Clean Price

The clean price of a bond does not include accrued interests. Accrued interest is the accumulation of interest between two scheduled payments. When an investor checks a bond’s price online, they are looking at the clean price, hence it is also known as a clean quote or quoted price.

In contrast, there is a concept of dirty price. A dirty price is the culmination of the bond’s quoted price and accrued interests. The dirty price is either equal to or higher than the clean price of the bond.

• The clean price of a bond does not include the interest accumulated between two coupon payments; it is also known as the bond's quoted price or a flat price.
• A bond’s quoted price can be derived by subtracting accrued interests from the dirty price.
• The difference between a bond’s quoted and dirty price becomes an added profit for the bond issuer.
• Investors use the clean quote to compare between bonds, as it does not fluctuate based on the date. The clean quote fluctuates concerning market conditions.

A clean price is the price of a bond without including accrued interest. It is also called the bond’s quoted price or clean quote.

To comprehend the meaning of bond price, we must first define a bond. Bonds are debt instruments issued by governments or corporations. Bonds are fixed-income securities that allow the bondholders to earn periodic interest—in the form of coupon payments. Thus, bond issuers are borrowers, and bondholders are the lenders (or investors). Bonds are the safest form of investment because the government backs them.

Every bond is issued at a specific coupon rate and an interest rate. Investors receive periodic repayments based on a fixed schedule. Based on the particular schedule, bondholders receive payments every month, every quarter, twice a year, or once a year. Most US bonds repay investors twice a year. It also comes with a maturity date; it is completely an investor's choice to hold the bond till its maturity or sell it in the secondary market.

Typically, bonds are priced according to their present value. Once the coupon payment is done, investors do not receive any amount till the next scheduled repayment. The fund accumulates interest between two scheduled payments—this is known as accrued interest. Thus, on the payment date, accrued interest is reset, and starts back at zero.

A bond quote reflects the most recent price or market price at the time of trading. If a bond’s price includes accrued interest, it is called a dirty price. Therefore, the terms clean quote or a clean price signifies that it does not include accrued interests.

Now, let us look at the clean price formula.

• Clean Price = Dirty Price - Accrued Interest

Similarly, the dirty price formula is as follows:

• Dirty Price = Clean Price + Accrued Interest

Also, accrued interest formula is as follows:

Accrued Interest = F x C/M x D/T

• Here, F is the face value.
• C denotes the annual coupon rate.
• M denotes coupon payments per year.
• D stands for days since the last payment.
• T denotes the accrual period.

Now, let us calculate the clean price of a bond.

Susan bought a government bond with a coupon rate of 5%; it will mature in 2023. The bond offers semiannual payments, one on December 1 and another on June 1. Susan bought it in January 2021, at a price of $1,800.

Usually, a bond’s quoted price is the clean price, there is no particular reason to calculate it. But a bond issuer might present a dirty price to an investor.

Thus, to determine if the quoted price, is dirty or not, we have to calculate the accrued interest. The accrued interest is calculated from the last payment date to the date of purchase. Susan bought the bond on January 1, 2022. Thus, interests were accumulated from December 1, 2020, to January 1, 2021 (31 days have elapsed).

• Accrued interest = F x C/M x D/T
• Accrued interest = 1800 x 0.05/2 x 31/182.5
• Accrued Interest = 1800 x 0.025 x 0.169
• Accrued Interest = $7.60

Now, let us apply the dirty price formula:

• Dirty Price = Clean Price + Accrued Interest
• Dirty Price = 1800 + 7.60
• Dirty Price = $1807.60

Thus, on January 1, 2022, the bond’s dirty price was $1807.60. This proves that Susan received, a clean quote from the broker. We can also derive the clean quote by subtracting accrued interests from the dirty price.

• Clean Quote = The Dirty Price - Accrued Interest
• Clean Quote = 1807.60 - 7.60
• Clean Quote = $1800

Investors receive a clean quote from a broker. But, It is important to note, that investors end up paying the dirty price nonetheless. Therefore, Susan pays $7.60 over the clean quote, this amount becomes a profit to the bond issuer.

This has been a guide to what is Clean Price. Here, we explain it with its formula, calculation, and an example. You can learn more about it from the following articles -

• Price Action
• Bond Quote
• Overtrading