INVESTMENTS: Analysis and Management Second Canadian Edition INVESTMENTS: Analysis and Management Second Canadian Edition W. Sean Cleary Charles P. Jones

Chapter 7 Expected Return and Risk

Explain how expected return and risk for securities are determined. Explain how expected return and risk for portfolios are determined. Describe the Markowitz diversification model for calculating portfolio risk. Learning Objectives

Involve uncertainty Focus on expected returns  Estimates of future returns needed to consider and manage risk Goal is to reduce risk without affecting returns  Accomplished by building a portfolio  Diversification is key Investment Decisions

Risk that an expected return will not be realized Investors must think about return distributions, not just a single return Use probability distributions  A probability should be assigned to each possible outcome to create a distribution  Can be discrete or continuous Dealing with Uncertainty

Weighted average of the individual security expected returns  Each portfolio asset has a weight, w, which represents the percent of the total portfolio value  The expected return on any portfolio can be calculated as: Portfolio Expected Return

Portfolio risk is not simply the sum of individual security risks Emphasis on the risk of the entire portfolio and not on risk of individual securities in the portfolio Individual stocks are risky only if they add risk to the total portfolio Portfolio Risk

Assume all risk sources for a portfolio of securities are independent The larger the number of securities, the smaller the exposure to any particular risk  “Insurance principle” Only issue is how many securities to hold Risk Reduction in Portfolios

Random diversification  Diversifying without looking at relevant investment characteristics  Marginal risk reduction gets smaller and smaller as more securities are added A large number of securities is not required for significant risk reduction International diversification is beneficial Risk Reduction in Portfolios

 p % Number of securities in portfolio Total Portfolio Risk Market Risk Portfolio Risk and Diversification

Act of randomly diversifying without regard to relevant investment characteristics 15 or 20 stocks provide adequate diversification Random Diversification

 p % Number of securities in portfolio Domestic Stocks only Domestic + International Stocks International Diversification

Non-random diversification  Active measurement and management of portfolio risk  Investigate relationships between portfolio securities before making a decision to invest  Takes advantage of expected return and risk for individual securities and how security returns move together Markowitz Diversification

Statistical measure of relative co-movements between security returns  mn = correlation coefficient between securities m and n   mn = +1.0 = perfect positive correlation   mn = -1.0 = perfect negative (inverse) correlation   mn = 0.0 = zero correlation Correlation Coefficient

When does diversification pay?  Combining securities with perfect positive correlation provides no reduction in risk Risk is simply a weighted average of the individual risks of securities  Combining securities with zero correlation reduces the risk of the portfolio  Combining securities with negative correlation can eliminate risk altogether Correlation Coefficient

Encompasses three factors  Variance (risk) of each security  Covariance between each pair of securities  Portfolio weights for each security Goal: select weights to determine the minimum variance combination for a given level of expected return Calculating Portfolio Risk

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