly is only correct when ρ = +1, and is the single most common arithmetic error here.
What is the difference between the SML and the CML?
The security market line (SML) plots required return against beta (systematic risk) and prices individual assets — this is where CAPM and the cost of equity live. The capital market line plots return against total standard deviation and applies only to efficient portfolios. Confusing the two, or reading a cost of equity off the CML, is a flagged error.
Is CAPM the only way to get the cost of equity?
CAPM is the primary route in this subject. The alternative is the Gordon-growth DCF route, ke = D1/P0 + g, which backs the cost of equity out of the dividend valuation. It is useful as a cross-check when a reliable beta is hard to find.
Exam move
Split your practice into the two exam flavours. For the mechanical questions, drill the recipe: E[R], then variance and SD, then a two-asset portfolio return (weighted average) and risk (the variance formula with the covariance term — never average the SDs). For the CAPM plug-in, memorise the three-step recipe: get the market risk premium (subtract Rf from E(RM) if needed), multiply by beta for the stock's risk premium, add Rf. Always sanity-check direction against the SML (β > 1 means above the market return). For the conceptual MCQ, be able to state in one line why only systematic risk is priced and why diversification removes only the unsystematic half. The single trap that recurs: use beta, never total SD, in CAPM.
