FINM7006 Chap.8 Portfolio Risk, Return and CAPM
Portfolio Risk, Return and CAPM
Expected return describes the centre of a return distribution, while standard deviation describes total dispersion. Portfolios add a second layer: return remains a weighted average, but risk depends on covariance and correlation. This chapter uses that co-movement to explain diversification and efficient combinations, then distinguishes total volatility from systematic beta.
CAPM translates beta into a required return that can enter valuation and NPV when the risk match is appropriate.
What this chapter covers
- 01
Expected return and probability weights
- 02
Variance and standard deviation
- 03
Covariance and correlation
- 04
Portfolio diversification
- 05
Systematic risk and beta
- 06
CAPM required return
Worked example · free
Calculate risk for a two-asset portfolio
- +1Return: 0.5(12%) + 0.5(6%) = 9%.
- +2Variance: add two weighted variance terms and the covariance term to obtain 0.0145.
- +2Risk: square root of 0.0145 is 0.1204, or 12.04%.
- +1Interpret: risk is below the 15% weighted average because correlation is below positive one.
Key terms
- Expected return
- Expected return is the probability-weighted mean of possible investment returns.
- Correlation
- Correlation standardises the direction and strength of co-movement between two returns.
- Diversification
- Diversification reduces portfolio risk by combining assets whose returns do not move perfectly together.
- Systematic risk
- Systematic risk is market-related exposure that remains after broad diversification.
Portfolio Risk, Return and CAPM FAQ
Why is portfolio risk not a weighted average of standard deviations?
Assets move together to different degrees, so covariance contributes to portfolio variance. Expected return is linear in weights, but variance contains squared weights and cross-product terms. Ignoring covariance treats every pair as though their co-movement did not matter and misses the source of diversification benefit.
What does beta measure?
Beta measures sensitivity to market returns within the CAPM framework. A beta above one indicates greater systematic responsiveness than the market benchmark in the model. It is not a percentage, a probability or total volatility. Asset-specific variation can raise standard deviation without producing the same beta.
When can a CAPM return be used in NPV?
Use it when the project or security's systematic risk is reasonably represented by the beta input and the CAPM assumptions are acceptable for the task. A company-wide beta should not be applied automatically to a project with different operating risk. Explain the risk match and test sensitive estimates.
Exam move
Calculate expected return and variance from a small state distribution, then build a two-asset portfolio and vary correlation through positive one, zero and negative one. Explain why the expected-return line does not change while portfolio risk does. Keep beta, standard deviation and correlation in separate boxes with their units and roles.
Practise CAPM as risk-free rate plus beta times market premium, then carry the resulting return into one NPV and state the model limitation. For a state distribution, verify that probabilities sum to one before calculating the expected return. Build a three-column table for outcome, deviation from the mean and squared deviation weighted by probability.
Keep returns consistently in decimals or percentages throughout; mixing units can enlarge variance by a factor of ten thousand. Take the square root only after summing variance and restore the return unit when interpreting standard deviation. For portfolios, confirm that weights describe proportions of market value and sum to one in a fully invested long-only case.
Calculate expected return linearly, then write the complete two-asset variance expression including the covariance term. Replace covariance with correlation times both standard deviations only once. Recalculate at correlations of positive one, zero and negative one while holding weights and individual volatility fixed. Explain why expected return remains the weighted average while risk changes through co-movement.
Use the extreme negative-correlation case to understand possible offset, without assuming that real asset returns maintain perfect correlation. Keep a measure card for standard deviation, covariance, correlation and beta. State what each measures, its unit or scale, and whether diversification can remove the risk it describes.
For CAPM, calculate the market risk premium first, scale it by beta and add the risk-free rate exactly once. Interpret beta as sensitivity, not a probability or percentage volatility. Carry the required return into one security or project valuation only after checking that the beta is relevant to that exposure. Add sensitivity around beta and the market premium because estimated inputs are uncertain.
In closed-book preparation, use mixed prompts that ask you to identify the measure before calculation. Finish each with a sentence on diversification, systematic risk or value. Mark separately any error in probabilities, units, covariance, market premium, beta interpretation or discount-rate application, then rebuild that component from definitions.
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