How are interest rates, bond prices related?

There is an inverse relationship between bond prices and interest rates. When bond prices go up interest rates fall and when interest rates rise bond prices fall.

Even though it is clear that bond prices and interest rates are inversely related, there are also many other bond pricing relationships that an investor needs to understand. Mentioned below are some pricing relationships between bonds and interest rates.

  • An increase in a bond’s yield to maturity leads to a lesser price decrease than the price increase related with a decline of equal scale in yield. This is known as convexity.

  • Prices of long term bonds are likely to be more perceptive to interest rate amendments than prices of short term bonds.

  • For coupon bonds, as maturity increases, the likeliness of bond prices to change in yield increases at a declining rate.

  • Interest rate risk is inversely related to a bond’s coupon rate. (The sensitivity of a bond’s price to a change in yield is inversely related to the yield at maturity at which the bond is now selling.)

Let’s explain this with a help of an example

Let’s take the bond price as Rs.100 which pays a rate of interest called a coupon. Now, if the interest rates go up, the bond, in order to pay the same rates, will have to cost less. So, the same bond which was costing Rs.100 may be priced at Rs.90.

Now, let’s ignore the discount factor where the time frame of a bond is one year giving an interest rate of 4% and having principle amount as Rs.100. According to 4% rate of interest, the investor gets 4%*100= Rs.4. You pay Rs.100 for a bond today. At the end of year 1, you receive Rs.4.  Now you can buy a new 1 year bond which pays 4.25% on Rs.100 bond.

Thus, you tend to pay less for a bond which will now pay 4.25 % as interest and was originally paying 4% interest.

Now the question is much less are you required to pay.

Today: You Pay X.

Year 1: You Receive Rs4.00

Year 1 (Maturity): You Receive Rs.100

The interest you receive + the difference between the redemption price (Rs.100) and the initial price paid (X) should give you 4.25%: [(Rs100 - X) + Rs4.00] / X = 4.25%

Rs.104 - X = 4.25% * X

Rs.104 = 4.25% * X + X

Rs.104 = X (4.25% + 1)

Rs.104 / (1.0425) = X

X = Rs 99.76

So, to get a 4.25% yield, you would pay Rs.99.75 for a bond with a 4% coupon.

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