FNCE90065 Chap.6 Portfolio Risk and Diversification
Portfolio Risk and Diversification
Portfolio expected return is a weighted average, but portfolio risk depends on component volatility and co-movement. This chapter interprets covariance and correlation, calculates two-asset variance and explains why imperfect correlation can reduce risk. It distinguishes asset-specific risk from common market exposure and asks how a new security changes the portfolio already held.
The key move is writing the covariance cross-term and reasoning about its sign before calculating.
What this chapter covers
- 01
Portfolio expected return uses component weights and expected returns
- 02
Covariance measures the direction of joint deviations from each mean
- 03
Correlation standardises covariance between negative one and positive one
- 04
Two-asset variance includes weighted component variances and a cross-term
- 05
Imperfect correlation creates diversification benefit
- 06
Broad portfolios retain risk from common economic factors
Worked example · free
Combine two assets with zero correlation
- 1Check that the two weights sum to one.
- 1Compute expected return of 6.8 percent.
- 1Square each weight and each component volatility.
- 1Set the covariance cross-term to zero because correlation is zero.
- 1Sum to portfolio variance of 0.004176 in decimal units.
- 1Take the square root to obtain portfolio volatility of approximately 6.46 percent.
Key terms
- Covariance
- Covariance measures whether two returns tend to deviate from their means in the same direction.
- Correlation
- Correlation standardises covariance by both standard deviations and lies between negative one and positive one.
- Portfolio weight
- A portfolio weight is the share of total portfolio value invested in an asset.
- Diversification benefit
- Diversification benefit is the reduction in portfolio risk produced by imperfect return co-movement.
- Market risk
- Market risk is common exposure that remains after asset-specific risk has been diversified.
Portfolio Risk and Diversification FAQ
Why is portfolio volatility not a weighted average?
Portfolio returns combine across the same states, so co-movement matters. The variance formula includes a covariance term in addition to weighted component variances. A weighted average of standard deviations ignores offsetting or reinforcing movements and therefore misses the mechanism that creates diversification.
What does lower correlation do to portfolio risk?
Holding weights and individual volatilities constant, lower correlation reduces the covariance cross-term and therefore lowers portfolio variance. Expected portfolio return is unchanged because correlation does not enter its weighted-average formula. The strongest two-asset offset occurs at perfect negative correlation.
Can diversification remove all investment risk?
Diversification can remove much company-specific risk when holdings do not move perfectly together. It cannot generally remove exposure to common economic forces that affect many assets at once. Correlations can also rise during stress, so a historical diversification benefit should be tested under less favourable co-movement.
Exam move
Write expected return and variance on separate lines so their rules do not blend. Memorise the two-asset variance structure by meaning: own contribution from Asset A, own contribution from Asset B and one cross-term for co-movement. Predict how variance changes when correlation rises or falls before calculating.
Use scatter plots to connect the sign and strength of correlation with a return cloud, then stress-test the same portfolio at higher correlation. Finish each practice answer by explaining whether the new asset reduces total portfolio risk, not merely whether its own volatility is high or low. Build a two-asset worksheet with rows for weights, expected returns, standard deviations and correlation.
Check that weights sum to one before multiplying anything. Calculate expected return first because it is a weighted average, then expand variance into the two own-variance terms and the covariance term. Mark every squared weight and both standard deviations in the cross-term; these are common omissions. Repeat the same inputs at correlations of positive one, zero and negative one.
Before using a calculator, sketch the expected ordering of portfolio standard deviations and identify whether a perfect hedge is feasible from the relative volatilities and weights. Next, hold correlation fixed and vary the portfolio weight in regular increments. Record expected return and standard deviation, plot the opportunity set and label the minimum-variance point.
Explain why portfolios below that point are dominated by portfolios with the same risk and higher expected return. For a diversification explanation, separate firm-specific risk from market-wide risk and name the economic shock that produces each. Do not claim that adding securities removes all risk.
Finish with a comparison drill: one proposed asset has high standalone volatility but low covariance with the existing portfolio, while another has low standalone volatility but high covariance. Decide which contribution is more valuable and defend it using the cross-term rather than an unsupported slogan. Recalculate the selected mix after the correlation estimate rises during market stress.
This final case tests whether the diversification argument survives changing co-movement rather than relying on a single historical estimate.
Working through Portfolio Risk and Diversification in FNCE90065? Sia is AskSia’s AI Finance tutor — ask any FNCE90065 Portfolio Risk and Diversification question and get a clear, step-by-step explanation grounded in how FNCE90065 is taught and assessed. Read this chapter free, then take your hardest questions to Sia.
