**Investing in bonds may seem simple. However, the level of complexity of the fixed income market is very high. For this reason, it is essential to understand metrics. Here we will analyze one of the most important: the yield of bonds.**

## Content

- Introduction
- What is the Yield on a Bond?
- Bond Yield Formula
- Assumptions made in the Bond Yield Calculation
- Negative Bond Yields
- Bond Prices Move with Yields
- Conclusion

## Introduction

The bond market is by far the largest in the world, being much bigger than the global stock market. However, it receives very little attention from the financial press. This is probably the reason why there is a lot of ignorance about what bonds are and how they work.

In fact, the bond market is only spoken about in the news if there are macroeconomic problems. If interest rates are spiking because inflation is under control, or because certain governments or companies are unable to service their debts, we will hear about the bond market. That proves how important it is.

Nonetheless, the bond market is always there, and having a proper understanding of how it works is key regardless of the asset classes in which you invest.

## What is the Yield on a Bond?

The yield on a bond is a metric often used to indicate the potential return of a bond at any given time under certain future circumstances. For example, a US Treasury bond maturing in 10 year may have a yield of 4%. This means that, under certain circumstances, we can expect to make about 4% per annum by investing in this bond.

However, if we look more closely at the bond, we may see that it pays a coupon (interest) of only 3% per year. How is the bond offering a return of 4% if it only pays 3% in annual interest? Because bond prices move. And depending on how much we have to pay to buy the bond, the return we can expect from it will be different. That is what bond yields indicate.

The face value of a bond is the money that we are going to receive at maturity. The price of a bond trades relative to 100. 100 means 100% of par. So, if we want to buy $100,000 of a bond and the price is 100, we will pay $100,000.

If the bond was trading at 90, we would only have to pay $90,000 today. On the other hand, if the bond was trading at 120, we would have to pay $120,000. Regardless of how much we pay, we would still get $100,000 when the bond matures.

When the price is below 100, the yield on the bond is higher than the coupon it pays. This may happen because the bond is paying a 3% coupon, but we only pay 90 to buy it. The 3% coupon would still be calculated on $100,000 (not $90,000) and that is also the amount we would receive at maturity.

### Consequently, the calculation of bond yields takes the following inputs into account:

- Bond price (90 per 100 of notional value)
- Coupon or interest rate payment (3%)
- Maturity date (when we will receive the 100 of notional value)

By taking all these values into consideration, we end up with a bond yield of 4%. In another section we will discuss what conditions must be met to achieve exactly that annual return over the next 10 years.

## Bond Yield Formula

The yield of a bond is the interest at which we must discount future coupon and maturity payments so that the current value of these is equal to the price of the bond. I know this may sound complicated, so let us analyze an example.

A hypothetical bond pays an interest of 2% per annum and matures in exactly 3 years. Therefore, we can expect three payments from this bond:

- In 1 year: $2 of coupon payment
- In 2 years: $2 of coupon payment
- In 3 years: $102 of both coupon and maturity payment

The bond yield would be the “**i**” in this formula:

If the price is 100, the yield **(i)** will be 2%. When the price of a bond is 100, its yield is usually exactly the same as its coupon.

When the price is above 100, the yield is lower than the coupon. This happens because we are “overpaying” for the bond. If we overpay for a bond, the return we will get is set to be lower than the interest the bond pays.

When the price is less than 100, the opposite happens. The bond yield is now higher than the coupon. This is because we “underpay” for the bond. A lower purchase price leads to higher returns.

## Assumptions made in the Bond Yield Calculation

For the future annual return of our investment to be exactly the same as the bond yield today, three conditions must be met:

- We must keep the bond until maturity
- There will be no defaults or delays: this means we will receive all our payments on time
- Any coupon payments we receive during the life of the bond must be reinvested at that same yield: this is usually not feasible, but it can be ignored in most situations

## Negative Bond Yields

There have been in the past bonds trading at negative interest rates. A lot of people have difficulty understanding what that means. After all, how can a bond have a negative interest rate?

The answer is simple. First, please note that we are using the term interest rates to refer to bond yields. A bond with a negative interest rate is one that guarantees that, if we hold it until maturity, we will lose money. There is total certainty about that.

Mathematically, a negative bond yield appears when the bond price today is higher than all the cash flows we will receive from that bond, including both coupon payments and notional amount.

The easiest example to illustrate that would be with a bond that pays no coupon, i.e., it has a 0% coupon, but its price is above 100. If we pay $102 for a bond that will pay us no interest, and we will only receive $100 at maturity, our return will be negative.

Bonds with negative yields were very common during the last few years as many central banks implemented negative interest rates and bond buying programs, precisely with the goal to bring interest rates into negative territory.

## Bond Prices Move with Yields

As you have already seen, the yield on a bond will only become our realized return if we hold that bond until maturity. But there are bonds maturing in 30, 50 and even 100 years. Therefore, it is very likely we will have to sell them at some point.

Bond prices fluctuate constantly, and they can move in either direction. These price movements are often very pronounced, especially for long-dated bonds. The further into the future the maturity, the higher its price volatility. This is because such movements are exposed to what is called **duration or interest rate risk**.

For this reason, if you plan to invest in bonds but have a short investment horizon, it is usually better to focus on short-dates bonds. The realized return in short-dated bonds will be very similar to their yield, unless there is a default of course.

The realized return on long-dated bonds in the short term will be mostly determined by how its price has moved.

Therefore, if we want to invest for the short term and have a quasi-guaranteed return, it is better to stick to short-dated bonds.

## Conclusion

We have talked quite extensively about bonds yield. As you can see, bond yields are only an indication of the annual return we can expect from bonds if we invest in them for the long term and no default occurs.

For this reason, if you are interested in investing in bonds, it is very important to know what the bond yield is. Even if you plan on investing in bonds through an investment fund or ETF, you can check what the average bond yield for the fund is.

Bonds play an important role in a diversified portfolio. If you want to learn about it, check out this link:**The Role of Bonds in a Portfolio**

I also encourage you to subscribe to my newsletter:**Clear Finances**

Comments are closed.