Understanding Bond Prices and Yields

Bond prices are worth watching from day to day as a useful indicator of the direction of interest rates and, more generally, future economic activity. Not incidentally, they’re an important component of a well-managed and diversified investment portfolio.

Everybody knows that high-quality bonds are a relatively safe investment. But far fewer understand how bond prices and yields work.

In fact, much of this information is irrelevant to the individual investor. It is used only in the secondary market, where bonds are sold for a discount to their face value.

That is, if you buy a bond that pays 1% interest for 3 years, that’s exactly what you’ll get. And when the bond matures, its face value will be returned to you. Its value at any time in between is of no interest to you unless you want to sell it.

And that’s when it becomes important to understand the movements of bond prices.

Reading Bond Quotes

The chart below is taken from Bloomberg. Note that Treasury bills, which mature in a year or less, are quoted differently from bonds. T-bills are quoted at a discount from face value, with the discount expressed as an annual rate based on a 360-day year. For example, you will get a 0.07*90/360=1.75% discount when you purchase the T-bill. 

Figure 1:

Let’s look at how we calculated this number. A bond’s price consists of a handle, or the whole number part of the price quote. In the two-year Treasury, for example, that’s 99. It’s colloquially called the “big number.” The two-year Treasury’s handle is 99, and the 32nds are 29. We must convert those values into a percentage to determine the dollar amount we will pay for the bond. To do so, we first divide 29 by 32. This equals .90625. We then add that amount to 99 (the handle), which equals 99.90625. So, 99-29 equals 99.90625% of the par value of $100,000, which equals $99,906.25.

Calculating a Bond’s Dollar Price

A bond’s dollar price represents a percentage of the bond’s principal balance, otherwise known as par value. A bond is simply a loan, after all, and the principal balance, or par value, is the loan amount. So, if a bond is quoted at 99-29, and you were to buy a $100,000 two-year Treasury bond, you would pay $99,906.25.

The two-year Treasury is trading at a discount, which means that it is trading at less than its par value. If it were “trading at par,” its price would be 100. If it were trading at a premium, its price would be greater than 100.

To understand discount versus premium pricing, remember that when you buy a bond, you buy them for the coupon payments. While different bonds make their coupon payments at different frequencies, the payments are typically dispersed semi-annually.

When you buy a bond, you are entitled to the percentage of the coupon that is due from the date that the trade settles until the next coupon payment date. The previous owner of the bond is entitled to the percentage of that coupon payment from the last payment date to the trade settlement date.

Because you will be the holder of record when the actual coupon payment is made and will receive the full coupon payment, you must pay the previous owner his or her percentage of that coupon payment at the time of trade settlement.

In other words, the actual trade settlement amount consists of the purchase price plus accrued interest.

Discount Vs. Premium Pricing

When would someone pay more than a bond’s par value? The answer is simple: when the coupon rate on the bond is higher than current market interest rates.

In other words, the investor will receive interest payments from a premium-priced bond that are greater than could be found in the current market environment.

The same holds true for bonds priced at a discount; they are priced at a discount because the coupon rate on the bond is below current market rates.

Yield Tells (Almost) All

A yield relates a bond’s dollar price to its cash flows. A bond’s cash flows consist of coupon payments and return of principal. The principal is returned at the end of a bond’s term, known as its maturity date.

A bond’s yield is the discount rate that can be used to make the present value of all of the bond’s cash flows equal to its price. In other words, a bond’s price is the sum of the present value of each cash flow. Each cash flow is present-valued using the same discount factor. This discount factor is the yield.

Intuitively, discount and premium pricing makes sense. Because the coupon payments on a bond priced at a discount are smaller than on a bond priced at a premium, if we use the same discount rate to price each bond, the bond with the smaller coupon payments will have a smaller present value. Its price will be lower.

In reality, there are several different yield calculations for different kinds of bonds. For example, calculating the yield on a callable bond is difficult because the date at which the bond might be called is unknown. The total coupon payment is unknown.

However, for non-callable bonds such as U.S. Treasury bonds, the yield calculation used is a yield to maturity. In other words, the exact maturity date is known and the yield can be calculated with near-certainty.

But even yield to maturity has its flaws. A yield to maturity calculation assumes that all the coupon payments are reinvested at the yield to maturity rate. This is highly unlikely because future rates can’t be predicted.

Why a Bond’s Yield Moves Inversely to Its Price

A bond’s yield is the discount rate (or factor) that equates the bond’s cash flows to its current dollar price. So, what is the appropriate discount rate or conversely, what is the appropriate price?

When inflation expectations rise, interest rates rise, so the discount rate used to calculate the bond’s price increases, and the bond’s price falls.

The opposite would occur when inflation expectations fall.

How to Determine the Appropriate Discount Rate

Inflation expectation is the primary variable that influences the discount rate investors use to calculate a bond’s price. But as you can see in Figure 1, each Treasury bond has a different yield, and the longer the maturity of the bond, the higher the yield.

That’s because the longer a bond’s term to maturity is, the greater the risk is that there could be future increases in inflation. That determines the current discount rate that is required to calculate the bond’s price.

The credit quality, or the likelihood that a bond’s issuer will default, is also considered when determining the appropriate discount rate. The lower the credit quality, the higher the yield and the lower the price. 

Bond Prices and the Economy

Inflation is a bond’s worst enemy. When inflation expectations rise, interest rates rise, bond yields rise, and bond prices fall.

That’s why bond prices/yields, or the prices/yields of bonds with different maturities, are an excellent predictor of future economic activity.

To see the market’s prediction of future economic activity, all you have to do is look at the yield curve. The yield curve in Figure 1 predicts a slight economic slowdown and a slight drop in interest rates between months six and 24. After month 24, the yield curve is telling us that the economy should grow at a more normal pace.

Why It Matters 

Understanding bond yields is key to understanding expected future economic activity and interest rates. That helps inform everything from stock selection to deciding when to refinance a mortgage. Use the yield curve as an indication of potential economic conditions to come.