Portfolio Theory and Asset Allocation
Core Concepts
Modern Portfolio Theory (MPT) is central: diversification reduces unsystematic risk; the efficient frontier represents optimal risk-return combinations; the Capital Asset Pricing Model (CAPM) links expected return to systematic risk (beta). Candidates must understand asset allocation strategies (strategic vs tactical), correlation, and the impact of risk tolerance and investment horizon. Key concepts: mean-variance optimisation, Sharpe ratio, Treynor ratio, and the security market line. Traps often involve misapplying beta (systematic risk) vs standard deviation (total risk), confusing the efficient frontier with the capital market line, and misunderstanding the assumptions of CAPM (e.g., no taxes, homogeneous expectations). Also, the distinction between active and passive management, and the role of rebalancing. Candidates should know how to calculate portfolio expected return and risk for a two-asset portfolio, and understand the benefits of international diversification (currency risk, correlation). Another trap: the impact of risk-free rate changes on the efficient frontier.
Worked Example / Rule of Thumb
Two assets: A with expected return 10%, std dev 15%; B with expected return 5%, std dev 8%; correlation 0.2. Portfolio 50/50: expected return = 7.5%; portfolio variance = (0.5^2 * 0.15^2) + (0.5^2 * 0.08^2) + 20.50.50.150.08*0.2 = 0.005625 + 0.0016 + 0.0012 = 0.008425; std dev ≈ 9.18%. Diversification reduces risk below weighted average (11.5%). Rule of thumb: lower correlation → greater diversification benefit.
Key Points
- MPT: diversification reduces unsystematic risk; efficient frontier shows optimal portfolios.
- CAPM: expected return = risk-free + beta * market risk premium.
- Beta measures systematic risk; standard deviation measures total risk.
- Sharpe ratio = (return - risk-free) / std dev; Treynor = (return - risk-free) / beta.
- Strategic asset allocation aligns with long-term goals; tactical adjusts for short-term views.
- Rebalancing maintains target allocation and controls risk.