Question

The term structure is flat at 8%. Consider an 8% coupon bond with semiannual payouts that matures in 10 years. If yields increased by 1 basis point (y = 8.01%) what would be the effect on price? If the yield curve was flat at 9% and increased by 1 basis point, would the price effect be bigger or smaller. Explain

Answer 1

Lets assume the Face value be $100.

Now Coupon rate - 8% p.a with semiannual payment.

=> Semiannual coupon rate = 8%/2= 4%

=>Semiannual Interest = $100*4%=$4.

Total semiannual = 10 year*2 =20

Price of the Bond = Present value of the Future cash inflows discounted at Market Yield.

If market Yield= coupon rate	then Bond price= face value
If market yield < Coupon rate	Bond price > Face value
If market yield > Coupon rate	then Bond price< Face value

Now if YTM = 8.01% Per annum or 4.005% per semiannual, then the Bond price will be -

	A		B	A*B
Semiannual	Cash Inflow		Present value discount [email protected]%	Present value of the Future cash flows
1	$4	Semiannual coupon	0.961492236	$3.85
2	$4	Semiannual coupon	0.9244673198	$3.70
3	$4	Semiannual coupon	0.8888681504	$3.56
4	$4	Semiannual coupon	0.8546398254	$3.42
5	$4	Semiannual coupon	0.8217295566	$3.29
6	$4	Semiannual coupon	0.7900865887	$3.16
7	$4	Semiannual coupon	0.7596621208	$3.04
8	$4	Semiannual coupon	0.7304092311	$2.92
9	$4	Semiannual coupon	0.7022828048	$2.81
10	$4	Semiannual coupon	0.6752394642	$2.70
11	$4	Semiannual coupon	0.6492375023	$2.60
12	$4	Semiannual coupon	0.6242368177	$2.50
13	$4	Semiannual coupon	0.6001988536	$2.40
14	$4	Semiannual coupon	0.5770865378	$2.31
15	$4	Semiannual coupon	0.5548642256	$2.22
16	$4	Semiannual coupon	0.5334976449	$2.13
17	$4	Semiannual coupon	0.5129538434	$2.05
18	$4	Semiannual coupon	0.4932011379	$1.97
19	$4	Semiannual coupon	0.4742090648	$1.90
20	$104	Semiannual coupon+face value	0.455948334	$47.42
			Bond price	$99.93

Bond price at 8% YTM = $100

Bond price at 8.01% YTM = $99.93

Effect on price = ($99.93-$100) = -$0.07

% effect = -$0.07/$100 = -0.07%

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Yield Curve =9% means the YTM or yield to maturity = 9%

If YTM =9% per annum or 4.50% per semiannul,then the price will be =

	A		B	A*B
Semiannual	Cash Inflow		Present value discount [email protected]%	Present value of the Future cash flows
1	$4	Semiannual coupon	0.956937799	$3.83
2	$4	Semiannual coupon	0.9157299512	$3.66
3	$4	Semiannual coupon	0.8762966041	$3.51
4	$4	Semiannual coupon	0.8385613436	$3.35
5	$4	Semiannual coupon	0.8024510465	$3.21
6	$4	Semiannual coupon	0.7678957383	$3.07
7	$4	Semiannual coupon	0.7348284577	$2.94
8	$4	Semiannual coupon	0.703185127	$2.81
9	$4	Semiannual coupon	0.6729044277	$2.69
10	$4	Semiannual coupon	0.643927682	$2.58
11	$4	Semiannual coupon	0.6161987388	$2.46
12	$4	Semiannual coupon	0.5896638649	$2.36
13	$4	Semiannual coupon	0.564271641	$2.26
14	$4	Semiannual coupon	0.5399728622	$2.16
15	$4	Semiannual coupon	0.5167204423	$2.07
16	$4	Semiannual coupon	0.4944693228	$1.98
17	$4	Semiannual coupon	0.4731763854	$1.89
18	$4	Semiannual coupon	0.4528003688	$1.81
19	$4	Semiannual coupon	0.4333017884	$1.73
20	$104	Semiannual coupon+face value	0.4146428597	$43.12
			Bond price@9% YTM	$93.50

$ Effect on price = [($93.50-$100) / $100]*100 = -6.50%

If yield or YTM is 9.01% per annum or 4.505% per semiannum, then the price will be-

	A		B	A*B
Semiannual	Cash Inflow		Present value discount [email protected]%	Present value of the Future cash flows
1	$4	Semiannual coupon	0.9568920147	$3.83
2	$4	Semiannual coupon	0.9156423279	$3.66
3	$4	Semiannual coupon	0.8761708319	$3.50
4	$4	Semiannual coupon	0.8384008726	$3.35
5	$4	Semiannual coupon	0.8022591001	$3.21
6	$4	Semiannual coupon	0.7676753267	$3.07
7	$4	Semiannual coupon	0.73458239	$2.94
8	$4	Semiannual coupon	0.7029160231	$2.81
9	$4	Semiannual coupon	0.6726147296	$2.69
10	$4	Semiannual coupon	0.6436196637	$2.57
11	$4	Semiannual coupon	0.6158745167	$2.46
12	$4	Semiannual coupon	0.5893254072	$2.36
13	$4	Semiannual coupon	0.5639207762	$2.26
14	$4	Semiannual coupon	0.5396112877	$2.16
15	$4	Semiannual coupon	0.5163497322	$2.07
16	$4	Semiannual coupon	0.4940909356	$1.98
17	$4	Semiannual coupon	0.4727916708	$1.89
18	$4	Semiannual coupon	0.4524105744	$1.81
19	$4	Semiannual coupon	0.4329080661	$1.73
20	$104	Semiannual coupon+face value	0.4142462715	$43.08
			Bond price	$93.43

% Effect on price if Yield increaded from 9% to 9.01% = [($93.43-$93.50) / $93.50] *100 = -0.075 %

Hence the price effect will be bigger.

Because when the Yield change from 8% to 8.01% then the effect was -0.07%

Now when the Yield change from 9% to 9.01 % then the effect was -0.075 %