Efficient Investment Portfolios
Efficient portfolio construction begins with the risk–return trade-off. Modern portfolio theory shows that combining assets with less-than-perfect correlation can reduce portfolio volatility without proportionally reducing expected return. The efficient frontier is the set of portfolios offering the highest expected return for each level of risk; the optimal portfolio depends on the client’s risk aversion and constraints, not on the frontier alone. Adding a risk-free asset produces the capital market line, and the Sharpe ratio measures excess return per unit of volatility.
Candidates should understand diversification, covariance, correlation, systematic versus unsystematic risk, and the difference between strategic asset allocation and tactical shifts. Policy portfolio weights should reflect goals, time horizon, liquidity needs, taxes, and costs. Rebalancing controls drift but creates transaction and tax consequences. Mean-variance optimization is sensitive to inputs, especially expected returns and correlations, so sensible constraints and judgment are essential.
Traps: confusing expected with realized returns; assuming diversification eliminates market risk; treating the highest-Sharpe portfolio as right for every client; ignoring taxes, fees, and liquidity; and using historical inputs as if they were forecasts.
Worked example: Two assets have volatilities of 10% and 20%, equal weights, and correlation 0.2. Portfolio variance = 0.25(0.10²) + 0.25(0.20²) + 2(0.5)(0.5)(0.10)(0.20)(0.2) = 0.0145, so standard deviation is about 12.0%, below the 15% weighted-average volatility. Rule of thumb: add an asset only if it improves the portfolio’s risk-adjusted expected return, not merely because it lowers volatility.