Lecture Notes: Portfolio Management and Modern Portfolio Theory

Introduction

• Course is designed to show the application of math to real-world industry, particularly in finance.
• Feedback from students indicated a preference for more focus on application rather than math theory.
• Important topics include Modern Portfolio Theory and its application in the real world.

Portfolio Construction Exercise

• Students asked to construct a portfolio from scratch using their intuition.
• Example given: constructing a portfolio with $1,000 allowance from parents.
• Purpose is to connect theory with practice through real-life examples.

Learning through Observation

• Start with observation, collect data, find patterns.
• Build models and theories, verify predictions, and refine models.

Concepts of Portfolio Theory

• Efficient Frontier: Curve representing optimal portfolios that offer the highest return for a given level of risk.
• Risk: Often measured by standard deviation of returns.
• Diversification: Combining uncorrelated assets to minimize risk and achieve higher returns.

Special Cases in Portfolio Theory

• Discussed various portfolio scenarios:
  • Cash vs. lottery vs. coin flipping
  • Government bonds, stocks, venture capital
• Efficient Frontier examples with two assets, special cases with correlations
  • Zero correlation, perfectly negative correlation, etc.

Practical Application

• Real-world application of portfolio theory involves understanding goals, objectives, and risk tolerance.
• Risk Parity: Allocating risk equally among assets instead of based on market value.

Risk Parity and Leverage

• Risk parity strategy uses leverage to balance risk among different asset classes.
• Discussed the impact of leverage on risk and portfolio return.

Sharpe Ratio and Beta

• Sharpe Ratio: Measure of risk-adjusted return.
• Beta: Measure of a portfolio's volatility in relation to the market.

Real-world Considerations

• Market dynamics and interconnectedness can affect portfolio strategies.
• Examples such as the Millennium Bridge and metronome synchronization illustrate systemic risk.

Conclusion

• Emphasized the importance of a dynamic approach to portfolio management.
• Diversification is beneficial but not a guaranteed free lunch.
• Encouraged students to think broadly and adapt to market changes.

Discussion and Q&A

• Topics covered included game theory, risk management, and the role of human judgment in portfolio management.
• Discussion on the limitations of relying solely on historical data for forecasting.

Additional Resources and Reading

• Recommended reading on Kelly Criterion and its application in multi-period investments.
• Mentioned the book "Fortune's Formula" for further exploration of investment theory.

Key Takeaways

• Portfolio management involves blending theoretical models with practical considerations.
• Continuous observation, adaptation, and innovation are crucial in the field of finance.

No homework assigned for this lecture.