Question

COULD YOU PRETTY PLEASE show this in WORKING NOT EXCEL

5. A bond has maturity of 7 years and pays a 7% coupon rate (with coupon paid annually).The bond sells at par value.

(1) Calculate the duration and convexity of the bond. 2

(2) Assuming its yield to maturity increases from 7% to 8% with maturity unchanged. Calculate the predicted price using modified duration rule, and the percentage error of this rule.

(3) Assuming its yield to maturity increases from 7% to 8% with maturity unchanged. Calculate the predicted price using the modified duration with convexity rule, and the percentage error of this rule.

Answer 1

Solution

1) Duration and Convexity of Bond

Duration of Bond

Time until Payment	Cash flow	PV of CF(discount factor 7%)	Weight	Col 1 * col 4
1	$7	$6.542	0.06542	0.06542
2	$7	$6.114	0.06114	0.12228
3	$7	$5.714	0.05714	0.17142
4	$7	$5.340	0.05340	0.21361
5	$7	$4.991	0.04991	0.24955
6	$7	$4.664	0.04664	0.27986
7	$107	$66.634	0.66634	4.66438
Total		$100.000	1.00000	5.76652

Duration of Bond : 5.767 Years

Convexity of Bond

Time until Payment	Cash flow	PV of CF(discount factor 7%)	T2+t	Col4*Col3
1	$7	$6.542	2	13.084
2	$7	$6.114	6	36.684
3	$7	$5.714	12	68.568
4	$7	$5.340	20	106.805
5	$7	$4.991	30	149.727
6	$7	$4.664	42	195.888
7	$107	$66.634	56	3731.504
Total		$100.000		4302.26

Covexity = 4302.26 / P(1+y)^2

= 4302.26 / 100(1.07)^2

= 4302.26/114.49

= 37.578

Convexity of Bond : 37.578

2) Predicted price using Modified duration rule and % of error rule

Duration rule assuming YTM increases to 8%

Predicted price change =

   = 7.515 /(1.08)*.01*100

= 6.96

Predicted Price change = 100-6.96 = $93.04

% of error rule

Duration rule predicts a % price change of = (7.515/1.07 )*0.01 = 0.0702 (7.02%)

Decrease in price of 0.06% (7.02-6.96)

3) Predicted price using modified duration with convexity rule & % of error rule if YTM increases to 8%

Duration with convexity rule

{(Duration/(1+y) * delta y ) +(0.5*convexity*(delta y)^2)} * Po

= {7.515/(1.07)*.01)+(0.5*37.578*(0.01)^2)} * 100

=(0.0702 + 0.00188)*100

= 7.208

Predicted Price Change = 100 - 7.208 = 92.792

% error is 0.248%

% error using duration with convexity rule is less than duration rule