Question

Interest Rate Risk. Both Bond Bill and Bond Ted have 6.2 percent coupons, make semiannual payments, and are priced at par value. Bond Bill has 5 years to maturity, whereas Bond Ted has 25 years to maturity. If interest rates suddenly rise by 2 percent, what is the percentage change in the price of Bond Bill? Of Bond Ted? Both bonds have a par value of $1,000. If rates were to suddenly fall by 2 percent instead, what would the percentage change in the price of Bond Bill be then? Of Bond Ted? Illustrate your answers by graphing bond prices versus YTM. What does this problem tell you about the interest rate risk of longer-term?

Answer 1

At 2% increase	Bill	Ted
Price	$919.29	$788.81
% Change	-8.07%	-21.12%
At 2% decline
Price	$1,089.36	$1,307.73
% Change	8.94%	30.77%

Longer term bonds have greater risk.

AutoSaver HD Book1 - Excel Sign in - 0 X File Home Insert Draw Page Layout Formulas Data Review View Help Tell me what you want to do Share Comments - 10 A = = 0 insert E 47 Z - Calibri BIU - B -A A = E Paste - General 3$ -% Numberto Delete - Format . Conditional Format as Formatting Table - Styles Cell Styles Sort & Find & Filter - Select Editing Font Alignment Cells Clipboard FZ - for E к 1 Bill 2 0.062 3 1000 4 1000 Ted 0.062 1000 1000 F G H Rate Bill Ted 0.062 1000 1000 0.082 =C10 =D10 0.042 =C13 =D13 Bond Prices 25 1400 1200 1000 800 7 0.062 0.062 00 Bill Ted 10 --PV(8.2%/2,$C$5*2,$C$2*$C$4/2,$C$4) --PV18.2%/2,$D$5*2,$D$2$D$4/2,$D$4) 11 =(C10-C3}/C3 =D10-D3)/D3 13 --PV(4.2%/2,$C$5*2,$C$2*$C$4/2,$C$4) --PV[4.2%/2,$D$5*2,$D$2$D$4/2,$D$4) 14 =(C13-04/04 =(D13-04)/D4 6.20% 8.209 Bill Ted - 17 18 19 Sheet1 Sheet2 Sheet3 Sheet4 Sheets Sheet6 Sheet7 Ready

Answer 2

- x V fc =(B7-B3)/B3 Change in bond prices 1 2 Current price: 3 Bond Bill 4 Bond Ted 5 6 If interest rate rise by 2% $ 1,000.00 $ 1,000.00 7 Bond Bill $ 919.29 -8.07% =PV(8.2%/2,5*2,62/2,1000)*-1 $ 788.81 -21.12% =PV(8.2%/2,25*2,62/2,1000)*-1 8 Bond Ted 9 10 If interest rate fall by 2% 11 Bond Bill $ 1,089.36 8.94% =PV(4.2%/2,5*2,62/2,1000)*-1 12 Bond Ted $ 1,307.73 30.77% =PV(4.2%/2,25*2,62/2,1000)*-1 13 14 Lower coupon bonds will have high interest rate risk.

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