Why do interest rates have an inverse relationship with bond prices?

Bonds have an inverse relationship to interest rates - when interest rates rise bond prices fall, and vice-versa. At first glance, the inverse relationship between interest rates and bond prices seems somewhat illogical, but upon closer examination, it makes good sense.

An easy way to grasp why bond prices move in the opposite direction as interest rates is to consider zero-coupon bonds, which don't pay coupons but derive their value from the difference between the purchase price and the par value paid at maturity: For instance, if a zero-coupon bond is trading at $950 and has a par value of $1,000 (paid at maturity in one year), the bond's rate of return at the present time is approximately 5.26%, which is equal to (1000 - 950) ÷ 950.

For a person to pay $950 for this bond, he or she must be happy with receiving a 5.26% return. But his or her satisfaction with this return depends on what else is happening in the bond market.

Bond investors, like all investors, typically try to get the best return possible. If current interest rates were to rise, giving newly issued bonds a yield of 10%, then the zero-coupon bond yielding 5.26% would not only be less attractive, it wouldn't be in demand at all. Who wants a 5.26% yield when they can get 10%?

To attract demand, the price of the pre-existing zero-coupon bond would have to decrease enough to match the same return yielded by prevailing interest rates. In this instance, the bond's price would drop from $950 (which gives a 5.26% yield) to $909.09 (which gives a 10% yield).

This is why zero-coupon bonds tend to be more volatile, as they do not pay any periodic interest during the life of the bond. Upon maturity, a zero coupon bondholder receives the face value of the bond.

Thus, the only value in zero-coupon bonds is the closer they get to maturity, the more the bond is worth. Further, there is limited liquidity for zero coupon bonds since their price is not impacted by interest rate changes. This makes their value even more volatile.

Zero coupon bonds are issued at a discount to par value. Yields on zero coupon bonds are a function of the purchase price, the par value and the time remaining until maturity. However, zero coupon bonds also lock in the bond’s yield, which may be attractive to some investors.

Still, zero-coupon bonds have unique tax implications that investors should understand before investing in them. Even though no periodic interest payment is made on a zero-coupon bond, the annual accumulated return is considered to be income, which is taxed as interest. The bond is assumed to gain value as it approaches maturity. The gain in value is not taxed at the capital gains rate but is treated as income.

Taxes must be paid on these bonds annually, even though the investor does not receive any money until the bond maturity date. This may be burdensome for some investors. However, there are some ways to limit these tax consequences.

Now that we have an idea of how a bond's price moves in relation to interest rate changes, it's easy to see why a bond's price would increase if prevailing interest rates were to drop. If rates dropped to 3%, our zero-coupon bond – with its yield of 5.26% – would suddenly look very attractive. More people would buy the bond, which would push the price up until the bond's yield matched the prevailing 3% rate.

In this instance, the price of the bond would increase to approximately $970.87. Given this increase in price, you can see why bond holders (the investors selling their bonds) benefit from a decrease in prevailing interest rates.

These examples also show how a bond's coupon rate is directly affected by national interest rates, and consequently, its market price. Newly-issued bonds tend to have coupon rates that match or exceed the current national interest rate.

When people refer to "the national interest rate" or "the fed," they're most often referring to the federal funds rate set by the Federal Open Market Committee (FOMC). This is the rate of interest charged on the interbank transfer of funds held by the Federal Reserve and is widely used as a benchmark for interest rates on all kinds of investments and debt securities.

For this reason, when the Federal Reserve increased interest rates in March 2017 by a quarter percentage point, the bond market fell. The yield on 30-year Treasury bonds dropped to 3.108% from 3.2%, the yield on 10-year Treasury notes fell to 2.509% from 2.575%, and the two-year notes' yield fell from 1.401% to 1.312%.

The Fed raised interest rates four times in 2018. After the last raise of the year announced on December 19, 2018, the yield on 10-year Treasury notes fell from 2.868% to 2.794%.

For a more detailed explanation of bond pricing and yield calculations, check out Advanced Bond Concepts.