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# Bond Yield

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Bond yield is how much money you make from a bond. It’s the profit you get from investing in a bond. Bond yield and bond prices are linked but opposite: when one goes up, the other goes down. When a bond is first sold, its yield matches its coupon rate. There are various ways to figure out bond yields, like coupon yield and current yield. More complicated calculations, like yield to maturity (YTM), also help find a bond’s yield.

## Formula and Calculation of a Bond Yield

The easiest way to figure out a bond’s yield is by dividing its annual coupon payment by the bond’s face value. This is known as the coupon rate.

Coupon Rate = Annual Coupon Payment / Bond Face Value

For example, if a bond is worth \$1,000 and it pays \$100 in interest or coupons each year, then its coupon rate is 10%, calculated as \$100 divided by \$1,000.

## Understanding Bond Yields

Bonds act like loans to those who issue them. They’re seen as safe investments because their values don’t swing as much as stock prices do. They offer a steady income to investors and give bondholders a fixed amount of money regularly.

Investors earn interest on bonds over time and get the bond’s full value back when it matures. Bonds can be bought for more (premium) or less (discount) than their face value, which affects the yield they produce.

Bond ratings, determined by SEC-approved services, range from “AAA” for low-risk bonds to “D” for default or high-risk bonds.

The profit a bond investor makes is called the yield. Different types of yields include:

• Coupon Yield: This is the yearly interest rate set when the bond is issued, staying the same throughout the bond’s life.
• Current Yield: This depends on the bond’s price and its coupon. If the bond’s price changes, its yield changes too.

## Bond Yield vs. Bond Price

The relationship between price and yield in bonds is inverse. This means when a bond’s price rises, its yield drops, and when its yield rises, the bond’s price falls.

For instance, imagine an investor buys a \$1000 bond that matures in five years with a 10% annual coupon rate, meaning it pays \$100 in interest each year. If interest rates rise above 10%, the bond’s price falls if the investor sells it.

If rates climb to 12%, the original bond still pays \$100, which is less appealing compared to bonds paying \$120. To sell the original bond, its price can drop to make its payments match a 12% yield.

Conversely, if rates fall, the bond’s price rises since its coupon payment becomes more attractive. The steeper the rate drops, the higher the bond’s price climbs. In these situations, the coupon rate isn’t meaningful for new investors. Instead, dividing the annual coupon payment by the bond’s price helps determine the current yield, providing an estimate of the bond’s actual yield.

However, the current yield and coupon rate alone don’t fully show a bond’s yield. They don’t consider the time value of money, maturity value, payment frequency, and other factors, which require more complex calculations.

In addition to the methods mentioned earlier, there are other ways to calculate a bond’s yield. These include Yield to Maturity (YTM), Bond Equivalent Yield (BEY), and Effective Annual Yield (EAY).

### Yield to Maturity (YTM)

A bond’s yield to maturity (YTM) is the interest rate that makes the present value of all the bond’s future cash flows equal to its current price. These cash flows include all the coupon payments and the maturity value. Solving for YTM involves a trial-and-error process, which can be done using a financial calculator, but the formula is as follows:

Price = ∑ (Cash Flows / (1 + YTM)^t)

where:

• Price is the current price of the bond,
• ∑ denotes the sum of all cash flows from time t = 1 to T,
• Cash Flows represents the cash flows at each time t,
• YTM is the yield to maturity.

In the previous example, a bond with a face value of \$1,000, five years to maturity, and \$100 annual coupon payments is worth \$927.90 to match a new YTM of 12%. The bond’s six cash flows include the five coupon payments and the \$1,000 maturity value.

Determining the present value of each of these six cash flows using an interest rate of 12% will establish the bond’s current price.

### Bond Equivalent Yield (BEY)

Bond yields are usually mentioned as a bond equivalent yield (BEY), which takes into account the bond coupon paid in two semi-annual payments. In the last example, since the bonds’ cash flows happened yearly, the YTM is the same as the BEY.

But, if the coupon payments were made every six months, the semi-annual YTM would be 5.979%. The BEY is a straightforward yearly version of the semi-annual YTM, found by multiplying the YTM by two.

For instance, in a bond that pays semi-annual coupon payments of \$50, the BEY would be 11.958% (5.979% X 2 = 11.958%). However, the BEY doesn’t consider the time value of money for adjusting from a semi-annual YTM to a yearly rate.

### Effective Annual Yield (EAY)

Investors can calculate a more accurate annual yield called the effective annual yield (EAY) by considering the time value of money in the calculation, based on the BEY for a bond. For a bond with semi-annual coupon payments, the EAY is calculated using this formula:

EAY = ((1 + YTM/2)^2) – 1

Where:
EAY = Effective annual yield

If an investor knows that the semi-annual YTM is 5.979%, they can apply the formula to find the EAY, which equals approximately 12.32%. Since the EAY includes an additional compounding period, it will be higher than the BEY.

## Bond Yield Calculation Issues

Calculating the yield of a bond can be tricky because of some factors. In the examples before, we assumed the bond had exactly five years left, which is not common. Sometimes bonds have fractional periods, making it harder to figure out the interest earned.

Let’s say a bond has four years and eight months until it matures. We need to turn the time into a decimal for our calculations, considering the partial year.

Here’s the thing: four months of the current coupon period have passed, and two are left. This means we have to adjust the interest earned so far. When someone new buys the bond, they’ll get the full coupon payment. To make up for the four months already passed, the bond’s price goes up a bit.

Bonds can be priced in two ways: clean price and dirty price. The clean price doesn’t include the accrued interest, while the dirty price does. Systems like Bloomberg or Reuters usually use the clean price when quoting bonds.

## FAQs

What Does a Bond’s Yield Tell Investors?

A bond’s yield is how much money an investor gets back from the bond’s interest payments. You can figure it out in a simple way or using a more complicated method called yield to maturity. When yields are higher, it means bond investors receive more interest payments, but it might also mean there’s more risk involved. If a borrower is risky, investors want a higher yield. Bonds with longer timeframes usually have higher yields.

Are High-Yield Bonds Better Investments Than Low-Yield Bonds?

Investing in bonds relies on what the investor needs, aims for, and how much risk they can handle. If someone wants a safe investment or wants to balance their investments with low risk, they might choose low-yield bonds. On the other hand, if someone is okay with taking some risk to get more money back, they might go for high-yield bonds.

How Do Investors Utilize Bond Yields?

Yields help in doing advanced analyses. Traders can trade bonds with various maturity dates to benefit from the yield curve, which shows the interest rates of bonds with the same credit quality but different maturity dates.
The slope of the yield curve gives insight into future interest rate changes and economic activity. Analysts also compare interest rates between different types of bonds while keeping some characteristics the same.
A yield spread is the difference between yields on different debt instruments like maturities, credit ratings, issuers, or risk levels. It’s calculated by subtracting one instrument’s yield from another, such as the difference between AAA corporate bonds and U.S. Treasuries. This difference is usually measured in basis points (bps) or percentage points.

## Conclusion

Bond yield tells investors how much they’ll earn from a bond. It’s important to understand two basic concepts: the coupon rate and current yield. The coupon rate is the fixed interest rate that the bond pays, while the current yield is the annual return on the bond’s current price. Another crucial aspect is a bond rating, which grades the bond based on its credit quality and the risk level for investors.