# Bond Yield Calculator

Created by Wei Bin Loo
Reviewed by Dominik Czernia, PhD and Jack Bowater
Based on research by
Gürkaynak RS, Brian Sack B, Wright JH. The U.S. Treasury Yield Curve: 1961 to the Present Federal Reserve Board (June 2006)
Last updated: Jan 15, 2023

We have prepared this bond yield calculator to help you to calculate the bond yield on different bonds. Bond yield is usually taken as the rate of return for bond investors (see rate of return calculator). As this metric is one of the biggest factors impacting the bond price, we need to fully understand the bond yield definition.

We have written this article to help you understand what a bond yield is, how to calculate bond yield, and what causes bond yields to rise. We will also demonstrate some examples to help you understand the concept.

## What is a bond yield? Bond yield definition

Before we talk about calculating the current bond yield, we must first understand what a bond is. A bond is a financial instrument that governments and companies issue to get debt funding from the public. The size of the bond market, also known as the fixed-income market, is twice the size of the stock market. This tells us how active this market actually is.

Bond yield meaning, also often known as the yield to maturity (YTM), is often understood as the rate of return for bond investors, given that the bond investors hold the bond until it matures and reinvest the coupons at an interest rate equal to the YTM. As bond yield is very volatile and sensitive to the economic climate, it is of the essence that we understand its dynamics and calculation.

Now that we know the bond yield definition, let's take a look at some examples to understand how to calculate bond yields.

## How to calculate bond yield? The bond yield calculator

The bond yield formula needs five inputs:

• bond price – Price of the bond;
• face value – Face value of the bond;
• coupon rate – Annual coupon rate (see coupon rate calculator);
• frequency – Number of times the coupon is distributed in a year; and
• n – Years to maturity.

Let's take Bond A, issued by Company Alpha, which has the following data, as an example:

• Bond price: $980 • Face value:$1,000
• Annual coupon rate: 5%
• Coupon Frequency: Annual
• Years to maturity: 10 years
1. Determine the bond price.

The bond price is the money an investor has to pay to acquire the bond. You can find it on most financial data websites. The bond price of Bond A is $980. 2. Determine the face value. The face value is equivalent to the principal of the bond. In our example, face value =$1,000.

3. Determine the annual coupon rate and the coupon frequency.

The coupon rate is the annual interest you will receive by investing in the bond, and frequency is the number of times you will receive it in a year.

In our example, Bond A has a coupon rate of 5% and an annual frequency. This means that the bond will pay $1,000 × 5% =$50 as interest annually.

4. Determine the years to maturity.

The n is the number of years from now until the bond matures. The n for Bond A is 10 years.

5. Calculate the bond yield.

The bond yield can be seen as the internal rate of return of the bond investment if the investor holds it until it matures and reinvests the coupons at the same interest rate. Hence, the bond yield formula involves deducing the bond yield r in the equation below:

$\qquad p = \sum_{k=1}^{n} \frac{{\rm cf}}{(1 + r)^k}$

where $p$ is the bond price, $\rm cf$ is the cash flows (coupons or the principal), $r$ is the bond yield, and $n$ is the years to maturity.

This calculation involves complex iteration, and it is nearly impossible to do it by hand. And that's why we have built this calculator for you!

For Bond A, the equation looks like this:

$\footnotesize \! \begin{split} 980 = \frac{\50}{(1 + r)^1}\! +\! \frac{\50}{(1 + r)^2}\! +\! \frac{\50}{(1 + r)^2}\\[1.5em] + \frac{\50}{(1 + r)^3} + ... + \frac{\50}{(1 + r)^9} + \frac{\1050}{(1 + r)^{10}} \end{split}$

After performing the estimation, our bond yield calculator gives bond yield $r = 5.26\%$.

💡 You might also be interested in our bond price calculator or debt to asset ratio calculator.

## Why do bond yields rise and fall?

Now that you understand the meaning of bond yield and how to calculate it, let's explore its economics, i.e., why do bond yields rise and fall?

• The most important factor in determining the bond yield is inflation. When inflation is higher than expected, bond yields will rise. This is because investors anticipate that the central banks will increase the interest rates to curb and control inflation (see interest rate calculator).

• The other important factor is the uncertainty of the market conditions. Investors despise uncertainty in general. The more volatile the market conditions, the more uncertainty investors will face. Owing to the higher uncertainty, investors will demand a higher rate of return to compensate for the risks they undertake. Therefore, this is what causes bond yields to rise.

The bond yield curve is one of the best instruments to analyze the evolution of bond yields. The bond yield curve plots the bond yields against time. For instance, if the bond yield curve is upward-sloping, it generally means long-term bond yields, such as the 10-year bond yield, is higher than short-term bond yields, such as the 2-year bond yield. On the other hand, if the bond yield curve is trending downwards, the 10-year bond yield will be lower than the 2-year bond yield.

## FAQ

### Does bond yield equal yield to maturity?

Technically, yes. The bond yield will equal the yield to maturity if you hold to the bond until its maturity and reinvest at the same rate as the yield to maturity.

### What is a yield curve?

The yield curve is a graph drawn of bond yield against time. It shows the evolution of bond yield with time. If the yield curve is trending upwards, it means that long-term bond yields are higher than short-term bond yields.

### What causes bond yields to fall?

There are several factors that can make bond yields fall. For instance, the lower the inflation, the lower the bond yield. The less volatile the market condition, the lower the bond yields.

### Can bond yield be negative?

Yes, bond yield can be negative. It happens every now and then, even though it is not common. This situation typically occurs when inflation is out of control and the market is unstable.

In such a situation, even a negative yield is still better than storing cash since hyperinflation might happen.

Wei Bin Loo
Face value
$Bond price$
Annual coupon rate
%
Coupon frequency
Annually
Years to maturity
year(s)
Bond yield
%
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