BFF2140 Chap.6 Risk, Diversification and CAPM
Risk, Diversification and CAPM
Risk, Diversification and CAPM separates an asset's standalone volatility from its contribution to a portfolio. Expected return is weighted linearly, but portfolio variance also depends on covariance and correlation. Diversification removes firm-specific risk, while beta captures systematic exposure and CAPM translates that exposure into a required return on the security market line.
Probability-weighted returns describe expectation, while variance and standard deviation measure dispersion around it. Portfolio return remains a weighted average, but portfolio risk includes how each pair of assets moves together. Correlation below one can reduce risk without reducing expected return, creating the curved opportunity set and the efficient frontier.
This benefit does not eliminate market-wide shocks, so well-diversified investors focus on systematic rather than specific exposure. Beta measures sensitivity to the market portfolio, and CAPM adds a beta-scaled market risk premium to the risk-free rate. The security market line then compares expected return with the return required for beta.
A security above the line appears underpriced within the model and one below appears overpriced, but this conclusion depends on estimated beta, the market proxy and expected-return assumptions. The chapter combines calculation with those model boundaries so diversification is not confused with guaranteed safety and CAPM is not treated as a forecast promise.
What this chapter covers
- 01
Expected return
- 02
Variance and standard deviation
- 03
Covariance and correlation
- 04
Portfolio diversification
- 05
Beta and systematic risk
- 06
CAPM and the SML
- 07
Model checks linking covariance, correlation, portfolio variance, beta and the gap between expected return and required return
Worked example · free
Calculate two-asset portfolio risk
- 2Expected return is 0.60 times 12% plus 0.40 times 6%, which equals 9.6%.
- 5Apply the two-asset variance formula including the covariance term, then take the square root to obtain 11.86%.
Key terms
- Covariance
- A measure of how two asset returns move together.
- Beta
- A security's systematic return sensitivity relative to the market portfolio.
- Market risk premium
- The expected market return above the risk-free rate.
Risk, Diversification and CAPM FAQ
Why is portfolio risk not a weighted average?
Risk depends on how returns move together as well as each asset's volatility. The covariance term can reduce total variance when correlation is below one, which is the mathematical source of diversification.
What risk does CAPM reward?
CAPM rewards systematic risk measured by beta because diversified investors can remove firm-specific risk without sacrificing expected return. Bearing avoidable specific risk therefore does not earn a separate premium in the model.
What does a beta above one mean?
A beta above one means the asset has greater systematic sensitivity than the market. CAPM therefore assigns it a required return above the market return when the market risk premium is positive.
Exam move
Separate the three layers of risk analysis: individual outcomes, portfolio co-movement and market exposure. For a single security, build the probability distribution, verify probabilities sum to one, calculate expected return and then measure dispersion around that expectation.
For a two-asset portfolio, compute expected return as a weighted average but write the entire variance formula, including the covariance term, before substituting numbers. Translate correlation into covariance using both standard deviations and check the result by comparing portfolio risk with sensible bounds. Change correlation while holding weights and standalone risks fixed so the source of diversification becomes visible.
Explain why combining perfectly positively correlated assets provides little risk reduction, while lower correlation bends the attainable set leftward. Do not describe diversification as eliminating all volatility; it removes firm-specific components while systematic shocks remain. Estimate beta conceptually as sensitivity to market movements and distinguish it from total standard deviation.
Sketch the security market line with beta on the horizontal axis, required return on the vertical axis, the risk-free intercept and the market-risk-premium slope. Calculate CAPM return and then compare a stated expected return with the required return. A point above the line appears underpriced within the model, while one below appears overpriced; include the expected price adjustment and keep the claim conditional.
Practise interpreting betas below zero, between zero and one, equal to one and above one without confusing beta with correlation. Use calculator and spreadsheet exercises to verify variance, but retain a paper formula that exposes weights squared and the factor of two in the covariance term.
Keep error categories for omitted covariance, variance reported as standard deviation, weights not summing to one and market premium confused with market return. Finish each problem by naming which risk is rewarded and why a diversified investor does not receive compensation for avoidable specific risk.
Review model limits such as estimated beta, an unobservable true market portfolio and unstable correlations, particularly during stressed periods.
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