IBBC CAPITAL ACADEMY / 2027
Diversification, utility and efficient risky portfolios
Independent IBBC Capital draft content for self-study. Not affiliated with or endorsed by CFA Institute. New lessons await subject-matter review. No CFA designation or official PSM credit is awarded.
Learning goals
- Explain risk and preferences using mechanisms and limitations.
- Explain covariance mechanics using mechanisms and limitations.
- Explain efficient choices using mechanisms and limitations.
Draft · approximately 25 minutes, excluding further revision.
Risk and preferences
Cash, bonds, equity and real assets differ in income, horizon, liquidity and drawdown behavior; an asset class label cannot replace a risk and cash-flow description.
A risk-averse investor requires compensation for greater uncertainty; a quadratic mean–variance utility is a model of preferences, not a universal psychological law.
Covariance mechanics
Portfolio expected return is the weighted sum of asset expected returns; standard deviation also depends on covariances and is not generally the weighted sum of asset volatilities.
Historical covariance averages paired deviations from their means with a consistent sample denominator; correlation scales covariance by the two standard deviations.
Efficient choices
Correlation below positive one can reduce portfolio volatility relative to a perfectly correlated mix, but correlation estimates and diversification benefits can change in crises.
The efficient frontier offers highest expected return at each modeled risk above the global minimum-variance point; the investor’s optimal choice also depends on risk preferences.
Formula and assumptions
σp²=w1²σ1²+w2²σ2²+2w1w2ρ12σ1σ2; U≈E(R)−½Aσ²
Original applied case: Diversification, utility and efficient risky portfolios
- Two equally weighted assets have volatilities 20% and 10%, correlation zero.
- Variance=0.5²×0.2²+0.5²×0.1²=0.0125; volatility=11.1803%.
- This is below the 15% weighted volatility; the covariance term explains the difference.
Errors to catch
- Do not assume: All asset classes have identical liquidity and drawdowns.
- Do not assume: Risk aversion means refusing every risky asset.
- Do not assume: Portfolio volatility is always a weighted mean of volatilities.
Original knowledge check
Answer every question before checking. Review explanations after submitting; retry starts a new attempt.
Sources and coverage status
These original lessons are drafts. Public outlines are used to check scope; the official learning-outcome text and proprietary question banks are not reproduced here. Follow the source for exam-year requirements and updates.