Ch 27

Future and present values Suppose a relative has promised to give you $1,000 as a wedding gift the day you get engaged. Assuming a constant interest rate of 6%, consider the present and future values of this gift, depending on when you become engaged. Complete the first row of the following table by determining the value of the gift in one and two years with interest if you become engaged today and save the money. Table: Date Received; Present Value ($); Value in 1 yr ($); Value in 2 yrs ($) Today; 1,000.00; __________; ___________ In 1 year; _______; 1,000.00 In 2 years; ________; BLANK; 1,000.00

1,060.00; 1,123.60 943.40 890.00

Risk and return Suppose Frances currently allocates 25% of her portfolio to a diversified group of stocks and 75% of her portfolio to risk-free bonds; that is, she chooses combination B. She wants to increase the average annual return on her portfolio from 4.5% to 9.5%. In order to do so, she must do which of the following? Check all that apply. The table uses the standard deviation of the portfolio's return as a measure of risk. A normal random variable, such as a portfolio's return, stays within two standard deviations of its average approximately 95% of the time. Suppose Frances modifies her portfolio to contain 75% diversified stocks and 25% risk-free government bonds; that is, she chooses combination D. The average annual return for this type of portfolio is 9.5%, but given the standard deviation of 15%, the returns will typically (about 95% of the time) vary from a gain of ____% to a loss of _____% .

Accept more risk Sell more of her bonds &use the proceeds to purchase stocks 39.5 -20.5

Problems in insurance markets Consider the following story: Coverall, Inc., an insurance company, recently moved into the motorcycle insurance market. Coverall was concerned that the most likely motorcycle insurance customers are those who ride their motorcycles recklessly, because they would benefit most from insurance coverage. Since Coverall cannot distinguish perfectly between high-risk and low-risk cyclists, it raised its motorcycle premiums in an effort to account for the reckless riders. The economic problem in this story is known as:

Adverse Selection

How interest rate changes affect present and future value Suppose you will receive a payment of $200 one year from now. True or False: If during the year the interest rate rises, this increases the present value of your future payment.

False

Diversification and risk The graph shows the relationship between risk, measured as the standard deviation of a stock portfolio's return, and the number of different stocks in the portfolio for a hypothetical stock market. Points: (1,50); (4,32); (10,25); (20,21.5); (30,20) True or False: Increasing the number of stocks in a portfolio reduces market risk. Consider two stock portfolios. Portfolio Y consists of four different stocks from firms in different industries. Portfolio X consists of 20 different stocks, also from firms in different industries. The return on Portfolio Y is likely to be ______ volatile than that of Portfolio X.

False More

Future and present values Now complete the first column of the previous table by computing the present value of the gift if you get engaged in one year or two years. The present value of the gift is ________ if you get engaged in one year than it is if you get engaged in two years.

Greater

Risk and return Suppose Frances is choosing how to allocate her portfolio between two asset classes: risk-free government bonds and a risky group of diversified stocks. The following table shows the risk and return associated with different combinations of stocks and bonds. Table: Combination; Fraction of Portfolio in Diversified Stocks (%); Average Annual Return (%); Standard Deviation of Portfolio Return (risk; %) A; 0; 2.00; 0 B; 25; 4.50; 5 C; 50; 7.00; 10 D; 75; 9.50; 15 E; 100; 12.00; 20 If Frances reduces her portfolio's exposure to risk by opting for a smaller share of stocks, he must also accept a ______ average annual return.

Lower

Which lottery payout scheme is better? Suppose you win a small lottery and have the choice of two ways to be paid: You can accept the money in a lump sum or in a series of payments over time. If you pick the lump sum, you get $2,750 today. If you pick payments over time, you get three payments: $1,000 today, $1,000 1 year from today, and $1,000 2 years from today. At an interest rate of 6% per year, the winner would be better off accepting the _______ sum , since that choice has the greater present value.

Payments over time

Diversification and risk Suppose a stock analyst recommends buying stock in the following companies: Table: Company; Industry Toyonda; Automotive Saalvo; Automotive GMW; Automotive Honsubishi; Automotive Shexxon; Oil & gas Mobron; Oil & gas Airing; Aircraft Boebus; Aircraft Goohoo; Technology Pherk; Pharmaceutical Each of the following portfolios contains four of the stock picks. Which portfolio is the most diversified?

Pher, Toyonda, Goohooo, Shexxon

Understanding risk aversion Suppose your friend Jacques offers you the following bet: He will flip a coin and pay you $1,000 if it lands heads up and collect $1,000 from you if it lands tails up. Currently, your level of wealth is $3,000. The graph shows your utility function from wealth. Use the graph to answer the following questions. Points: A. (2,55) B. (4,70) C. (3,65) The shape of your utility function implies that you are a ________ individual, and, therefore, you ______ accept the wager because the difference in utility between A and C is _______ the difference between C and B.

Risk-averse Would not Greater than

Using the rule of 70 Consider an imaginary economy that has been growing at a rate of 6% per year. Government economists have proposed a number of policies to increase the growth rate but first need to convince the president that the policies will pay off. To do so, they want to present a comparison of the number of years it will take for the economy to double, depending on the growth rate. Using the rule of 70, determine the number of years it will take the economy to double at each growth rate. Table: Growth Rate (percentage); Yrs Required to Double (nearest whole # of yrs) 6; ____ 7; ____ 8; ___

Rule of 70 @ growth rate = 70/% Growth rate 12; 70/6 10; 70/7 9; 70/8

Efficient markets hypothesis Which of the following are consistent with the efficient markets hypothesis? Check all that apply.

Stock markets reflect all available information about the value of stocks. An average person in the market will believe that all stocks are fairly valued.

Understanding risk aversion Which of the following best explain why the pain of losing $1,000 exceeds the pleasure of winning $1,000 for risk-averse people? Check all that apply.

The More Wealth that risk-averse people have, the less satisfaction they receive from an additional dollar.

Which lottery payout scheme is better? At an interest rate of 10% per year, the winner would be better off accepting ________, since it has the greater present value. Years after you win the lottery, a friend in another country calls to ask your advice. By wild coincidence, she has just won another lottery with the same payout schemes. She must make a quick decision about whether to collect her money under the lump sum or the payments over time. What is the best advice to give your friend?

The lump sum It will depend on the interest rate; advise her to get a calculator.