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name: matlab-optimize-portfolio description: Help users formulate and solve portfolio optimization problems using Financial Toolbox's Portfolio object. Covers mean-variance (Markowitz), maximum Sharpe ratio (tangency), and efficient frontier workflows. Use when users ask about portfolio optimization, Markowitz, efficient frontier, Sharpe ratio, or attempt to use generic solvers (quadprog, fmincon, ga, problem-based optimize) for portfolio problems. license: https://www.mathworks.com/content/dam/mathworks/license/pmrl/license.md metadata: author: MathWorks version: "1.0"

Portfolio Optimization with Financial Toolbox

You are helping a user formulate and solve a portfolio optimization problem using MATLAB's Financial Toolbox Portfolio object.

When to Use

• User wants to optimize a portfolio (minimize variance, maximize Sharpe ratio, trace efficient frontier)
• User asks about Markowitz, mean-variance, minimum-variance, or tangency portfolios
• User asks about the efficient frontier or target-return portfolios
• User is trying to use fmincon, quadprog, ga, or problem-based optimize for portfolio optimization (redirect to Portfolio object)
• User asks how to set up constraints for portfolio optimization (bounds, groups, turnover, one-way turnover, cardinality, semicontinuous)
• User asks about mean-variance with cardinality or semi-continuous constraints
• User gets errors from Portfolio, estimateMaxSharpeRatio, estimateFrontier, or related methods

When NOT to Use

• User has a general optimization problem (QP, NLP, MILP) that is NOT financial asset allocation (e.g., filter design, resource allocation, mixture proportions) — use matlab-solve-optimization
• User needs to retrieve market data from Bloomberg, FRED, or Haver Analytics — use matlab-access-datafeed
• User wants to predict returns or portfolio weights using neural networks or ML — use matlab-train-network
• User only wants to clean, explore, or summarize a returns table without optimization — use matlab-analyze-data
• User wants Experiment Manager parameter sweeps (not portfolio frontier) — use matlab-use-experiment-manager
• User wants CVaR, MAD, or other non-mean-variance risk measures — use PortfolioCVaR or PortfolioMAD classes (not covered by this skill)

Key Principle

Always use the Portfolio class — never let users manually code the optimization with fmincon or quadprog. The toolbox handles solver configuration, constraint management, and frontier computation automatically.

If the user is already attempting a manual solver approach, acknowledge their work, then show how the Portfolio object achieves the same result with less code and fewer pitfalls.

Step 1: Identify the Formulation

Determine which problem the user is trying to solve:

| User wants to... | Formulation | Reference | |------------------|-------------|-----------| | Minimize portfolio risk (no return target) | Mean-variance (min-variance) | formulation-mean-variance.md | | Minimize risk for a given target return | Mean-variance (target-return) | formulation-mean-variance.md | | Trace the efficient frontier | Mean-variance (frontier) | formulation-mean-variance.md | | Maximize risk-adjusted return (Sharpe ratio) | Max Sharpe / tangency | formulation-max-sharpe.md |

Consult the relevant formulation file for problem-specific guidance and methods.

Step 2: Determine What Data the User Has

Ask (if not clear) whether they have:

• A matrix of historical asset returns (or prices that need converting)
• Pre-computed mean returns (mu) and covariance matrix (Sigma)
• A risk-free rate (relevant for Sharpe ratio; defaults to 0 if unspecified)

Step 3: Create the Portfolio Object

See reference-core.md for all creation patterns. The most common:

From return statistics:

p = Portfolio('AssetMean', mu, 'AssetCovar', Sigma);

From historical returns:

p = Portfolio;
p = setAssetMoments(p, mean(returns)', cov(returns));

Step 4: Set Constraints

Always set constraints. At minimum, use default constraints (fully invested, long-only):

p = setDefaultConstraints(p);

For other constraint types (bounds, groups, turnover, one-way turnover, cardinality), see reference-core.md.

Step 5: Solve

Use the method appropriate to the formulation (see the formulation file). Common patterns:

wMinVar = estimateFrontierLimits(p, 'Min');       % minimum-variance
wTarget = estimateFrontierByReturn(p, targetRet); % target-return
wSharpe = estimateMaxSharpeRatio(p);              % max Sharpe ratio
wFrontier = estimateFrontier(p, 20);              % efficient frontier

Step 6: Analyze and Visualize

Use built-in methods for portfolio statistics — never compute them manually:

portRisk = estimatePortRisk(p, w);
portRet  = estimatePortReturn(p, w);
[risk, ret] = estimatePortMoments(p, w);

Always use plotFrontier as the primary frontier visualization — add custom annotations (special portfolios, CAL line) with hold on/hold off afterward:

wFrontier = estimateFrontier(p, 20);
plotFrontier(p, wFrontier);
hold on
[risk, ret] = estimatePortMoments(p, wSpecial);
plot(risk, ret, 'r*', 'MarkerSize', 12);
hold off

Common Pitfalls

1. Manual solver usage — quadprog/fmincon for portfolio problems is error-prone; Portfolio handles it.
2. Missing constraints — A Portfolio without constraints is underdetermined.
3. Redundant solves — Pass weights to plotFrontier, not a number of portfolios, if you already solved.
4. Manual risk/return formulas — Use estimatePortRisk, estimatePortReturn, estimatePortMoments.
5. Cardinality/semicontinuous constraints — When calling estimateMaxSharpeRatio, specify 'Method','iterative' (MATLAB auto-selects with a warning if omitted, but explicit is cleaner). Frontier methods (estimateFrontier, estimateFrontierLimits, estimateFrontierByReturn) auto-detect these constraints and select the mixed-integer solver internally — do NOT pass 'Method','iterative' to them.

Tone

Be direct and practical. Show working MATLAB code. If the user provides data, use their actual data. If not, use a small illustrative example so they can see the pattern and adapt.

Reference Materials

• reference-core.md — Portfolio setup, constraints API, visualization (shared across formulations)
• formulation-mean-variance.md — Min-variance, target-return, efficient frontier
• formulation-max-sharpe.md — Max Sharpe ratio / tangency portfolio
• examples.md — Complete runnable examples for all formulations

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