Question

A coupon bond pays out 2% every year on a principal of $100. The bond matures in six years and has a market value of $92. Calculate the yield to maturity, duration and convexity for the bond.

(Please provide a well detailed answer with the equations used for each part. Thank you!)

Answer 1

K = N

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

k=1

K =6

92 =∑ [(2*100/100)/(1 + YTM/100)^k]     +   100/(1 + YTM/100)^6

k=1

YTM% = 3.5

Duration

Period	Cash Flow	Discounting factor	PV Cash Flow	Duration Calc
0	($92.00)	=(1+YTM/number of coupon payments in the year)^period	=cashflow/discounting factor	=PV cashflow*period
1	2.00	1.04	1.93	1.93
2	2.00	1.07	1.87	3.73
3	2.00	1.11	1.80	5.41
4	2.00	1.15	1.74	6.97
5	2.00	1.19	1.68	8.42
6	102.00	1.23	82.98	497.86
			Total	524.33

Macaulay duration =(∑ Duration calc)/(bond price*number of coupon per year)

=524.33/(92*1)

=5.7

Modified duration = Macaulay duration/(1+YTM)

=5.7/(1+0.035)

=5.51

Convexity

Period	Cash Flow	Discounting factor	PV Cash Flow	Duration Calc	Convexity Calc
0	($92.00)	=(1+YTM/number of coupon payments in the year)^period	=cashflow/discounting factor	=PV cashflow*period	=duration calc*(1+period)/(1+YTM/N)^2
1	2.00	1.04	1.93	1.93	3.61
2	2.00	1.07	1.87	3.73	10.46
3	2.00	1.11	1.80	5.41	20.21
4	2.00	1.15	1.74	6.97	32.54
5	2.00	1.19	1.68	8.42	47.16
6	102.00	1.23	82.98	497.86	3,253.32
			Total	524.33	3,367.29

Convexity =(∑ convexity calc)/(bond price*number of coupon per year^2)

=3367.29/(92*1^2)

=36.6