💰Intro to Finance Unit 13 – Introduction to Portfolio Theory

What's Portfolio Theory?

• Focuses on how risk-averse investors can construct portfolios to optimize or maximize expected return based on a given level of market risk
• Emphasizes that risk is an inherent part of higher reward
• Includes the efficient frontier, a concept that describes the set of optimal portfolios that offer the highest expected return for a defined level of risk
• Pioneered by Harry Markowitz with his paper "Portfolio Selection" published in 1952 by the Journal of Finance
• Assumes that investors are rational, markets are efficient, and that the future performance of investments is normally distributed
• Investors should select portfolios that yield the highest returns while considering their risk tolerance
• Provides a mathematical framework for assembling a portfolio of assets such that the expected return is maximized for a given level of risk

Key Concepts and Terms

• Risk-averse investor prefers lower returns with known risks rather than higher returns with unknown risks
• Standard deviation measures the dispersion of data from its mean, used as a measure of risk in Portfolio Theory
• Efficient frontier represents the set of optimal portfolios that offer the highest expected return for a defined level of risk or the lowest risk for a given level of expected return
• Optimal portfolio is the portfolio which maximizes the risk-adjusted return
• Risk-free asset is an asset which has a certain future return (government bonds are usually used as a proxy)
• Market portfolio is a theoretical portfolio in which every available type of asset is included at the level of its market value
• Capital Asset Pricing Model (CAPM) describes the relationship between systematic risk and expected return for assets
• Correlation coefficient measures the degree to which two securities move in relation to each other (-1 to +1)

Risk vs. Return Basics

• Return is the gain or loss of a security in a particular period, consists of the income and the capital gains relative on an investment
• Risk is the chance that an investment's actual return will differ from the expected return, includes the possibility of losing some or all of the original investment
• High risk is associated with high probability of higher return and lower risk with a lower return
• Determining what risk level is most appropriate for you isn't an easy question to answer
  • Risk tolerance is a key factor, it measures how much volatility or market risk an investor can tolerate
  • Time horizon should also be considered, if you're saving for retirement in 30 years, you may be able to afford more risk than someone who needs the money in 5 years
• Standard deviation is a statistical measure of volatility, often used as a proxy for risk
• Beta is a measure of the volatility of a security or a portfolio in comparison to the market as a whole

Diversification: The Free Lunch

• Refers to the reduction of risk that results from investing in a variety of assets
• Aims to maximize return by investing in different instruments that would each react differently to the same event
• "Don't put all your eggs in one basket" is a common expression that describes the concept of diversification
• Benefits of diversification include reducing portfolio risk while maintaining return
  • Owning stocks in many companies in many industries reduces industry-specific risk (Enron)
  • Owning other asset classes like bonds reduces market-specific risk
• Diversification is limited to the number of assets with non-correlated returns
• Modern Portfolio Theory shows that an investor can reduce portfolio risk simply by holding instruments which are not perfectly positively correlated

Building Efficient Portfolios

• Optimal portfolios are those which provide the highest expected return for a given level of risk
• These can be determined by plotting risk (standard deviation) against expected return in mean-variance space and identifying the efficient frontier
• Portfolios that lie below the efficient frontier are sub-optimal because they do not provide enough return for the level of risk
• Portfolios that cluster to the right of the efficient frontier are sub-optimal because they have a higher level of risk for the defined rate of return
• Optimal portfolios that comprise the efficient frontier tend to have a higher degree of diversification
  • For every level of return, there is one portfolio that offers the lowest possible risk, and for every level of risk, there is a portfolio that offers the highest return
• Goal is to select investments that have a high return, but also to select investments that move independently of each other

Modern Portfolio Theory (MPT)

• A theory on how risk-averse investors can construct portfolios to maximize expected return based on a given level of market risk
• Describes how to find the best possible diversification strategy to minimize risk given a desired return
• Key insight is that an asset's risk and return should not be assessed by itself, but by how it contributes to a portfolio's overall risk and return
• MPT assumes that investors are risk-averse, meaning that given two portfolios that offer the same expected return, investors will prefer the less risky one
• Under the model:
  • An investor can reduce portfolio risk simply by holding combinations of instruments that are not perfectly positively correlated
  • Investors can reduce their exposure to individual asset risk by holding a diversified portfolio of assets
• MPT mathematically formulates the concept of diversification, with the aim of selecting a collection of investment assets that has collectively lower risk than any individual asset

Practical Applications

• Investors use MPT to determine their acceptable level of risk tolerance and then allocate money between a risk-free asset (bonds) and a risky asset (stocks)
• This allocation is known as the asset allocation decision and is a personal decision
• Passive investors create a well-diversified portfolio and then rebalance annually to maintain appropriate asset allocation
• Active investors may engage in tactical asset allocation to find short-term opportunities to boost returns
• Robo-advisors often use MPT to formulate optimal portfolios for their clients, based on each individual's risk tolerance and investment horizon
• Target-date funds have become a popular default option in many retirement plans, they automatically adjust asset allocation as the target date approaches
• Portfolio managers may run optimization algorithms on securities based on historical data to find the most efficient portfolio

Limitations and Criticisms

• MPT assumes that asset returns follow a Gaussian distribution or normal distribution, returns in reality have shown to have fat tails
• Theory assumes that correlations between assets are fixed and constant forever, correlations depend on systemic relationships between the underlying assets
• MPT does not account for behavioral aspects of investing, such as the influence of investor emotions on investment decisions
• Assumes markets are efficient and investors are rational, real markets are not always efficient and investors can be irrational
• Assumes that all investors aim to maximize economic utility, but some investors may have other goals
• Model assumes a single-period transaction, and does not account for the impact of compounding returns over multiple periods
• Standard deviation assumes returns are normally distributed, but asset returns often have non-normal distributions
• Theory is based on historical data, and past performance does not guarantee future results