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# Bond prices and interest rates

Dec 16, 2010

Why do bond prices have an inverse relationship with interest rates? While it seems illogical that the value of a bond will fall when interest rates increase and rise when the interest rates fall, on close examination it makes sense. In this article we will explain to you how this works.

For this, we will consider a zero coupon bond. A zero coupon bond does not pay coupons (or interest payments). These bonds return the accrued interest and principal (or par value) to the investor at the time of maturity. Zero coupon bonds derive their value from the difference between the purchase price and the par value (also the face value of the bond) paid at maturity.

Let us assume that a hypothetical company had to raise money. For this it issues a zero coupon bond with a par value of Rs 1,000 and a coupon rate of 10% with a maturity of 2 years.

The price at which the bond should trade is derived by the following formula.

##### Par Value -------------------------------------------------- (1+coupon rate)^time for maturity

Using this formula (1000/(1+10%)^2), we arrive at a price of = Rs 826

Hence when issued, an investor will buy this bond at Rs 826 which is a discount to par value. This will be as only at this price, the investors will receive 10% returns on his investment when the bond matures. However, say the interest rates go up and the same company now has to pay 15% to raise money. A bond investor like an equity investor also seeks to maximise his return. Hence, in case an investor now buys the same bond, he will pay only Rs 756. This is because only at this rate will he be able to receive 15% on his investment. Hence when interest rates move up, the value of the bond falls.

Similarly, if the interest rate falls to 5%, the bond's value will increase. A 10% coupon bond will be more attractive in the market as the bonds are now being issued by the same company with a coupon rate of only 5%. Hence an investor will pay more for the 10% bond. By our calculation, the bond will now be worth Rs 907.

Conclusion:

We have seen how bond prices are affected when interest rates move. With a number of companies now issuing bonds, an investor should keep this basic relationship in mind for investing profitably.

2 Responses to "Bond prices and interest rates"

pramod

Dec 22, 2010

Rule of thumb, longer the period more the risk. Hence investors would seek a premium for that. Higher rate of return for long term bonds is expected, but comparing two offerings of different maturity is speculative as it depends on how interest rates pan out in future.

Dec 16, 2010

What about the time value of money? How is the comparison done between zero coupon bond effectively paying 10% and maturing in the next two years and another bond effectively paying 15% but maturing in 10 years from now? How does maturity period impact the price of a bond?

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