Return and Risk: The Capital Asset Pricing Model,Chapter 11,Copyright 2010 by the McGraw-Hill Companies, Inc. All rights reserved.,McGraw-Hill/Irwin,Key Concepts and Skills,Know how to calculate expected returns Know how to calculate covariances, correlations, and betas Understand the impact of diversification Understand the systematic risk principle Understand the security market line Understand the risk-return tradeoff Be able to use the Capital Asset Pricing Model,Chapter Outline,11.1 Individual Securities 11.2 Expected Return, Variance, and Covariance 11.3 The Return and Risk for Portfolios 11.4 The Efficient Set for Two Assets 11.5 The Efficient Set for Many Assets 11.6 Diversification 11.7 Riskless Borrowing and Lending 11.8 Market Equilibrium 11.9 Relationship between Risk and Expected Return (CAPM),11.1 Individual Securities,The characteristics of individual securities that are of interest are the: Expected Return Variance and Standard Deviation Covariance and Correlation (to another security or index),11.2 Expected Return, Variance, and Covariance,Consider the following two risky asset world. There is a 1/3 chance of each state of the economy, and the only assets are a stock fund and a bond fund.,Expected Return,Expected Return,Variance,Variance,Standard Deviation,Covariance,“Deviation” compares return in each state to the expected return.,“Weighted” takes the product of the deviations multiplied by the probability of that state.,Correlation,11.3 The Return and Risk for Portfolios,Note that stocks have a higher expected return than bonds and higher risk. Let us turn now to the risk-return tradeoff of a portfolio that is 50% invested in bonds and 50% invested in stocks.,Portfolios,The rate of return on the portfolio is a weighted average of the returns on the stocks and bonds in the portfolio:,Portfolios,The expected rate of return on the portfolio is a weighted average of the expected returns on the securities in the portfolio.,Portfolios,The variance of the rate of return on the two risky assets portfolio is,where BS is the correlation coefficient between the returns on the stock and bond funds.,Portfolios,Observe the decrease in risk that diversification offers. An equally weighted portfolio (50% in stocks and 50% in bonds) has less risk than either stocks or bonds held in isolation.,11.4 The Efficient Set for Two Assets,We can consider other portfolio weights besides 50% in stocks and 50% in bonds.,100% bonds,100% stocks,The Efficient Set for Two Assets,100% stocks,100% bonds,Note that some portfolios are “better” than others. They have higher returns for the same level of risk or less.,Portfolios with Various Correlations,100% bonds,return,100% stocks, = 0.2, = 1.0, = -1.0,Relationship depends on correlation coefficient -1.0 r +1.0 If r = +1.0, no risk reduction is possible If r = 1.0, complete risk reduction is possible,11.5 The Efficient Set for Many Securities,Consider a world with many risky assets; we can still identify the opportunity set of risk-return combinations of various portfolios.,return,P,Individual Assets,The Efficient Set for Many Securities,The section of the opportunity set above the minimum variance portfolio is the efficient frontier.,return,P,minimum variance portfolio,efficient frontier,Individual Assets,Announcements, Surprises, and Expected Returns,The return on any security consists of two parts. First, the expected returns Second, the unexpected or risky returns A way to write the return on a stock in the coming month is:,Announcements, Surprises, and Expected Returns,Any announcement can be broken down into two parts, the anticipated (or expected) part and the surprise (or innovation): Announcement = Expected part + Surprise.,Diversification and Portfolio Risk,Diversification can substantially reduce the variability of returns without an equivalent reduction in expected returns. This reduction in risk arises because worse than expected returns from one asset are offset by better than expected returns from another. However, there is a minimum level of risk that cannot be diversified away, and that is the systematic portion.,Portfolio Risk and Number of Stocks,Nondiversifiable risk; Systematic Risk; Market Risk,Diversifiable Risk; Nonsystematic Risk; Firm Specific Risk; Unique Risk,n,In a large portfolio the variance terms are effectively diversified away, but the covariance terms are not.,Portfolio risk,Risk: Systematic and Unsystematic,A systematic risk is any risk that affects a large number of assets, each to a greater or lesser degree. An unsystematic risk is a risk that specifically affects a single asset or small group of assets. Unsystematic risk can be diversified away. Examples of systematic risk include uncertainty about general economic conditions, such as GNP, interest rates or inflation. On the other hand, announcements specific to a single company are examples of unsystem