Principles of Investing FIN 330 CHAPTER 8 MODERN PORTFOLIO THEORY CAPITAL ASSET PRICING THEORY Dr David P Echevarria All Rights Reserved

STUDENT LEARNING OBJECTIVES What is Modern Portfolio Theory (MPT) What does MPT tell us about managing risk and diversification? How do we measure investment risk? What is the Capital Asset Pricing Model? How does CAPM describe the efficient frontier? Dr David P Echevarria All Rights Reserved

Some Background on MPT Prior to MPT there was no real quantitative method for constructing portfolios or measuring their investment efficiency. Harry Markowitz developed the idea of mean and variance efficient portfolios. The locus of which would later be identified as the Efficient Frontier. Mean and Variance Efficiency = the best rate of return for a given level of risk. All assets meeting this criteria fall on the efficient frontier.

Assumptions of MPT 1. Risk of a portfolio is based on the variability of returns from the said portfolio. 2. Investors are risk averse. 3. The investor's utility function is convex and increasing, due to risk aversion and consumption preference. 4. Analysis is based on single period model of investment. 5. An investor either maximizes portfolio return for a given level of risk or maximizes return for the minimum risk. 6. An investor is rational in nature.

Investment RISK The probability of losing some or all of your investment Risk is a function of the dispersion of possible future outcomes Expected Value: probability of a particular outcome times the magnitude Risk is measured as the standard deviation of expected outcomes Dr David P Echevarria All Rights Reserved

Modern Portfolio Theory (H. Markowitz) The expected return of a portfolio is a weighted average of the expected returns of each of the securities in the portfolio E(Rp) = S Xi Ri The weights (Xi) are equal to the percentage of the portfolio’s value which is invested in each security and Ri is the [expected] return for each asset i in the portfolio. Dr David P Echevarria All Rights Reserved

Modern Portfolio Theory The riskiness of a portfolio is more complex; it is the square root of the sum of the weighted (X2i) times the variances (s2) of each security and the correlation (r - rho) between the 2 securities in a 2-Asset Portfolio. sp = (X2i s2i + X2j s2j + 2 Xi Xj ri,j si sj)1/2 2 Sources of Risk: Variance and Covariance Dr David P Echevarria All Rights Reserved

Modern Portfolio Theory sp = (X2i s2i + X2j s2j + 2 Xi Xj ri,j si sj)1/2 The correlation coefficient (ri,j) can be positive (+1), zero, or negative (-1) If the average correlation of securities in the portfolio is positive – the riskiness of the portfolio will be larger. If the average correlation of securities in the portfolio is negative – the riskiness of the portfolio is smaller: the third term will be negative Dr David P Echevarria All Rights Reserved

Example of Efficient Frontier 2-Asset Portfolio Two assets are positively correlated but r is less than 1 Minimum Variance Investment Portfolio Dr David P Echevarria All Rights Reserved

Modern Portfolio Theory D. Correlation: Range from +1 to 0 to -1 When the holding period returns of two securities move in the same direction, by the same amount at the same time, the pair is perfectly positively correlated: rho = 1 When the holding period returns of two securities are totally unrelated to each other, the pair is uncorrelated; rho = 0 When they move in opposite directions, the pair are negatively correlated: rho = -1 Dr David P Echevarria All Rights Reserved

Modern Portfolio Theory MPT Efficient Portfolios Mean & Variance Efficient portfolios form a curvilinear frontier Assets that are efficiently price will fall on the frontier as will all efficient portfolios. Assets lying below or above the efficient Frontier are not mean-variance efficient. Assets below the EF are said to be overpriced. Assets above the EF are said to be underpriced. Dr David P Echevarria All Rights Reserved

Modern Portfolio Theory The risk of a portfolio is the weighted average of the risk of each security in the portfolio, and the correlations between each pair of securities in the portfolio Some textbooks use the covariance terms in the third term: si,j = ri,j si sj sp = (X2i s2i + X2j s2j + 2 Xi Xj sj,j)1/2 Dr David P Echevarria All Rights Reserved

Risk Reduction: Benefits of Diversification Portfolio diversification Diversification can increase the risk/return tradeoff if the average correlation coefficient between individual securities in the portfolio is less than 1.0 The benefits of diversification increase as the correlation coefficient gets smaller Dr David P Echevarria All Rights Reserved

Risk Reduction: Benefits of Diversification B. Diversification across securities As the number of securities in a portfolio increases the portfolio risk decreases and approaches the risk of the total market Market risk is inherent from business cycles, inflation, interest rates, and economic factors Firm-specific risk is tied to the company’s labor contracts, new product development and other company related factors Dr David P Echevarria All Rights Reserved

Risk Reduction: Benefits of Diversification Forms of Diversification Mathematical: Increasing the number of stocks reduces the portfolio risk Diversification across time Dollar cost averaging Dr David P Echevarria All Rights Reserved

Risk Reduction: Benefits of Diversification 4. Naive Diversification Naive diversification occurs when investors select stocks at random, and purchase and equal dollar amount of each security When N becomes large enough, naive diversification averages out the firm-specific (unsystematic) risk of the stocks in the portfolio, so that only the market (or systematic) risk remains Dr David P Echevarria All Rights Reserved

Capital Asset Pricing Model (CAPM) Equation that defines the risk/return relationship The CAPM assumes two assets: the risk-free asset and the risky market portfolio The two asset CAPM world results in a linear efficient frontier: Capital Market Line (CML) Dr David P Echevarria All Rights Reserved

Capital Asset Pricing Model (CAPM) The risk aversion characteristic of the investor will determine how much is invested in the risk-free asset and how much is invested in the risky market portfolio The standard deviation of the risk-free asset is zero. Based on the idea that investors accept a higher risk only for a higher return Dr David P Echevarria All Rights Reserved

Capital Asset Pricing Model (CAPM) Assumptions of the CAPM Investors have cost-free and equal access to information leading to homogenous expectations Frictionless capital markets No transaction costs or taxes (perfect) Securities infinitely divisible (complete) Investors are rewarded for systematic risk (b) Non-systematic risk is diversified away. Dr David P Echevarria All Rights Reserved

Capital Asset Pricing Model (CAPM) B. Assumptions of the CAPM (cont.) Investors are rational and seek to maximize their expected utility functions All investment is for the same time period All investors can borrow or lend at the risk-free rate Dr David P Echevarria All Rights Reserved

The Capital Market Line (CML) Expected Portfolio Return: E(Rp) = (X) E(Rp) + (1 - X) RF Where: X = % of Wealth Invested Portfolio Risk: sP = S Xi si Where: Xi = proportion invested in asset i, si = the standard deviation (riskiness) of asset i CML is locus of all combinations of the risk-free asset and the risky market portfolio. The CML is also termed the Borrowing-Lending line. Dr David P Echevarria All Rights Reserved

The Capital Market Line (CML) The Market Portfolio The Market Portfolio (point M) must be the only risky portfolio chosen by all risk-averse investors. Because it is demanded by all investors, it must contain all the securities and other traded assets Portfolio M’s risk = Market risk Dr David P Echevarria All Rights Reserved

The Capital Market Line (CML) Measuring Relative Risk (Beta b) Relative risk contribution of security i Known as beta, b , it measures security risk, or volatility relative to the market portfolio Beta greater than 1.0 is riskier than the market Beta less than 1.0 is less risky than the market Dr David P Echevarria All Rights Reserved

The Capital Market Line (CML) The value of beta implies something about returns relative to the market portfolio The choice of a proxy affects beta: e.g. S&P 500, Wilshire 5000, Russell 1000, etc. Dr David P Echevarria All Rights Reserved

The Capital Market Line (CML) Types of CAPM Risk Systematic or non-diversifiable risk: Beta is the measure of systematic risk Non Systematic or diversifiable risk Risk due to firm specific attributes Become irrelevant in a well-diversified portfolio Decisions made by total risk (standard deviations) instead of beta ignore the systematic risk and diversifiable risk components of total risk Dr David P Echevarria All Rights Reserved

The Capital Market Line (CML) F. The Security Market Line (SML) The SML addresses the risk-return characteristics for individual securities The slope of the SML is equal to the stock’s beta coefficient. Dr David P Echevarria All Rights Reserved

HOMEWORK Dr David P Echevarria All Rights Reserved