Use the following information to determine duration and convexity, and then use those metrics to predict...

Use the following information to determine duration and convexity, and then use those metrics to predict a percentage change in the price of the bond assuming a 130 basis-point increase in yield. Time-to-maturity = 7 years, Coupon rate = 4%, paid semi-annually, Current bond-equivalent yield-to-maturity = 6.0%.

Expert Solution

We use excel to find the duration and convexity

We first chalk out the cash-flows

Bond pays (4%/2) 2% coupon every 6 months and has a face value of $1000

Duration = Time weighted PV / PV

Convexity = Time^2 weighted PV / (PV*(1+ytm/2)^2)

Term	Period	Cash-flow	Present value	Time weighted PV	Time^2 weighted PV
0.5	1	20	19.41747573	9.708737864	9.708737864
1	2	20	18.85191818	18.85191818	28.27787727
1.5	3	20	18.30283319	27.45424978	54.90849956
2	4	20	17.76974096	35.53948192	88.84870479
2.5	5	20	17.25217569	43.13043922	129.3913177
3	6	20	16.74968513	50.2490554	175.8716939
3.5	7	20	16.26183023	56.91640579	227.6656232
4	8	20	15.78818469	63.15273875	284.1873244
4.5	9	20	15.32833465	68.97750591	344.8875296
5	10	20	14.8818783	74.40939149	409.2516532
5.5	11	20	14.44842553	79.46634043	476.7980426
6	12	20	14.0275976	84.16558562	547.0763066
6.5	13	20	13.6190268	88.5236742	619.6657194
7	14	1020	674.3401619	4720.381134	35402.8585
			887.0392686	5420.926658	38799.39753

		Duration	6.111258937
		Convexity	41.22946377

We get

Duration	6.111258937
Convexity	41.22946377

Percentage change in price of the bond = -Duration*Change in yield + 0.5*Convexity*(Change in yield)^2

For a 130 basis-point increase in yield

Percentage change in price of the bond = -6.111258937*0.013+0.5*41.22946377*(0.013*0.013)

Percentage change in price of the bond = -0.0759 = -7.59%

jeff jeffy answered 2 years ago

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