Question

2) Assume that you have a 10 year Treasury Bond with a yield of 2.76%, coupon rate of 2.35%,   paying annual coupon payments. Assume the face value of the bond is $1,000. Shock the yield on the bond by 100 basis points up and down to determine the approximate duration and approximate convexity of the bond. Determine the approximate percentage change in the price of the bond because of the effects of duration and convexity when there is a 100 basis point increase in interest rates. How does this compare to the actual changes in the bond? What would be the approximate percentage change in the price of the bond because of the effects of duration and convexity when there is a 100 basis point decrease in interest rates?    Determine if you are immunized if your planning horizon is 7.32 years. Please explain your answer.

Answer 1

Lets first understand the concept of duration of the bond:- It is measure of the sensitivity of price of the bond or other debt instrument to change in the interest rate. You can also say that bond duration is the time period in to which the bond holder will receive the principle value of the bond. Higher the duration will be more prone to the credit and interest rate risk. Lower duration is favorable.

Lets get the duration from the above financial:-

Face Value	$1,000
Coupon	2.35%
Yield	2.76%
Time	10

Calculation of the duration is given below:-

Time	Cash flow	PV of cash flow	(PV/Total)* Time
1	$24	$22.87	0.0237
2	$24	$22.25	0.0461
3	$24	$21.66	0.0674
4	$24	$21.08	0.0874
5	$24	$20.51	0.1063
6	$24	$19.96	0.1241
7	$24	$19.42	0.1409
8	$24	$18.90	0.1568
9	$24	$18.39	0.1716
10	$1,024	$779.56	8.0817
Total		$964.59	9.0061

Duration given in the above table is 9.0061 years.

Lets shock the yield by 100 basis point upwards.

Face Value	$1,000
Coupon	2.35%
Yield	3.76%
Time	10

Calculation of the duration is given below:-

Time	Cash flow	PV of cash flow	(PV/Total)* Time
1	$24	$22.65	0.0256
2	$24	$21.83	0.0494
3	$24	$21.04	0.0714
4	$24	$20.27	0.0917
5	$24	$19.54	0.1105
6	$24	$18.83	0.1278
7	$24	$18.15	0.1437
8	$24	$17.49	0.1582
9	$24	$16.86	0.1716
10	$1,024	$707.60	8.0022
Total		$884.26	8.9520

Duration in this is 8.9520 years.

Change in percent when yield changes 100 basis point upward is 0.6007%.

Lets shock the yield by 100 basis point Downwards.

Face Value	$1,000
Coupon	2.35%
Yield	1.76%
Time	10

Calculation of the duration is given below:-

Time	Cash flow	PV of cash flow	(PV/Total)* Time
1	$24	$23.09	0.0219
2	$24	$22.69	0.0431
3	$24	$22.30	0.0635
4	$24	$21.92	0.0832
5	$24	$21.54	0.1022
6	$24	$21.16	0.1205
7	$24	$20.80	0.1382
8	$24	$20.44	0.1552
9	$24	$20.09	0.1716
10	$1,024	$859.64	8.1585
Total		$1,053.67	9.0579

Duration in this is 9.0579 years.

Change in percent when yield changes 100 basis point upward is 0.5751%.