Chapter 9_Asset Pricing Models

The expected return for the market is 12 percent , and the risk - free rate is 8 percent . The following information is estimated for each of five stocks . Stock Beta R , ( % ) 1 0.9 12 * 2 1.3 13 3 0.5 11 4 1.1 12.5 5 1.0 12 a . Calculate the required return for each stock . b . Assume that an investor , using fundamental analysis , develops the estimated returns , R. , for these stocks . Based on the investor's estimates , determine which C. What is the market risk premium

( a ) From the SML : Stock 1: 8 % + 9 ( 4 % ) - 11.6 % Stock 2: 8 % +1.3 ( 4 % ) = 13.2 % Stock 3: 8 % + 5 ( 4 % ) - 10.0 % Stock 4: 8 % +1.1 ( 4 % ) - 12.4 % Stock 5: 8 % +1.0 ( 4 % ) - 12.0 % Funds 1, 3, and 4 are undervalued because each has an expected return greater than its required return as given by the SML. (c) The market risk premium is the slope of the SML, or (12-8) = 4%.

The market has an expected return of 12 percent , and the risk - free rate is 5 percent . Activalue Corp's systematic risk is 80 percent that of the market as a whole . What is the required return for Activalue ?

5 % + . 8 [ 12 % -5 % ] -10.6 %

Electron Corporation's returns are 50 percent more sensitive to market moves than the average stock . The market risk premium is 7 percent . The risk - free rate is 5 percent . What is the required return for Electron ?

5 % + 1.57 % ] - 15.5 %

The market has an expected return of 11 percent , and the risk - free rate is 5 percent . Pfizer has a beta of 0.9 . What is the required return for Pfizer ?

5 % +9 [ 11 % -5 % ) - 10.4 %

Draw a diagram of the SML , Label the axes and the intercept . a . Assume the risk - free rate shifts upward . Draw the new SML . b . Assume that the risk - free rate remains the same as before the change in ( a ) but that investors become more pessimistic about the stock market . Draw the new SML .

A diagram of the SML is simply an upward - sloping tradeoff between required return on the vertical axis and risk as measured by beta on the horizontal axis . In effect , this is a diagram of the whole concept of investing , which is , in fact , best described simply as an upward - sloping tradeoff between expected return and risk ( a ) If the risk - free rate shifts upward , and nothing else changes , the diagram would show a new upward sloping line above the old line , running parallel with it . The difference between the two vertical intercepts would reflect the increase in the risk - free rate . - ( b ) In this case , the SML would rotate upward to the left to reflect a greater tradeoff . As investors become pessimistic , market risk premium ( E ( Ra ) -RF ) increases because investors would like to require more compensation for the same risk , so the line becomes steeper ( rotates upward to the left ) ; as they become optimistic , the line rotates downward to the right , approach

What What is a factor model ?

A factor model is based on the view that there are underlying risk factors that affect realized and expected security returns . These risk factors represent broad economic forces and not company - specific characteristics and , by definition , they represent the element of surprise in the risk factor - the difference between the actual value for the factor and its expected value .

Why is the standard deviation of a security's returns an inadequate measure of the contribution of that security to the risk of a portfolio that is well diversified ?

A security's contribution to the risk of the market portfolio is determined by the security's covariance with the market , not the security's standard deviation . A security's contribution to the risk of the market portfolio is given by : Kam ( M ) where Cov - the covariance between stock ( and the market portfolio .

What is meant by an " arbitrage profit " ? What ensures that investors could act quickly to take advantage of such opportunities ?

An arbitrage profit in the context of the APT , refers to a situation where a zero investment portfolio can be constructed that will yield a risk - free profit . If arbitrage profits arise , a relatively few investors can act to restore equilibrium .

The arbitrage pricing theory ( APT ) differs from the capital asset pricing model because the APT : A ) places more emphasis on market risk . B ) minimizes the importance of diversification . C ) recognizes multiple unsystematic risk factors . D ) recognizes multiple systematic risk factors .

D ( note that APT involves systematic factors )

Assume that the risk - free rate is 7 percent and the market risk premium is 6 percent . Show that the security market line is E ( R ) 7.0 + 6.08 Assume that an investor has estimated the following values for six different corporations : Corporation B₁ R ; ( % ) GF 0.8 12 PepsiCo 0.9 13 IBM 1.0 14 NCNB 1.2 11 EG & G 1.2 21 EAL 1.5 10 Calculate the expected return for each corporation using the SML . , and evaluate which securities are overvalued and which are undervalued .

E(Ri) = 7.0% + (13.0%-7.0%)βi = 7.0 + 6.0βi GF 7% + 6%( .8) = 11.8% < 12% undervalued PepsiCo 7% + 6%( .9) = 12.4% < 13% undervalued IBM 7% + 6%(1.0) = 13.0% < 14% undervalued NCNB 7% + 6%(1.2) = 14.2% > 11% overvalued EG&G 7% + 6%(1.2) = 14.2% < 21% undervalued EAL 7% + 6%(1.5) = 16.0% > 10% overvalued

What is the market portfolio ?

In theory , the market portfolio ( portfolio M ) is the portfolio of all risky assets , both financial and real , in their proper proportions . Such a portfolio would be completely diversified ; however , it is a risky portfolio . In equilibrium , all risky assets must be in portfolio M because all investors are assumed to hold the same risky portfolio . If they do , in equilibrium this portfolio must be the market portfolio consisting of all risky assets . The market portfolio is often proxied by the portfolio of all common stocks , which , in turn , is proxied by a market index such as the Standard & Poor's 500 Composite Index .

How does an investor decide where to be on the new efficient frontier represented by the CML ?

Investors decide where they are to be on the new efficient frontiee- ( the straight line dominating the Markowitz efficient frontier ) by their risk preferences . If they are conservative , they will be on the lower end of the line toward RF ; if aggressive , they will be on the upper end , which represents larger expected returns and larger risks .

How do lending ( borrowing ) possibilities change the Markowitz model ?

Lending possibilities change part of the Markowitz efficient frontier from an are to a straight line . The straight line extends from RF , the risk - free rate of return , to M , the market portfolio This new opportunity set , which dominates the old Markowitz efficient frontier , provides investors with various combinations of the risky asset portfolio M and the riskless asset . Borrowing possibilities complete the transformation of the Markowitz efficient frontier into a straight line extending from RF through M and beyond. Investors can use borrowed funds to lever their portfolio position beyond point M, increasing the expected return and risk beyond that available at point M.

Why does Roll argue that the CAPM is untestable ?

Roll has argued that the CAPM is untestable because the market portfolio , which consists of all risky assets , is unobservable .

The CAPM provides required returns for individual securities or portfolios . What uses can you see for such a model ?

The CAPM is a useful model for estimating required returns . These requifd returns can be used in conjunction with independently derived expected returns to determine overvalued and undervalued securities . This model is also useful in estimating the cost of equity capital for a security . And , as we shall see in Chapter 22 , the CAPM provides a basis for measuring portfolio performance .

Why does the CML contain only efficient portfolios ?

The CML extends from RF , the risk - free asset , through M , the market portfolio of all risky securities ( weighted by their respective market values ) . This portfolio is efficient , and the CML consists of combinations of this portfolio and the risk - free asset . All asset combinations on the CML are efficient portfolios consisting of M and the risk - free asset .

What is the relationship between the CML and the Markowitz efficient frontier ?

The CML is drawn tangent to the Markowitz efficient frontier. When this is done, it can be seen that the CML dominates the Markowitz efficient frontier. The CML is a straight line tangent to the efficient frontier at point M, the market portfolio, and with an intercept of RF.

The CML can be described as representing a trade - off . What is this trade - off ? Be specific .

The CML is the trade off between expected returns and risk for efficient portfolios . The slope of the CML indicates the equilibrium price of risk in the market .

In terms of their appearance as a graph , what is the difference between the CML and the SML ?

The basic difference between graphs of the SML and the CML is the label on the horizontal axis . For the CML , it is standard deviation while for the SML , beta . Also , the CML is applicable to portfolios while the SML applies to individual securities and to portfolios .

How can we measure a security's contribution to the risk of the market portfolio ?

The contribution of each security to the standard deviation of the market portfolio depends on the size of its covariance with the market portfolio . Therefore , investors consider the relevant measure of risk for a security to be its covariance with the market portfolio .

What is " the law of one price " ?

The law of one price states that two otherwise identical assets cannot sell at different prices .

Explain the separation theorem .

The separation theorem states that the investment decision ( what portfolio of assets to hold ) is separate from the financing decision ( how much of one's funds to put in risky assets vs. riskless assets ) . The separation theorem leads to the idea that one portfolio of risky assets is optimal for all investors .

What is the slope of the CML ? What does it measure ?

The slope of the CML is where E(RM) is the expected return on the market M portfolio, RF is the rate of return on the risk-free asset, and M is the standard deviation of the returns on the market portfolio. The slope of the CML is the market price of risk for efficient portfolios; that is, it indicates the equilibrium price of risk in the market. It shows the additional return that the market demands for each percentage increase in a portfolio's risk.

Briefly explain whether investor should expect a higher return from holding Portfolio A versus Portfolio B under CAPM . Assume that both portfolios are fully diversified . Portfolio A Portfolio B Systematic Risk ( beta ) 1.0 1.0 Specific risk for each individual security High Low

Under CAPM , the only risk that investors should be compensated for bearing is the risk that cannot be diversified away ( systematic risk ) . Because systematic risk ( measured by beta ) is equal to one for both portfolios , an investor would expect the same return for Portfolio A and B. Since both portfolios are fully diversified , it doesn't matter if the specific risk for each individual security is high or low . The specific risk has been diversified away for both portfolios .

Why , under the CAPM , do all investors hold identical risky portfolios ?

Under the CAPM , all investors hold the market portfolio because it is the optimal risky portfolio . Because it produces the highest attainable return for any given risk level , all rational investors will seek to be on the straight line tangent to the efficient set at the steepest point , which is the market portfolio .

How can the SML be used to identify over- and undervalued securities ?

Using some methodology to estimate the expected returns for securities , investors can compare these expected returns to the required returns obtained from the SML . Securities whose expected returns plot above the SML are undervalued because they offer more expected return than investors require ; if they plot below the SML , they are overvalued because they do not offer enough expected return for their level of risk .

What happens to the price and return of a security when investors recognize it as undervalued ?

When a security is recognized by investors as undervalued , they will purchase it because it offers more return than required , given its risk . This demand will drive up the price of the security as more of it is purchased . The return will be driven down until it reaches the level indicated by the SML as appropriate for its degree of risk .

Suppose that the risk - free rate is 5 percent and the expected return on the market portfolio is 13 percent . An investor with $ 1 million to invest wants to achieve a 17 percent return on a portfolio combining the risk - free asset and the market portfolio . Calculate how much this investor would need to borrow at the risk - free rate in order to establish this target expected return .

With RM the return on the market portfolio, we have E(RP) = wE (RM) + (1 - w)RF 17% = 13%w + 5%(1 - w) w = 1.5 Thus 1 - 1.5 = -0.5 of initial wealth goes into the risk-free asset. The negative sign indicates borrowing: -0.5($1 million) = -$500,000, so the investor borrows $500,000.

Suppose that the best predictor for a stock's future beta is determined to equal 0.33 + 0.67 ( historical beta ) . The historical beta is calculated as 1.2 . The risk - free rate is 5 percent , and the market risk premium is 8.5 percent . Calculate the expected return on the stock using adjusted beta in the CAPM .

βadj = 0.33 + (0.67)(1.2) = 0.33 + 0.80 = 1.13 E(RP)= E (Ri) = RF + βi[E(RM) - RF] = 5% + 1.13 (8.5%) = 14.6%