INTRODUCTION TO MODERN PORTFOLIO THEORY

Introduction to Modern Portfolio Theory

• Definition: Modern Portfolio Theory (MPT) provides a framework for constructing and selecting portfolios based on the expected performance of the investments and the risk appetite of the investor.
• Details: MPT quantifies the concept of diversification by introducing the statistical notion of covariance, or correlation between investment assets.

Key Concepts

• Framework for Constructing Portfolios: MPT provides a framework for constructing and selecting portfolios based on the expected performance of the investments and the risk appetite of the investor.
• Assumptions of the Theory:
  • Investors want to maximize return for a given level of risk.
  • Investors maximize one-period expected utility.
  • Utility curves demonstrate diminishing marginal utility of wealth.
  • Investors estimate the risk of the portfolio on the basis of the variability of expected returns of constituent assets.
  • Investors base decisions solely on expected return and risk.
• Definition of Risk Averse, Risk Seeking, and Risk Neutral Investor:
  • Risk Averse Investor: Rejects fair games and demands a risk premium for bearing risk.
  • Risk Seeking Investor: Engages in fair games and makes an upward adjustment for utility.
  • Risk Neutral Investor: Evaluates investment opportunities solely on the basis of expected return with no regard to risk.
• Calculation of Risk and Return:
  • Expected Rate of Return: The sum of the potential returns multiplied with the corresponding probability of the returns.
  • Variance of Return: A measure of the variation of possible rates of return, from the expected rate of return.
  • Standard Deviation: The square root of the variance.
• Graphical Presentation of Portfolio Risk/Return:
  • Two Securities Portfolio: The portfolio return and standard deviation are linear combinations of the individual securities.
  • Efficient Frontier: A set of optimal portfolios that offer the highest expected return for a given level of risk or the lowest risk for a given level of expected return.
• Portfolio Optimization Process:
  • Optimum Portfolio: A combination of investments having desirable individual risk–return characteristics for a given set of constraints.
  • Estimation Requirements: Expected return, standard deviation, and correlation coefficient among the entire set of asset class, securities, and investment opportunities.
• Estimation Issues:
  • Estimation Risk: The potential source of error that arises from estimating returns, risk, and correlations among the securities in the investment universe.
  • Variance-Covariance Matrix: A matrix of variance and covariance estimates used to calculate portfolio risk.