DURATION
You must use LOTUS or another Spreadsheet software. You must turn in your diskette with the
worksheet and your printed results.
The Merchant's Bank and Trust Co. has $750,000 in bonds maturing from the existing portfolio. You
have received interest rate forecasts from two well known investment firms. Firm A predicts short term
interest rates, 0-6 months, to average between 3% to 5%. This same firm forecasted long term rates
will fluctuate between 1% to 3%. Firm B predicts a downward sloping curve with long term interest
rates in the 2% to 4%.
Using Firm A and Firm B's forecast of long term interest rates and attached table:
(1)
Calculate the duration of each bond under Firm A and Firm B's forecast (use the average
of each firm's long term interest range).
(2)
Construct a portfolio using the 4 bonds listed and calculate the portfolio's duration under
Firm A's and Firm B's forecast.
(3)
Using the elasticity formula, what would be Firm A's portfolio value change if interest
rates decrease 1% from Firm A's forecasted long-term average rate?
Table
Bond Being Considered for Purchase
Amount*
Name
Coupon Rate
Maturity
$150,000
Agency A
10.90%
three years
$200,000
Government 1
10.85%
three years
$200,000
Agency D
11.35%
five years
$200,000
Government 6
12.50%
ten years
*
All bonds are purchased at par and are assumed to have an annual coupon.
DURATION
Financial Analyses of Long-Term Bonds
Dominique Domingue, head of investments for Middletown National Bank, is considering the
purchase of a series of Treasury bonds which have just become available for sale. The coupon rate on
the bonds is 7.0% per year and interest is payable on a semi-annual basis. Originally, the bonds had a
twenty year maturity but they were issued ten years ago, so they have another ten years until maturity.
The face value of each individual bond is $1,000.
Dominique has checked the yield-to-maturity on similar bonds and has determined that bonds of
similar maturity and risk are yielding 7.5% on a yield-to-maturity basis. She would like to earn no
less than this rate on her purchase of any bonds for the bank.
Dominique is intrigued by this particular issue of bonds. She knows that bonds of this series
have been held by large property and casualty insurance companies. However, the decade's largest
hurricane has recently swept through the country. The eye of the storm hit the Caribbean coast near the
Louisiana-Mississippi state line, traveled through the Mississippi and Ohio river valleys, and exited the
country in the vicinity of Maryland. The damage created by the storm has created large claims on
insurance policies and the insurance companies are selling off securities from their portfolios to meet
these claims. The selling pressure from the large amount of bonds available for sale has depressed
prices across the board but certain bond issues are depressed more than others.
That is what intrigues Dominique about this particular issue. She suspects that it has been held
by an insurance company and the company is very anxious to sell. The asking price (i.e. the price for
which the bond can be purchased) is $975.00.
Dominique is confident that the maturity and default risk characteristics of the bond issue is
appropriate for her bank. However, she has two major questions regarding the bonds:
1.
Is the bond too volatile for the bank, given its conservative investment policy?
2.
Does the asking price of the bond represent an attractive price?
To answer the first question, Dominique has decided to use the bonds' duration
to measure the price volatility risk. Given the current interest rate outlook, Dominique
has decided to invest in bonds which have a duration of eight years or less. This would
limit the market risk (or price volatility risk) of the bank.
To answer the second question, Dominique can do one of the two things. First,
she can determine the fair price to pay for the bond, then compare it to the asking price.
If she can buy the bond for less than its fair price, it would represent an attractive
investment. Second, as an alternate way of evaluating it, she could calculate the yield-tomaturity (YTM) on the bond, given its asking price of $975.00. If the yield-to-maturity is
greater than the YTM of similar risk bonds, it would represent an attractive investment.
1.
A.Calculate the duration of the Treasury bond issue.
B. Does the bond issue meet Dominique's criteria or price volatility risk?
2.
Given its duration, how would the price of the bond be expected to change if
Dominique bought the bond and then interest rates increased by one percent?
(Answer in terms of percentage change and dollar value change.)
3.
A. What is the fair price to pay for the bond, given the yield on other bonds of
equal risk?
B. Should Dominique buy the bond issue at the current asking price of $975.00?
4.
A. What is the approximate yield-to-maturity of the bond issue at its current
asking price?
B. Calculate the exact yield to maturity. How close is this to the bond's true
yield-to-maturity?