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. Bond prices and bond yields are always at risk of fluctuating in value, especially in periods of rising or falling interest rates. Let's discuss the relationship between bond prices and yields.

Bond Prices and Yields: An Overview

If you buy a bond at issuance, the bond price is the face value of the bond, and the yield will match the coupon rate of the bond. That is, if you buy a bond that pays 1% interest for three years, that's exactly what you'll get. 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.

However, imagine you buy the same bond above. Then, six months after your purchase, the same bond issues another public offering. However, this bond is now offering 2% interest. You've already locked into your rate, but surely this change in interest rates will impact the value of your bond?

In secondary markets, bonds may be sold for a premium or discount on their face value. Therefore, although you might've paid $1,000 for your bond when it was issued, the same bond may now be worth $980 or $1,020, depending on external factors like prevailing interest rates.

Three factors primarily determine the price of a bond on the open market. They are the credit quality of the bond, the term till bond maturity, and the current supply and demand for bonds.

Reading Bond Quotes

The image below pulls the prevailing bond prices for United States Treasury bills and bonds with varying maturities. Note that Treasury bills, which mature in a year or less, are quoted differently from bonds, hence the wide difference in price.

Looking at the Treasury bonds with maturities of two years or greater, you'll notice the price is relatively similar around $100. For bonds, $100 is often used as the benchmark par value. That is, if a bond was purchased at issuance, it would often be purchased in fixed, "clean" increments like $100 and would receive only coupon rate payments.

However, none of these prices reflect $100. Since their issuance, their price has either increased (see the five-year bond) or decreased (see the two-year, 10-year, or 30-year bond). You'll also note each bond's coupon rate no longer matches the current yield.

The two furthest columns measure the change in yield. This change is often measured in basis points, or hundredths of a percent. Therefore, the 30-year bond has increased 33 basis points over the past month, or 0.33%.

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 $98.90 and you were to buy a $100,000 two-year Treasury bond, you would pay ~$98,900.

In the example above, the two-year Treasury is trading at a discount. This means 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. Trading at a discount means the price of the bond has declined since it was issued; it is now cheaper to buy the bond than when it was issued.

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.

Considering Bond Prices (Discount vs. Premium)

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

Consider an example where a bond pays a coupon of 5%. All issuances of this bond are sold at par value. Then, macroeconomic conditions in the world worsen, and the Federal Reserve begins lower the federal funds rate. By extension, many other rates begin to drop, and the prevailing rate of interest in the market now is only 2%.

Instead of settling for 2%, investors realize they can instead try to buy the 5% bond in secondary markets. However, secondary markets often price in prevailing rates. Instead of being able to buy the bonds at par value, the bond's price has become more expensive. You'll still get your 5% coupon rate; however, you'll have overpaid for the bonds and your true yield will be closer to 2%.

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. Because you can earn a better return simply by buying new issuances of bonds, sellers must entice buyers to buy secondary bonds by marking their securities down to a discounted price.

Considering Bond Yields

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 make 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.

Even yield to maturity does have 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.

Considering Inflation

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?

The answer lies in the prevailing market rate. Therefore, as the Federal Reserve assesses inflation, the bond market is at risk for valuation changes. When inflation is a concern, the Fed may consider raising interest rates. Higher interest rates make the existing lower interest rates less desirable. In addition, the discount rate used to calculate the bond's price increases. For these two reasons, the bond's price falls.

The opposite would occur when inflation expectations fall. As inflation concerns decrease, the Federal Reserve may be more willing to decrease interest rates. Lower rates make existing bonds more desirable in secondary markets. In addition, lower rates mean the discount rate used to calculate the bond's price decreases. For these two reasons, the bond's price increases.

Considering the Discount Rate

Inflation expectation is the primary variable that influences the discount rate investors use to calculate a bond's price. From the photo above, each Treasury bond has a different yield, and the longer maturities often have higher yields than shorter yields.

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. You'll note this always isn't the case, as the five-year bond has a higher maturity than the 10-year bond. This means the broad market is placing more risk surrounding interest rates during the shorter period compared to the longer period.

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. 

The Bottom Line

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. When interest rates are on the rise, bond prices generally fall. When interest rates are lower, bond prices tend to rise. Bond price and bond yield are often inversely related.