Question

1. We consider to purchase 5-years zero-coupon bond with the nominal value of 1000 USD and YTM of 4 %. We would like to invest in this bond

a) For 3 years

b) For 7 years

What would be your yield/loss if the day after the bond purchase

a) YTM will increase by 1 %

b) YTM will decrease by 1 %

Answer 1

Today's Price of Bond:

(NOTE: Coupons will not be paid in zero coupon bonds. They are redeemed at Nominal Value and Issued at a discount. Therefore, Value at anytime will simply be the Present Value at that time)

Present Value = Future Value ÷ (1+i)ⁿ

where, i = interest rate and n = number of years

(i) For 3 years

Present Value = 1000 ÷ (1+0.04)³ = 1000 ÷ 1.1249 = $888.97

(ii) For 7 years

Present Value = 1000 ÷ (1+0.04)⁷ = 1000 ÷ 1.3159 = $759.94

Yield or Loss after 1 day:

(i) If yield increase by 1%:

New i = 4+1 = 5% = 0.05

For 3 years, Value of Bond = 1000 ÷ (1+0.05)³ = 1000 ÷ 1.1576 = $863.86

For 7 years, Value of Bond = 1000 ÷ (1+0.05)⁷ = 1000 ÷ 1.4071 = $710.68

Loss = Old Value - New Value

For 3 years = 888.97-863.86 = $25.11 and for 7 years = 759.94-710.68 = $49.26

(ii) If yield decreses by 1%:

New i = 4-1 = 3% = 0.03

For 3 years, Value of Bond = 1000 ÷ (1+0.03)³ = 1000 ÷ 1.0927 = $915.16

For 7 years, Value of Bond = 1000 ÷ (1+0.03)⁷ = 1000 ÷ 1.2299 = $813.07

Gain = New Value - Old Value

For 3 years = 915.16-888.97 = $26.19 and for 7 years = 813.07-759.94 = $53.13

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