FNCE90056 Chap.1 Return, Risk and Investor Utility
Return, Risk and Investor Utility
Return, Risk and Investor Utility develops this reasoning route: Compute state-contingent return moments and use risk aversion to compare complete investment opportunities. Start with expected return, which is The probability-weighted average return across possible states. Then use variance as a separate analytical move: The probability-weighted squared dispersion of returns around expected return.
For expected return, a definition must classify an observed fact rather than decorate a paragraph; variance must then carry a mechanism or test an inference. The chapter application asks you to Compare two risky funds for investors with different risk aversion after computing expected return, variance and utility under the same state probabilities.
The controlling limit is: Utility rankings depend on the stated preference model and inputs; they are not universal measures of investment quality. A defensible expected return response compares risk aversion under the same criteria, identifies uncertainty and closes with a responsible actor, action and review trigger. Build the variance evidence chain in four passes.
First, state the decision and define expected return without importing a conclusion. Second, choose only facts that activate or challenge variance. Third, explain the intermediate mechanism so the first unsupported variance move is visible. Fourth, change one condition attached to risk aversion and decide whether the result remains, narrows or reverses.
That risk aversion variation turns the vocabulary into a transferable method and makes correction more precise than rereading. Keep definitions, observations, assumptions and judgements about expected return in separate sentences, especially when the case leaves evidence incomplete. Before finalising, audit the conclusion backwards from mean-variance utility.
Ask which fact supports each claim, which concept gives that fact relevance and which uncertainty could defeat the mean-variance utility connection. If expected return and variance appear to do the same job, rewrite one paragraph until their different effects become observable. When the risk aversion alternative cannot change the action, strengthen the comparison or remove it.
Finally, translate mean-variance utility into a practical sequence: identify who decides, what happens next, which evidence is retained and when the judgement is reviewed. These controls keep the expected return conclusion from outrunning the chapter evidence.
What this chapter covers
- 01
Expected return
- 02
Variance
- 03
Risk aversion
- 04
Mean-variance utility
- 05
Applied decision method
- 06
Boundary and transfer test
Apply expected return to a changed case
- 1Define expected return and state the decision boundary.
- 1Connect the material facts to variance through an explicit mechanism.
- 1Use risk aversion to test a credible alternative.
- 1State the qualified conclusion and review condition.
Key terms
- Expected return
- The probability-weighted average return across possible states. Use it by tying the definition to a fact and a consequence in the chapter case.
- Variance
- The probability-weighted squared dispersion of returns around expected return. Use it by tying the definition to a fact and a consequence in the chapter case.
- Risk aversion
- A preference for a less risky prospect when expected return is held constant. Use it by tying the definition to a fact and a consequence in the chapter case.
Return, Risk and Investor Utility FAQ
Which inputs must be identified before calculating expected return?
State the definition first: The probability-weighted average return across possible states. Identify the fact that establishes the starting object, explain why it matters to the decision and keep the conclusion inside this boundary: Utility rankings depend on the stated preference model and inputs; they are not universal measures of investment quality.
How would variance move if one stated assumption changed?
Use variance to carry the central relationship rather than repeat the opening label. Its chapter meaning is: The probability-weighted squared dispersion of returns around expected return. Show the intermediate step and the evidence that could make that mechanism fail.
When is risk aversion the appropriate benchmark for this comparison?
Reverse the case condition closest to risk aversion and retrace only the affected steps. The relevant meaning is: A preference for a less risky prospect when expected return is held constant. State whether the action remains, narrows or reverses and why.
What can and cannot be inferred from mean-variance utility alone?
Treat mean-variance utility as a constraint with analytical force: A preference score combining expected return with a penalty for variance scaled by risk aversion. Name the uncertainty, responsible actor and review trigger instead of presenting the chapter judgement as universal.
Exam move
Retrieve expected return, variance, risk aversion, mean-variance utility without notes, apply them to a changed version of the case and repair the first step that violates this limit: Utility rankings depend on the stated preference model and inputs; they are not universal measures of investment quality.
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