Consider the following analysis: “The rise and fall of a bond’s price has a dire

Question

Consider the following analysis: “The rise and fall of a bond’s price has a direct inverse relationship to its yield to maturity or interest rate. As prices go up, the yield declines and vice versa. For example, a $1,000 bond might carry a stated annual yield, known as the coupon of 8%, meaning that it pays $80 a year to the bondholder. If that bond was bought for $870, the actual yield to maturity would be 9.2% ($80 annual interest on $870 of principal)”. Do you agree with this analysis? Briefly explain.

Explanation / Answer

Yes, I agree with the analysis.

Bonds pay a fixed percentage of interest, called the coupon rate, which is calculated on their face value. In the example given, a $1,000 face value bond having a coupon rate of 8 percent, pays $80 in interest each year.

But the interest rates are bound to vary, ie; go up and down, according to the market conditions.

For instance, if in the example given, one year after the issue, the interest rates for similar bonds of maturity of 9 years goes up to 9%, then nobody will buy the bond for $1000, as the buyer will get only $80 or 8% return per year. Instead the prospective buyer can buy similar bonds from the market that would yield 9%. In other words the bond in our example would have a price on which $80 works out to 9%, ie; it may have a price equal to 80/.0.09 = $888.89.

Reverse is the case if the interest rates fall. For instance if the market interest rate falls to 7%, the bond holder would like to sell it at a higher price only, so that the interest of $80 works out to 7%. The price of the bond could be 80/0.07 = $1142.86.

Price and yield:

If the bond price falls to $800, one has to invest less to buy the bond. The effective interest rate (yield) would be $80 divided by $800which is equal to 10 percent. This reverse is true as well. If the bond price rises above the face value, one has to invest more and the yield comes down.

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