Investment Analysis- Risk and Return
You purchased a share of stock for $20. One year later you received $1 as dividend and sold the share for $29. What was your holding period return? a. 45% b. 50% c. 5% d. 40% e. none of the above
b. 50% ($1 + $29 - $20)/$20 = 0.5000, or 50%
According to the mean-variance criterion, which of the statements below is correct? Investment/ E(r)/ Std Dev A/ 10%/ 5% B/ 21%/ 11% C/ 18%/ 23% D/ 24%/ 16% a. Investment B dominates Investment A b. Investment B dominates Investment C c. Investment D dominates all of the other investments d. Investment D dominates only Investment B e. Investment C dominates investment A
b. Investment B dominates Investment C
An investor invests 70 percent of his wealth in a risky asset with an expected rate of return of 0.11 and a variance of 0.12 and 30 percent in a T-bill that pays 3 percent. His portfolio's expected return and standard deviation are ___ and ___, respectively a. 0.086; 0.242 b. 0.087; 0.267 c. 0.295; 0.123 d. 0.087; 0.182 e. none of the above
a. 0.086; 0.242 E(r P) = 0.7(11%) + 0.3(3%) = 8.6% s P = 0.7(0.12)^1/2 = 24.2%
You purchased a share of stock for $65. One year later you received $2.37 as dividend and sold the share for $63. What was your holding period return? a. 0.57% b. -0.2550% c. -0.89% d. 1.63% e. none of the above
a. 0.57% ($2.37 + $63 - $65)/$65 = 0.0056, or 0.57%
What is the expected holding period return for KMP stock? State of Economy/ Prob/ HPR Boom/ 0.30/ 18% Normal growth/ 0.50/ 12% Recession/ 0.20/ -5% a. 10.40% b. 9.32% c. 11.63% d. 11.54% e. 10.88%
a. 10.40% (0.3 * 0.18) + (0.5 * 0.12) + (0.2 * -0.05) = .104
You purchased a share of stock for $12. One year later you received $0.25 as dividend and sold the share for $12.92. What was your holding period return? a. 9.75% b. 10.65% c. 11.75% d. 11.25% e. none of the above
a. 9.75% ($0.25 + $12.92 - $12)/$12 = 0.975, or 9.75%.
The first major step in asset allocation is a. assessing risk tolerance b. analyzing financial statements c. estimating security betas d. identifying market anomalies e. none of the above
a. assessing risk tolerance
The expected return of a portfolio of risky securities a. is a weighted average of the securities' returns b. is the sum of the securities' returns c. is the weighted sum of the securities' variances and covariances d. A and C e. none of the above
a. is a weighted average of the securities' returns
The efficient frontier of risky assets is a. the portion of the investment opportunity set that lies above the minimum variance portfolio b. the portion of the investment opportunity set that represents the highest standard deviations c. the portion of the investment opportunity set which includes the portfolios with the lowest standard deviation d. the set of portfolios that have zero standard deviation e. both A and B are true
a. the portion of the investment opportunity set that lies above the minimum variance portfolio Portfolios on the efficient frontier are those providing the greatest expected return for a given amount of risk. Only those portfolios above the minimum variance portfolio meet this criterion
An investor invests 30 percent of his wealth in a risky asset with an expected rate of return of 0.15 and a variance of 0.04 and 70 percent in a T-bill that pays 6 percent. His portfolio's expected return and standard deviation are ___and ____, respectively a. 0.114; 0.12 b. 0.087; 0.06 c. 0.295; 0.12 d. 0.087; 0.12 e. none of the above
b. 0.087; 0.06 E(r P) = 0.3(15%) + 0.7(6%) = 8.7%; s P = [(0.3^2)(0.04)]^1/2 = 6%
You are considering investing $1,000 in a T-bill that pays 0.05 and a risky portfolio, P, constructed with 2 risky securities, X and Y. The weights of X and Y in P are 0.60 and 0.40, respectively. X has an expected rate of return of 0.14 and variance of 0.01, and Y has an expected rate of return of 0.10 and a variance of 0.0081. If you want to form a portfolio with an expected rate of return of 0.11, what percentages of your money must you invest in the T-bill and P, respectively? a. 0.25; 0.75 b. 0.19; 0.81 c. 0.65; 0.35 d. 0.50; 0.50 e. cannot be determined
b. 0.19; 0.81 E(r p) = 0.6(14%) + 0.4(10%) = 12.4%; 11% = 5x + 12.4(1 - x); x = 0.189 (T-bills) (1-x) =0.811 (risky asset)
You purchase a share of CAT stock for $90. One year later, after receiving a dividend of $4, you sell the stock for $97. What was your holding period return? a. 14.44% b. 12.22% c. 13.33% d. 5.56% e. none of the above
b. 12.22% HPR = ([97 - 90] + 4) / 90 = 12.22%
Efficient portfolios of N risky securities are portfolios that a. are formed with the securities that have the highest rates of return regardless of their standard deviations b. have the highest rates of return for a given level of risk c. are selected from those securities with the lowest standard deviations regardless of their returns d. have the highest risk and rates of return and the highest standard deviations e. have the lowest standard deviations and the lowest rates of return
b. have the highest rates of return for a given level of risk Portfolios that are efficient are those that provide the highest expected return for a given level of risk
The presence of risk means that a. investors will lose money b. more than one outcome is possible c. the standard deviation of the payoff is larger than its expected value d. final wealth will be greater than initial wealth. e. terminal wealth will be less than initial wealth
b. more than one outcome is possible
The measure of risk in a Markowitz efficient frontier is a. specific risk b. standard deviation of returns c. reinvestment risk d. beta e. none of the above
b. standard deviation of returns Markowitz was interested in eliminating diversifiable risk (and thus lessening total risk) and thus was interested in decreasing the standard deviation of the returns of the portfolio
The holding period return (HPR) on a share of stock is equal to a. the capital gain yield during the period, plus the inflation rate b. the capital gain yield during the period, plus the dividend yield c. the current yield, plus the dividend yield. d. the dividend yield, plus the risk premium. e. the change in stock price.
b. the capital gain yield during the period, plus the dividend yield The HPR of any investment is the sum of the capital gain and the cash flow over the period, which for common stock is B
Portfolio theory as described by Markowitz is most concerned with a. the elimination of systematic risk b. the effect of diversification on portfolio risk c. the identification of unsystematic risk d. active portfolio management to enhance returns e. none of the above
b. the effect of diversification on portfolio risk
When two risky securities that are positively correlated but not perfectly correlated are held in a portfolio, a. the portfolio standard deviation will be greater than the weighted average of the individual security standard deviations b. the portfolio standard deviation will be less than the weighted average of the individual security standard deviations c. the portfolio standard deviation will be equal to the weighted average of the individual security standard deviations d. the portfolio standard deviation will always be equal to the securities' covariance e. none of the above is true
b. the portfolio standard deviation will be less than the weighted average of the individual security standard deviations
An investor invests 40 percent of his wealth in a risky asset with an expected rate of return of 0.18 and a variance of 0.10 and 60 percent in a T-bill that pays 4 percent. His portfolio's expected return and standard deviation are ___and ___, respectively a. 0.114; 0.112 b. 0.087; 0.063 c. 0.096; 0.126 d. 0.087; 0.114 e. none of the above
c. 0.096; 0.126 E(r P) = 0.4(18%) + 0.6(4%) = 9.6% s P = [(0.4^2)(0.10)]^1/2 = 12.6
You are considering investing $1,000 in a T-bill that pays 0.05 and a risky portfolio, P, constructed with 2 risky securities, X and Y. The weights of X and Y in P are 0.60 and 0.40, respectively. X has an expected rate of return of 0.14 and variance of 0.01, and Y has an expected rate of return of 0.10 and a variance of 0.0081. If you want to form a portfolio with an expected rate of return of 0.10, what percentages of your money must you invest in the T-bill, X, and Y, respectively if you keep X and Y in the same proportions to each other as in portfolio P? a. 0.25; 0.45; 0.30 b. 0.19; 0.49; 0.30 c. 0.32; 0.41; 0.27 d. 0.50; 0.30; 0.20 e. cannot be determined
c. 0.32; 0.41; 0.27 E(r p) = .100.10 = 5w + 12.4(1 - w); x = 0.32 (weight of T-bills); As composition of X and Y are .6 and .4 of P, respectively, then for 0.68 weight in P, the respective weights must be 0.41 and 0.27; .6(.68) = 41%; .4(.68) = 27%
For a two-stock portfolio, what would be the preferred correlation coefficient between the two stocks? a. +1.00 b. +0.50 c. 0.00 d. -1.00 e. none of the above
d. -1.00
An investor chooses to invest in a stock with expected returns of 15% per year and a standard deviation of 30% per year. The other option was to invest in t-bills with a return of 6% per year. Assume the investor is risk averse, and cares only about expected returns and risk (variance). What is the maximum level of risk aversion for this investor? a. 0.3 b. 0.7 c. 1 d. 1.2 e. 1.5
c. 1 Utility from riskless asset = 0.06. The maximum level of risk aversion must yield a utility greater than or equal to 0.06. 0.06 = 0.15 - lambda x 0.3^2. Solve for lambda: lambda = (0.15 - 0.06)/0.09 = 1
Assume an investor with the following utility function: U = E(r) - 3/2(s^2). To maximize her expected utility, she would choose the asset with an expected rate of return of ___ and a standard deviation of ___, respectively. (s^2 denotes variance) a. 12%; 20% b. 10%; 15% c. 10%; 10% d. 8%; 10% e. none of the above
c. 10%; 10% U = 0.10 - 3/2(0.10)^2 = 8.5%; highest utility of choices
You invest $100 in a risky asset with an expected rate of return of 0.12 and a standard deviation of 0.15 and a T-bill with a rate of return of 0.05. What percentages of your money must be invested in the risk-free asset and the risky asset, respectively, to form a portfolio with a standard deviation of 0.06? a. 30% and 70% b. 50% and 50% c. 60% and 40% d. 40% and 60% e. cannot be determined
c. 60% and 40%
You invest $100 in a risky asset with an expected rate of return of 0.11 and a standard deviation of 0.20 and a T-bill with a rate of return of 0.03. What percentages of your money must be invested in the risk-free asset and the risky asset, respectively, to form a portfolio with a standard deviation of 0.08? a. 30% and 70% b. 50% and 50% c. 60% and 40% d. 40% and 60% e. cannot be determined
c. 60% and 40% 0.08 = x(0.20); x = 40% in risky asset
You invest $100 in a risky asset with an expected rate of return of 0.11 and a standard deviation of 0.20 and a T-bill with a rate of return of 0.03. What percentages of your money must be invested in the risky asset and the risk-free asset, respectively, to form a portfolio with an expected return of 0.08? a. 85% and 15% b. 75% and 25% c. 62.5% and 37.5% d. 57% and 43% e. cannot be determined
c. 62.5% and 37.5%
Which of the following statements is (are) true regarding the variance of a portfolio of two risky securities? a. The higher the coefficient of correlation between securities, the greater the reduction in the portfolio variance b. There is a linear relationship between the securities' coefficient of correlation and the portfolio variance c. The degree to which the portfolio variance is reduced depends on the degree of correlation between securities d. A and B e. A and C
c. The degree to which the portfolio variance is reduced depends on the degree of correlation between securities
Consider a T-bill with a rate of return of 5 percent and the following risky securities: Security A: E(r) = 0.15; Variance = 0.04 Security B: E(r) = 0.10; Variance = 0.0225 Security C: E(r) = 0.12; Variance = 0.01 Security D: E(r) = 0.13; Variance = 0.0625 From which set of portfolios, formed with the T-bill and any one of the 4 risky securities, would a risk-averse investor always choose his portfolio? a. The set of portfolios formed with the T-bill and security A b. The set of portfolios formed with the T-bill and security B c. The set of portfolios formed with the T-bill and security C d. The set of portfolios formed with the T-bill and security D e. Cannot be determined
c. The set of portfolios formed with the T-bill and security C
The variance of a portfolio of risky securities a. is a weighted sum of the securities' variances b. is the sum of the securities' variances c. is the weighted sum of the securities' variances and covariances d. is the sum of the securities' covariances e. none of the above
c. is the weighted sum of the securities' variances and covariances
Which of the following statements regarding risk-averse investors is true? a. they only care about the rate of return b. they accept investments that are fair games c. they only accept risky investments that offer risk premiums over the risk-free rate d. they are willing to accept lower returns and high risk e. A and B
c. they only accept risky investments that offer risk premiums over the risk-free rate
Toyota stock has the following probability distribution of expected prices one year from now: State: 1, 2, 3 Probability: 25%, 40%, 35% Price: $50, $60, $70 If you buy Toyota today for $55 and it will pay a dividend during the year of $4 per share, what is your expected holding period return on Toyota? a. 17.72% b. 18.89% c. 17.91% d. 18.18% e. none of the above
d. 18.18% E(P1) = .25 (54/55 - 1) + .40 (64/55 - 1) + .35 (74/55 - 1) = 18.18%
You purchase a share of Boeing stock for $90. One year later, after receiving a dividend of $3, you sell the stock for $92. What was your holding period return? a. 4.44% b. 2.22% c. 3.33% d. 5.56% e. none of the above
d. 5.56% HPR = (92 - 90 + 3) / 90 = 5.56%
You invest $100 in a risky asset with an expected rate of return of 0.12 and a standard deviation of 0.15 and a T-bill with a rate of return of 0.05. What percentages of your money must be invested in the risky asset and the risk-free asset, respectively, to form a portfolio with an expected return of 0.09? a. 85% and 15% b. 75% and 25% c. 67% and 33% d. 57% and 43% e. cannot be determined
d. 57% and 43% 9% = w 1(12%) + (1 - w 1)(5%); 9% = 12%w 1 + 5% - 5%w 1; 4% = 7%w 1; w 1 = 0.57; 1 - w 1 = 0.43; 0.57(12%) + 0.43(5%) = 8.99%
A portfolio has an expected rate of return of 0.15 and a standard deviation of 0.15. The risk-free rate is 6 percent. An investor has the following utility function: U = E(r) - (A/2)s^2. Which value of A makes this investor indifferent between the risky portfolio and the risk-free asset? a. 5 b. 6 c. 7 d. 8 e. none of the above
d. 8 0.06 = 0.15 - A/2(0.15) 2; 0.06 - 0.15 = -A/2(0.0225); -0.09 = -0.01125A; A = 8; U = 0.15 - 8/2(0.15) 2 = 6%; U(R f) = 6%.
The risk premium for common stocks a. cannot be zero, for investors would be unwilling to invest in common stocks b. must always be positive, in theory c. is negative, as common stocks are risk d. A and B e. A and C
d. A and B cannot be zero, for investors would be unwilling to invest in common stocks & must always be positive, in theory
Asset allocation a. may involve the decision as to the allocation between a risk-free asset and a risky asset b. may involve the decision as to the allocation among different risky assets c. may involve considerable security analysis d. A and B e. A and C
d. A and B may involve the decision as to the allocation between a risk-free asset and a risky asset & may involve the decision as to the allocation among different risky assets
Based on their relative degrees of risk tolerance a. investors will hold varying amounts of the risky asset in their portfolios b. all investors will have the same portfolio asset allocations c. investors will hold varying amounts of the risk-free asset in their portfolios d. A and C e. none of the above
d. A and C investors will hold varying amounts of the risky asset in their portfolios & investors will hold varying amounts of the risk-free asset in their portfolios
Which of the following statements about the efficient frontier is (are) false? a. Portfolios on the efficient frontier earn the highest returns for any given level of risk b. The minimum variance portfolio is not an efficient portfolio c. Even if short selling is allowed, investors cannot take positions in which more than 100% of their wealth is allocated to 1 stock d. B and C e. A and C
d. B and C The MVP is an efficient portfolio, and if short selling is allowed then you can have positions with more than 100% of your wealth allocated to 1 stock. The only restriction is that the sum of portfolio weights must equal 1
The riskiness of individual assets a. should be considered for the asset in isolation b. should be considered in the context of the effect on overall portfolio volatility c. combined with the riskiness of other individual assets (in the proportions these assets constitute of the entire portfolio) should be the relevant risk measure d. B and C e. none of the above
d. B and C should be considered in the context of the effect on overall portfolio volatility & combined with the riskiness of other individual assets (in the proportions these assets constitute of the entire portfolio) should be the relevant risk
Because historical returns on US Treasury bills are less volatile than common stock returns, it follows that: a. Treasury bills should offer a higher risk premium than common stock. b. The standard deviation of Treasury bill returns is negative. c. The real return on Treasury bills has frequently been negative. d. Common stocks should offer a higher return than Treasury bills. e. Treasury bills should become more volatile in the future
d. Common stocks should offer a higher return than Treasury bills. Stocks are riskier than Treasury bills. Investors are risk averse so require compensation for bearing additional risk
Which of the following statements regarding the Capital Market Line (CML) is false? a. The CML shows risk-return combinations b. The slope of the CML equals the increase in the expected return of a risky portfolio per unit of additional standard deviation c. The slope of the CML is also called the reward-to-risk ratio d. The CML is also called the efficient frontier of risky assets in the absence of a risk-free asset e. Both A and C are true
d. The CML is also called the efficient frontier of risky assets in the absence of a risk-free asset The CML consists of combinations of a risky asset and a risk-free asset whose slope is the reward-to-variability ratio; thus, all statements except d are true
Elias is a risk-averse investor. David is a less risk-averse investor than Elias. Therefore, a. for the same risk, David requires a higher rate of return than Elias. b. for the same return, Elias tolerates higher risk than David. c. for the same risk, Elias requires a lower rate of return than David. d. for the same return, David tolerates higher risk than Elias. e. cannot be determined.
d. for the same return, David tolerates higher risk than Elias.
Given the capital market line, an investor's optimal portfolio is the portfolio that a. maximized her expected profit b. maximizes her risk c. maximized both her risk and return d. maximizes her expected utility e. none of the above
d. maximizes her expected utility
Other things equal, diversification is mostly effective when a. securities' returns are uncorrelated b. securities' returns are positively correlated c. securities' returns are high d. securities' returns are negatively correlated e. B and C
d. securities' returns are negatively correlated Negative correlation among securities results in the greatest reduction of portfolio risk, which is the goal of diversification
The standard deviation of a two-asset portfolio is a linear function of the assets' weights when a. the assets have a coefficient less than zero b. the assets have a coefficient equal to zero c. the assets have a coefficient greater than zero d. the assets have a coefficient equal to one e. the assets have a coefficient less than one
d. the assets have a coefficient equal to one
Which of the following statement(s) is (are) true regarding the selection of a portfolio from those that lie on the Capital Market Line? a. Less risk-averse investors will invest more in the risk-free security and less in the optimal risky portfolio than more risk-averse investors b. More risk-averse investors will invest less in the optimal risky portfolio and more in the risk-free security than less risk-averse investors c. Investors choose the portfolio that maximizes their expected utility d. A and C e. B and C
e. B and C All rational investors select the portfolio that maximizes their expected utility; for investors who are relatively more risk-averse, doing so means investing less in the optimal risky portfolio and more in the risk-free asset
You purchased a share of CSCO stock for $20. One year later you received $2 as dividend and sold the share for $31. What was your holding period return? a. 45% b. 50% c. 60% d. 40% e. none of the above
e. none of the above
You purchased a share of stock for $120. One year later you received $1.82 as dividend and sold the share for $136. What was your holding period return? a. 15.67% b. 22.12% c. 15.67% d. 13.25% e. none of the above
e. none of the above ($1.82 + $136 - $120)/$120 = 0.1485, or 14.85%