FNCE90056 Chap.3 Portfolio Variance and Diversification
Portfolio Variance and Diversification
Portfolio Variance and Diversification develops this reasoning route: Trace how weights, variances and covariances determine portfolio risk and the minimum-variance opportunity set. Start with covariance, which is A measure of the linear co-movement between two asset returns. Then use portfolio variance as a separate analytical move: The weighted combination of asset variances and pairwise covariances.
For covariance, a definition must classify an observed fact rather than decorate a paragraph; portfolio variance must then carry a mechanism or test an inference. The chapter application asks you to Recompute a two-asset portfolio after changing correlation while holding individual expected returns and volatilities fixed.
The controlling limit is: Diversification changes portfolio risk through covariance; averaging standalone volatilities is not a valid calculation. A defensible covariance response compares diversification under the same criteria, identifies uncertainty and closes with a responsible actor, action and review trigger. Build the portfolio variance evidence chain in four passes.
First, state the decision and define covariance without importing a conclusion. Second, choose only facts that activate or challenge portfolio variance. Third, explain the intermediate mechanism so the first unsupported portfolio variance move is visible. Fourth, change one condition attached to diversification and decide whether the result remains, narrows or reverses.
That diversification variation turns the vocabulary into a transferable method and makes correction more precise than rereading. Keep definitions, observations, assumptions and judgements about covariance in separate sentences, especially when the case leaves evidence incomplete. Before finalising, audit the conclusion backwards from minimum-variance frontier.
Ask which fact supports each claim, which concept gives that fact relevance and which uncertainty could defeat the minimum-variance frontier connection. If covariance and portfolio variance appear to do the same job, rewrite one paragraph until their different effects become observable. When the diversification alternative cannot change the action, strengthen the comparison or remove it.
Finally, translate minimum-variance frontier into a practical sequence: identify who decides, what happens next, which evidence is retained and when the judgement is reviewed. These controls keep the covariance conclusion from outrunning the chapter evidence.
What this chapter covers
- 01
Covariance
- 02
Portfolio variance
- 03
Diversification
- 04
Minimum-variance frontier
- 05
Applied decision method
- 06
Boundary and transfer test
Apply covariance to a changed case
- 1Define covariance and state the decision boundary.
- 1Connect the material facts to portfolio variance through an explicit mechanism.
- 1Use diversification to test a credible alternative.
- 1State the qualified conclusion and review condition.
Key terms
- Covariance
- A measure of the linear co-movement between two asset returns. Use it by tying the definition to a fact and a consequence in the chapter case.
- Portfolio variance
- The weighted combination of asset variances and pairwise covariances. Use it by tying the definition to a fact and a consequence in the chapter case.
- Diversification
- Risk reduction produced by combining imperfectly co-moving assets. Use it by tying the definition to a fact and a consequence in the chapter case.
Portfolio Variance and Diversification FAQ
Which inputs must be identified before calculating covariance?
State the definition first: A measure of the linear co-movement between two asset returns. Identify the fact that establishes the starting object, explain why it matters to the decision and keep the conclusion inside this boundary: Diversification changes portfolio risk through covariance; averaging standalone volatilities is not a valid calculation.
How would portfolio variance move if one stated assumption changed?
Use portfolio variance to carry the central relationship rather than repeat the opening label. Its chapter meaning is: The weighted combination of asset variances and pairwise covariances. Show the intermediate step and the evidence that could make that mechanism fail.
When is diversification the appropriate benchmark for this comparison?
Reverse the case condition closest to diversification and retrace only the affected steps. The relevant meaning is: Risk reduction produced by combining imperfectly co-moving assets. State whether the action remains, narrows or reverses and why.
What can and cannot be inferred from minimum-variance frontier alone?
Treat minimum-variance frontier as a constraint with analytical force: The portfolios with the lowest variance available for each expected return. Name the uncertainty, responsible actor and review trigger instead of presenting the chapter judgement as universal.
Exam move
Retrieve covariance, portfolio variance, diversification, minimum-variance frontier without notes, apply them to a changed version of the case and repair the first step that violates this limit: Diversification changes portfolio risk through covariance; averaging standalone volatilities is not a valid calculation.
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