FOUNDATION 09 / Markets & risk
Portfolios, diversification & risk
Combine assets, calculate a two-asset risk model and connect risk to goals and constraints.
By the end of this lesson
- Calculate weighted expected return.
- Explain covariance and diversification.
- Distinguish willingness, capacity and liquidity needs.
IBBC Capital Finance Foundations · Original content drafted with AI assistance. IBBC Capital is responsible for editorial review and content. General education, not an official CFA Institute curriculum or credential.
Weights and expected return
For fully invested, unlevered holdings, weights sum to one. Portfolio expected return = Σ wᵢE[Rᵢ]. A 60% weight in an 8% expected-return asset and 40% in a 3% asset produces 6%, not a guaranteed result.
Weights can drift when prices change. Rebalancing restores intended exposures but can incur transaction costs and taxes. A target allocation is a policy choice; this lesson does not prescribe a personal allocation.
Risk depends on co-movement
For two assets, σp² = w²σA² + (1−w)²σB² + 2w(1−w)σAσBρ. Correlation ρ describes linear co-movement. Standard deviation is the square root of variance, not a weighted average of the two standard deviations in general.
For two risky assets with positive weights, imperfect positive correlation can reduce dispersion relative to a perfectly correlated combination. Negative correlation can reduce it further in the model, but estimates can change in stress.
What diversification cannot promise
Holding many names in one industry can leave substantial common exposure. Diversification can reduce some security-specific risk, but it does not eliminate market-wide losses, liquidity shortages or model error.
Volatility is only one view of risk. Drawdown, inflation shortfall, leverage, currency and inability to meet a payment can matter more for a particular objective. Describe risk in relation to the objective, not just one statistic.
Goals and constraints before products
Separate willingness to bear losses from financial capacity to bear them. Time horizon, near-term spending, liabilities and emergency liquidity can constrain capacity even when stated willingness is high.
A sound exercise records objective, horizon, liquidity, currency, restrictions and assumptions. Monitoring asks whether those inputs changed. It is not a promise that a historical optimal portfolio remains optimal.
Two equal-weight assets
- Both assets have 10% standard deviation and zero correlation. Weights are 50% each.
- Variance = 0.5²×0.1² + 0.5²×0.1² = 0.005.
- Portfolio standard deviation = √0.005 = 7.0711%. If correlation were +1, it would be 10%.
Try before looking at the explanation
Change one input in the practice tool below. Predict the direction first, calculate second, then explain why it changed.
Work the numbers
Common mistakes to catch
- Averaging volatilities while ignoring correlation.
- Treating many holdings as automatic diversification.
- Mistaking historical expected returns for promised future outcomes.
Knowledge check · 6 original questions
Answer all six. At least five correct marks the lesson complete for self-study. You can retry; this is not a credential.
Keep these ideas
- Return combines weights; risk combines weights and co-movement.
- An allocation should answer a goal with explicit constraints.