# Understand bond prices and yields

Bond prices are worthy of attention every day as a useful indicator of the direction of interest rates and more generally the direction of future economic activity. Not accidentally, they are an important part of a well-managed and diversified investment portfolio.

Everyone knows that high-quality bonds are a relatively safe investment. But few people understand how bond prices and yields work.

In fact, most of the information has nothing to do with individual investors. It is only used in the secondary market, and bonds are sold at prices below face value.

In other words, if you buy a bond with an interest rate of 1% for 3 years, this is exactly what you get. When the bond matures, its face value will be returned to you. Unless you want to sell it, you are not interested in its value at any time in between.

This is when understanding bond price trends becomes important.

## Read bond market

The picture below is from Bloomberg. Please note that the quotes for Treasury bills maturing in one year or less are different from bonds. Treasury bills are quoted at a discount on face value, and the discount is expressed as an annual interest rate based on 360 days a year.For example, when you buy Treasury bills, you will get a discount of 0.07*90/360=1.75%.

Let’s see how we calculated this number. The price of a bond consists of the “handle” or the integer part of the quote. For example, in a two-year Treasury bond, it is 99. Commonly known as “Large Number”. The handle of the two-year treasury bond is 99, and the 32nd place is 29. We must convert these values ​​into percentages to determine the dollar amount we will pay for the bond. To do this, we first divide 29 by 32. This is equal to 0.90625. Then we add the amount to 99 (handle), which equals 99.90625. Therefore, 99-29 is equal to 99.90625% of the face value of US\$100,000, or US\$99,906.25.

## Calculate the dollar price of the bond

The dollar price of a bond represents a percentage of the bond’s principal balance, also known as the face value. After all, a bond is just a loan, and the principal balance or face value is the loan amount. Therefore, if the bond is quoted at 99-29 and you want to buy a two-year Treasury bond of 100,000 USD, you will pay 99,906.25 USD.

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### Key points

• The bond yield is the discount rate that links the bond’s cash flow to its current dollar price.​​​
• When inflation expectations increase, interest rates increase, and so does the discount rate used to calculate bond price increases.
• This makes the price of bonds fall.
• When inflation expectations fall, the situation is just the opposite.

Two-year Treasury bonds are traded at a discount, which means that its trading price is lower than its face value. If it is a “parity transaction”, its price is 100. If it is a premium transaction, its price will be greater than 100.

To understand discount and premium pricing, remember that when you buy bonds, you buy them to pay for coupons. Different bonds pay coupons at different frequencies. The coupon payment is in arrears.

When you buy a bond, you have the right to obtain the coupon percentage from the date of settlement of the transaction to the maturity of the next coupon payment date. The previous owner of the bond is entitled to the percentage of coupon payment from the last payment date to the transaction settlement date.

Because you will become the record holder when the coupon is actually paid and you will receive the full coupon payment, you must pay the former owner his or her percentage of the coupon payment when the transaction is settled.

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

## Discount vs. premium pricing

When will someone pay more than the face value of the bond? The answer is simple: when the coupon rate of the bond is higher than the current market interest rate.

In other words, investors will receive higher interest payments from high-priced bonds that are higher than the current market environment.

The same is true for bonds priced at discounted prices; they are priced at discounted prices because the coupon rate of the bond is lower than the current market interest rate.

## Yield tells (almost) everything

The rate of return relates the dollar price of the bond to its cash flow. The cash flow of bonds includes coupon payment and principal return. The principal is returned at the end of the bond term, which is called the maturity date.

Bond prices and bond yields are excellent indicators of the overall economy, especially inflation indicators.

The bond yield is the discount rate that can be used to make the present value of all bond cash flows equal to its price. In other words, the price of a bond is the sum of the present value of each cash flow. Each cash flow uses the same discount factor for present value. This discount factor is the rate of return.

Intuitively, discounts and premium pricing make sense. Since the par payment amount of discount bonds is less than the par payment amount of premium bonds, if we use the same discount rate to price each bond, the present value of the bond with the smaller par payment amount is smaller. Its price will be lower.

In fact, there are several different yield calculations for different types of bonds. For example, it is difficult to calculate the yield of a callable bond because the date when the bond may be redeemed is unknown. The total amount of coupon payment is unknown.

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

But even the yield to maturity has its drawbacks. The yield to maturity calculation assumes that all coupon payments are reinvested at the yield to maturity. This is extremely unlikely because it is impossible to predict future interest rates.

## Why bond yield is inversely proportional to its price

The bond yield is the discount rate (or factor) that equals the bond’s cash flow 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 bond prices rises and bond prices fall.

When inflation expectations fall, the situation is just the opposite.

## How to determine the appropriate discount rate

Inflation expectations are the main variable that affects the discount rate investors use to calculate bond prices. 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.

This is because the longer the maturity of the bond, the greater the risk of rising inflation in the future. This determines the current discount rate required to calculate bond prices.

When determining the appropriate discount rate, credit quality or the possibility of default by the bond issuer is also considered. The lower the credit quality, the higher the yield and the lower the price.

## Bond prices and the economy

Inflation is the biggest enemy of bonds. When inflation expectations rise, interest rates rise, bond yields rise, and bond prices fall.

This is why the bond price/yield rate, or the price/yield rate of bonds of different maturities, is an excellent predictor of future economic activity.

To understand the market’s forecast of future economic activity, you only need to look at the yield curve. The yield curve in Figure 1 predicts that between the 6th and 24th months, the economy will slow down slightly and interest rates will drop slightly. After 24 months, the yield curve tells us that the economy should grow at a more normal rate.

## Why is it important

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

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