CAPM APT 1 Capital Market Theory An Overview

CAPM & APT 1

Capital Market Theory: An Overview u Capital market theory extends portfolio theory and develops a model for pricing all risky assets u Capital asset pricing model (CAPM) will allow you to determine the required rate of return for any risky asset 2

Capital Asset Pricing Model (CAPM) u The asset pricing models aim to use the concepts of portfolio valuation and market equilibrium in order to determine the market price for risk and appropriate measure of risk for a single asset. u Capital Asset Pricing Model (CAPM) has an observation that the returns on a financial asset increase with the risk. CAPM concerns two types of risk namely unsystematic and systematic risks. The central principle of the CAPM is that, systematic risk, as measured by beta, is the only factor affecting the level of return. 3

Capital Asset Pricing Model u Introduction u Systematic and unsystematic risk u Fundamental risk/return relationship revisited 4

Introduction u The Capital Asset Pricing Model (CAPM) is a theoretical description of the way in which the market prices investment assets • The CAPM is a positive theory 5

Systematic and Unsystematic Risk u Unsystematic risk can be diversified and is irrelevant u Systematic risk cannot be diversified and is relevant • Measured by beta – Beta determines the level of expected return on a security or portfolio (SML) 6

CAPM u The more risk you carry, the greater the expected return: 7

CAPM (cont’d) u The CAPM deals with expectations about the future u Excess returns on a particular stock are directly related to: • The beta of the stock • The expected excess return on the market 8

CAPM (cont’d) u CAPM assumptions: • Variance of return and mean return are all investors care about • Investors are price takers – They cannot influence the market individually • All investors have equal and costless access to information • There are no taxes or commission costs 9

CAPM (cont’d) u CAPM assumptions (cont’d): • Investors look only one period ahead • Everyone is equally adept at analyzing securities and interpreting the news 10

SML and CAPM u If you show the security market line with excess returns on the vertical axis, the equation of the SML is the CAPM • The intercept is zero • The slope of the line is beta 11

Market Model Versus CAPM u The market model is an ex post model • It describes past price behavior u The CAPM is an ex ante model • It predicts what a value should be 12

Market Model Versus CAPM (cont’d) u The market model is: 13

Note on the CAPM Assumptions u Several assumptions are unrealistic: • People pay taxes and commissions • Many people look ahead more than one period • Not all investors forecast the same distribution u Theory is useful to the extent that it helps us learn more about the way the world acts • Empirical testing shows that the CAPM works reasonably well 14

Diversification and the Elimination of Unsystematic Risk u The purpose of diversification is to reduce the standard deviation of the total portfolio u This assumes that imperfect correlations exist among securities u As you add securities, you expect the average covariance for the portfolio to decline u How many securities must you add to obtain a completely diversified portfolio? 15

Diversification and the Elimination of Unsystematic Risk Observe what happens as you increase the sample size of the portfolio by adding securities that have some positive correlation 16

Determining the Expected Rate of Return for a Risky Asset RFR = 6% (0. 06) RM = 12% (0. 12) Implied market risk premium = 6% (0. 06) Assume: E(RA) = 0. 06 + 0. 70 (0. 12 -0. 06) = 0. 102 = 10. 2% E(RB) = 0. 06 + 1. 00 (0. 12 -0. 06) = 0. 120 = 12. 0% E(RC) = 0. 06 + 1. 15 (0. 12 -0. 06) = 0. 129 = 12. 9% E(RD) = 0. 06 + 1. 40 (0. 12 -0. 06) = 0. 144 = 14. 4% E(RE) = 0. 06 + -0. 30 (0. 12 -0. 06) = 0. 042 = 4. 2% 17

Price, Dividend, and Rate of Return Estimates 18

Comparison of Required Rate of Return to Estimated Rate of Return 19

Arbitrage Pricing Theory u APT background u The APT model u Comparison of the CAPM and the APT 20

Arbitrage Pricing Theory u u Arbitrage Pricing Theory was developed by Stephen Ross (1976). His theory begins with an analysis of how investors construct efficient portfolios and offers a new approach for explaining the asset prices and states that the return on any risky asset is a linear combination of various macroeconomic factors that are not explained by this theory namely. Similar to CAPM it assumes that investors are fully diversified and the systematic risk is an influencing factor in the long run. However, unlike CAPM model APT specifies a simple linear relationship between asset returns and the associated factors because each share or portfolio may have a different set of risk factors and a different degree of sensitivity to each of them. 21

APT Background u Arbitrage pricing theory (APT) states that a number of distinct factors determine the market return • Roll and Ross state that a security’s long-run return is a function of changes in: – Inflation – Industrial production – Risk premiums – The slope of the term structure of interest rates 22

APT Background (cont’d) u Not all analysts are concerned with the same set of economic information • A single market measure such as beta does not capture all the information relevant to the price of a stock 23

Arbitrage Pricing Theory (APT) u CAPM is criticized because of the difficulties in selecting a proxy for the market portfolio as a benchmark u An alternative pricing theory with fewer assumptions was developed: u Arbitrage Pricing Theory 24

Arbitrage Pricing Theory - APT Three major assumptions: 1. Capital markets are perfectly competitive 2. Investors always prefer more wealth to less wealth with certainty 3. The stochastic process generating asset returns can be expressed as a linear function of a set of K factors or indexes 25

Arbitrage Pricing Theory (APT) For i = 1 to N where: Ri = return on asset i during a specified time period Ei = expected return for asset i = reaction in asset i’s returns to movements in a common bik factor = a common factor with a zero mean that influences the returns on all assets = a unique effect on asset i’s return that, by assumption, is completely diversifiable in large portfolios and has a mean of zero N = number of assets Multiple factors expected to have an impact on all assets 26

Arbitrage Pricing Theory (APT) Multiple factors expected to have an impact on all assets: • • • Inflation Growth in GNP Major political upheavals Changes in interest rates And many more…. Contrast with CAPM insistence that only beta is relevant 27

Arbitrage Pricing Theory (APT) Bik determine how each asset reacts to this common factor Each asset may be affected by growth in GNP, but the effects will differ In application of theory, the factors are not identified Similar to the CAPM, the unique effects are independent and will be diversified away in a large portfolio 28

Arbitrage Pricing Theory (APT) u APT assumes that, in equilibrium, the return on a zero-investment, zero-systematic-risk portfolio is zero when the unique effects are diversified away u The expected return on any asset i (Ei) can be expressed as: 29

Example-market risk u Suppose the risk free rate is 5%, the average investor has a risk-aversion coefficient of A* is 2, and the st. dev. Of the market portfolio is 20%. u A) Calculate the market risk premium. u B) Find the expected rate of return on the market. u C) Calculate the market risk premium as the riskaversion coefficient of A* increases from 2 to 3. u D) Find the expected rate of return on the market referring to part c. 30

Answer-market risk u A) E(rm-rf)=A*σ2 m u Market Risk Premium =2(0. 20)2=0. 08 u B) E(rm) = rf +Eq. Risk prem u = 0. 05+0. 08=0. 13 or 13% u C) Market Risk Premium =3(0. 20)2=0. 12 u D) E(rm) = rf +Eq. Risk prem u = 0. 05+0. 12=0. 17 or 17% 31

Example-risk premium l Suppose an av. Excess return over Treasury bill of 8% with a st. dev. Of 20%. l A) Calculate coefficient of risk-aversion of the av. investor. l B) Calculate the market risk premium as the risk-aversion coefficient is 3. 5 32

Answer-risk premium u A) A*= E(rm-rf)/ σ2 m =0. 085/0. 202=2. 1 u B) E(rm)-rf =A*σ2 m =3. 5(0. 20)2=0. 14 or 14% 33

Example-Portfolio beta and risk premium Beta Risk prem. Portfolio Weight X 1. 2 9% 0. 5 Y 0. 8 6 0. 3 Z 0. 0 0 0. 2 Port. 0. 84 1. 0 Asset u u u Consider the following portfolio: A) Calculate the risk premium on each portfolio B) Calculate the total portfolio if Market risk premium is 7. 5%. 34

Answer-Portfolio beta and risk premium u A) (9%) (0. 5)=4. 5 u (6%) (0. 3)=1. 8 u =6. 3% u B) 0. 84(7. 5)=6. 3% 35

Example-risk premium u Suppose the risk premium of the market portfolio is 8%, with a st. dev. Of 22%. u A) Calculate portfolio’s beta. u B) Calculate the risk premium of the portfolio referring to a portfolio invested 25% in x motor company with beta 0 f 1. 15 and 75% in y motor company with a beta of 1. 25. 36

Answer-risk premium u A) βy= 1. 25, βx= 1. 15 u βp=wy βy+ wx βx =0. 75(1. 25)+0. 25(1. 15)=1. 225 u u B) E(rp)-rf=βp[E(rm)-rf] u =1. 225(8%)=9. 8% 37