8.2 Asset allocation and portfolio optimization algorithms

Modern Portfolio Theory revolutionized investing by emphasizing diversification and risk-return trade-offs. It guides asset allocation decisions, balancing stocks and bonds based on an investor's risk tolerance. MPT's principles underpin many investment strategies used today.

Portfolio optimization algorithms have evolved beyond traditional mean-variance optimization. Newer approaches like risk parity and machine learning techniques aim to create more robust portfolios, addressing limitations of earlier models and adapting to changing market conditions.

Modern Portfolio Theory and Asset Allocation

Principles of modern portfolio theory

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• Modern Portfolio Theory (MPT) developed by Harry Markowitz in 1952 maximizes expected return for given risk level
• Key concepts: diversification reduces portfolio risk, efficient frontier represents optimal portfolios, risk-return trade-off balances potential gains and losses
• Portfolio construction allocates assets based on investor's risk tolerance and considers correlation between assets (stocks, bonds)
• Mean-variance optimization creates optimal portfolios using expected returns, variances, and covariances of assets
• Capital Asset Pricing Model (CAPM) extends MPT by introducing systematic (market) and unsystematic (company-specific) risk
• MPT guides investment decisions by determining optimal asset mix balancing risk and return objectives (60/40 stock/bond split)

Algorithms for portfolio optimization

• Mean-variance optimization (MVO) traditional approach based on MPT sensitive to input parameters
• Black-Litterman model combines market equilibrium with investor views addressing MVO limitations
• Risk parity allocates based on risk contribution aiming for equal risk from each asset (equities, fixed income)
• Hierarchical risk parity clusters correlated assets allocates within and between clusters
• Monte Carlo simulation generates multiple scenarios for stress testing and optimization (1000+ simulations)
• Genetic algorithms use evolutionary approach handling complex constraints and objectives
• Machine learning techniques employ neural networks for return prediction and reinforcement learning for dynamic allocation

Risk Assessment and Robo-Advisor Platforms

Risk tolerance assessment techniques

• Questionnaires gather demographic information, financial goals, time horizon, risk capacity, and risk perception
• Psychometric testing assesses emotional responses to financial scenarios measuring risk aversion
• Scenario analysis presents hypothetical market situations (market crash, economic boom) gauging investor reactions
• Risk capacity evaluation assesses ability to withstand losses considering income, assets, and liabilities
• Goal-based risk assessment aligns risk tolerance with specific financial objectives (retirement, home purchase)
• Dynamic risk profiling adjusts risk profile based on changing circumstances incorporating behavioral finance insights

Asset allocation in robo-advisors

• Strategic vs tactical allocation: strategic focuses on long-term MPT-based approach while tactical makes short-term market adjustments
• Passive vs active management: passive uses index-based ETFs while active selectively picks securities
• Factor-based allocation focuses on specific risk factors (value, momentum, quality) capturing risk premia
• Goal-based allocation tailors portfolios to specific financial goals using separate sub-portfolios (education fund, retirement account)
• Tax-aware strategies incorporate tax-loss harvesting and asset location optimization
• ESG integration considers environmental, social, and governance factors varying across platforms
• Rebalancing approaches differ in frequency and methodology using time-based or threshold-based triggers (quarterly, 5% deviation)