Definition of clean price
How clean price works
Clean price vs. dirty price
What this means for individual investors
Definition of clean price
The clean price is the price of a bond without accounting for interest accrued between coupon payments. Bonds are generally quoted at the clean price in financial publications. The clean price of a bond changes as interest rates and other bond market conditions change. The clean price plus accrued interest equals the dirty price of the bond. The clean price is typically used as a standard to compare bonds.
How clean price works
Bonds are often issued with a face value of $1,000. Bond prices are typically quoted as a percentage of the face value. For example, if XYZ Corporation issues a bond with a face value of $1,000 and it is priced at 95, it has a market value of $950. The clean price of the bond is $950. If XYZ Corporation pays a 6% coupon paid semi-annually, the clean price of the bond remains $950. The “market price” is another term for the clean price of the bond.
If the bond is trading below its face value, also known as par value, it is considered to be trading at a discount. If the bond is trading above its face value, it is trading at a premium.
The clean price is also used to calculate the dirty price. The dirty price is the price of the bond that takes into account the accumulated interest.
Dirty price = clean price + accrued interest
Assume XYZ Corporation pays its coupons on January 1 and July 1 of each year. In the United States, corporate bonds typically follow a 30/360 convention, which means that interest on the bond is calculated as accruing over 30 days in a month and 360 days in a year.
Accrued interest is calculated as follows:
Accrued interest = face value × coupon rate / number of coupon payments per year × number of days since the last coupon payment × number of days between payments or accumulation period
If you want to calculate the dirty price on April 1, you would first need to calculate the accrued interest using the formula above. Although there are fewer days in February, the convention is to follow 30/360, so you would use 90 (30 × 3) for “D”. You would use 180 (360 divided by two) for “T”, or the number of days between coupon payments, even though the coupon is semi-annual and there are 365 days in a year.
Accrued interest = $1,000 × 0.06 / 2 × 90/180 = $15
Dirty price = $950 clean price + $15 accrued interest = $965
Clean price vs. dirty price
The clean price and dirty price of a bond differ not only in how they are calculated. Due to its reliance on accrued interest, the dirty price changes daily, while the clean price moves with fluctuations in the bond market.
Clean price = quoted percentage of face value
Dirty price = clean price + accrued interest
The clean price changes with changes in interest rates and other bond market conditions, while the dirty price changes daily with the accumulation of interest.
The clean price is usually used as a context for comparing different bonds, while the dirty price is used to determine the total cost of the bond.
What this means for individual investors
Investors typically use the clean price as a benchmark to compare other bonds. The change in yield for the dirty price is not affected by changes in accrued interest, making it a better tool for comparison. The dirty price is used to calculate the expected yield from buying or selling a specific bond.
The clean price should always be equal to or less than the dirty price. The two prices will be equal on the day a coupon payment is made, but the dirty price increases every day that interest accrues.
Will be
The dirty price is higher before the coupon payment. Once that happens, the clean price and the dirty price will be equal. Then the dirty price will start to increase again as interest accrues.
Source: https://www.thebalancemoney.com/what-is-clean-price-5198398
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