Portfolio Optimization - Handbook

Type: LP (Linear Programming)

This handbook explains the Portfolio Optimization sample problem in the LP Black Box platform.

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The Problem

Scenario

Invest $100,000 across three asset types to maximize returns while managing risk.

Asset	Return (%)	Risk Level	Cost ($)
Stocks	12	15	1
Bonds	5	3	1
Real Estate	8	8	1

Your Goal

Maximize total expected return while staying within risk and policy limits.

The Constraints

1. Budget: Cannot invest more than $100,000

   Formula: 1×stocks + 1×bonds + 1×real_estate ≤ 100000

2. Risk Limit: Total risk score cannot exceed 500

   Formula: 15×stocks + 3×bonds + 8×real_estate ≤ 500

3. Minimum Bonds: Must invest at least $20,000 in bonds (diversification)

   Formula: 1×bonds ≥ 20000

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How to Use

Step 1: Load the Sample

Select Portfolio Optimization from the dropdown.

Step 2: Solve

The solver finds the optimal allocation that maximizes return while respecting risk tolerance.

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Try It Yourself

• Increase risk limit to 600
• Add a minimum real estate allocation

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This demonstrates investment optimization with risk constraints.