FNCE90065 Chap.5 Measuring Investment Risk and Return
Measuring Investment Risk and Return
Investment return combines price change and cash distributions over a stated holding period. This chapter separates realised return from a forward-looking distribution of possible returns, then calculates expected return, variance and standard deviation. It uses mean-standard-deviation space to explain dominance and shows why a high realised outcome is not proof of a high expected return.
The core habit is keeping probabilities, return units and the distribution centre consistent.
What this chapter covers
- 01
Realised return includes both price change and distributions received
- 02
Expected return is the probability-weighted centre of possible outcomes
- 03
Variance measures squared deviations from expected return
- 04
Standard deviation expresses dispersion in the same units as return
- 05
Historical sample statistics estimate rather than guarantee future parameters
- 06
Dominance requires higher return for the same risk or lower risk for the same return
Worked example · free
Measure a three-state return distribution
- 1Confirm the probabilities sum to one.
- 1Compute expected return as 8.8 percent.
- 1Find each return deviation from 8.8 percent.
- 1Square deviations and multiply by their probabilities.
- 1Sum to variance of 156.16 percentage-points squared.
- 1Take the square root to obtain standard deviation of approximately 12.50 percent.
Key terms
- Realised return
- Realised return is the price change plus distributions received, divided by the beginning investment.
- Expected return
- Expected return is the probability-weighted average of possible returns.
- Variance
- Variance is the probability-weighted average of squared deviations from expected return.
- Standard deviation
- Standard deviation is the positive square root of variance and a common measure of volatility.
- Dominance
- Dominance occurs when one asset offers at least as much return and no more risk, with one strict improvement.
Measuring Investment Risk and Return FAQ
What belongs in realised share return?
Include the ending price minus beginning price and any dividend received during the holding period, then divide by beginning price. State the holding period alongside the percentage. Omitting the dividend understates performance, while using ending price as the denominator changes the meaning of the measure.
Why use standard deviation instead of variance?
Variance is necessary for aggregation because deviations are squared, but its units are return squared. Standard deviation takes the square root and returns to the same units as return, making it easier to compare with expected return. Both contain the same information about dispersion.
Does a high historical return mean a high expected return?
Not necessarily. A realised return is one outcome from an uncertain process, while expected return is the centre of a distribution. Historical samples can estimate future parameters only when the sample remains relevant. A favourable draw or changing conditions can make the latest outcome a poor forecast.
Exam move
Use state tables with columns for outcome, probability, probability-weighted return, deviation and probability-weighted squared deviation. Check the probability total before calculating. Work once in decimal units and once in percentage-point units so you understand how the final standard deviation converts.
Practise dominance questions visually in expected-return and volatility space, and state when neither asset dominates because one has both more return and more risk. Keep realised, sample and expected labels explicit in every sentence to avoid presenting an estimate as a promise. Begin with holding-period return questions that include both price change and dividend. State the horizon and use beginning price as the denominator.
Then create a three-state distribution and calculate expected return, variance and standard deviation in a table. Recompute after moving probability toward a tail outcome and predict that volatility should rise. This creates an intuitive check on the squared-deviation arithmetic. Next, plot several assets in expected-return and volatility space.
Mark clear dominance only where one asset has no less return and no more risk, with one strict improvement. Where one asset has more of both, write that preference is not determined from those coordinates alone. For historical samples, distinguish sample mean and sample standard deviation from future parameters. Change the sample window and discuss whether extra observations improve precision or mix different regimes.
Keep a separate note on units: decimals through the variance calculation, percentage output after the square root. The final revision test is verbal: explain why one excellent realised year does not prove a high expected return and why a low-volatility sample is not a guarantee about the next period. Add a downside scenario with the same mean as a symmetric distribution but a different shape.
Explain what standard deviation captures and what it omits, especially when an investor cares more about losses than equally sized gains.
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