Question

(Use Excel or similar) Pick a coupon rate, yield-to-maturity, and maturity length, T (don’t pick something stupid like zero percent). Compute the price of the bond. Compute the duration of the bond. One at a time, vary each of the three chosen numbers while allowing the price to adjust. See how the duration changes. Create three graphs with duration on the y-axis and coupon rate, ytm, and T on the x-axis.

Answer 1

Coupon rate	5%
Yield - to maturity	6%
Maturity (T)	10
Frequency	Annual

Face value 1000

Period	1	2	3	4	5	6	7	8	9	10
Cash flow	50	50	50	50	50	50	50	50	50	1050
PV	47.2	44.5	42.0	39.6	37.4	35.2	33.3	31.4	29.6	586.3
Bond price	926.4

Duration calculation
PV * period	47.2	89.0	125.9	158.4	186.8	211.5	232.8	251.0	266.4	5863.1
Macaulay Duration	8.0	years

Now, if we change coupon rate to 4%.

Coupon rate	4%
Yield - to maturity	6%
Maturity (T)	10
Frequency	Annual
Face value	1000
Period	1	2	3	4	5	6	7	8	9	10
Cash flow	40	40	40	40	40	40	40	40	40	1040
PV	37.7	35.6	33.6	31.7	29.9	28.2	26.6	25.1	23.7	580.7
Bond price	852.8
Duration calculation
PV * period	37.7	71.2	100.8	126.7	149.5	169.2	186.2	200.8	213.1	5807.3
Macaulay Duration	8.3	years

If we increase YTM to 7%.

Coupon rate	5%
Yield - to maturity	7%
Maturity (T)	10
Frequency	Annual
Face value	1000
Period	1	2	3	4	5	6	7	8	9	10
Cash flow	50	50	50	50	50	50	50	50	50	1050
PV	46.7	43.7	40.8	38.1	35.6	33.3	31.1	29.1	27.2	533.8
Bond price	859.5
Duration calculation
PV * period	46.7	87.3	122.4	152.6	178.2	199.9	218.0	232.8	244.8	5337.7
Macaulay Duration	7.9	years

If we increase YTM to 4%.

Coupon rate	5%
Yield - to maturity	4%
Maturity (T)	10
Frequency	Annual
Face value	1000
Period	1	2	3	4	5	6	7	8	9	10
Cash flow	50	50	50	50	50	50	50	50	50	1050
PV	48.1	46.2	44.4	42.7	41.1	39.5	38.0	36.5	35.1	709.3
Bond price	1081.1
Duration calculation
PV * period	48.1	92.5	133.3	171.0	205.5	237.1	266.0	292.3	316.2	7093.4
Macaulay Duration	8.2	years

If we increase the maturity to 14 years.

Coupon rate	5%
Yield - to maturity	6%
Maturity (T)	10
Frequency	Annual
Face value	1000
Period	1	2	3	4	5	6	7	8	9	10	11	12	13	14
Cash flow	50	50	50	50	50	50	50	50	50	50	50	50	50	1050
PV	47.2	44.5	42.0	39.6	37.4	35.2	33.3	31.4	29.6	27.9	26.3	24.8	23.4	464.4
Bond price	907.1
Duration calculation
PV * period	47.2	89.0	125.9	158.4	186.8	211.5	232.8	251.0	266.4	279.2	289.7	298.2	304.7	6501.8
Macaulay Duration	10.2	years