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šŸ’¼ Portfolio Optimization

Quantum algorithms for optimal asset allocation and risk management

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Quantum Optimization Problems

šŸ’¼ The Trillion-Dollar Problem

Portfolio optimization is the cornerstone of modern finance: allocate capital across assets to maximize returns while minimizing risk. With $100+ trillion in managed assets globally, even 1% improvement means billions in gains. Quantum computing offers exponential speedups for these complex quadratic optimization problems.

šŸ’” Why Quantum?

Classical optimization struggles with high-dimensional portfolios (100+ assets) and complex constraints. Quantum algorithms like QAOA and quantum annealing can explore exponentially large solution spaces efficiently, finding better risk-return tradeoffs.

Classical portfolio optimization:O(nĀ³) complexity

šŸŽÆ What You'll Master

šŸ“Š
Modern Portfolio Theory
Markowitz, efficient frontier, Sharpe ratio
āš›ļø
Quantum Algorithms
QAOA for quadratic programming
šŸ”’
Real Constraints
Cardinality, transaction costs, ESG
šŸ¦
Industry Applications
Banks, hedge funds, pension funds

šŸ“ˆ The Optimization Challenge

šŸŽÆObjective
Maximize return:Ī£ wiri
Minimize risk:wTĪ£w
Balance:Risk-adjusted
āš–ļøConstraints
Budget:Ī£ wi = 1
No shorting:wi ā‰„ 0
Cardinality:Max K assets

šŸ’° Market Impact

Global AUM
Assets under management
$103T
Quantum Advantage
Potential improvement
0.5-2%
Annual Value
With quantum optimization
$500B-$2T