many broad-based, market-value-weighted indexes are computed daily. These include the Standard & Poor’s 500 Stock Index, the NYSE index, the Nasdaq index, the Wilshire 5000 Index, and indexes of many non-U.S. stock markets.
8. A call option is a right to purchase an asset at a stipulated exercise price on or before a ma- turity date. A put option is the right to sell an asset at some exercise price. Calls increase in value while puts decrease in value as the price of the underlying asset increases.
9. A futures contract is an obligation to buy or sell an asset at a stipulated futures price on a maturity date. The long position, which commits to purchasing, gains if the asset value increases while the short position, which commits to purchasing, loses.
PROBLEMS
1. The following multiple-choice problems are based on questions that appeared in past CFA examinations.a. A firm’s preferred stock often sells at yields below its bonds because:
i. Preferred stock generally carries a higher agency rating.
ii. Owners of preferred stock have a prior claim on the firm’s earnings.
iii. Owners of preferred stock have a prior claim on a firm’s assets in the event of liquidation.
iv. Corporations owning stock may exclude from income taxes most of the divi- dend income they receive.
b. A municipal bond carries a coupon of 63⁄4% and is trading at par; to a taxpayer in a 34% tax bracket, this bond would provide a taxable equivalent yield of:
i. 4.5%
ii. 10.2%
iii. 13.4%
iv. 19.9%
c. Which is the most riskytransaction to undertake in the stock index option markets if the stock market is expected to increase substantially after the transaction is com- pleted?
i. Write a call option.
ii. Write a put option iii. Buy a call option.
iv. Buy a put option.
2. A U.S. Treasury bill has 180 days to maturity and a price of $9,600 per $10,000 face value. The bank discount yield of the bill is 8%.
a. Calculate the bond equivalent yield for the Treasury bill. Show calculations.
b. Briefly explain why a Treasury bill’s bond equivalent yield differs from the discount yield.
3. A bill has a bank discount yield of 6.81% based on the asked price, and 6.90%
based on the bid price. The maturity of the bill is 60 days. Find the bid and asked prices of the bill.
4. Reconsider the T-bill of Problem 3. Calculate its bond equivalent yield and effective annual yield based on the ask price. Confirm that these yields exceed the discount yield.
5. Which security offers a higher effective annual yield?
a. i. A three-month bill selling at $9,764.
ii. A six-month bill selling at $9,539.
b. Calculate the bank discount yield on each bill.
6. A Treasury bill with 90-day maturity sells at a bank discount yield of 3%.
a. What is the price of the bill?
b. What is the 90-day holding period return of the bill?
c. What is the bond equivalent yield of the bill?
d. What is the effective annual yield of the bill?
7. Find the price of a six-month (182-day) U.S. Treasury bill with a par value of $100,000 and a bank discount yield of 9.18%.
8. Find the after-tax return to a corporation that buys a share of preferred stock at $40, sells it at year-end at $40, and receives a $4 year-end dividend. The firm is in the 30%
tax bracket.
CFA
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9. Turn to Figure 2.10 and look at the listing for Honeywell.
a. What was the firm’s closing price yesterday?
b. How many shares could you buy for $5,000?
c. What would be your annual dividend income from those shares?
d. What must be its earnings per share?
10.Consider the three stocks in the following table. Ptrepresents price at time t, and Qt represents shares outstanding at time t. Stock C splits two for one in the last period.
P0 Q0 P1 Q1 P2 Q2
A 90 100 95 100 95 100
B 50 200 45 200 45 200
C100 200 110 200 55 400
a. Calculate the rate of return on a price-weighted index of the three stocks for the first period (t0 to t1).
b. What must happen to the divisor for the price-weighted index in year 2?
c. Calculate the rate of return for the second period (t1 to t2).
11. Using the data in Problem 10, calculate the first-period rates of return on the following indexes of the three stocks:
a. A market-value-weighted index.
b. An equally weighted index.
12.An investor is in a 28% tax bracket. If corporate bonds offer 9% yields, what must mu- nicipals offer for the investor to prefer them to corporate bonds?
13.Short-term municipal bonds currently offer yields of 4%, while comparable taxable bonds pay 5%. Which gives you the higher after-tax yield if your tax bracket is:
a. Zero.
b. 10%.
c. 20%.
d. 30%.
14.Find the equivalent taxable yield of the municipal bond in the previous problem for tax brackets of zero, 10%, 20%, and 30%.
15.The coupon rate on a tax-exempt bond is 5.6%, and the rate on a taxable bond is 8%.
Both bonds sell at par. The tax bracket (marginal tax rate) at which an investor would be indifferent between the two bonds is:
a. 30.0%.
b. 39.6%.
c. 41.7%.
d. 42.9%.
16.Which security should sell at a greater price?
a. A 10-year Treasury bond with a 9% coupon rate versus a 10-year T-bond with a 10%
coupon.
b. A three-month maturity call option with an exercise price of $40 versus a three- month call on the same stock with an exercise price of $35.
c. A put option on a stock selling at $50, or a put option on another stock selling at $60 (all other relevant features of the stocks and options may be assumed to be identical).
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d. A three-month T-bill with a discount yield of 6.1% versus a three-month bill with a discount yield of 6.2%.
17.Look at the futures listings for the Russell 2000 index in Figure 2.14.
a. Suppose you buy one contract for September delivery. If the contract closes in Sep- tember at a price of $510, what will your profit be?
b. How many September maturity contracts are outstanding?
18.Turn back to Figure 2.13 and look at the Hewlett Packard options. Suppose you buy a March maturity call option with exercise price 35.
a. Suppose the stock price in March is 40. Will you exercise your call? What are the profit and rate of return on your position?
b. What if you had bought the call with exercise price 40?
c. What if you had bought a March put with exercise price 35?
19.Why do call options with exercise prices greater than the price of the underlying stock sell for positive prices?
20.Both a call and a put currently are traded on stock XYZ; both have strike prices of $50 and maturities of six months. What will be the profit to an investor who buys the call for $4 in the following scenarios for stock prices in six months? What will be the profit in each scenario to an investor who buys the put for $6?
a. $40.
b. $45.
c. $50.
d. $55.
e. $60.
21.Explain the difference between a put option and a short position in a futures contract.
22.Explain the difference between a call option and a long position in a futures contract.
23.What would you expect to happen to the spread between yields on commercial paper and Treasury bills if the economy were to enter a steep recession?
24.Examine the first 25 stocks listed in the stock market listings for NYSE stocks in your local newspaper. For how many of these stocks is the 52-week high price at least 50%
greater than the 52-week low price? What do you conclude about the volatility of prices on individual stocks?
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SOLUTIONS TO CONCEPT C H E C K S
1. The discount yield at bid is 6.03%. Therefore
P10,000 [1 .0603 (86/360)] $9,855.95
2. If the bond is selling below par, it is unlikely that the government will find it optimal to call the bond at par, when it can instead buy the bond in the secondary market for less than par. Therefore, it makes sense to assume that the bond will remain alive un- til its maturity date. In contrast, premium bonds are vulnerable to call because the government can acquire them by paying only par value. Hence it is more likely that the bonds will repay principal at the first call date, and the yield to first call is the sta- tistic of interest.
3. A 6% taxable return is equivalent to an after-tax return of 6(1 .28) 4.32%.
Therefore, you would be better off in the taxable bond. The equivalent taxable yield of the tax-free bond is 4/(l .28) 5.55%. So a taxable bond would have to pay a 5.55% yield to provide the same after-tax return as a tax-free bond offering a 4%
yield.
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SOLUTIONS TO CONCEPT C H E C K S
4. a. You are entitled to a prorated share of IBM’s dividend payments and to vote in any of IBM’s stockholder meetings.
b. Your potential gain is unlimited because IBM’s stock price has no upper bound.
c. Your outlay was $50 100 $5,000. Because of limited liability, this is the most you can lose.
5. The price-weighted index increases from 62.5 [i.e., (100 25)/2] to 65 [i.e., (110 20)/2], a gain of 4%. An investment of one share in each company requires an outlay of $125 that would increase in value to $130, for a return of 4% (i.e., 5/125), which equals the return to the price-weighted index.
6. The market-value-weighted index return is calculated by computing the increase in the value of the stock portfolio. The portfolio of the two stocks starts with an initial value of $100 million $500 million $600 million and falls in value to $110 million
$400 million $510 million, a loss of 90/600 .15 or 15%. The index portfolio re- turn is a weighted average of the returns on each stock with weights of 1⁄6on XYZ and
5⁄6on ABC (weights proportional to relative investments). Because the return on XYZ is 10%, while that on ABC is 20%, the index portfolio return is 1⁄610% 5⁄6 (20%) 15%, equal to the return on the market-value-weighted index.
7. The payoff to the call option is $4 per share at maturity. The option cost is $3.50 per share. The dollar profit is therefore $.50. The put option expires worthless. There- fore, the investor’s loss is the cost of the put, or $3.40.
E-INVESTMENTS:
INTEREST RATES
Go to http://www.bloomberg.com/markets/index.html. In the markets section under RATES & Bonds, find the rates in the Key Rates and Municipal Bond Rates sections.
Describe the trend over the last six months in Municipal Bonds Yields
AAA Rated Industrial Bonds 30-year Mortgage Rates