RETURN AND RISK: The Capital Asset Pricing Model

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1 RETURN AND RISK: The Capital Asset Pricing Model (BASED ON RWJJ CHAPTER 11) Return and Risk: The Capital Asset Pricing Model (CAPM) Know how to calculate expected returns Understand covariance, correlation, and betas Understand the impact of diversification Understand the systematic risk principle Understand the security market line (SML) Understand the risk-return tradeoff Be able to apply the capital asset pricing model (CAPM) 1 1

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. 2 Expected Return 3 2

3 Variance 4 Standard Deviation 5 3

4 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. 6 Correlation 7 4

5 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. 8 Portfolios The rate of return on the portfolio is a weighted average of the returns on the stocks and bonds in the portfolio: 9 5

6 Portfolios The expected rate of return on the portfolio is a weighted average of the expected returns on the securities in the portfolio. 10 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. 11 6

7 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. 12 The Efficient Set 100% stocks 100% bonds Note that some portfolios are better than others. They have higher returns for the same level of risk or less. 13 7

8 Portfolios with Various Correlations return = % stocks Relationship depends on correlation coefficient -1.0 < < % bonds = 1.0 = 0.2 If = +1.0, no risk reduction is possible If = 1.0, complete risk reduction is possible 14 The Efficient Set for Many Securities return minimum variance portfolio Individual Assets P Consider a world with many risky assets; we can still identify the opportunity set of risk-return combinations of various portfolios. The section of the opportunity set above the minimum-variance portfolio is the efficient frontier. 15 8

9 Risk: Systematic and Unsystematic Systematic Risk - factors that affect a large number of assets Also known as non-diversifiable risk or market risk Includes such things as changes in GDP, inflation, interest rates, etc. Unsystematic Risk - factors that affect a limited number of assets Also known as unique risk and asset-specific risk Includes such things as labor strikes, part shortages, etc. 16 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. 17 9

10 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 18 Diversifiable Risk The risk that can be eliminated by combining assets into a portfolio Often considered the same as unsystematic, unique, or asset-specific risk If we hold only one asset, or assets in the same industry, then we are exposing ourselves to risk that we could diversify away

11 Total Risk Total risk = systematic risk + unsystematic risk The standard deviation of returns is a measure of total risk. For well-diversified portfolios, unsystematic risk is very small. Consequently, the total risk for a diversified portfolio is essentially equivalent to the systematic risk. 20 Riskless Borrowing and Lending return Efficient fund 1 r f In addition to stocks and bonds, consider a world that also has a risk-free security like a T-bill. Now investors can allocate money across the T-bills and one of the funds that offers a risk return combo on the efficient frontier. 11

12 Riskless Borrowing and Lending return r f Efficient fund 1 Can borrow at risk-free rate, invest own money and borrowed money to get to these combinations of risk & return In addition to stocks and bonds, consider a world that also has a risk-free security like a T-bill. Now investors can allocate money across the T-bills and one of the funds that offers a risk return combo on the efficient frontier. Riskless Borrowing and Lending return Efficient fund 1 Efficient fund 2 r f In addition to stocks and bonds, consider a world that also has a risk-free security like a T-bill. Now investors can allocate money across the T-bills and one of the funds that offers a risk return combo on the efficient frontier. 12

13 Riskless Borrowing and Lending return Efficient fund 1 Efficient fund 2 Effic. Fund 3 r f In addition to stocks and bonds, consider a world that also has a risk-free security like a T-bill. Now investors can allocate money across the T-bills and one of the funds that offers a risk return combo on the efficient frontier. Riskless Borrowing and Lending return Balanced fund Capital Market Line r f In addition to stocks and bonds, consider a world that also has a risk-free security like a T-bill. Now investors can allocate money across the T-bills and one of the funds that offers a risk return combo on the efficient frontier. 13

14 Market Equilibrium return M r f 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. Just where the investor chooses along the Capital Market Line depends on his risk tolerance. The big points are that all investors have the same CML and use the same M. 26 Risk When Holding the Market Portfolio Researchers have shown that the best measure of the risk of a security in a large portfolio is the beta () of the security. Beta measures the responsiveness of a security to movements in the market portfolio (i.e., systematic risk). Clearly, your estimate of beta will depend upon your choice of a proxy for the market portfolio. 14

15 Estimating with Regression Security Returns % Slope = i Return on market % R i = i + i R m + e i Estimating of the Market Return on market % Slope = Return on market % The beta of the market is 1 15

16 Estimating of Risk-Free Asset Risk-free Ret. % Slope = Return on market % The beta of a risk-free asset is 0 Risk and Return (CAPM) Expected Return on the Market: Expected return on an individual security: Market Risk Premium This applies to individual securities held within welldiversified portfolios

17 Expected Return on a Security This formula is called the Capital Asset Pricing Model (CAPM): Ticky-tack Technically, Should be Required Return Expected return on a security = Riskfree rate + Beta of the security Market risk premium Assume i = 0, then the expected return is R F. Assume i = 1, then 32 Examples: R M = 8.0% & R F = 2.0% Market Risk Premium = 6.0% Thought of as the extra reward (extra return) that you should be able to require for taking on however much market risk the market has Boeing has a β = 1.1 How much extra return? 1.1 x ( 8.0% 2.0% ) E(r BOE ) = 2.0% x ( 8.0% 2.0% ) = 8.6% Axiall has a β = 2.4 How much extra return? 2.4 x ( 8.0% 2.0% ) E(r AXI ) = 2.0% x ( 8.0% 2.0% ) = 16.4% 17

18 Relation Between Risk and Return SECURITY MARKET LINE Summary statements regarding risk and return for a portfolio. The expected return on a portfolio is always a weighted average of the expected returns on the portfolio's components. The risk of a portfolio's return, as measured by standard deviation, is generally less than the weighted average of the risks of the portfolio s components. Risk generally declines when new assets are added to a portfolio. Risk declines more if: the new asset's standard deviation is lower, the correlations between the new asset's payoffs and the various existing assets payoffs are lower. Beta measures the amount of Portfolio Risk 18

Lecture 5. Return and Risk: The Capital Asset Pricing Model

Lecture 5. Return and Risk: The Capital Asset Pricing Model Lecture 5 Return and Risk: The Capital Asset Pricing Model Outline 1 Individual Securities 2 Expected Return, Variance, and Covariance 3 The Return and Risk for Portfolios 4 The Efficient Set for Two Assets