Classical and Adaptive Asset Allocation: Markowitz Meets Momentum

Harry Markowitz's mean-variance optimization framework, published in 1952, remains the theoretical foundation of modern portfolio construction. The idea is elegant: given estimates of expected returns, volatilities, and correlations, there exists an optimal set of portfolio weights that maximizes return for any given level of risk. The problem — and it is a serious one — is that the optimizer's outputs are extremely sensitive to its inputs. Small errors in expected return estimates can produce wildly different portfolios, and historical estimates are notoriously poor forecasts of future behavior.

The strategies covered in this article — Classical Asset Allocation (CAA), Adaptive Asset Allocation (AAA), and Keller's Defensive Allocation (KDA) — each address this input sensitivity problem differently, while preserving the mathematical rigor of the optimization framework. They replace static historical estimates with dynamic, momentum-based inputs that adapt to changing market conditions.

Classical Asset Allocation (CAA)

CAA, developed by Wouter Keller, takes the Markowitz optimizer and feeds it momentum-derived expected returns instead of long-term historical averages. The result is a portfolio that is optimized anew each month using the most recent performance data.

The CAA Offensive Variant (CAA_OFF)

Parameter	Value
Universe	SPY, EFA, EEM, QQQ, EWJ, HYG, BIL, IEF (8 assets)
Defensive Assets	BIL, IEF
Momentum Method	K13612U = average(R1, R3, R6, R12)
Allocation	CLA_TARGET_VOL (target volatility = 10%)
Position Cap	25% max on risky assets; BIL and IEF uncapped

How the CLA Optimizer Works

The Critical Line Algorithm (CLA) is a specialized optimizer designed specifically for portfolio allocation with inequality constraints. Unlike general-purpose quadratic programming, CLA efficiently handles the long-only constraint (no short selling) and position size limits that are essential for practical portfolio construction.

Each month, the engine feeds the CLA optimizer two inputs:

1. Expected returns: Computed as K13612U — the average of each asset's 1-month, 3-month, 6-month, and 12-month returns. This multi-period composite captures both recent momentum and longer-term trends, producing return estimates that are more stable than any single-period lookback.
2. Covariance matrix: Computed from trailing 12-month returns. This captures the current correlation structure between assets, which can shift significantly between risk-on and risk-off environments.

The optimizer then finds the portfolio on the efficient frontier that achieves a target volatility of 10% annualized for CAA_OFF. Risky assets (SPY, EFA, EEM, QQQ, EWJ, HYG) are capped at 25% each. BIL and IEF are uncapped, allowing the optimizer to allocate heavily to cash and bonds when risk assets have poor momentum or high correlations.

CAA Defensive (CAA_DEF)

CAA_DEF uses the identical universe, momentum method, and optimizer — the only difference is the target volatility, which is set to 5% instead of 10%. This lower volatility target forces the optimizer to allocate significantly more to BIL and IEF, producing a portfolio that is structurally more conservative. In practice, CAA_DEF typically holds 60-80% in cash and bonds, with only modest allocations to the risky assets that show the strongest momentum.

Adaptive Asset Allocation (AAA)

Parameter	Value
Universe	SPY, VGK, EWJ, EEM, VNQ, RWX, IEF, TLT, DBC, GLD (10 assets)
Top-N	5
Lookback	6 months
Momentum Method	REL_STR_1P (6-month return)
Allocation	MIN_VAR (minimum variance, long-only, 126-day covariance)

Two-Stage Process

AAA uses a two-stage approach that separates asset selection from weight optimization:

1. Momentum filter (stage 1): Rank all 10 assets by their trailing 6-month return. Select the top 5. This stage is pure momentum — no optimization, no covariance.
2. Minimum variance optimization (stage 2): Take the 5 selected assets and compute their minimum variance portfolio using a 126-day (approximately 6-month) covariance matrix. Long-only constraint applies. The optimizer finds weights that minimize portfolio volatility.

The minimum variance approach differs from Markowitz's original mean-variance framework in a crucial way: it ignores expected returns entirely during the optimization step. Instead of trying to maximize the Sharpe ratio (which requires accurate return forecasts), it simply minimizes risk. Research has consistently shown that minimum variance portfolios are more robust out-of-sample than mean-variance portfolios, precisely because they depend only on covariance estimates, which are more stable than return estimates.

An important behavioral note: the optimizer may concentrate into fewer than 5 assets when the selected assets are highly correlated. If three of the five selected assets are all developed-market equities with correlations above 0.9, the optimizer may allocate almost nothing to two of them and concentrate in the least volatile one. This is mathematically correct — diversification provides no benefit among highly correlated assets — but can produce unintuitive portfolios.

Keller's Defensive Allocation (KDA)

Parameter	Value
Universe	SPY, VGK, EWJ, EEM, RWX, DBC, GLD, VNQ, TLT, IEF (10 assets)
Risk-Off	IEF
Canary Assets	VWO, BND
Top-N	5
Lookback	12 months
Momentum	K13612W (weighted: 12×R1 + 4×R3 + 2×R6 + R12)
Protection	CANARY (graduated: 0 neg = full, 1 neg = 50%, 2 neg = 100% IEF)
Allocation	MIN_VAR (252-day covariance)

KDA's Three-Layer Architecture

KDA combines three independent mechanisms — canary signals, momentum ranking with absolute filter, and minimum variance optimization — into a single strategy:

1. Canary check: Evaluate the 13612W scores of VWO and BND. If neither is negative: proceed with full risk-on allocation. If one is negative: 50% of the portfolio goes to IEF, the other 50% is allocated to risk-on assets. If both are negative: 100% IEF.
2. Momentum ranking: Rank the 10 universe assets by K13612W score. Select up to 5 with positive scores. The absolute momentum filter ensures only assets with upward momentum are included — if fewer than 5 have positive scores, the strategy holds fewer positions.
3. Min-var optimization: The selected assets are passed into a minimum variance optimizer with a 252-day (1-year) covariance matrix. Note the longer covariance window compared to AAA's 126 days — this produces more stable weight estimates at the cost of slower adaptation.

The graduated canary system is particularly elegant. Rather than a binary risk-on/risk-off switch, it creates three regimes: full risk-on, half defensive, and full defensive. This graduated approach reduces whipsaw during transitional periods when one canary asset is signaling danger but the other is not. For deeper analysis of how canary signals work across the platform, see the article on Vigilant Asset Allocation, which pioneered the canary concept.

Comparing Optimization Approaches

Feature	CAA	AAA	KDA
Optimizer	CLA (target vol)	Min variance	Min variance
Uses Return Estimates	Yes (K13612U)	No (selection only)	No (selection only)
Covariance Window	12 months	126 days	252 days
Defensive Mechanism	Optimizer shifts to BIL/IEF	None (always top 5)	Canary graduated + absolute
Max Risk-On Weight	25% per risky asset	No cap	No cap

CAA is the most faithful to Markowitz — it uses both return estimates and covariance in the optimizer. This gives it the theoretical advantage of targeting a specific risk-return trade-off, but the disadvantage of sensitivity to return estimation errors. AAA and KDA sidestep this by using momentum only for asset selection and relying solely on covariance for weighting, which is a more robust approach empirically.

Investors who prefer simpler allocation methods — equal weight, inverse volatility, or fixed tiers — will find detailed comparisons in the risk parity with trend filters article. The optimizer-based strategies covered here trade simplicity for mathematical precision, which can be an advantage during periods of rapidly shifting correlations.

All three strategies represent a bridge between the academic elegance of modern portfolio theory and the practical demands of tactical asset allocation. By replacing static assumptions with dynamic momentum signals, they preserve the optimizer's mathematical rigor while adapting to the market conditions of the moment.