Question

A bond with a face value of $1000 and maturity of exactly 20 years pays 10% annual coupon. This bond is currently selling at an annual yield-to-maturity (YTM) of 12%. Answer the following questions for this bond.

a. Calculate the current price of the bond by discounting all the cash flows of the bond using the timeline method. b. Calculate the modified duration of the bond without using any Excel built-in function. (calculate PV of each cash flow, find the weight of each cash flow and then multiply time with the weight) c. Using modified Duration, calculate what would be the new price of the bond when YTM is 11%. d. Using modified Duration, what is the percentage change in price from the original level (found in part a) when YTM is 11%? e. Calculate convexity of the bond without using any Excel built-in function. f. Using the modified duration plus convexity model, what is the new price of the bond when YTM is 13%? g. Using the modified duration plus convexity model, what is the percentage price change from the original level (found in part a) of the bond when YTM is 13%.

Please only answer parts E,F & G

Answer 1

K = N

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

k=1

K =20

Bond Price =∑ [(10*1000/100)/(1 + 12/100)^k]     +   1000/(1 + 12/100)^20

k=1

Bond Price = 850.61

Period	Cash Flow	Discounting factor	PV Cash Flow	Duration Calc	Convexity Calc
0	($850.61)	=(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	100.00	1.12	89.29	89.29	142.36
2	100.00	1.25	79.72	159.44	381.31
3	100.00	1.40	71.18	213.53	680.91
4	100.00	1.57	63.55	254.21	1,013.26
5	100.00	1.76	56.74	283.71	1,357.05
6	100.00	1.97	50.66	303.98	1,696.31
7	100.00	2.21	45.23	316.64	2,019.42
8	100.00	2.48	40.39	323.11	2,318.21
9	100.00	2.77	36.06	324.55	2,587.28
10	100.00	3.11	32.20	321.97	2,823.43
11	100.00	3.48	28.75	316.22	3,025.10
12	100.00	3.90	25.67	308.01	3,192.07
13	100.00	4.36	22.92	297.93	3,325.07
14	100.00	4.89	20.46	286.47	3,425.55
15	100.00	5.47	18.27	274.04	3,495.46
16	100.00	6.13	16.31	260.99	3,537.08
17	100.00	6.87	14.56	247.60	3,552.87
18	100.00	7.69	13.00	234.07	3,545.40
19	100.00	8.61	11.61	220.60	3,517.27
20	1,100.00	9.65	114.03	2,280.67	38,180.84
			Total	7,317.04	83,816.25

e

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

=83816.25/(850.61*1^2)

=98.54

g

Using convexity adjustment to modified duration

Convexity adjustment = 0.5*convexity*Yield_Change^2*Bond_Price

0.5*98.54*0.01^2*850.61

=4.19

%age change in bond price=(Mod.duration pred.+convex. Adj.)/bond price

=(-65.33+4.19)/850.61

=-7.19%

New bond price = bond price+Mod.duration pred.+convex. Adj.

=850.61-65.33+4.19

=789.47

h

%age change = (789.48/850.61-1)*100=-7.19%