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A 9%, 16-year annual pay bond has a yield to maturity of 11% and Macaulay duration of 9

Business Oct 13, 2022

A 9%, 16-year annual pay bond has a yield to maturity of 11% and Macaulay duration of 9.25 years. If the market yield declines by 32 basis points, answer the following question:

 

Will the price of the bond go up or down, given the change in rates?

 

Why is the duration of the bond much lower than the maturity of the bond?

Expert Solution

THE CORRECT ANSWER IS AS FOLLOWS :-

Step-by-step explanation

PART - 1)

 

EFFECT OF FALL IN YIELDS ON BOND PRICE

A FALL IN YIELD OF BOND WILL LEAD TO A INCREASE IN PRICE OF THE BOND SINCE THE EXPECTATION OR REQUIRED RATE FALLS AND HENCE THE CASH FLOWS ARE TO BE DISCOUNTED AT LOWER YTM , LEADING TO HIGHER PRICE .

 

 

PART - 2)

 

WHY IS DURATION OF BOND LOWER THAN MATURITY

THE DURATION OF BOND IS GENERALLY LOWER THAN THE MATURITY SINCE THE CASH-FLOW IN FORM OF INTEREST OR COUPONS ARE RECEIVED BEFORE THE MATURITY OF BOND HENCE THE DURATION OF A COUPON PAYING BOND IS LOWER THAN MATURITY SINCE. CASHFLOWS OCCUR BEFORE THE MATURITY OF BOND ALSO .

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