MVO, the Efficient Frontier, SAA vs TAA

Learning objectives

By the end you can:

1. **Generalize the two-asset efficient frontier of M3.02 §4.5 to n assets in matrix form**, build a covariance matrix Σ from volatilities and a correlation matrix, state the Markowitz problem as minimize w′Σw subject to w′μ = target, w′1 = 1, and explain why the two-asset formula you already own is the n = 2 special case of everything here.
2. Compute the global minimum-variance (GMV) portfolio and the unconstrained efficient frontier in Python, verify the GMV's first-order condition (Σw proportional to 1) to machine precision, and state, and demonstrate, the non-obvious fact that GMV weights depend on Σ alone and never on μ.
3. Compute the tangency (maximum-Sharpe) portfolio from w ∝ Σ⁻¹(μ − Rf·1), both unconstrained and under a long-only and a single-asset-cap constraint, and quantify the Sharpe ratio a real-world constraint costs relative to the unconstrained optimum.
4. Distinguish Strategic Asset Allocation (SAA) from Tactical Asset Allocation (TAA), build an SAA at a stated risk target on a constrained frontier, apply a bounded tactical tilt, and judge the tilt on risk-adjusted terms rather than on whether the tilted asset simply went up.
5. Expose, reproduce, and explain the MVO input-sensitivity failure, recompute, in Python, how a change of roughly one percentage point in a single expected-return assumption can swing a tangency weight by ten-plus percentage points and flip its sign, name the phenomenon (the "estimation-error maximizer" critique) and its sources, and state why this makes an unverified, AI- or solver-generated "optimal allocation" the single highest AI-over-trust risk in this Ring.
6. Correctly attribute the industry's most misquoted statistic, state what Brinson, Hood & Beebower (1986) actually found, why "asset allocation explains 90% of returns" is a documented misreading of it, and how Ibbotson & Kaplan (2000) corrected the record.
7. Assemble a defensible capital-market-assumptions (CMA) table, verify a correlation matrix is a valid (positive semi-definite) input before trusting anything downstream of it, and know where to pull real CMAs (a published institutional CMA set, or the historical/implied-ERP toolkit of M3.02 re-purposed for the equity leg) versus where this node's own numbers are explicitly synthetic teaching inputs.

Say this once, plainly (R10). Of every region in this program, asset allocation is the one where a tool will most confidently hand you a wrong-shaped answer that looks like sophistication. Worked Example 6 proves, in your own re-run Python, that the tangency portfolio's composition can reverse on an input change smaller than any honest confidence interval around that input, while the optimizer's own scorecard (its Sharpe ratio) moves almost nothing. That is AI0.01's "optimizes for plausible, not true" wearing a spreadsheet's clothing: the output is precise, confident, and only as trustworthy as the assumptions nobody shows you the error bars on. The by-hand and Python-verified understanding of why the optimizer is this fragile, not just that it exists, is the gated skill here; letting a tool run the optimization before you can reproduce and stress-test its answer yourself is exactly the failure mode this node exists to immunize you against.

Prerequisites & connections

Builds on. M3.02 §4.3–§4.5 is this entire node's foundation and is not re-derived: the two-asset portfolio-variance formula (σp² = w²σA² + (1−w)²σB² + 2w(1−w)ρσAσB), the minimum-variance weight formula, the bowed efficient frontier, the tangency portfolio, two-fund separation, the Sharpe ratio, and CAPM/beta/the equity risk premium. If any of those is not automatic, stop and go back, everything below is that same machinery, scaled from one correlation number to a full covariance matrix, and solved in Python because a napkin no longer suffices past two or three assets. M9.01 and M9.02 supply the concentrated-investor lens this node's positioning line keeps faith with: M9.01 argues risk is permanent capital impairment, not benchmark-relative wobble, and sizes single positions by conviction and Kelly logic; M9.02 stages the concentration-versus-diversification debate honestly and gives factor investing and the active-passive question their first hearing. Read what follows as the separate institutional dialect for a different mandate, a multi-asset policy portfolio, not a rebuttal of that view. M3.03 supplies the clean, currency-matched risk-free rate (its Station 1: strip the sovereign default spread out of a raw government-bond yield, add country risk back once through the ERP) that this node reuses without re-deriving as the risk-free leg of every capital allocation line below.