2. You are thinking about buying a bond and you want to consider your interest r
ID: 2730101 • Letter: 2
Question
2. You are thinking about buying a bond and you want to consider your interest rate exposure. The bond in question is a semiannual note issued by Bank of America that has a $1,000 face value, four years left until maturity and pays a coupon rate of 4.375%. It is currently yielding 5.875%. Because of a slowing economy, you expect a 75 basis point downward shift in the yield curve this year.
Calculate the following:
a. Price, duration, modified duration and convexity (manually, though you can confirm your answers using the Excel functions or one of the online calculators).
b. the approximate dollar and percentage change in price due to duration and convexity
c. the actual dollar and percentage change in price
Explanation / Answer
Calculation of interest
Stated Coupon rate = 4.375%
As it is a semiannual bond the rate if halved therefore rate = 2.1875%
Interest at 2.1875% on $1,000 = $21.875
Now find out the present value of annuity for 2.9375% rounded off to 3% at 8 years = 7.02
(Note 8 years is taken as it is 4 ears and interest is paid semiannually and half of the market rate is taken as it is semiannually)
Present value of Interest = $21.875* 7.02 = $153.57
Present value of $1 at 3% for 8 years = 0.98741
Present Face value of the bond = $1,000 * 0.98741 = $ 987.41
Bond price = $21.875 + $ 987.41 = $990.30 (rounded off)
Calculation of duration
Duration = Present value of a bond's cash flows, weighted by length of time to receipt and divided by the bond's current market value
No of years
Cash flow
Period * cash flow
PV of $ 1 @ 2.1% or 2%
Present value of cash flows
1
$21.875
$21.88
0.98039
$21.45
2
$21.875
$43.75
0.96117
$42.05
3
$21.875
$65.63
0.94232
$61.84
4
$21.875
$87.50
0.92385
$80.84
5
$21.875
$109.38
0.90573
$99.06
6
$21.875
$131.25
0.88797
$116.55
7
$21.875
$153.13
0.87056
$133.30
8
$21.875
$175.00
0.85349
$149.36
Total
$175.00
$704.45
Macaulay duration = $704.45 / $ 987.41= 0.71
Modified duration = Macaulay's Duration/ (1 + yield/k)
Where k = the number of periods: two for semi-annual
Hence
Modified duration = 0.71/ (1+ 0.75/ 2) = 0.71/ (1.75/2)
= 0.71/ 0.875 = 0.811
No of years
Cash flow
Period * cash flow
PV of $ 1 @ 2.1% or 2%
Present value of cash flows
1
$21.875
$21.88
0.98039
$21.45
2
$21.875
$43.75
0.96117
$42.05
3
$21.875
$65.63
0.94232
$61.84
4
$21.875
$87.50
0.92385
$80.84
5
$21.875
$109.38
0.90573
$99.06
6
$21.875
$131.25
0.88797
$116.55
7
$21.875
$153.13
0.87056
$133.30
8
$21.875
$175.00
0.85349
$149.36
Total
$175.00
$704.45
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