Frozen Holdings Portfolio Optimization (MPT)

This demonstration shows how ClearLedger Analytics optimizes a real DOW 30 portfolio when certain positions must remain unchanged — including an overweight legacy holding in Apple (AAPL) and a fixed‑income GIC position.

Download Spreadsheet

You can download the exact ClearLedger Analytics export used in this demonstration:

• Download Frozen Holdings Demo Spreadsheet (XLSX)

About This Demo

This ClearLedger Analytics export shows how a real DOW 30 portfolio behaves today — and how its return and risk profile improves when optimized using Modern Portfolio Theory (MPT) while respecting frozen holdings.

In this example, AAPL is frozen at 25.4% because the investor does not want to realize a capital gain. A GIC position at 8.28% acts as a fixed‑income anchor. ClearLedger adjusts all other weights around these constraints.

What Are Frozen Holdings?

Frozen holdings are positions the investor chooses not to change during optimization — typically due to tax considerations, long‑term conviction, or compliance restrictions. In this demo, AAPL remains fixed at 25.4%, and the GIC remains at 8.28%. These constraints create a realistic optimization scenario where ClearLedger must improve efficiency without altering key positions.

Buy / Hold / Sell Signals

These signals do not mean buy or sell the stock. They are mathematical weight‑adjustment signals used to move your portfolio toward the efficient frontier.

How ClearLedger Optimizes a Portfolio with Frozen Holdings

Frozen holdings introduce real‑world constraints into the optimization process. ClearLedger evaluates the remaining DOW 30 equities using a full covariance matrix derived from the selected time horizon. Each security’s variance, covariance, and correlation contributes to total portfolio risk.

With AAPL frozen, the optimizer must rebalance the remaining holdings to improve diversification and reduce concentration. Positions such as CAT, CSCO, CVX, INTC, JNJ, KO, MRK, TRV, UNH exhibit strong risk‑adjusted characteristics and receive higher weights. Meanwhile, correlated or less efficient positions — including GS, MSFT, AMZN, AXP, BA, CRM, DIS, JPM, MCD, MMM, PG, V, VZ, WMT — are reduced or trimmed to zero.

The engine builds the efficient frontier by solving a constrained quadratic optimization problem. Weight limits, frozen positions, and risk‑adjusted efficiency targets ensure the optimized portfolio remains realistic and investable.

Total Portfolio Technical Summary

The Technicals table in Demo‑6.xlsx shows how the entire portfolio behaves today versus after optimization.

Expected Return

The optimized portfolio increases expected return from 0.3165 to 0.5816.

Risk

Total portfolio risk decreases from 0.1218 to 0.1167.

Sharpe Ratio

The Sharpe ratio improves from 2.1351 to 4.3970.

Alpha

Portfolio alpha increases from 0.1363 to 0.3434.

Beta

Portfolio beta decreases from 0.7217 to 0.5443.

Correlation

Overall correlation improves from 0.3008 to 0.1780.

Actual vs Expected Return

Actual vs Expected Return improves from 0.1456 to 0.3037.

Benchmark Comparison

The benchmark gap improves from 0.7410 to 16.5553.

Every metric improves because the optimizer focuses on the total portfolio — not individual stocks — even when major positions are frozen.