Question

Question is stated on the excel sheet

Example Same Yield Change Different Maturities .......-5%, 5-year Note- 5% coupoi 5% yield 4% yield PV PV Recreate this example with yields rising to 6% instead of falling. What happenings to the price changes 50 50 50 50 1050 47.62 45.35 43.19 41.14 822.70 48.08 46.23 44.45 42.74 863.02 50 50 NUWE -5%, 20-year Bond 5% coupoi 5% yield 4% yield PV PY 50 47.62 48.08 50 45.35 46.23 50 43.19 44.45 41.14 42.74 39.18 41.10 37.31 39.52 35.53 38.00 33.84 36.53 50 32.23 35.13 50 30.70 33.78 29.23 32.48 27.84 31.23 26.52 30.03 25.25 28.87 24.05 27.76 22.91 26.70 21.81 25.67 20.78 24.68 19.79 23.73 1050 395.73 479.21 1000 sum Percentage change 1044.52 4.45 1000 1135.90 13.591

Answer 1

The value of the bond is inversely related to the Yield of the Bond ie Higher the yield lower will be the bond value as proved by the calculations in the table below.

The longer the duration of the bonds the more the bonds tend to be volatile compared to short term bonds. As you can see the from the above example the 20 years bond is more volatile as the changes in its value of bond are more compared to the changes in the values of shorter duration bond.

Therefore we see more changes in value of longer duration bonds ie from 1000 to 1135,90(4% yield) and 885.30(6%yield).
However, the changes in the value of 5 year bond changed only from 1000 to 1044.518(4% yield) and 957.876(6%yield).

5% 5 year Bond
Year	5% Coupon	5% Yield PV	4% Yield PV	6% Yield PV
1	50	47.619	48.077	47.170
2	50	45.351	46.228	44.500
3	50	43.192	44.450	41.981
4	50	41.135	42.740	39.605
5	1050	822.702	863.023	784.621
Present value		1000.000	1044.518	957.876
Percentage change			4.452	-4.212

5% 20 year Bond
Year	5% Coupon	5% Yield PV	4% Yield PV	6% Yield PV
1	50	47.62	48.08	47.17
2	50	45.35	46.23	44.50
3	50	43.19	44.45	41.98
4	50	41.14	42.74	39.60
5	50	39.18	41.10	37.36
6	50	37.31	39.52	35.25
7	50	35.53	38.00	33.25
8	50	33.84	36.53	31.37
9	50	32.23	35.13	29.59
10	50	30.70	33.78	27.92
11	50	29.23	32.48	26.34
12	50	27.84	31.23	24.85
13	50	26.52	30.03	23.44
14	50	25.25	28.87	22.12
15	50	24.05	27.76	20.86
16	50	22.91	26.70	19.68
17	50	21.81	25.67	18.57
18	50	20.78	24.68	17.52
19	50	19.79	23.73	16.53
20	1050	395.73	479.21	327.39
Present Value		1000	1135.90	885.30
Percentage change			13.590	-11.470