Elliot Karlin is a 35-year-old bank executive who has just inherited a large sum of money. Having spent several years in the bank's investments department, he's well aware of the concept of duration and decides to apply it to his bond portfolio. In particular, Elliot intends to use $1 million of his inheritance to purchase 4 U.S. Treasury bonds:
1. An %8.64%, 13-year bond that's priced at $1,095.38 to yield 7.48%.
2. A 7.788%, 15-year bond that's priced at $1022.96 to yield 7.53%.
3. A 20-year stripped Treasury (zero coupon) that's priced at $197.00 to yield 8.29%.
4. A 24-year, 7.47% bond that's priced at $962.34 to yield 7.82%. Note that these bonds are semiannual compounding bonds.
a. Find the duration and the modified duration of each bond.
b. Find the duration of the whole bond portfolio if Elliot puts $250,000 into each of the 4 U.S. Treasury bonds.
c. Find the duration of the portfolio if Elliot puts $360,000 each into bonds 1 and 3 and $140,000 each into bonds 2 and 4.
d. Which portfolio âb or câshould Elliot select if he thinks rates are about to head up and he wants to avoid as much price volatility as possible? Explain. From which portfolio does he stand to make more in annual interest income? Which portfolio would you recommend, and why?
Elliot Karlin is a 35-year-old bank executive who has just inherited a large sum of money. Having spent several years in the bank's investments department, he's well aware of the concept of duration and decides to apply it to his bond portfolio. In particular, Elliot intends to use $1 million of his inheritance to purchase 4 U.S. Treasury bonds:
1. An %8.64%, 13-year bond that's priced at $1,095.38 to yield 7.48%.
2. A 7.788%, 15-year bond that's priced at $1022.96 to yield 7.53%.
3. A 20-year stripped Treasury (zero coupon) that's priced at $197.00 to yield 8.29%.
4. A 24-year, 7.47% bond that's priced at $962.34 to yield 7.82%. Note that these bonds are semiannual compounding bonds.
a. Find the duration and the modified duration of each bond.
b. Find the duration of the whole bond portfolio if Elliot puts $250,000 into each of the 4 U.S. Treasury bonds.
c. Find the duration of the portfolio if Elliot puts $360,000 each into bonds 1 and 3 and $140,000 each into bonds 2 and 4.
d. Which portfolio âb or câshould Elliot select if he thinks rates are about to head up and he wants to avoid as much price volatility as possible? Explain. From which portfolio does he stand to make more in annual interest income? Which portfolio would you recommend, and why?
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Minicase 1
Interest Rates, Bond Yields, and Duration
CONCEPTS IN THIS CASE
simple loans
fixed-payment loans
coupon bonds
present value
yield-to-maturity
current yield
nominal and real interest rates
rate of return
capital gain
interest-rate and reinvestment risk
duration
You have been hired to analyze the debt securities of your organization. The firm has outstanding loans and bonds. A quick review of the balance sheet shows the following:
| Liability | Nominal | Years to | |
| Selected Liabilities of the firm | |||
| Simple Loans | 800 | 5% | 1 |
| Fixed-Payment Loans | 5,000 | 12% | 19 |
| Long-term Bonds #1 | 500,000 | 10% | 4 |
| Long-term Bonds #2 | 1,080,000 | 10% | 10 |
| Liabilities Total | 1,585,800 | ||
| Market Price for Bond #1 | 930.50 | ||
| Market Price for Bond #2 | 859.50 | ||
| Face Value of Each Bond | 1,000.00 | ||
| Selected Current Assets of the firm | |||
| Marketable Securities: | |||
| Treasury Bills | 100,000 | ||
Note: Treasury Bills have a $10,000 face value, which matures in one year. Each Treasury Bill has a cost of $9,580.00
How much interest would the firm pay each year on the simple-interest loan?
How much would you write a cheque for to pay off the loan in one year?
What is the monthly payment needed to pay off the fixed-payment loans?
What is the current yield for each bond if the current price is:
$930.50 for Bond #1?
$859.50 for Bond #2?
What is the expected yield to maturity for each bond?
Bond #1 selling for $930.50?
Bond #2 selling for $859.50
What is the rate of capital gain if both bonds sell for $900.00 in one year?
Bond #1 selling for $930.50 today?
Bond #2 selling for $859.50 today?
If the Yield to Maturity expected by investors changes to 11%:
What will be the market price of Bond #1?
What will be the market price for Bond #2?
What will be the dollar change in price for Bond #1?
What will be the dollar change in price for Bond #2?
What will be the percent change in price for Bond #1?
What will be the percent change in price for Bond #2?
Since the change in expected yield to maturity is the same, why is the amount of change different between the bonds?
If investors holding our 4-year bonds (Bond #1) receive interest income annually for four years, plus the face value of the bonds at maturity,
What will be the total interest earned on the bond over the next four years?
What will be the face value received at maturity?
Given the following projected income stream for Bond #1:
| Projected Reinvestment Rates | ||||
| Year | Coupon | Face | 10% | 5% |
| 1 | 100 | |||
| 2 | 100 | 10.00 | 5.00 | |
| 3 | 100 | 21.00 | 10.25 | |
| 4 | 100 | 1000 | 33.10 | 15.76 |
| Total Income | 400 | 1000 | 64.10 | 31.01 |
What is the total cash available over the next four years to the bond holder earning
10%
15%
What is the average annual rate of return for the bond holder earning
10%
15%
Why does the reinvestment rate affect the annual rate of return for the same bond?
If the expected rate of return on our bonds is 10%, what is the duration of Bond #1?
What is the yield to maturity on the Treasury Bills (a discount bond)?
What is the real rate of interest if the nominal rate is 10% and the inflation rate is 3%?
Copyright © 2000â2001 Addison Wesley Longman, a division of Pearson Education
Adaptation copyright © 2002 Pearson Education Canada
