Principles of Asset Allocation

This module turns capital market expectations into a strategic asset allocation. It starts with mean-variance optimization and the techniques that make it usable in practice (reverse optimization, Black-Litterman, constraints and resampling), tests the result with Monte Carlo simulation, scenarios, liquidity analysis and risk budgets, and then adapts the method to investors with liabilities and to individuals with several goals. It closes with popular heuristics and the factors that set a sensible rebalancing policy.

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What you will learn

1. Apply mean-variance optimization and evaluate its limitations, including the use of reverse optimization, Black-Litterman, constraints, resampling and the global market portfolio as a starting point.

Utility = E(R) - 0.005 x lambda x sigma squared (in percent); pick the efficient portfolio with the highest utility.
MVO is input-sensitive, maximizes estimation error and produces concentrated portfolios.
Reverse optimization backs out implied excess returns from market weights: Pi = lambda x Sigma x w.
Black-Litterman blends equilibrium returns with views weighted by confidence.
Resampling averages many optimizations for more diversified weights but lacks theoretical foundation.

2. Use Monte Carlo simulation, scenario analysis, liquidity analysis and risk budgeting to test and refine an asset allocation.

Monte Carlo handles many periods, cash flows, taxes and path dependence and gives probabilities of meeting goals.
Stress tests show that correlations rise in crises and diversifiers can fail together.
Liquidity analysis compares liquid assets with spending, capital calls, collateral and redemptions under stress; beware the denominator effect.
MCTR = beta x portfolio volatility; ACTR = weight x MCTR; the ACTRs sum to portfolio volatility.
Optimal risk budget: excess return divided by MCTR is equal across assets.

3. Recommend liability-relative allocations, including surplus optimization, the hedging and return-seeking portfolio approach and integrated asset-liability approaches.

Surplus utility = E(surplus return) - 0.005 x lambda x surplus variance; liability-mimicking bonds are the low-risk asset.
Two-portfolio approach: a hedging portfolio sized by dollar duration plus a return-seeking portfolio for the surplus.
Hedging portfolio value = liability value x liability duration / hedging asset duration.
Underfunded plans hedge partially and raise the hedge ratio along a glide path as funding improves.
Derivative-based hedges save capital but create collateral and liquidity risk.

4. Recommend goals-based allocations by mapping each goal to a sub-portfolio that meets its horizon and required probability of success.

Each goal has an amount, a horizon and a required probability of success that reflects its urgency.
Minimum expected return at probability p over T years is approximately mu - z x sigma / square root of T.
Pick the module with the highest minimum expected return for the goal's horizon and probability.
Capital required = goal / (1 + minimum expected return)^T; discounting at the expected return would set aside too little.
Excess capital beyond all goals is discretionary and can be invested for growth.

5. Evaluate heuristic approaches to asset allocation, such as the 60/40 portfolio, 1/N and risk parity, and the factors that determine a rebalancing policy.

60/40 puts most of the risk in equities and relies on bonds hedging stocks, which fails in inflationary shocks.
Risk parity equalizes risk contributions, ignores expected returns and usually needs leverage.
1/N avoids estimation error but depends on how assets are grouped; 120 minus age ignores the full balance sheet.
Wider corridors: higher costs, illiquidity, higher risk tolerance, higher correlation with the rest of the portfolio, taxes.
Narrower corridors: higher volatility of the asset class or of the rest of the portfolio.

Module at a glance

Choose the efficient portfolio with the highest utility: E(R) - 0.005 x lambda x sigma squared.
MVO is input-sensitive; reverse optimization, Black-Litterman, constraints and resampling make it usable.
Test allocations with Monte Carlo (paths and cash flows), stress tests, liquidity analysis and risk budgets.
Risk contribution = weight x beta x portfolio volatility; the optimal budget equalizes excess return per unit of MCTR.
Liability-relative investors optimize the surplus or split assets into a dollar-duration-matched hedging portfolio and a return-seeking portfolio.
Goals-based: pick the module with the highest minimum expected return and discount each goal at it.
Heuristics such as 60/40 and risk parity rely on bonds diversifying equities; corridors widen with costs and narrow with volatility.

This free module has 5 lessons, 18 practice questions with full explanations and 1 essay case with a model answer.

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