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- Global Frameworks: CFA Level 1 & 2 (Portfolio Management), EFPA (European Financial Planning Association) Syllabus.
1. Mean-Variance Optimization FrameworkModern Portfolio Theory (MPT), pioneered by Harry Markowitz, operates on the foundational assumption that rational, risk-averse investors look at assets not in isolation, but based on how they impact a total portfolio’s risk and return profile.The portfolio expected return is a linear combination of asset weights:
E(R_p) = Σ_{i=1..n} w_i E(R_i)The portfolio variance, however, is structurally non-linear because it integrates the co-movement between all asset pairs:σp^2 = Σ{i=1..n} (w_i^2 σi^2) + Σ{i=1..n} Σ_{j≠i..n} (w_i w_j σ_i σ_j ρ_ij)
where ρ_ij is the correlation coefficient between asset i and asset j.
, risk reduction is achieved without a proportional reduction in expected returns.
2. The Efficient Frontier and Global Minimum Variance PortfolioBy plotting every possible combination of risky assets in an expected return vs. standard deviation space, an analyst maps out the Feasible Set.The upper boundary of this set forms the Efficient Frontier. Portfolios resting on this frontier offer the maximum possible expected return for a specific level of risk, or the lowest possible risk for a targeted level of return.Expected Return E(R) ▲ │ * Optimal Portfolio (Tangent to CAL) │ / │ ┌─┴─────────────── Efficient Frontier │ / │ * Global Minimum Variance Portfolio (GMVP) │ / │ │ └────┴─────────────────────────────────────────► Risk (σ)The turning point of this curve is the Global Minimum Variance Portfolio (GMVP), which represents the absolute lowest risk portfolio achievable using only the available risky assets.3. The Capital Allocation Line (CAL) and Two-Fund SeparationWhen a risk-free asset (\(R_{f}\)) is introduced, investors can blend this riskless asset with a portfolio of risky assets (p). This combination creates a linear risk-return tradeoff known as the Capital Allocation Line (CAL):E(R_c) = R_f + ((E(R_p) – R_f) / σ_p) · σ_c- The Tangency Portfolio: The unique risky portfolio that maximizes the slope of the CAL is the tangency portfolio. At this point, the Sharpe ratio is maximized.
- Two-Fund Separation Theorem: States that regardless of individual risk preferences, all rational investors will hold the exact same optimal portfolio of risky assets (the tangency portfolio) and simply adjust their allocation by borrowing or lending at the risk-free rate.