Question

Consider the follwing bond:annual coupon 5%, .maturity 5 years, annual compounding frequency.

1. What is its relative price change if its required yield increases from 10% to 11%

2. What is its relative price change if its required yield increases from 5% to 6%

3. What conclusion can you draw from theses examples? Explain

Answer 1

1.let the FV of these bonds be $100.

PMT = $5

N = 5 YEARS

YTM = 10%

PV = $81.05

THE I/Y IS 11%

THE PV IS = $77.82

THE RELATIVE PRICE CHANGE IS ( 77.82-81.05)/ 81.05 * 100 = -3.98%

2. NOW THE YTM IS 5%

THE PV IS = 100

WHEN THE YTM IS 6%

THE PV IS = $95.78 .

THE RELATIVE CHANGE IN PRICE IS : ( 95.78 - 100)/ 100 * 100 = -4.22%

3.THE HIGHER THE YIELD THE LOWER WILL BE THE PRICE. THE PRICE OF THE BOND AND THE YIELD HAS AN INVERSE RELATIONSHIP. AS THE YIELD RISES THE PRICE OF THE BOND FALLS.