Portfolio Optimization

Overview

Portfolio optimization helps investors and fund managers allocate capital across assets to achieve the best possible return for a given level of risk. Rather than picking stocks by intuition, you define your investment universe, expected returns, risk tolerances, and diversification rules -- then let the solver find the allocation that maximizes your risk-adjusted returns.

This is one of the foundational problems in quantitative finance, first formalized by Harry Markowitz in 1952 and still used daily by asset managers worldwide.

When to Use This

• Scenario: You have a fixed budget to invest across stocks, bonds, real estate, and other assets, and you need to find the allocation that maximizes expected return while keeping risk within acceptable bounds
• Industry: Asset management, wealth management, pension funds, insurance investment, corporate treasury
• ROI: Typical improvement of 0.5-2% in risk-adjusted returns (Sharpe ratio), which compounds significantly over multi-year horizons

Step-by-Step Walkthrough

1. Define your investment universe

List available assets with their expected annual returns, historical volatility, and any asset-class labels. For example: US Large Cap (8.5% return, 15% volatility), Investment Grade Bonds (3.5% return, 5% volatility).

2. Set risk and allocation constraints

Define your risk tolerance and regulatory or policy constraints:

• Maximum portfolio volatility or Value-at-Risk
• Minimum and maximum allocation per asset class
• Sector or geographic diversification requirements
• Liquidity constraints (minimum allocation to liquid assets)

3. Configure the objective

Common approaches:

• Maximize expected return subject to a risk budget
• Minimize risk (volatility) for a target return level
• Maximize Sharpe ratio (return per unit of risk)

4. Run the optimization

5. Interpret the efficient allocation

The solver returns the optimal percentage allocation per asset. Review the results against your investment committee's guidelines. Run multiple scenarios with different risk budgets to map out the efficient frontier.

Example Parameters

import httpx

API_URL = "https://api.jaot.io/api/v2"
headers = {"Authorization": "Bearer ok_live_your_key_here"}

# Maximize expected return for a $1M portfolio with diversification rules
response = httpx.post(f"{API_URL}/solve", headers=headers, json={
    "variables": [
        {"name": "us_large_cap_pct", "type": "continuous", "lb": 0, "ub": 0.40},
        {"name": "us_small_cap_pct", "type": "continuous", "lb": 0, "ub": 0.20},
        {"name": "intl_developed_pct", "type": "continuous", "lb": 0, "ub": 0.25},
        {"name": "emerging_markets_pct", "type": "continuous", "lb": 0, "ub": 0.15},
        {"name": "investment_grade_bonds_pct", "type": "continuous", "lb": 0.10, "ub": 0.50},
        {"name": "real_estate_pct", "type": "continuous", "lb": 0, "ub": 0.15},
    ],
    "objective": {
        "sense": "maximize",
        "coefficients": {
            "us_large_cap_pct": 8.5,
            "us_small_cap_pct": 10.2,
            "intl_developed_pct": 7.0,
            "emerging_markets_pct": 11.5,
            "investment_grade_bonds_pct": 3.5,
            "real_estate_pct": 6.8,
        },
    },
    "constraints": [
        {
            "name": "fully_invested",
            "coefficients": {
                "us_large_cap_pct": 1, "us_small_cap_pct": 1,
                "intl_developed_pct": 1, "emerging_markets_pct": 1,
                "investment_grade_bonds_pct": 1, "real_estate_pct": 1
            },
            "sense": "==",
            "rhs": 1.0,
        },
        {
            "name": "max_equity_exposure",
            "coefficients": {
                "us_large_cap_pct": 1, "us_small_cap_pct": 1,
                "intl_developed_pct": 1, "emerging_markets_pct": 1
            },
            "sense": "<=",
            "rhs": 0.70,
        },
        {
            "name": "min_domestic_allocation",
            "coefficients": {
                "us_large_cap_pct": 1, "us_small_cap_pct": 1,
                "investment_grade_bonds_pct": 1
            },
            "sense": ">=",
            "rhs": 0.40,
        },
    ],
})
result = response.json()

print(f"Expected portfolio return: {result['objective_value']:.2f}%")
for var in result["variables"]:
    print(f"  {var['name']}: {var['value'] * 100:.1f}%")

Templates

Next Steps

• Insurance Risk Modeling -- Apply portfolio allocation principles to insurance risk pools advanced
• Real Estate Investment -- Optimize property investment portfolios with location and budget constraints intermediate
• Budget Allocation -- Extend allocation optimization to marketing and advertising budgets beginner