Question

A 5-year bond with a yield of 10% (continuously compounded), with a face value of $100, pays an 10% coupon at the end of each year.

What is the bond’s price?

A 5-year bond with a yield of 10% (continuously compounded) pays an 10% coupon at the end of each year.

What is the bond’s duration?

A 5-year bond with a yield of 10% (continuously compounded),   with a face value of $100, pays an 10% coupon at the end of each year.

Use the duration from the previous question to calculate the effect on the bond’s price of a 0.1% decrease in its yield. What is the new bond price?

(Remember if the yield goes down what happens to the the bond price?)

A 5-year bond with a yield of 10% (continuously compounded) pays an 10% coupon at the end of each year.

Check the results from your previous duration calculation the long way.  Recalculate the bond’s price on the basis of a 9.9% per annum yield and verify that the result is in agreement with your answer to the previous question.

Answer 1

EAR =[ e^(Annual percentage rate) -1]*100

Effective Annual Rate=(e^(10/100)-1)*100

Effective Annual Rate% = 10.52

K = N

Bond Price =∑ [(Annual Coupon)/(1 + YTM)^k]     +   Par value/(1 + YTM)^N

k=1

K =5

Bond Price =∑ [(10*100/100)/(1 + 10.52/100)^k]     +   100/(1 + 10.52/100)^5

k=1

Bond Price = 98.05

Period	Cash Flow	PV Cash Flow	Duration Calc
0	($98.05)
1	10.00	9.05	9.05
2	10.00	8.19	16.37
3	10.00	7.41	22.22
4	10.00	6.70	26.81
5	110.00	66.71	333.55
		Total	408.00

Macaulay Duration	4.16
Modified Duration	3.77

Modified duration prediction = -Mod_Duration*Yield_Change*Bond_Price = -3.77*(-.001)*98.05

Modified Duration Predicts

0.37

bond price new = 98.06+0.37 = 98.419

bond price by actual method:

K = N

Bond Price =∑ [( Coupon)/(1 + YTM)^k]     +   Par value/(1 + YTM)^N

k=1

K =5

Bond Price =∑ [(10*100/100)/(1 + 10.42/100)^k]     +   100/(1 + 10.42/100)^5

k=1

Bond Price = 98.42