In: Finance
A company just issued a bond with the following characteristics:
Maturity = 3 years
Coupon rate = 8%
Face value = $1,000
YTM = 10%
Interest is paid annually and the bond is noncallable.
Calculate the bond’s Macaulay duration ?Round "Present value" to 2 decimal places and "Duration" to 4 decimal place.?
Calculate the bond’s modified duration
Assuming the bond’s YTM goes from 10% to 9.5%, calculate an estimate of the price change without considering convexity
Calculate the convexity of the bond.
Macaulay Duration
Period | Cash Flow | Period * Cash flow | PV @8% | PV of cash flow |
1 | 80 | 80 | 0.926 | 74.08 |
2 | 80 | 160 | 0.857 | 137.12 |
3 | 1080 | 3240 | 0.794 | 2572.56 |
Total | 2783.76 |
Macaulay Duration = Sum of PV of cash flow / Face value of bond
= 2783.76 / 1000 = 2.7837 Years
Modified Duration
Modified Duration = Macaulay Duration / [1 + (YTM/2)]
= 2.7837 / [1 + (0.1 / 2)]
= 2.6511 years
Price Change
factor change in yield = 0.095 / 0.1 = 0.95
assuming price of bond is $1000
New price = 1000 / 0.95 = $1052.63
Change in price = $52.63
Covexity of bond
convexity of bond = [P(i decreases) + P(i Increases) - 2*FV] / [2 * FV * dY^2]
where P(i decreases) - price of bond in case of decrease in interest rate
P (i increases) - price when interest rate increases
FV - Face value of bond
dY = change in interest rate
dY = 0.5% = 0.005
if YTM increases from 10% to 10.5%, then
Price of bond = $952.38 (calculation is done as per above mentioned method and assumption)
Convexity of bond = [1052.63 + 952.38 - 2*1000] / [2*1000*0.005^2]
= 5.01 / 0.05 = 100.2