Question

22. Now, suppose that the answer from question 21 that you got for Macaulay's duration was 2.65 years (it isn't), and using the same information given in that problem (3-year semi-annual coupon bond with a $1,000 par value, an 8 percent annual coupon rate, and a 6 percent annual yield to maturity) use modified duration to calculate the estimated percent change in the bond's price if interest rates were to fall by ½ percent and state whether the price rises or falls.

Answer 1

Duration

Period	CF	PVF@3%	Disc CF	Weights	Weights * Period
1	$      40.00	0.9709	$      38.83	0.0368	0.0368
2	$      40.00	0.9426	$      37.70	0.0358	0.0715
3	$      40.00	0.9151	$      36.61	0.0347	0.1042
4	$      40.00	0.8885	$      35.54	0.0337	0.1349
5	$      40.00	0.8626	$      34.50	0.0327	0.1637
6	$      40.00	0.8375	$      33.50	0.0318	0.1907
6	$1,000.00	0.8375	$    837.48	0.7944	4.7667
Duration of the Bond	5.4684

Modified duaration :
Modified duration = Duration / [ 1 + YTM ]
It specifies% change in Price in opposite direction due to 1% change in YTM.

= 5.4684 / (1+0.06)

= 5.4684 / (1.06)

= 5.1589

i,e., for 1 % change in YTM the price of the bond changes by 5.16 %

in the given question YTM changes by 0.5% so the modifies duration will be 5.1589*0.5

= 2.5794

i,e., for 0.5 % change in YTM the price of the bond changes by 2.58 %

In the given scenario as the YTM falls by 0.5% the price of the bond increases by 2.58%

Pls do rate, if the answer is correct and comment, if any further assistance is required.