Principles of Corporate Finance Eighth Edition Introduction to

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Key Concepts and Skills Ø Know how to calculate expected returns Ø Know how to calculate covariances, correlations, and betas Ø Understand the impact of diversification Ø Understand the systematic risk principle Ø Understand the security market line Ø Understand the risk-return tradeoff Ø Be able to use the Capital Asset Pricing Model Mc. Graw-Hill/Irwin Copyright © 2006 by The Mc. Graw-Hill Companies, Inc. All rights reserved 7 - 2

Chapter Outline 10. 1 Individual Securities 10. 2 Expected Return, Variance, and Covariance 10. 3 The Return and Risk for Portfolios 10. 4 The Efficient Set for Two Assets 10. 5 The Efficient Set for Many Assets 10. 6 Diversification: An Example 10. 7 Riskless Borrowing and Lending 10. 8 Market Equilibrium 10. 9 Relationship between Risk and Expected Return (CAPM) Mc. Graw-Hill/Irwin Copyright © 2006 by The Mc. Graw-Hill Companies, Inc. All rights reserved 7 - 3

10. 1 Individual Securities Ø 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) Mc. Graw-Hill/Irwin Copyright © 2006 by The Mc. Graw-Hill Companies, Inc. All rights reserved 7 - 4

7 - 5 10. 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 a bond fund. Mc. Graw-Hill/Irwin Copyright © 2006 by The Mc. Graw-Hill Companies, Inc. All rights reserved

Covariance 7 - 11 Deviation compares return in each state to the expected return. Weighted takes the product of the deviations multiplied by the probability of that state. Mc. Graw-Hill/Irwin Copyright © 2006 by The Mc. Graw-Hill Companies, Inc. All rights reserved

7 - 13 10. 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. Mc. Graw-Hill/Irwin Copyright © 2006 by The Mc. Graw-Hill Companies, Inc. All rights reserved

Portfolios The rate of return on the portfolio is a weighted average of the returns on the stocks and bonds in the portfolio: Mc. Graw-Hill/Irwin Copyright © 2006 by The Mc. Graw-Hill Companies, Inc. All rights reserved 7 - 14

Portfolios The expected rate of return on the portfolio is a weighted average of the expected returns on the securities in the portfolio. Mc. Graw-Hill/Irwin Copyright © 2006 by The Mc. Graw-Hill Companies, Inc. All rights reserved 7 - 15

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. Mc. Graw-Hill/Irwin Copyright © 2006 by The Mc. Graw-Hill Companies, Inc. All rights reserved 7 - 16

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. Mc. Graw-Hill/Irwin Copyright © 2006 by The Mc. Graw-Hill Companies, Inc. All rights reserved 7 - 17

7 - 18 1)Suppose you invest equal amounts in a portfolio with an expected return of 20% and a standard deviation of returns of 16% and a risk-free asset with an interest rate of 4%; calculate the expected return on the resulting portfolio? Ø 0. 5(20) + 0. 5(4) = 12% 2) calculate the standard deviation of the returns on the resulting portfolio: 0. 5(16) = 8% Mc. Graw-Hill/Irwin Copyright © 2006 by The Mc. Graw-Hill Companies, Inc. All rights reserved

7 - 19 10. 4 The Efficient Set for Two Assets 100% stocks 100% bonds We can consider other portfolio weights besides 50% in stocks and 50% in bonds … Mc. Graw-Hill/Irwin Copyright © 2006 by The Mc. Graw-Hill Companies, Inc. All rights reserved

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. Mc. Graw-Hill/Irwin Copyright © 2006 by The Mc. Graw-Hill Companies, Inc. All rights reserved 7 - 20

7 - 21 return Portfolios with Various Correlations 100% stocks = -1. 0 100% bonds = 1. 0 = 0. 2 Ø Relationship depends on correlation coefficient -1. 0 < < +1. 0 Ø If = +1. 0, no risk reduction is possible Ø If = – 1. 0, complete risk reduction is possible Mc. Graw-Hill/Irwin Copyright © 2006 by The Mc. Graw-Hill Companies, Inc. All rights reserved

7 - 22 return 10. 5 The Efficient Set for Many Securities Individual Assets P Consider a world with many risky assets; we can still identify the opportunity set of risk-return combinations of various portfolios. Mc. Graw-Hill/Irwin Copyright © 2006 by The Mc. Graw-Hill Companies, Inc. All rights reserved

7 - 23 return The Efficient Set for Many Securities r nt ie ffic e tie ron f minimum variance portfolio Individual Assets P The section of the opportunity set above the minimum variance portfolio is the efficient frontier. Mc. Graw-Hill/Irwin Copyright © 2006 by The Mc. Graw-Hill Companies, Inc. All rights reserved

Diversification and Portfolio Risk Ø Diversification can substantially reduce the variability of returns without an equivalent reduction in expected returns. Ø This reduction in risk arises because worse than expected returns from one asset are offset by better than expected returns from another. Ø However, there is a minimum level of risk that cannot be diversified away, and that is the systematic portion. Mc. Graw-Hill/Irwin Copyright © 2006 by The Mc. Graw-Hill Companies, Inc. All rights reserved 7 - 24

7 - 25 Portfolio Risk and Number of Stocks In a large portfolio the variance terms are effectively diversified away, but the covariance terms are not. Diversifiable Risk; Nonsystematic Risk; Firm Specific Risk; Unique Risk Portfolio risk Nondiversifiable risk; Systematic Risk; Market Risk n Mc. Graw-Hill/Irwin Copyright © 2006 by The Mc. Graw-Hill Companies, Inc. All rights reserved

Systematic Risk Ø Risk factors that affect a large number of assets Ø Also known as non-diversifiable risk or market risk Ø Includes such things as changes in GDP, inflation, interest rates, etc. Mc. Graw-Hill/Irwin Copyright © 2006 by The Mc. Graw-Hill Companies, Inc. All rights reserved 7 - 26

Unsystematic (Diversifiable) Risk Ø Risk factors that affect a limited number of assets Ø Also known as unique risk and asset-specific risk Ø Includes such things as labor strikes, part shortages, etc. Ø The risk that can be eliminated by combining assets into a portfolio Ø If we hold only one asset, or assets in the same industry, then we are exposing ourselves to risk that we could diversify away. Mc. Graw-Hill/Irwin Copyright © 2006 by The Mc. Graw-Hill Companies, Inc. All rights reserved 7 - 27

Total Risk Ø Total risk = systematic risk + unsystematic risk Ø The standard deviation of returns is a measure of total risk. Ø For well-diversified portfolios, unsystematic risk is very small. Ø Consequently, the total risk for a diversified portfolio is essentially equivalent to the systematic risk. Mc. Graw-Hill/Irwin Copyright © 2006 by The Mc. Graw-Hill Companies, Inc. All rights reserved 7 - 28

return Optimal Portfolio with a Risk-Free Asset 7 - 29 100% stocks rf 100% bonds In addition to stocks and bonds, consider a world that also has risk-free securities like T-bills. Mc. Graw-Hill/Irwin Copyright © 2006 by The Mc. Graw-Hill Companies, Inc. All rights reserved

7 - 30 return 10. 7 Riskless Borrowing and Lending L CM 100% stocks Balanced fund rf 100% bonds Now investors can allocate their money across the T-bills and a balanced mutual fund. Mc. Graw-Hill/Irwin Copyright © 2006 by The Mc. Graw-Hill Companies, Inc. All rights reserved

7 - 31 return Riskless Borrowing and Lending L CM efficient frontier rf P With a risk-free asset available and the efficient frontier identified, we choose the capital allocation line with the steepest slope. Mc. Graw-Hill/Irwin Copyright © 2006 by The Mc. Graw-Hill Companies, Inc. All rights reserved

return 10. 8 Market Equilibrium 7 - 32 L CM efficient frontier M rf P With the capital allocation line identified, all investors choose a point along the line—some combination of the risk-free asset and the market portfolio M. In a world with homogeneous expectations, M is the same for all investors. Mc. Graw-Hill/Irwin Copyright © 2006 by The Mc. Graw-Hill Companies, Inc. All rights reserved

return Market Equilibrium L M C 7 - 33 100% stocks Balanced fund rf 100% bonds Where the investor chooses along the Capital Market Line depends on his risk tolerance. The big point is that all investors have the same CML. Mc. Graw-Hill/Irwin Copyright © 2006 by The Mc. Graw-Hill Companies, Inc. All rights reserved

7 - 34 Risk When Holding the Market Portfolio Ø Researchers have shown that the best measure of the risk of a security in a large portfolio is the beta (b)of the security. Ø Beta measures the responsiveness of a security to movements in the market portfolio (i. e. , systematic risk). Mc. Graw-Hill/Irwin Copyright © 2006 by The Mc. Graw-Hill Companies, Inc. All rights reserved

Security Returns Estimating b with Regression ine L ic ist ter c ra ha C Slope = bi Return on market % Ri = a i + b i Rm + e i Mc. Graw-Hill/Irwin Copyright © 2006 by The Mc. Graw-Hill Companies, Inc. All rights reserved 7 - 35

The Formula for Beta Clearly, your estimate of beta will depend upon your choice of a proxy for the market portfolio. Mc. Graw-Hill/Irwin Copyright © 2006 by The Mc. Graw-Hill Companies, Inc. All rights reserved 7 - 36

10. 9 Relationship between Risk and Expected Return (CAPM) ØExpected Return on the Market: • Expected return on an individual security: Market Risk Premium This applies to individual securities held within welldiversified portfolios. Mc. Graw-Hill/Irwin Copyright © 2006 by The Mc. Graw-Hill Companies, Inc. All rights reserved 7 - 37

Expected Return on a Security ØThis formula is called the Capital Asset Pricing Model (CAPM): Expected return on a security Risk-free Beta of the = + × rate security Market risk premium • Assume bi = 0, then the expected return is RF. • Assume bi = 1, then Mc. Graw-Hill/Irwin Copyright © 2006 by The Mc. Graw-Hill Companies, Inc. All rights reserved 7 - 38

Quick Quiz Ø How do you compute the expected return and standard deviation for an individual asset? For a portfolio? Ø What is the difference between systematic and unsystematic risk? Ø What type of risk is relevant for determining the expected return? Ø Consider an asset with a beta of 1. 2, a risk-free rate of 5%, and a market return of 13%. – What is the expected return on the asset? Mc. Graw-Hill/Irwin Copyright © 2006 by The Mc. Graw-Hill Companies, Inc. All rights reserved 7 - 41