Deck 3: Models of Equilibrium in the Capital Markets

Question 1

For the following three questions, assume that: $\bar { R } _ { m } = 15 \%$ , $\bar { R } _ { A } = 13 \%$ , $R _ { F } = 5 \%$ , $\sigma _ { m } = 16 \%$ , the market portfolio is a tangency portfolio, and that A is an efficient portfolio on the Capital Market Line.

-What would be the expected rate of return of portfolio A if its standard deviation was 32%?

A) 25%
B) 15%
C) 30%
D) 20%

Answer 1

25%

Question 2

For the following three questions, assume that: $\bar { R } _ { m } = 15 \%$ , $\bar { R } _ { A } = 13 \%$ , $R _ { F } = 5 \%$ , $\sigma _ { m } = 16 \%$ , the market portfolio is a tangency portfolio, and that A is an efficient portfolio on the Capital Market Line.

-What is the standard deviation of portfolio A?

A) 12.8%
B) 13.8%
C) 10.7%
D) 28.6%

Answer 2

12.8%

Question 3

Security A has a greater level of systematic risk than security B.The expected equilibrium return for A must be greater than that for B because:

A) B's price will fall as investors realize that B offers lower returns.
B) if it is not, then A's price will fall and B's price will rise as investors sell A and buy B.
C) the Security Market Line is negatively sloped.
D) the standard deviation of A's return is greater than B's.

Answer 3

B

Question 4

In a CAPM framework,prohibiting short sales:

A) will prohibit investors from holding the market portfolio in equilibrium.
B) will make the security market line steeper.
C) will encourage investors to hold more riskless assets.
D) will not change the equilibrium.

Question 5

What is the expected return on asset A if it has a beta of 0.6,the expected market portfolio return is 15%,and the risk-free rate is 6%?

A) 12.4%
B) 11.4%
C) 11.8%
D) 10.2%

Question 6

Which statement of the following statements is true?

A) All portfolios that plot on the Security Market Line are efficient.
B) All portfolios that plot on the Security Market Line are inefficient.
C) Both efficient and inefficient portfolios plot on the Capital Market Line.
D) Only individual securities plot on the Capital Market Line.

Question 7

Assume that the risk-free rate is 9% and that the market portfolio has an expected return of 17%.What expected return would be consistent with the CAPM for a security with a beta of 1.5?

A) 13%
B) 21%
C) 25.5%
D) 17%

Question 8

The existence of riskless lending and borrowing at the same rate and homogeneous expectations means:

A) all investors hold the same portfolio of risky assets.
B) all investors will either borrow or lend.
C) all investors place at least some of their wealth in the riskless asset.
D) none of the above.

Question 9

The standard CAPM implies:

A) investors are compensated for all risk they take.
B) investors are compensated for all market risk they take.
C) portfolio diversification does not matter.
D) high-return investments have higher variances than low-return investments.

Question 10

Discuss whether the following statement is true or false:
Under the assumption of the standard CAPM,an investor who is very risk averse will only invest in the riskless asset and risky assets with very low variances.

Question 11

Which statement of the following statements is true?

A) In equilibrium, every security and combination of securities lies on the Capital Market Line.
B) In equilibrium, every security and combination of securities lies on the Security Market Line.
C) Only efficient portfolios lie on the Security Market Line.
D) In equilibrium, every security and combination of securities lies lower than the Capital Market Line.

Question 12

In case of a simple CAPM being used to estimate a time series data:

A) the mean of a residual risk should be equal to zero.
B) the regression coefficient should be equal to zero.
C) the difference between the market return and the riskfree rate of return should be equal to zero.
D) the beta of the portfolio should be equal to zero.

Question 13

Assume that the assumptions underlying the standard CAPM hold.Indicate whether each of the following statements is true or false.
a. A firm with a high variance will have a higher beta than a firm with a low variance.
b. A portfolio is efficient if it has no unsystematic risk.
c. A firm that is highly correlated with the market will have a higher beta than a firm that is less correlated.
d. If the variance of the market portfolio goes up, the betas of all securities will go down.
e. A well-managed firm will have a lower beta than a poorly managed firm.
f. The market portfolio is efficient. Therefore, it contains only the best stocks in the market.
g. A risk-seeking investor should hold the riskiest stocks in the market, and a risk-averse investor should hold the safest stocks.
h. If the riskless rate increases, the slope of the capital market line will decrease.

Question 14

For the following three questions, assume that: $\bar { R } _ { m } = 15 \%$ , $\bar { R } _ { A } = 13 \%$ , $R _ { F } = 5 \%$ , $\sigma _ { m } = 16 \%$ , the market portfolio is a tangency portfolio, and that A is an efficient portfolio on the Capital Market Line.

-What would be the expected return and standard deviation of a portfolio with equal proportions invested in Treasury bills and the market portfolio?

A) 7.5%, 8%
B) 10%, 8%
C) 10%, 16%
D) 25%, 32%

Question 15

Discuss whether the following statement is true or false:
If there were no riskless assets in the economy,then there would be no security market line.

Question 16

Assume that the risk-free rate is 9% and that the market portfolio has an expected return of 17%.Under equilibrium conditions as described by the CAPM,what would be the expected return for a portfolio having no diversifiable risk and a beta of 0.75?

A) 17%
B) 9%
C) 20%
D) 15%

Question 17

The CAPM implies that:

A) investors may invest in assets with expected returns lower than the riskless interest rate.
B) no investor should invest in the risk-free asset.
C) the only relevant measure of risk is standard deviation.
D) the expected return on an efficient portfolio may be lower than the riskless interest rate.

Question 18

The beta of an efficient portfolio:

A) must be 1 since an efficient portfolio is perfectly positively correlated with the market portfolio.
B) is proportional to 1, depending on the proportion invested in the market portfolio.
C) is equivalent to the portfolio's standard deviation, since standard deviation is the measure of risk for an efficient portfolio.
D) is always less than 1.

Question 19

A long-short investment strategy is used in the case where the target is being tracked vastly differs from a diversified market portfolio.In such a situation,a _____ model is being used.

A) multi-index
B) single-index
C) multi-asset pricing
D) value at risk

Question 20

If the standard CAPM holds,a security with a high variance of return and a beta of zero should be expected to earn:

A) a zero rate of return.
B) the market rate of return.
C) the risk-free rate of return.
D) higher rate of return

Question 21

Consider the following data for assets A and B: $\bar { R } _ { A } = 12 \%$ ; $\bar { R } _ { B } = 8 \%$ ; $\sigma _ { \mathrm { A } } = 10 \%$ ; $\sigma _ { B } = 4 \%$ ; $\rho _ { A B } = - 1.0$
a. If only assets A and B are available, draw the efficient frontier.
b. If the riskless lending and borrowing rate is 10%, why is this a disequilibrium situation and what is the arbitrage that will restore equilibrium?

Question 22

Consider the following data:
$\begin{array}{lccc}&\underline{\text { ABC }} & \underline{\text { XYZ}}&\underline{\text { Market }}\\\text { Price } & \$ 20 & \$ 50 & - \\\text { Dividend } & \$ 0.40 & \$ 2 & 6 \% \\\text { Beta } & 1.5 & 1.0 & 1.0 \\\text { Alpha } & -1.0 \% & 2.0 \% & -\end{array}$ The riskless rate is 10%,and the expected return on the market is 20%.Your portfolio consists of 50,000 shares of ABC and 10,000 shares of XYZ.
a. Give the values of the following statistics for your portfolio: dividend yield; expected prices for ABC and XYZ in one year; beta; and alpha.
b. Suppose you are in the 40% effective marginal tax bracket and you plan to hold your portfolio more than one year. What is the expected after-tax return on your portfolio? What is the expected after-tax return on the market portfolio?

Question 23

You use the single-factor model $R _ { i t } = \alpha _ { i } + \beta _ { i } R _ { m t } + e _ { i t }$
and have obtained the following estimates for stock A and stock B:
$\begin{array} { l l l l } \text { Stock } & \alpha & \beta & \sigma _ { e } \\\text { A } & 2 \% & 1.3 & 30 \% \\\text { B } & 10 \% & 1.2 & 40 \%\end{array}$
You also estimate that the expected return on the market portfolio is 16%,the standard deviation of the market portfolio is 20%,and the riskless rate is 8%.
a. Based on the single-factor model, what are the expected returns and standard deviations of stock A and stock B?
b. Based on the single-factor model, the Security Market Line, and the Capital Market Line, state whether each of the following statements is completely true, completely false, or uncertain. Explain your answers.
1) In any given year, stock B is certain to outperform stock A.
2) An investor would consider stock B to be riskier than stock A.
3) Stock A is undervalued.
4) If an investor had to select one investment to combine with the riskless asset, the investor would prefer stock A to the market portfolio.

Question 24

For questions 1-3 use the information from the following table
$\begin{array} { l c c l } \text { Security } & \text { Return } & \text { Standard Deviation } & \text { Beta } \\\text { A } & 16 \% & 20 \% & 1.2 \\\text { B } & 12 \% & 25 \% & 0.8 \\\text { Risk-free asset } & 4 \% & 2 ? ? & \text { ??? }\end{array}$

-What is the portfolio expected return and the portfolio beta if
you invest 35% in A,45% in B and 20% in the risk-free asset?

Question 25

Discuss whether the following statement is true or false:
It is possible for a stock to have an expected rate of return that is negative.

Question 26

If one accepts the Sharpe single-index model,and the simple form of the CAPM holds,what is $\alpha _ { i }$ (the intercept term in the Sharpe single-index model)equal to?

Question 27

For questions 1-3 use the information from the following table
$\begin{array} { l c c l } \text { Security } & \text { Return } & \text { Standard Deviation } & \text { Beta } \\\text { A } & 16 \% & 20 \% & 1.2 \\\text { B } & 12 \% & 25 \% & 0.8 \\\text { Risk-free asset } & 4 \% & 2 ? ? & \text { ??? }\end{array}$

-Which of A and B has the least total risk? Which of A and B has the least
systematic risk?

Question 28

For questions 1-3 use the information from the following table
$\begin{array} { l c c l } \text { Security } & \text { Return } & \text { Standard Deviation } & \text { Beta } \\\text { A } & 16 \% & 20 \% & 1.2 \\\text { B } & 12 \% & 25 \% & 0.8 \\\text { Risk-free asset } & 4 \% & 2 ? ? & \text { ??? }\end{array}$

-What is the value of systematic risk for a portfolio with 2/3 of
the funds invested in A and 1/3 of the funds invested in B?

Question 29

An efficient portfolio has an expected return of 20%.The riskless rate is 5%,the return on the market portfolio is 15%,and the standard deviation of the market portfolio is 20%.What is the efficient portfolio's beta,standard deviation,and correlation coefficient with the market portfolio?

Question 30

Discuss whether the following statement is true or false:
A very risk-averse investor should buy predominantly low-beta stocks.

Question 31

Consider the following data for funds A,B,C,and D: $\bar { R } _ { A } = 20 \%$ ; $\bar { R } _ { B } = 15 \%$ ; $\bar { R } _ { C } = 10 \%$ ; $\bar { R } _ { D } = 18 \%$ ; $\beta _ { \mathrm { A } } = 1.5$ ; $\beta _ { B } = 1.0$ ; $\beta _ { C } = 0.8$ ; $\beta _ { D } = 1.2$ .
Assume that the zero-beta form of the CAPM is a reasonable description of reality and that funds A and B are accurately priced.Which funds' returns are not in equilibrium and by how much? What is the arbitrage that would restore equilibrium?

Question 32

Consider the following data for securities A and B: $\bar { R } _ { A } = 20 \%$ ; $\bar { R } _ { B } = 10 \%$ ; $\beta _ { \mathrm { A } } = 1.5$ ; $\beta _ { B } = 0.5$ .
Assume that the zero-beta CAPM holds and that all securities are in equilibrium.Plot the Security Market Line.Be sure to label all points.

Question 33

Plot the standard CAPM and the zero-beta CAPM on the same diagram.Be sure to label all points.

Question 34

Discuss whether the following statement is true or false:
Under the assumption of a CAPM with no riskless lending or borrowing,every investor holds the same portfolio of risky assets.

Question 35

Consider the following data for stocks A and B: $\bar { R } _ { \mathrm { A } } = 10 \%$ ; $\bar { R } _ { B } = 19 \%$ ; $\sigma _ { \mathrm { A } } = 3 \%$ ; $\sigma _ { B } = 5 \%$ ; $\beta _ { \mathrm { A } } = 0.6$ ; $\beta _ { B } = 1.4$ ; $\rho _ { A B } = 0.4$
a. Calculate the expected return, variance, and beta of a portfolio constructed by investing 1/3 of your funds in stock A and 2/3 in stock B.
b. If the riskless rate of return were 5%, what percentage of money invested in risky stocks should an investor place in each stock (assuming A and B are the only risky assets available)?
c. If the security market line describes equilibrium, and stocks A and B are in equilibrium, what is the return on the market portfolio and the riskless rate of interest?
d. If an investor can lend and borrow at the riskless rate determined in part c, but is restricted to holding only one of the two risky stocks in this problem, which stock should be held?

Question 36

Discuss the two mutual fund theorem.Show why it arises.(A diagram may help.)

Question 37

Discuss whether the following statement is true or false:
If the post-tax form of the CAPM holds,then a tax-free institution should hold the market portfolio.

Question 38

You believe that Beta Alpha Watch Company will be worth $100 per share one year from now.How much are you willing to pay for one share today if the riskless rate is 8%,the expected return on the market is 18%,and the company's beta is 2?

Question 39

The expected return on the market portfolio is 20% and the riskless rate is 10%.XYZ gold mining has a beta of -0.2.What is the expected return on a short sale of 100 shares of XYZ,assuming you can get the proceeds of your short sale? What if you can't?

Question 40

Consider the following data for Dodger Corp.and the S&P 500:
$\begin{array}{|c|c|c|}\hline \text { Year } & \text { Dodger Corp. Price } & \text { S\&P } 500 \text { Level } \\\hline {1979} & 40.00 & 150.00 \\\hline 1980 & 36.00 & 150.00 \\\hline 1981 & 34.20 & 145.50 \\\hline 1982 & 20.52 & 160.05 \\\hline 1983 & 22.57 & 163.25 \\\hline 198 & 22.34 & 159.99 \\\hline\end{array}$

a. What is your estimate of beta for Dodger Corp.?
b. What portion of the firm's total variance is systematic, and what portion is unsystematic?
c. What is the required rate of return for Dodger Corp. if the riskless rate is 7% and the market risk premium is 8%?

Question 41

You have been hired as a consultant to advise a client on an appropriate measure of risk to use in judging the client's stock investments.What do you tell your client and why?

Question 42

Discuss possible bias inherent in estimating the true Beta value according to Lintner and Douglas.What are the findings of Miller and Scholes on the basis of this evaluation?

Question 43

Consider the following multi-index model: $R _ { \mathrm { it } } = R _ { F t } + \beta _ { i 1 } I _ { 1 t } + \beta _ { i 2 } I _ { 2 t } + \ldots + \beta _ { i j } I _ { j t } + e _ { i t }$ where: $R _ { it }$ is the return on asset i in period t $R _ { F t }$ is the risk-free rate in period $$t$$ $\beta _ { i j }$ is the sensitivity of asset $i$ to factor $j$ is the value of factor $j$ in period $t$ $e _ { i t }$ is a random error term for asset $i$ in period $t$
a. Assuming the APT holds, what is the expression for the expected return of asset i?
b. How can the APT be used in decision making?
c. Outline, in list form, the assumptions underlying the APT.

Question 44

Explain how the zero Beta version of CAPM is derived.

Question 45

List set of equity and fixed income factors that were shown to have generated historical premia.Define the value factor and its economic interpretation.

Question 46

Explain the essential features of the following three lines: the Security Market Line,and the Capital Market Line.How is each used in discussions of security price behavior? Suppose you know that portfolio P is an efficient portfolio.What does this tell you about its position with respect to each of the lines?