Question

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Suppose you have two bonds. The first one is a 1 year zero coupon bond. It...

Suppose you have two bonds. The first one is a 1 year zero coupon bond. It pays 1 at maturity and its price is 0.98 today. The second bond is a two year zero coupon bond that pays 1 at maturity and which price is 0.95 today.

a. What is the term structure of interest rate?

b. What is the duration and modified duration in these bonds?

c. What is the price movement in every bond after a 1% increase in the yield?

Expert Solution

A.

RATE ON 1 YEAR ZERO COUPON BOND

2.04% = (1/0.98) - 1

formula =(1/price)-1

B.

RATE ON 1 YEAR ZERO COUPON BOND

2.60% = (1/0.95)^(1/2) - 1

formula =(1/price)^(1/2)-1

YEAR

RATE OF INTEREST

1

2.04%

2

3.16%

(1.0260)^2/(1.0204^1)-1

C

DURATION OF 1 YEAR ZERO COUPON BOND = 1.0000 (NO COUPON THERE )

DURATION OF 2 YEAR ZERO COUPON BOND = 2.0000 (NO COUPON THERE )

C. MODIFIED DURATION ( DURATION / (1+ YIELD)

1 YEAR ZERO COUPON BOND

0.9800

1.0000

1.0000/(1+0.0204)

2 YEAR ZERO COUPON BOND

1.9493

2.0000

2.0000/(1+0.0260)

D.

CHANGE IN PRICE AFTER A 1% INCREASE IN YIELD

PRICE OF 1 YEAR ZERO COUPON BOND

0.9705

=PV(3.04%,1,,-1)

CHANGE IN PRICE = 0.9705 - 0.98 = -0.0095

PERCENTAGE CHANGE = -0.97% (-0.00095/0.98)

PRICE OF 2 YEAR ZERO COUPON BOND

0.9653

=PV (3.6%, 1,,-1)

CHANGE IN PRICE = 0.9653-0.95

0.0153

PERCENTAGE CHANGE = 1.61% (0.0153/0.95)

jeff jeffy answered 3 months ago

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