Frozen Holdings Portfolio Optimization (MPT)

How ClearLedger Optimizes Under Constraints

ClearLedger constructs the efficient frontier using a full variance‑covariance matrix and solves a constrained quadratic optimization problem. Every position in the portfolio is governed by a set of mathematical constraints that determine how the optimizer is allowed to adjust its weight.

Frozen Holdings

Some positions, such as AAPL (25.4%) and the GIC (8.28%), are locked for tax or structural reasons. These weights cannot move and act as hard constraints in the optimization model. Learn more about what happens when you freeze core holdings.

Directional Constraints (Buy / Hold / Sell)

Buy/Hold/Sell signals do not guarantee that a position will be increased, decreased, or selected. They define the allowed direction of movement for each security (read about how ClearLedger optimizes portfolio weights):

• Buy — the optimizer is permitted to increase the weight (up to its maximum constraint), but may still allocate 0% if the covariance structure does not justify the position.
• Sell — the optimizer is permitted to reduce the weight (down to its minimum constraint), but may retain the position if it contributes positively to diversification.
• Hold — the position is restricted to a narrow band around its current weight, allowing only limited movement.

These signals are permissions, not instructions. The solver ultimately selects weights based on risk‑adjusted efficiency, diversification, and the geometry of the efficient frontier — not on the Buy/Hold/Sell labels themselves.

Resulting Allocation Behavior

When the constraints are applied, the optimizer tends to increase weights in high‑efficiency positions such as CAT, CSCO, CVX, INTC, JNJ, KO, MRK, TRV, and UNH. These assets improve diversification and reduce concentration risk.

Conversely, positions with lower risk‑adjusted efficiency or high correlation — including GS, MSFT, AMZN, AXP, BA, CRM, DIS, JPM, MCD, MMM, PG, V, VZ, and WMT — are often trimmed or reduced to zero.

The final optimized portfolio reflects the combined effect of all constraints: frozen holdings, directional permissions, max/min boundaries, and the covariance structure of the underlying assets.

Tracing Metric Drivers & Variance Across the Model

To answer how performance and risk shifts are achieved and audited, the model breaks down performance via security-level attribution across all core metrics:

• Security-Level Attribution: Located in the engine sheet under the Variances and metrics blocks, individual asset columns isolate how specific holdings contribute to aggregate portfolio variance, expected return, and risk-adjusted efficiency based on their weight and covariance interactions.
• Key Portfolio Drivers: High-impact core leaders anchor the optimization by driving the largest positive expected return shifts when allocation weights are rebalanced toward efficient targets.
• Matrix Interactivity ($w^T \Sigma w$): Rather than relying on guesswork, the spreadsheet computes portfolio variance and risk metrics dynamically, letting you audit how shifting an individual holding's weight scales its marginal contribution to the portfolio's aggregate profile.

Total Portfolio Technical Summary

The optimized portfolio more than doubles its Sharpe ratio and reduces volatility despite locking over 33% of total assets in frozen holdings — demonstrating the power of disciplined, constraint‑aware optimization.