CHAPTER 12
RETURN DISTRIBUTIONS
a 71. A stock has an expected rate of return of 8.3 percent and a standard deviation of 6.4
percent. Which one of the following best describes the probability that this stock will lose 11 percent or more in any one given year?
a. less than 0.5 percent b. less than 1.0 percent c. less than 1.5 percent d. less than 2.5 percent e. less than 5 percent
RETURN DISTRIBUTIONS
d 72. A stock has returns of 3 percent, 18 percent, -24 percent, and 16 percent for the past
four years. Based on this information, what is the 95 percent probability range for any one given year?
a. -8.4 to 11.7 percent b. -16.1 to 22.6 percent c. -24.5 to 34.3 percent d. -35.4 to 41.9 percent e. -54.8 to 61.3 percent
RETURN DISTRIBUTIONS
c 73. A stock had returns of 8 percent, 14 percent, and 2 percent for the past three years.
Based on these returns, what is the probability that this stock will earn at least 20 percent in any one given year?
a. 0.5 percent b. 1.0 percent c. 2.5 percent d. 5.0 percent e. 16.0 percent
RETURN DISTRIBUTIONS
c 74. A stock had returns of 11 percent, 1 percent, 9 percent, 15 percent, and -6 percent for
the past five years. Based on these returns, what is the approximate probability that this stock will earn at least 23 percent in any one given year?
a. 0.5 percent b. 1.0 percent c. 2.5 percent d. 5.0 percent e. 16.0 percent
RETURN DISTRIBUTIONS
c 75. A stock had returns of 8 percent, 39 percent, 11 percent, and -24 percent for the past
four years. Which one of the following best describes the probability that this stock will NOT lose more than 43 percent in any one given year?
a. 84.0 percent b. 95.0 percent c. 97.5 percent d. 99.0 percent e. 99.5 percent
CHAPTER 12
RETURN DISTRIBUTIONS
b 76. Over the past five years, a stock produced returns of 14 percent, 22 percent, -16
percent, 2 percent, and 10 percent. What is the probability that an investor in this stock will NOT lose more than 8 percent nor earn more than 21 percent in any one given year?
a. 34 percent b. 68 percent c. 95 percent d. 99 percent e. 100 percent
ARITHMETIC AVERAGE
b 77. What are the arithmetic and geometric average returns for a stock with annual returns
of 4 percent, 9 percent, -6 percent, and 18 percent?
a. 5.89 percent; 6.25 percent b. 6.25 percent; 5.89 percent c. 6.25 percent; 8.33 percent d. 8.3 percent; 5.89 percent e. 8.3 percent; 6.25 percent
ARITHMETIC VS. GEOMETRIC AVERAGES
c 78. What are the arithmetic and geometric average returns for a stock with annual returns
of 21 percent, 8 percent, -32 percent, 41 percent, and 5 percent?
a. 5.6 percent; 8.6 percent b. 5.6 percent; 6.3 percent c. 8.6 percent; 5.6 percent d. 8.6 percent; 8.6 percent e. 8.6 percent; 6.3 percent
GEOMETRIC AVERAGE
b 79. A stock had returns of 6 percent, 13 percent, -11 percent, and 17 percent over the past
four years. What is the geometric average return for this time period?
a. 4.5 percent b. 5.7 percent c. 6.2 percent d. 7.3 percent e. 8.2 percent
CHAPTER 12
GEOMETRIC AVERAGE
b 80. A stock had the following prices and dividends. What is the geometric average return
on this stock?
Year Price Dividend 1 $23.19 ? 2 $24.90 $.23 3 $23.18 $.24 4 $24.86 $.25 a. 3.2 percent b. 3.4 percent c. 3.6 percent d. 3.8 percent e. 4.0 percent
IV. ESSAYS
EFFICIENT MARKETS
81. Define the three forms of market efficiency.
The student should present a straightforward discussion of weak (all past prices are in the current price), semi-strong (all public information is in the current price), and strong form (all information is in the current price) market efficiency.
HISTORICAL RETURNS
82. What securities have offered the highest average annual returns over the last several decades? Can we conclude that return and risk are related in real life? The purpose of this question is to check student understanding of the capital market history discussion of the chapter, as well as to reiterate the concept of the risk-return trade-off. The securities categories discussed in the chapter are listed below in descending order of historical returns (and risk): 1. small company stocks 2. large company stocks 3. long-term corporate bonds 4. long-term government bonds 5. U.S. Treasury bills By learning this hierarchy, and given that they are familiar with the attributes of each security, students should be left with little doubt that the maxim “The greater the risk, the greater the return” is an apt description of financial markets.
LESSONS
83. What are the lessons learned from capital market history? What evidence is there to suggest these lessons are correct? First, there is a reward for bearing risk, and second, the greater the risk, the greater the reward. As evidence, the students should provide a brief discussion of the historical rates of return and standard deviation of returns of the various asset classes discussed in the text.
CHAPTER 12
EFFICIENT MARKETS
84. Explain why it is that in an efficient market, investments have an expected NPV of zero. In an efficient market, prices are “fair” so that the cost of an investment is neither too high nor too low. Thus, on average, investments in that market will yield a zero NPV. Investors get exactly what they pay for when they buy a security in an efficient market and firms get exactly what their stocks and bonds are worth when they sell them.
EFFICIENT MARKETS
85. Do you think the lessons from capital market history will hold for each year in the future? That is, as an example, if you buy small stocks will your investment always outperform U.S. Treasury bonds? The student should realize that we are working with averages, so they should not expect riskier assets to always outperform less risky assets. The student should explain somewhere in their answer that this gets to the heart of what risk is. That is, the reason you expect to earn a higher return over the long haul is that your variability in price from year to year can be significant.
RISK AND RETURN
86. Suppose you have $30,000 invested in the stock market and your banker comes to you and tries to get you to move that money into the bank’s certificates of deposit (CDs). He explains that the CDs are 100% government insured and that you are taking unnecessary risks by being in the stock market. How would you respond? The usual response is that bank CDs typically will offer a very low rate of return because of their low level of risk. Even if students do not know the relationship between yields on CDs and historical returns on stocks, they should recognize that because of the risk differences the CDs must have a lower expected return. So, if the investor in the question is willing to trade off some safety in order to have the chance to earn larger returns, the stock market is the correct investment.
MARKET EFFICIENCY
87. Suppose your cousin invests in the stock market and doubles her money in a single year while the market, on average, earned a return of only about 15 percent. Is your cousin’s performance a violation of market efficiency? No, market efficiency does not preclude investors from “beating the market.” It is entirely possible to earn higher returns than the market at times. However, if your cousin is able to do so consistently, then there would certainly be some doubt cast upon market efficiency.
CHAPTER 12
INSIDER TRADING
88. How do you think the stock market would be affected if the laws were changed so that trading on insider information was no longer illegal? What would be the impact on the goal of the financial manager if such a change were to occur? This open-ended question allows students to ponder market efficiency from a different angle. By allowing insiders to trade on their information, it would be possible for insiders to take advantage of uninformed investors. This may keep some investors out of the market because they would perceive the prices observed as no longer being “fair.” This change would provide a serious blow to the efficiency of the market and would also further complicate the issue of who’s interest managers are working to satisfy.
MARKET EFFICIENCY
89. Why should a financial decision maker such as a corporate treasurer or CFO be concerned with market efficiency? Good answers to this question might indicate that market efficiency is a necessary condition for the “maximize shareholder wealth” rule. Unless we are confident that the market price is an economically meaningful number, seeking to maximize it is silly. Similarly, students should recognize that there is a very strong link between managerial decisions and the value of the firm, as reflected in security prices. Finally, as a preview of the cost of capital discussion in later chapters, instructors might point out that market efficiency ensures that the required returns on new securities will be directly related to the risk-return profile of the firm and, therefore, to managerial actions.
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