Chapter 9 Charles P. Jones, Investments: Analysis and Management, Twelfth Edition, John Wiley & Sons 9- 1 Capital Market Theory and Asset Pricing Models

 Positive rather than normative ◦ Describes how investors could behave not how they should be have  Focus on the equilibrium relationship between the risk and expected return on risky assets  Builds on Markowitz portfolio theory  Each investor is assumed to diversify his or her portfolio according to the Markowitz model 9- 2

9- 3  Assumes all investors: ◦ Use the same information to generate an efficient frontier ◦ Have the same one- period time horizon ◦ Can borrow or lend money at the risk-free rate of return  No transaction costs, no personal income taxes, no inflation  No single investor can affect the price of a stock  Capital markets are in equilibrium

 Risk free assets ◦ No correlation with risky assets ◦ Usually proxied by a Treasury security  Adding a risk-free asset extends and changes the efficient frontier  “Lending” because investor lends money to issuer  With borrowing, investor no longer restricted to own wealth 9- 4 Risk-Free Assets, Borrowing, Lending

 Riskless assets can be combined with any portfolio in the efficient set AB ◦ Z implies lending  Set of portfolios on line RF to T dominates all portfolios below it 9-5 Risk B A TE(R) RF L ZX

 Risk-free investing and borrowing creates a new set of expected return-risk possibilities  Addition of risk-free asset results in ◦ A change in the efficient set from an arc to a straight line tangent to the feasible set without the riskless asset ◦ Chosen portfolio depends on investor’s risk-return preferences 9- 6

 Line from RF to L is capital market line (CML)  x = risk premium =E(RM) - RF  y =risk =  M  Slope =x/y =[E(RM) - RF]/  M  y-intercept = RF 9-7 E(R M ) RF Risk MM L M y x

 Slope of the CML is the market price of risk for efficient portfolios, or the equilibrium price of risk in the market  Relationship between risk and expected return for portfolio P (Equation for CML): 9- 8

 Most important implication of the CAPM ◦ The portfolio of all risky assets is the optimal risky portfolio (called the market portfolio) ◦ The expected price of risk is always positive ◦ The optimal portfolio is at the highest point of tangency between RF and the efficient frontier ◦ All investors hold the same optimal portfolio of risky assets 9- 9

 All risky assets must be in portfolio, so it is completely diversified ◦ Includes only systematic risk  Unobservable but approximated with portfolio of all common stocks ◦ In turn approximated with S&P 500  All securities included in proportion to their market value 9- 10

 Investors use their preferences (reflected in an indifference curve) to determine optimal portfolio  Separation Theorem ◦ The investment decision about which risky portfolio to hold is separate from the financing decision  Investment decision does not involve investor  Financing decision depends on investor’s preferences 9- 11

 CML Equation only applies to markets in equilibrium and efficient portfolios  The Security Market Line depicts tradeoff between risk and expected return for individual securities  Under CAPM, all investors hold the market portfolio ◦ Relevant risk of any security is therefore its covariance with the market portfolio 9- 12

 Standardized measure of systematic risk  Relative measure of risk: risk of an individual stock relative to the market portfolio of all stocks  Relates covariance of an asset with the market portfolio to the variance of the market portfolio Beta

 Beta = 1.0 implies as risky as market  Securities A and B are more risky than the market ◦ Beta >1.0  Security C is less risky than the market ◦ Beta < A B C kMkM k RF SML Beta M E(R) Beta

 Required rate of return on an asset (k i ) is composed of ◦ risk-free rate (RF) ◦ risk premium (  i [ E(R M ) - RF ])  Market risk premium adjusted for specific security k i = RF +  i [ E(R M ) - RF ] ◦ The greater the systematic risk, the greater the required return 9- 15

 Treasury Bill rate used to estimate RF  Expected market return unobservable ◦ Estimated using past market returns and taking an expected value  Estimating individual security betas difficult ◦ Only company-specific factor in CAPM ◦ Requires asset-specific forecast 9- 16

 Market model ◦ Relates the return on each stock to the return on the market, assuming a linear relationship ◦ Produces an estimate of return for any stock R i =  i +  i R M +e i  Characteristic line ◦ Line fit to total returns for a security relative to total returns for the market index 9- 17

 Betas change with a company’s situation  Estimating a future beta ◦ May differ from the historical beta  R M represents the total of all marketable assets in the economy ◦ Approximated with a stock market index ◦ Approximates return on all common stocks 9- 18

 No one correct number of observations and time periods for calculating beta ◦ Therefore, estimates of beta vary  The regression calculations of the true  and  from the characteristic line are subject to estimation error  Portfolio betas more reliable than individual security betas 9- 19

 Assumptions are mostly unrealistic  Empirical evidence has not led to consensus  However, some points are widely agreed upon ◦ SML appears to be linear ◦ Intercept is generally higher than RF ◦ Slope of the CAPM is generally less than theory predicts ◦ It’s likely that only systematic risk is rewarded Tests of CAPM

 Based on the Law of One Price ◦ Two otherwise identical assets cannot sell at different prices ◦ Equilibrium prices adjust to eliminate all arbitrage opportunities  Unlike CAPM, APT does not assume ◦ single-period investment horizon, absence of personal taxes, riskless borrowing or lending, mean-variance decisions 9- 21

 APT assumes returns generated by a factor model  Factor Characteristics ◦ Each risk must have a pervasive influence on stock returns ◦ Risk factors must influence expected return and have non-zero prices ◦ Risk factors must be unpredictable to the market 9- 22

 Most important are the deviations of the factors from their expected values ◦ Expected return is directly related to sensitivity ◦ CAPM assumes risk is only sensitivity to market  The expected return-risk relationship for the APT can be described as: E(R i ) =RF +b i1 (risk premium for factor 1) +b i2 (risk premium for factor 2) +… +b in (risk premium for factor n) 9- 23

 Factors are not well specified ex ante ◦ To implement the APT model, need the factors that account for the differences among security returns  CAPM identifies market portfolio as single factor  Studies suggest certain factors are reflected in market ◦ Focus on cash flows and discount rate  Both CAPM and APT rely on unobservable expectations 9- 24

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