Question

Discuess the relationship between the bond fair price and the market interest rates

Answer 1

Answer to question

Bond fair price means the current market price of the bond i.e. the price we have to pay now to purchase the bond. And for this bond we will receive the fixed coupon amount every period till the maturity of the bond and at the end of the maturity we will receive an amount which will be equal to the face value of the bond.

Market interest rate means the rate of interest prevailing in the market and it is also called as Yield to Maturity i.e. Ytm. It is not fixed always. It is the rate by which we calculate the price of the bond today.

There is an inverse relationship between the bond fair price and the market interest rate. When the market interest rate decrease then the price of the bond increases and vice versa.

For example-

Take a 2 year bond of face value ₹100, coupon rate 10% annually i.e. ₹10, interest rate/ytm is 10%.

Then it's fair price will be= ₹10*PVAF(10%,2) + ₹100*PVIF(10%,2)
=₹17.36 + ₹82.65
=₹100 means the bond is at par because the ytm and coupon rates are same.

Now if the interest rate changes to 8% then the price of the bond will be= ₹10*PVAF(8%,2) + ₹100*PVIF(8%,2)
=₹17.83 + ₹85.74
=₹103.57
Price of bond increases due to decrease in interest rate.

Now if the interest rate changes to 12% then the price of the bond will be= ₹10*PVAF(12%,2) + ₹100*PVIF(12%,2)
=₹16.90 + ₹79.71
=₹96.61
Price of bond decreases due to increase in interest rate.

Conclusion :- We can see that there is an inverse relationship between the bond fair price and the market interest rate.