Learning objectives
By the end you can:
- Reverse-optimize equilibrium returns from a benchmark's market-cap weights and a covariance matrix (
Π = δΣw), explain what the risk-aversion coefficient δ and the scaling parameter τ each do, and verify the "no-view" sanity check that a correctly built model returns you exactly to the benchmark. - Blend a single view into the equilibrium using the closed-form Black-Litterman posterior, computed by hand for a 2–3 asset case, and correctly judge whether a stated view is more or less bullish than what the market already implies, the single most common Black-Litterman misreading.
- Compute marginal and component contribution to risk for any portfolio, show that capital weights and risk weights routinely diverge (a 60/40 book is not "60% equity risk"), and solve for risk-parity weights, by the 2-asset closed form and, for three or more assets, by a short iterative algorithm.
- Build a liability-relative allocation: compute a funded ratio and surplus, measure the asset–liability duration gap, and show numerically how an unmatched gap converts an ordinary rate move into a funded-ratio shock.
- Build a goals-based allocation using mental-accounting buckets, the required return to fund a goal, and Roy's safety-first ratio, and state, from your own computed numbers, exactly where that ratio's normal-distribution assumption breaks down for short, non-negotiable goals.
- Set and cost a rebalancing policy (calendar versus threshold) computing the number of trades, the transaction-cost drag, and the trade-off between the two disciplines from an explicit multi-period ledger.
- (R10 duality.) Know which parts of this toolkit are safely delegated to a solver (the N-asset, multi-view matrix algebra; the N-asset risk-parity iteration) versus which by-hand fluency you must retain to catch a broken scaffold, and apply the Primary-Source Guardrail (AI0.01) to every AI-assisted build.
The duality, stated once (R10). This branch carries the corpus's highest AI-over-trust risk: everything here is compute-heavy (matrix inversions, iterative solvers, multi-period ledgers) exactly the terrain where a fluent, wrong answer is hardest to eyeball. The gate below is earned by the by-hand mechanics (objectives 1–6); objective 7 is the payoff you keep. A solver can build you a beautiful Black-Litterman posterior from a transposed matrix and never tell you it's wrong.
Prerequisites & connections
Builds on. AA1.01 is this module's direct parent and its motivating failure: it built mean-variance optimization and the efficient frontier, then exposed MVO's acute input-sensitivity, plug in noisy trailing-sample expected returns and the optimizer answers with extreme, unstable, often nonsensical weights (large shorts, corner solutions). Black-Litterman exists because of that finding, and §4.4 below recomputes the exact contrast: the same optimizer, fed (a) a noisy historical-mean vector and (b) a Black-Litterman posterior, produces a reasonable allocation only in the second case. M3.02 supplied the foundations this module assumes without re-deriving: expected return and variance, the two-asset portfolio formula, systematic-vs-idiosyncratic risk, CAPM, beta, and the equity risk premium, you should be able to read Rf + β×ERP on sight. M9.01/M9.02 built the concentrated-investor's view of risk (permanent loss, not variance) and portfolio construction (concentration policy, hurdle rates, the "diworsification" math); this module puts that view in honest dialogue with the institutional, diversified-multi-asset-mandate view a family office, endowment, or pension trustee is actually required to hold. Both are legitimate, and a working analyst needs to speak both languages. M3.03 built the full cost-of-capital machine (clean risk-free rates, bottom-up beta) that supplies the discount-rate inputs a liability-relative build needs when discounting a stream of future obligations. This module does not re-teach duration mechanics (that by-hand skill, PVBP, and convexity belong to the Fixed Income branch, FI1.02) or the time-value-of-money compounding formula (M3.01), both are simply applied here, to a liability and to a goal respectively.
Feeds forward. AA1.03 (the crown of this branch) picks up where this module's weights leave off: once a portfolio is allocated and rebalanced through a live period, AA1.03 measures what actually happened, time- and money-weighted returns, Brinson attribution, Sharpe/Treynor/Information Ratio, and how a GIPS-compliant manager reports it all. None of that performance-measurement machinery is anticipated here; the GIPS seam is deliberate (AA1.03 owns it in full). PW1.01 (Private Wealth) inherits this module's goals-based and liability-relative frameworks directly and applies them to a single household's full financial life, tax location, estate transfer, decumulation, layered on top of, not duplicating, the allocation math built here. MS/AL modules occasionally reference "an allocation to X" in passing; this module is where "allocation" as a formal discipline lives.