Question

Bond	Coupon Rate	Yield	Maturity	Duration
A	7%	3.5%	4 Years
B	Zero Coupon	5.25%	8 Years

A) Compute the duration of each bond, assuming annual interest payments for the coupon bonds. Show your work below. (10 points)

B) What is the duration-predicted price change for each bond for a 1% increase in rates? Show your work below. (15 points)

Answer 1

(A) As bond B is a zero coupon bond, its duration should equal its maturity of 8 years. Hence, Bond B Duration = 8 years

Bond A duration is calculated as show below:

(B) Bond A:

Change in Yield = 1 %

% Change in Price = - Modified Duration x % Change in YTM = - 3.53 x (0.01) = - 0.0353 or -3.53 %

Original Price = $ 1128.56

Absolute Value of Price Change = 0.0353 x 1128.56 = $ 39.8382

New Bond Price = 1128.56 - 39.8382 = $ 1088..72

Bond B:

Bond Price = 1000 / (1.0525)^(8) = $ 664.084 (assuming a bond face value of $ 1000)

Change in Yield = 1 %

% Change in Price = - 8 x 0.01 = - 0.08 or - 8 %

Absolute Value of Price Change = (0.08 x 664.084) = $ 53.1267

New Price = 664.084 - 53.1267 = $ 610.957

Weighted Proportion of Bond | PV as % of Bond Price | Market Price Recouped (C x BOND Bond Parameters Year Cash Flow PV factor at 10 % PV of Cash Flow (D x E) 3.5% 2 YTM 3 Coupon Payments 4 Maturi 5 Coupon Rate 6 Face Value (in $) 70 70 70 1070 0.966183575 0.9335107 0.901942706 0.871442228 67.63 65.35 63.14 932.44 0.059928567 0.057901997 0.055943959 0.826225477 0.06 0.1 0.1 3.30 3.65 3.53 Annual 4 years 7%) 1000 Bond Price 1128.56 Macaulay's Duration Modified Duration

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