Model SOCPMarkowitzComparisonDemo

SOCPMarkowitzComparisonDemo — quantitative model tutorial

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Paper introduction

Harry Markowitz, Portfolio Selection (1952) explains diversification as a portfolio problem: an asset's risk cannot be judged independently of how its returns move with the other holdings. Expected portfolio return is a weighted mean; portfolio variance depends on the full covariance matrix.

The efficient set contains portfolios for which expected return cannot be improved without accepting more variance, or variance reduced without giving up expected return. An investor selects a tradeoff according to preferences and constraints. Holding many positively correlated assets need not provide much diversification.

The framework assumes the relevant return means and covariances are supplied. In practice, estimates can be unstable and constraints can materially change the answer. A solved optimization is therefore a set of weights under assumptions, not evidence of future outperformance. The original article was reviewed. Rolling calibration, rebalance schedules, costs and the dataset used here belong to the demo, not to the static 1952 formulation.

How this demo connects to the idea

Compares QP and SOCP representations under the configured constraints and data. Equality of mathematical formulations does not imply bit-identical numerical solutions; inspect the existing correlated-input TODO and solver tolerances.

What this example teaches

We compare the results from a QP solver (Markowitz) and from an SOCP solver. They should give more or less the same results given only QP constraints, subject to numerical differences.

The portfolio optimization problem is:

max rw-qw'Sigmaw s.t. sum(w)=1, w_i=1 for i in the black list.

We assume that the last index of w is in the black list.

Using this example. Compares quadratic and second-order-cone formulations using the same inputs and constraints. Numerical solver tolerances can produce different weights; inspect the existing TODO about correlated inputs rather than assuming universal agreement.

Model and publication. Related theory and the scope of this example are distinguished below.

Implementation in this tutorial. Compares QP and SOCP representations under the configured constraints and data. Equality of mathematical formulations does not imply bit-identical numerical solutions; inspect the existing correlated-input TODO and solver tolerances.

Verified execution record

Item	Value
Status	completed
Run	39114360151
UTC publication	2026-10-18 09:18 UTC
Source commit	355aa9242fc2a247b256aecc8406cbb409aa5ff3
Data mode	original main defaults
Exit code	0
Elapsed seconds	1.23
Time limit seconds	180
Maximum Java heap	1200m

The original main returned successfully. Read the output and model assumptions before interpreting it.

Reproduce the calculation

Follow the repository setup for JDK 8, Maven credentials and an external NM license. From the repository root:

mvn -U -Dmaven.test.skip=true clean package
mvn exec:java -Dexec.mainClass=tech.nmfin.algoquant.demo.model.portfoliooptimization.SOCPMarkowitzComparisonDemo

The automated run uses scripts/ModelDemoRunner.java to initialize the external license before the unchanged main, save JFreeChart windows as PNGs, and exit after main returns. It uses an isolated working directory with the repository datasets/configuration linked in. Running directly may leave desktop windows open.

Observed output

09:13:15.084 [main] INFO  t.n.a.d.m.p.SOCPMarkowitzComparisonDemo,107 - x1: [0.331978, 0.336715, 0.187407, 0.143901, 0.000000] 
09:13:15.092 [main] INFO  t.n.a.d.m.p.SOCPMarkowitzComparisonDemo,108 - x2: [0.341506, 0.345905, 0.181232, 0.131357, -0.000000] 
09:13:15.092 [main] INFO  t.n.a.d.m.p.SOCPMarkowitzComparisonDemo,109 - obj1 -0.0474881053881621 vs. obj2 -0.04741091251200159

Downloadable evidence

Download SOCPMarkowitzComparisonDemo.zip contains stdout, stderr, the execution record, checksums and any exported CSV/chart files.

Interpreting the result

Read the reported units: optimizer weights, model-fit coefficients, forecast correlations and simulated P/L are different outputs. Synthetic runs demonstrate the API rather than historical market returns. Inspect undefined values and open positions instead of replacing them with zero. Chart exports visualize exactly this run.

For model assumptions, original publications and adaptation limits, use the literature guide.