## Introduction

Bond is usually priced as a percentage of par, or face value. However, depending on a multitude of factors, bond prices fluctuate over the course of time. This is mainly because of the fact that there are numerous different factors, like interest rate, and compounding type, that impacts the overall bond price. For bond investors, it often gets confusing to fully understand bond prices and mechanisms. In this regard, two very commonly used terms are clean price and dirty price.

The main difference between both clean price and dirty price lies in the realms of technical differences. From the perspective of the investor, interest rate and accumulated interest calculation tend to be very crucial in making investment-related decisions. Therefore, regardless of either of the type of prices being used, the interest rates cannot be ignored in the bond pricing and analysis.

## What is a Clean Price?

The clean price is referred to as the price of a coupon bond that does not include any previously or currently accrued interest. In other words, a clean price implies that the price of the bond has not been incorporated with the accrued interest between the coupon payments. The clean price is the price that is normally quoted on financial news sites.

Given the fact that interest accrues evenly across the course of time in bonds, calculation of the amount that is earned can easily be calculated on a daily basis. However, this increment in interest over the course of time is not accounted for in the calculation of the dirty price. Normally, bonds are quoted at their face value or their par value. This means that if the bond’s face value is $1000, and it is quoted at 98%, this means that the clean price of the bond is going to be $980.

__Example of Clean Price__

For purpose of understanding how clean price is calculated and how it works, the following example is given:

Let’s assume the fact that Antsy Co. issued a bond that had a $1000 face value, with $960 being the published price of the bond. The bond is said to pay interest (or a coupon rate) of 5% annually in the form of semi-annual payments. Consequently, this implies that investors would continue to receive $25 every 6 months.

The clean price of the bond that is issued by Antsy Co. in this regard is said to be $960. However, when this amount is displayed and subsequently conveyed to the investors, it also factors in all the accumulated interest within the bond. This also implies that once a coupon payment has been duly made, the bond’s price is restored to the actual price. In other words, the clean price, and the dirty price are the same on and after the first day where coupon payments have been made. As soon as the bond begins to accrue interest again, clean price and dirty price are no longer the same.

## What is a Dirty Price?

A dirty price can be simply defined as the price that includes accrued interest alongside a bond’s coupon payment. This implies that the dirty price is over and above the clean price of the bond, simply because of the fact that it factors in accrued interest payments.

This concept can be explained using the notion of accrued interest on the bonds. Since interest is accrued evenly across these bonds, it is important to consider the fact that after every passing day, the accrued interest is meant to increase. Therefore, when buying or selling bonds, the investors need to account for coupon payments that are due in the near future, as well as coupon payments that have already been accounted for. Dirty price accumulates that, and this price is subsequently communicated to the investors for their consideration.

__Example of Dirty Price__

The calculation and usage of dirty price is explained in the following example:

Let’s assume the fact that Bitsy Co. issued a bond that had a $1000 face value, with $960 being the published price of the bond. The bond is said to pay interest (or a coupon rate) of 5% annually in the form of semi-annual payments. Consequently, this implies that investors would continue to receive $25 every 6 months.

In the example above, the clean price is going to stay the same. It will be maintained at $960 across the course of time. However, dirty price continues to change with the course of time. Every passing day, interest is accumulated on the bond, and hence, bond price from the perspective of the investor changes on the daily basis. For instance, in the case of Bitsy Co, it can be seen that there are semi-annual payments. Therefore, the dirty price of the bond is going to be $960 (par value) + $25 (accrued interest). The total amount, in that case, amounts to $985.

The dirty price of a bond continues to change with every passing day, because of the fact that interest keeps on accumulating over the course of time. When the coupon payment is made after 6 months, the dirty price and clean price would be the same since there would be no accumulated interest on the bond then. Therefore, the dirty price is the highest right before the coupon payment is about to be made, and it is the lowest (i.e. it is equal to the clean price) right after the bond has been issued, or right after the coupon payment has been made.

## How do Clean Prices and Dirty Prices work?

The mechanism of clean prices and dirty prices is illustrated via the following diagram:

## What are the differences between clean price and dirty price?

Despite the fact that clean price and dirty price essentially convey the same thing (the bond price with or without accumulated interest), yet there are a couple of differences between both these terminologies. These differences are given below:

- Firstly, the fundamental difference between the clean price and the dirty price is the fact that the clean price does not represent any accumulated interest. Dirty price, on the other hand, includes accumulated interest in the bond price.
- Clean Price is always less than or equal to the dirty price. Clean price can never be higher than the dirty price unless there’s a negative interest rate applied.
- Clean price just informs the investor about the face value of the bond. Other interest calculations need to be made by the investor himself. Dirty price is used by investors because it shows a lump sum value of the bond at a certain point in time.
- Clean Price is mainly used in the US. Dirty price is used in the UK.
- Clean price stays the same across the life of the bond. On the other hand, dirty price tends to increase till the point where coupon payment is due. After the coupon payment is due, the price restores back to the clean price.

However, the main difference between clean prices and dirty prices is the fact that clean prices do not include interest, whereas dirty prices are representative of the accumulated interest. In most cases, a clean price is a price that is used as a benchmark for comparisons. Dirty price is used for internal workings and calculations in order to estimate the expected payoff from purchasing a specific bond.

Therefore, it can be seen that clean price and dirty prices are two very commonly used that are often mixed upon by investors. However, there are numerous staunch differences between both these terminologies, predominantly on technical grounds.