Portfolio Optimization – Practical Applications

In the classroom, we use formulas. In the real world (Funds, Banks), we use Solvers and Algorithms to perform portfolio optimization.

The Objective Function

The goal is creating a mathematical problem for the computer to solve:

Maximize: Sharpe Ratio (Return / Risk) Subject to Constraints:

1. Weight of all assets = 100% (Budget Constraint).
2. No Short Selling (Weight >= 0).
3. Maximum allocation to one sector <= 20% (Risk Constraint).

Common Tools Used

1. Excel Solver

• Usage: Good for small portfolios (up to 20-30 assets).
• Method: Set up the Mean, Variance, and Covariance matrix. Use the "Data > Solver" add-in to maximize the Return cell while keeping Variance cell below a target.

2. Python (PyPortfolioOpt / SciPy)

• Usage: Professional standard. Can handle thousands of assets.
• Efficiency: Can fetch live data, compute the efficient frontier, and output trades in seconds.

3. Robo-Advisors

• Usage: For retail investors (e.g., Wealthfront, Zerodha).
• Method: Ask you 5 questions about risk, then automatically place you on the "Efficient Frontier" using low-cost ETFs.

Challenges in Practice

1. Garbage In, Garbage Out: If your expected return estimates are wrong, the "optimal" portfolio will be terrible.
2. Transaction Costs: Rebalancing too often eats up profits.
3. Instability: Optimization is sensitive. Small changes in data can lead to huge changes in recommended weights (Corner Solutions). Professional models add "Smoothing" constraints to prevent this.

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