FINM1001 Chap.6 Risk and Return
Risk and Return
Describe a distribution with centre and spread
A risky investment can produce several possible returns. Expected return is the probability-weighted average of those outcomes. It summarises the centre of the stated distribution, not the outcome that must occur and not necessarily the outcome with the highest probability.
Confirm probabilities sum to one before calculating.
Variance measures weighted squared deviations from expected return. Squaring prevents positive and negative deviations from cancelling. Standard deviation is the square root of variance and is easier to interpret because it uses the same return units as the outcomes.
Keep returns in one scale through the calculation; mixing whole percentages with decimals produces severe errors.
The order is fixed. Compute expected return first, subtract that same value from every possible outcome, square each deviation, weight by probability and add, then take the square root.
Rounding the expected return differently across rows creates an inconsistent variance, so retain precision until the final line.
Separate total and systematic risk
Standalone standard deviation captures total return dispersion. Part of that variation can be firm-specific, arising from events that need not affect other companies.
A diversified portfolio can reduce such unsystematic risk when holdings do not move perfectly together. Market-wide co-movement is systematic risk and remains relevant in a diversified portfolio.
This distinction prepares the CAPM, which uses beta rather than standalone standard deviation to price market exposure. A volatile asset can have moderate beta when much of its variation is unique.
Conversely, an asset with modest standalone spread can still contribute meaningfully to market risk when its returns move closely with the market.
Interpretation should remain conditional. Expected return and standard deviation depend on the assumed outcomes and probabilities. They do not guarantee a realised return or fully describe tail events.
State what the measure supports and avoid turning a statistical summary into a certainty.
What this chapter covers
- 01
Return distributions
- 02
Expected return
- 03
Variance
- 04
Standard deviation
- 05
Systematic and unsystematic risk
Worked example · free
Measure a three-state return
- 1Calculate probability-weighted expected return.
- 1Measure every deviation from that centre.
- 1Weight squared deviations to obtain variance.
- 1Take the square root and interpret units.
Key terms
- Return distribution
- A set of possible investment returns together with the probability assigned to each mutually exclusive outcome.
- Variance
- The probability-weighted average of squared deviations from expected return, expressed in squared return units.
- Unsystematic risk
- Firm-specific return variation that can be reduced by combining assets whose unique outcomes do not move together.
- Systematic risk
- Market-related co-movement that remains in a diversified portfolio and forms the risk focus of the CAPM.
Risk and Return FAQ
Is expected return the most likely outcome?
Not necessarily. It is a probability-weighted average and may not equal any possible outcome, even when one state has the highest individual probability in the specified distribution.
Why are deviations squared?
Squaring prevents positive and negative distances from cancelling and gives greater weight to outcomes farther from the expected-return centre before probabilities are applied and summed.
Why report standard deviation instead of variance?
Standard deviation returns the measure to ordinary return units, making it easier to compare with expected returns and observed percentage outcomes on the same horizon.
Does high volatility always mean high beta?
No. Standard deviation measures total standalone spread, while beta measures market co-movement. Large firm-specific movements can raise volatility without proportionally raising beta or the asset's priced systematic exposure.
Exam move
Create outcome-probability tables by hand, compute the mean before any deviation, and finish each problem by stating whether the measure describes total spread or market exposure. Use columns for outcome, probability, weighted return, deviation from the unrounded mean, squared deviation and weighted squared deviation. Sum the weighted-return column for the centre and the final column for variance.
This layout reveals omitted probabilities and inconsistent percentage conversion. Compare distributions only after confirming they use the same horizon and units. A higher expected return with higher standard deviation presents a trade-off, not an automatic ranking. When moving into portfolio analysis, keep each asset's expected return and standard deviation but add the relationship between returns.
When moving into CAPM, replace the total-spread question with market co-movement. Naming that transition aloud prevents every chapter's risk number from being treated as interchangeable. Before accepting a result, confirm probabilities total one, the mean lies between the smallest and largest outcomes, variance is non-negative and standard deviation uses the original return unit.
These four checks require no second full solution.
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