Financial Management, 12e (Titman/Keown/Martin)
An Introduction to Risk and Return-History of Financial Market Returns
7.1 Realized and Expected Rates of Return and Risk
1) You purchased the stock of Sargent Motors at a price of $75.75 one year ago today. If you sell the stock today for $89.00, what is your rate of return?
2) You have invested in a project that has the following payoff schedule:
|Payoff||Probability of Occurrence|
What is the expected value of the investment's payoff? (Round to the nearest $1.)
3) If there is a 20% chance we will get a 16% return, a 30% chance of getting a 14% return, a 40% chance of getting a 12% return, and a 10% chance of getting an 8% return, what is the expected rate of return?
4) You are considering investing in a project with the following possible outcomes:
|States||Probability of Occurrence||Investment Returns|
|State 1: Economic boom||15%||16%|
|State 2: Economic growth||45%||12%|
|State 3: Economic decline||25%||5%|
|State 4: Depression||15%||-5%|
Calculate the expected rate of return for this investment.
5) Spartan Sofas, Inc. is selling for $50.00 per share today. In one year, Spartan will be selling for $48.00 per share, and the dividend for the year will be $3.00. What is the cash return on Spartan stock?
6) What is the standard deviation of an investment that has the following expected scenario? 18% probability of a recession, 2.0% return; 65% probability of a moderate economy, 9.5% return; 17% probability of a strong economy, 14.2% return.
7) You are considering investing in a firm that has the following possible outcomes:
Economic boom: probability of 25%; return of 25%
Economic growth: probability of 60%; return of 15%
Economic decline: probability of 15%; return of -5%
What is the expected rate of return on the investment?
8) Which of the following best measures an asset's risk?
9) The cash return on an investment is calculated as purchase price-selling price.
10) Because returns are more certain for the least risky investments, the required return on these investments should be higher than the required returns on more risky investments.
11) Even though an investor expects a positive rate of return, it is possible that the actual return will be negative.
12) The expected rate of return is the weighted average of the possible returns for an investment.
13) The expected rate of return is the sum of each possible return times it likelihood of occurrence.
14) The higher the standard deviation, the less risk the investment has.
15) Using the following information for McDonovan, Inc.'s stock, calculate their expected return and standard deviation.
Ki = = (.20)(40%) + (.60)(15%) + (.20)(-20%)
= 8% + 9% - 4% = 13%
σi = ().
σi = ((40% - 13%)2(.2) + (15% - 13%)2 (.6) + (-20% - 13%)2 (.2)). = 19.13%
7.2 A Brief History of Financial Market Returns
1) Which of the following sequences is arranged in the correct order, from highest long-term returns to lowest?
2) Investments that have earned the highest rates of return over time also have
3) The difference between returns on stocks and government bonds is known as
4) An emerging market is
5) The risk-return tradeoff tells us that expected returns should be higher on investments that have higher risk.
6) Riskier investments have traditionally had lower returns than less risky investments have had.
7) Less risky investments have lower standard deviations than do more risky investments.
8) Investments in emerging markets have higher volatility than do U.S. Stocks.
9) Risky investments have the potential for higher returns, but also larger losses.
10) Historically, in the United States stocks have had higher returns and greater volatility than have government bonds.
11) Treasury Bills have less default risk than do Government Bonds.
12) Investors are always rewarded for taking higher risk with higher realized returns.
13) During the financial crisis of 2007-2009, returns on real estate investment trusts (REITS) and stocks moved in opposite directions.
7.3 Geometric vs. Arithmetic Average Rates of Return
1) Marcus Berger invested $9842.33 in Hawkeyehats, Inc. four years ago. He sold the stock today for $11,396.22. What is his geometric average return?
2) Michael Lynch invested $10,000 in the Rearguard Fund four years ago. All earnings were reinvested in the fund. If his compound annual rate of return was 7%, what is his investment worth today?
Roddy Richards invested $12014.88 in Wolverine Meat Distributors (W.M.D.) five years ago. The investment had yearly arithmetic returns of -9.7%, -8.1%, 15%, 7.2%, and 15.4%.
3) What is the arithmetic average return of Roddy Richard's investment?
4) What is the geometric average return of Roddy's Richard's investment?
5) How much money did Roddy Richards receive when he sold his shares of W.M.D.?
Susan Bright will get returns of 18%, -20.3%, -14%, 17.6%, and 8.3% in the next five years on her investment in CoffeeTown, Inc. stock, which she purchases for $73,419.66 today.
6) What is the arithmetic average return on her stock if she sells it five years from today?
7) What is the geometric average return on her stock if she sells it five years from today?
8) How much will Susan's stock be worth if she sells it five years from today?
9) Arithmetic average rate of return takes compounding into effect.
10) An investor who wishes to hold a stock for five years will be most interested in geometric average rather than in the arithmetic average return.
11) If an investor holds earns 10% on her investment in the first year and loses 10% the next year, she will have neither a gain nor a loss.
12) If an investor holds a stock for three years, the value at the end of three years will always be the initial cost of the stock times (1 + arithmetic average return) to the third power.
13) Why do the arithmetic average return and the geometric return differ?
Answer: The arithmetic average return does not take what the value of the investment was at the start of each period. Hence, even though a company may have the same arithmetic return for two consecutive years, the dollar amount of those returns will be different in later years than in the first year. For instance, if the investor started with $1,000, and earned 20% the first year, lost 20% the second year, and earned 15% the third year, the average arithmetic return would be 5%, and the 20% gain the first year would be $200, but the 20% loss the second year would be $240. The investment would be worth $1104 after three years, giving an average geometric return of 3.35%, different from the average arithmetic return.
7.4 What Determines Stock Prices?
1) Each of the following would tend to weaken the Efficient Market Hypothesis EXCEPT
2) Jayden spends a lot of time studying charts of stocks past performance, but his investment return are only average. This outcome supports
3) Which of the following is consistent with the efficient market hypothesis?
4) Madison was hired to design and decorate the offices of a large pharmaceutical company. She accidentally read a report indicating that a new drug had just been approved by the Food and Drug administration. She immediately bought the company's stock which doubled in price over the following week. This outcome is inconsistent with
5) Stock prices go up when there is positive information about a company, and go down when there is negative information about the company.
6) Strategies that exploit market inefficiencies tend to lose their effectiveness when they become widely known.
7) If a market is weak form efficient, an investor can make higher than expected profits by studying the past price patterns of a stock.
8) If an individual with inside information can make higher than expected profits, the market is no more than semi-strong form efficient.
9) Under the efficient market hypothesis, would securities be properly priced.
Answer: If markets were perfectly efficient, then investors would price a stock based on the company's expected future cash flows, so at any time the security would be properly priced. If good news becomes available, that would tend to increase the expected cash flows to a company, the stock price will go up, meaning that the new price is then the proper price for the stock.
10) Are markets moving toward being more efficient or toward being less efficient?
Answer: Empirical evidence shows that since about the year 2000 pricing anomalies have diminished considerably. Hedge funds have been trying to exploit pricing inefficiencies, and by doing so, eliminate the inefficiencies. Hence, the market appears to be becoming more efficient over time.
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