Question

W w ullameu espalatul (1). A portfolio of two bonds. Each bond has a face value of $100. The first 4-year bond, Bl pays a coupon 10% with yield 12% (continuously compounded). The second 3-year bond, B2 pays a coupon 8% with yield 10% (continuously compounded). Estimate (a) (5 points) what is the duration of B1 and B2? (b) (5 points) what is the duration of the bond portfolio? (C) (5 points) if the yield increases by 1%, how much the bond portfolio value will decrease?

Answer 1

Answer :

(1) (a)

Duration of Bond = (( 1 + YTM ) / YTM ) - (( 1+YTM) + Period X (Coupon rate - Yield rate ) ) / Coupon rate x [ (1+YTM ) ⁿ - 1 ] + YTM

Here, YTM = Yield to Maturity

Duration of Bond B1 = (( 1+0.12 ) / 0.12 ) - ( (1+0.12 ) + 4 X ( 0.1 - 0.12 ) )/ 0.12 X [ (1+0.12 )⁴ -1

= 9.33 - ( 1.04 / - 0.8426 ) = 10.56 Years

Duration of Bond B2 = (( 1+0.1 ) / 0.1 ) - ( (1+0.1 ) + 3  X ( 0.08 - 0.1 ) )/ 0.1 X [ (1+0.1 )³ -1

= 11 - ( 1.04 / - 0.867 ) = 12.20 Years

(1) (b) Duration of the Bond Portfolio ( Average ) = (10.56 years + 12.20 years ) /2 = 11.38 Years

(1) ( c ) If Yield increases by 1% then the bond portfolio value will be decrease by 10.28%

= Duration / ( 1+ YTM ) = 11.38 Years / ( 1+9.75% +1% ) = 10.28%

Working :

Average Yield of a Bond be (( 12+10 ) +  ( 12+10 ) + ( 12+10 ) + 12 ) / 4 x 2 = 9.75%