FIN 431 CH.7

What is the expected rate of return for a stock that has a beta of 1 if the expected return on the market is 15%?

It's expected return is exactly the same (15%) as the market return when beta is 1.0.

17.

Not possible. Given these data, the SML is: E(r) = 10% + β(18% - 10%) A portfolio with beta of 1.5 should have an expected return of: E(r) = 10% + 1.5 ´ (18% - 10%) = 22% The expected return for Portfolio A is 16% so that Portfolio A plots below the SML (i.e., has an alpha of -6%), and hence is an overpriced portfolio. This is inconsistent with the CAPM.

16.

Not possible. Portfolio A clearly dominates the market portfolio. It has a lower standard deviation with a higher expected return.

If the simple CAPM is valid, which of the situation in Problems 13-19 below are possible? Explain. Consider each situation independently. 13.

Not possible. Portfolio A has a higher beta than Portfolio B, but the expected return for Portfolio A is lower.

18.

Not possible. The SML is the same as in Problem 18. Here, the required expected return for Portfolio A is: 10% + (0.9 ´ 8%) = 17.2% This is still higher than 16%. Portfolio A is overpriced, with alpha equal to: -1.2%

15.

Not possible. The reward-to-variability ratio for Portfolio A is better than that of the market, which is not possible according to the CAPM, since the CAPM predicts that the market portfolio is the most efficient portfolio. Using the numbers supplied: SA = SM = These figures imply that Portfolio A provides a better risk-reward tradeoff than the market portfolio.

14.

Possible. If the CAPM is valid, the expected rate of return compensates only for systematic (market) risk as measured by beta, rather than the standard deviation, which includes nonsystematic risk. Thus, Portfolio A's lower expected rate of return can be paired with a higher standard deviation, as long as Portfolio A's beta is lower than that of Portfolio B.

19.

Possible. Portfolio A's ratio of risk premium to standard deviation is less attractive than the market's. This situation is consistent with the CAPM. The market portfolio should provide the highest reward-to-variability ratio.

Mutual Fund Theorem

states that all investors desire the same portfolio of risky assets and can be satisfied by a single mutual fund composed of that portfolio

Market Portfolio

the portfolio for which each security is held in proportion to its total market value

Which of the following statements is true.? a. It is possible that the APT is valid and the CAPM is not. b. Is is possible that the CAPM is valid and the APT is not.

A. is true. The APT may exist without the CAPM, but not the otherway. The reason is that the APT accepts the principle of risk and return, which is central to CAPM, without making any assumptions regarding individual investors and their portfolios.

Consider the statement: "If we can identify a portfolio that beats the S&P 500 index portfolio, then we should reject the single-index CAPM." Do you agree or disagree? Explain.

An example of this scenario would be an investment in the SMB and HML. As of yet, there are no vehicles (index funds or ETFs) to directly invest in SMB and HML. While they may prove superior to the single index model, they are not yet practical, even for professional investors

True or False: Stocks with a beta of zero offer an expected rate of return of zero

False. According to CAPM, when beta is zero, the "excess" return should be zero.

True of False: The CAPM implies that investors require a higher return to hold highly volatile securities.

False. CAPM implies that the investor will only require risk premium for systematic risk. Investors are not rewarded for bearing higher risk if the volatility results from the firm-specific risk, and thus, can be diversified.

You can construct a portfolio with beta of .75 by investing .75 of the investment budget in T-bills and the remainder in the market portfolio.

False. We can construct a portfolio with the beta of .75 by investing .75 of the investment budget in the market portfolio and the remainder in T-bills.

Suppose investors believe that the standard deviation of the market-index portfolio has increased by 50%. What does the CAPM imply about the effect of this change on the required rate of return on Google's investment projects?

The required rate of return on a stock is related to the required rate of return on the stock market via beta. Assuming the beta of Google remains constant, the increase in the risk of the market will increase the required rate of return on the market, and thus increase the required rate of return on Google.

Capital Asset Pricing Model (CAPM)

a model that relates the required rate of return on a security to its systematic risk as measured by beta

Security Characteristic Line (SCL)

a plot of a security's expected excess return over the risk-free rate as a function of the excess return on the market

Arbitrage Pricing Theory (APT)

a theory of risk-return relationships derived from no-arbitrage considerations in large capital markets

Factor Portfolio

a well-diversified portfolio constructed to have a beta of 1 on one factor and a beta of zero on any other factor

Arbitrage Portfolio

a zero-net-investment, risk-free portfolio with a positive return

Arbitrage

creation of riskless profits made possible by relative mispricing among securities

Security Market Line (SML)

graphical representation of the expected return-beta relationship of the CAPM

Expected return - beta relationship

implication of the CAPM that security risk premiums (expected excess returns) will be proportional to beta

multifactor models

models of security returns that respond to several systematic factors