Asset Allocation Essentials

Mean–Variance Optimization (MVO)

  • Purpose: choose weights that maximize expected return for a given risk or minimize risk for a given return.

  • Inputs: expected returns, standard deviations, correlation matrix.

  • Utility: U<em>m=E(R</em>m)−0.005λσm2U<em>m = E(R</em>m) - 0.005\lambda \sigma_m^2 ((\lambda): risk aversion).

  • Outputs: efficient frontier, global minimum-variance portfolio, tangency portfolio (highest Sharpe).

Reverse Optimization & Black–Litterman

  • Reverse optimization: infers equilibrium expected returns from global market weights, covariance matrix, and (\lambda).

  • Black–Litterman: blends reverse-optimized returns with investor views → more stable inputs.

Strategic Asset Allocation Steps

  1. Unconstrained MVO (baseline).

  2. Add real-world constraints (weights (\ge 0), sum to 11, liquidity limits, etc.).

  3. Evaluate results vs. economic balance sheet (include human capital, real estate).

Key Criticisms of MVO & Fixes

  • Extreme sensitivity to small input changes ➔ use reverse/robust/resampled MVO.

  • Concentration in few assets ➔ add weight limits / diversification constraints.

  • Single-period assumption ➔ multi-period or Monte-Carlo testing.

  • Mean–variance only ➔ consider CVaR, semivariance, skew/kurtosis models.

Risk Aversion & Probability Metrics

  • Typical (\lambda): 1!–!101!\text{–}!10.

  • Safety-first test: [E(R<em>P)−R</em>L]/σP[E(R<em>P)-R</em>L]/\sigma_P gauges chance of exceeding minimum return.

Monte Carlo Simulation (MCS)

  • Simulates thousands of return paths, cash flows, taxes, rebalancing.

  • Captures sequence risk, path dependency, multi-period dynamics.

  • Complements MVO by stress-testing allocations vs. long-term goals.

Asset-Only vs. Liability-Relative Frameworks

  • Asset-only: optimize assets in isolation.

  • Liability-relative: align assets with projected liabilities (duration, inflation drivers).
    • Methods: surplus optimization, hedging/return-seeking split, integrated ALM.

Surplus Optimization

  • Objective: maximize E(S)−0.005λσS2E(S) - 0.005\lambda \sigma_S^2 where S=A−LS = A - L.

  • Steps: choose assets, set constraints, estimate asset & liability covariances, trace surplus efficient frontier.

Factor-Based Allocation

  • Allocates to systematic factors (market, size, value, momentum, credit, duration, volatility).

  • Often yields similar frontier to asset-class approach but with lower correlations.

Goals-Based Asset Allocation (GBAA)

  • Split portfolio into sub-portfolios matched to explicit goals (“needs, wants, wishes”).

  • For each goal: define horizon, required success probability → select pre-built module with matching risk/return.

  • Discount goal cash flows at probability- & horizon-adjusted return; fund lowest-cost module.

Heuristic & Institutional Models

  • Age rules: “120−age120 - \text{age}” or “100−age100 - \text{age}” for equity weight.

  • 60/40 split: simple balanced benchmark ≈ global market portfolio.

  • Endowment (Yale) model: high illiquid alternatives; Norway model: passive 60/40, ESG focus.

Risk Parity

  • Equalizes each asset’s contribution to total portfolio variance (requires optimization; ignores expected return).

  • Can scale risk up/down with leverage or cash.

Rebalancing Principles

  • Disciplines: calendar vs. trigger (percent-range) methods.

  • Corridor width wider when: high transaction/tax costs, high risk tolerance, high asset correlation.

  • Narrower when: high volatility or tight risk control needed.

  • In GBAA, rebalance to prevent drift toward overly conservative mix as lower-risk buckets accumulate surplus.