FNCE10002 Chap.4 Risk, Return and Diversification

Risk, Return and Diversification

Define expected return

The course material gives this chapter a concrete anchor: Weeks 5 and 6 cover observed returns, variability, two-security portfolios, correlation and diversification limits.

That expected return anchor controls how variance is explained and how covariance is tested in changed practice.

Risk, Return and Diversification is a quantitative decision problem built from expected return, variance and covariance.

The aim is to combine assets by weight and co-movement rather than averaging risk; a numerical result earns meaning only when the variables, units, assumptions and comparison are all explicit.

Begin with expected return: state what quantity it represents, the scale on which it is measured and the condition under which it changes.

Then map every symbol in the Risk, Return and Diversification formula checkpoint to expected return before calculation begins.

Next connect variance to the calculation. Show the variance transformation line by line, preserve units and signs, and make any denominator or baseline visible.

A variance calculator output is not a method; the reader must be able to reconstruct why that operation answers the question.

Use covariance to interpret or stress-test the result. Ask whether the covariance magnitude is plausible, whether a boundary case behaves as expected and which conclusion would reverse if an assumption changed.

This is where computation becomes analysis rather than arithmetic.

When the task is to combine assets by weight and co-movement rather than averaging risk, separate inputs supplied by the problem from quantities you derive.

Then report the covariance result in the language of the course and attach the relevant uncertainty, limitation or decision consequence.

Trace variance

Build a representation check before solving.

Put expected return, variance and covariance into a small symbol-and-units table, mark which values are observed and which are calculated, and predict the direction of the result before doing arithmetic. A sign, scale or unit mismatch in expected return then becomes visible at setup instead of being hidden inside a polished final number.

Run one sensitivity test after the baseline answer.

Change the input most closely connected to variance, hold the remaining assumptions fixed and recompute only the affected steps. Explain whether the movement in covariance matches the mechanism.

This variance sensitivity shows which assumption controls the conclusion and prevents a single scenario from being presented as universal.

Use a three-column expected return error log for fnce10002: translation error, calculation error and interpretation error. Record the exact line where the variance solution first diverged, rewrite that line, and check it with a limiting case or an independent calculation.

Correcting the first failed variance move is more useful than copying the complete solution again.

A complete response should make the task visible before the detail: identify what must be decided, define the relevant terms, connect the evidence to variance, and use covariance to test the result.

The final sentence about covariance should answer the question actually asked rather than merely repeat the topic.

The controlling limit is specific: Historical estimates may not represent future distributions or extreme dependence.

Keep that covariance limit beside the worked example, because it separates a careful fnce10002 answer from one that sounds confident but claims more than the task or evidence supports.

For revision, retrieve expected return, variance and covariance without notes, explain their relationship aloud, then complete a changed version of the application: combine assets by weight and co-movement rather than averaging risk.

Record the first failed variance reasoning move and repair it before attempting another case.

What this chapter covers

• 01

  expected return

• 02

  variance

• 03

  covariance

• 04

  Applying expected return

• 05

  Limits of variance and covariance

Compute two-asset expected return

Key terms

expected return

Probability-weighted average of possible investment returns. This chapter uses the concept when students combine assets by weight and co-movement rather than averaging risk. Use this definition when the task is to combine assets by weight and co-movement rather than averaging risk.

variance

Expected squared deviation of return from its mean. It helps explain the reasoning required to combine assets by weight and co-movement rather than averaging risk. Use this definition when the task is to combine assets by weight and co-movement rather than averaging risk.

covariance

Measure of how two security returns move together. Its limit matters because historical estimates may not represent future distributions or extreme dependence. Use this definition when the task is to combine assets by weight and co-movement rather than averaging risk.

Risk, Return and Diversification FAQ

Exam move

Reconstruct the relationship among expected return, variance and covariance; complete the chapter application without notes; then test the result against this limit: Historical estimates may not represent future distributions or extreme dependence.

Working through Risk, Return and Diversification in FNCE10002? Sia is AskSia’s AI Finance tutor — ask any FNCE10002 Risk, Return and Diversification question and get a clear, step-by-step explanation grounded in how FNCE10002 is taught and assessed. Read this chapter free, then take your hardest questions to Sia.