Reference no: EM132277263
Exercise 1
BASED ON THE DATA BELOW COMPUTE AND PLOT THE DURATION AS A FUNCTION OF THE COUPON RATE WITH THE COUPON RATE GOING FROM 0% T0 11%, IN ONE-PERCENT INCREMENTS
| Current date |
4/6/2019 |
| Maturity, in years |
21 |
| Maturity date |
4/6/2040 |
| YTM |
12% |
| Coupon |
3% |
| Face value |
1,000 |
Exercise 2
BASED ON THE DATA BELOW COMPUTE AND PLOT THE DURATION AS A FUNCTION OF THE TIME TO MATURITY WITH TIME-TO-MATURITY GOING FROM 5 YEARS TO 70 YEARS, IN 5-YEAR INCREMENTS
| Current date |
4/6/2019 |
| Maturity, in years |
21 |
| Maturity date |
4/6/2040 |
| YTM |
10% |
| Coupon |
5% |
| Face value |
1,000 |
Exercise 3
DURATION MATCHING
You have a liability (obligation) with one payment of $6,000 due in 10 years.
Show that you can immunize yourself only by Bond 1 and not by Bond 2.
Show that if interest rate changes by 1% (immediately after you buy the bonds) Bond1 terminal value remains almost unchanged, near $6,000. (whereas the terminal values for Bond 2 depart much more significantly from $6,000)
The ongoing rate (YTM) is 6%, so assume the rate could jump to 7% and can go down to 5%.
Reminder: the terminal value includes the value of the re-invested coupons and the price of the bonds at time 10.
Hint: first verify that when the interest rate DOESN'T change (i.e. stays at 6%) you do have terminal values of exactly $6,000 for both Bond 1 and Bond 2. This will assure that you have the correct percentage of face value bought.
Only then can you check whether the terminal value stays constant for Bond 1 while it does not for the Bonds 2.
| Yield to maturity |
6.0% |
|
| Current Date |
4/6/2019 |
|
| Present Value of Future Obligation: |
$3,350.37 |
|
|
|
|
|
Bond 1 |
Bond 2 |
| Coupon rate |
7.00% |
6.000% |
| Maturity |
4/6/2034 |
4/6/2049 |
| Face value |
1,000 |
1,000 |
| Number of years to Maturity |
15.00 |
30 |
Exercise 4
DURATION MATCHING
You have a liability (obligation) with one payment of $6,000 due in 10 years.
Form a portfolio of bonds 2 and 3 and immunize yourself from the interest rate risks.
Show that if interest rate changes by 1% your portfolio terminal value still remains almost unchanged.
(whereas the terminal values for individual Bonds depart much more significantly from $6,000)
The ongoing rate (YTM) is 6%, so assume the rate could jump to 7% and can go down to 5%.
Reminder: the terminal value includes the value of the re-invested coupons and the price of the bonds at time 10.
Before starting to compute portfolio weights, first verify that when the interest rate DOESN'T change (i.e. stays at 6%) you do
have terminal values of exactly $6,000 for all Bonds. This will assure that you have the correct percentage of face value bought.
Only then can you start the duration matching (by computing the weights needed), and only then can you check whether the terminal value stays constant for your portfolio (weighted average of Bond2 and Bond3) while it does not for the individual Bonds.
Compute the terminal values of the individual bonds and the Portfolio (made up of Bonds 2 and 3) as a function of the interest rate (let r go from 0 to 10%) by using data tables.
Plot your results graphically to show that individual bonds are no match for the portfolio if rates swing wildly.
| Yield to maturity |
6.0% |
|
|
| Current Date |
4/6/2019 |
|
|
| Present Value of Future Obligation: |
$3,350.37 |
|
|
|
|
|
|
|
Bond 1 |
Bond 2 |
Bond 3 |
| Coupon rate |
7.00% |
6.000% |
6.700% |
| Maturity |
4/6/2032 |
4/6/2049 |
4/6/2029 |
| Face value |
1,000 |
1,000 |
1000 |
| Number of years to Maturity |
15.00 |
30 |
10 |
Exercise 5
Consider a bond that pays $100 annual interest (i.e. the CR =0.10) and has a remaining life of 15 years (matures on 4/6/2034). The bond currently (on 4/6/2019) sells for $985 and has a yield to maturity of 10.20%.
What is this bond's duration?
What is the actual Price change of the bond if interest rate (YTM) changes to 9.5%.
Compute the Price change of the bond using duration if interest rate (YTM) changes to 9.5%.
Compute the Convexity for the bond when interest rate changes from 10.2% to 9.5%.
Exercise 6
You have a liability (obligation) with one payment of $7,000 due in 9 years. Use Bonds 1, 3 and 4 below to immunize the portfolio "completely", i.e., matching the duration AND the convexity of a bond portfolio with the duration of the liability. Show that if the interest rate changes by 4% (large swing immediately after you buy the bonds) your portfolio terminal value still remains almost unchanged.
(whereas the terminal values for all individual Bonds depart much more significantly from it)
Show clearly what weights you obtain for Bond 1, 3 and 4. The ongoing rate (YTM) is 3%, so the rate could jump to 7%.
Reminder: the portfolio terminal value includes the value of the re-invested coupons (see the notes) and the price of the bonds at time 9.
Before starting to compute portfolio weights, first verify that when the interest rate DOESN'T change (i.e. stays at 3%) you do have terminal values of exactly $7,000 for all Bonds. This will assure that you have the correct percentage of face value bought.
Only then can you start the duration/convexity matching (by computing the weights needed), and only then can you check whether the terminal value stays constant for your portfolio (weighted average of Bond 1, Bond 3 and Bond 4) while it does not for the individual Bonds.
Compute the terminal values of both Bond 2 and the Portfolio (made up of Bonds 1, 3 and 4) as a function of the interest rate (let r go from 0 to 10%)
Plot your results graphically to show that even though Bond 2 performs well in the region nearby 3%, it is no match for the portfolio if rates swing wildly.
| Yield to maturity |
3% |
| Current Date |
4/6/2019 |
| Present Value of Future Obligation: |
|
|
|
|
|
Bond 1 |
Bond 2 |
Bond 3 |
Bond 4 |
| Coupon rate |
9.00% |
7.50% |
7.00% |
5.00% |
| Maturity |
4/6/2049 |
4/6/2031 |
4/6/2028 |
4/6/2032 |
| Face value |
1,000 |
1,000 |
1,000 |
1,000 |