# Zero coupon bond pricing

Find out how to calculate the yield to maturity of a zero-coupon bond, and learn why this calculation is simpler than one with a bond that has a.

## Price of a zero coupon bond

This means an investor knows his return in advance if he holds a zero coupon to maturity. The yield of a zero coupon bond is different than the yield of a normal bond of the same issuer. The individual coupons are the semi-annual interest payments due on the bond prior to maturity. The residual is the principle payable at maturity. Investment dealers exist to make a profit so the strips or zeros are sold to investors.

3.6 - Pricing a Coupon Bond as a Sum of Zero-Coupon Bonds

The dealers obviously make a healthy profit on stripping bonds. On the other hand, each strip bond is valued using the YTM of a comparable bond, a 5 year bond for a 5 year coupon and a 30 year bond for the 30 year residual.

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The sum of the parts is usually worth more than the whole bond was prior to stripping. Taken individually, each of these payments is an obligation of the issuer, in this case, the Government of Canada.

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This allows the components to be registered and traded as individual securities. Once a bond has been stripped, a trustee directs the appropriate amount of the interest or maturity payment to the security holders. The term discount bond is used to reference how it is sold originally at a discount from its face value instead of standard pricing with periodic dividend payments as seen otherwise.

To find the zero coupon bond's value at its original price, the yield would be used in the formula. After the zero coupon bond is issued, the value may fluctuate as the current interest rates of the market may change.

## Zero-Coupon Bond

The formula would be shown as. This site was designed for educational purposes. The current yield is simpler measure of the rate of return to a bond than the yield to maturity. The current yield is computed as:. This measure has the benefit of simplicity. It suffers from the drawback that it does not account for the time value of money.

Excel contains a set of specialized bond functions that can be used to account for several complications that arise in bond pricing, such as day-count conventions.

## Zero-Coupon Bond

Money market instruments e. Note that the settlement date and maturity date are represented as numerical values in Excel. The date January 1, is represented as 1; all later dates represent the number of days that have passed since January 1, As an example, suppose that a bond is sold on June 15, with a maturity date of June 15, What is the price of the bond? Note that the price of the bond is entered as Also note that represents June 15, and represents For example,.

This article is one part of a series on fixed income portfolios. Other articles in this series include:. Call us: These include: Face Value Coupon Rate Coupon Maturity Call Provisions Put Provisions Sinking Fund Provisions a Face Value The face value also known as the par value of a bond is the price at which the bond is sold to investors when first issued; it is also the price at which the bond is redeemed at maturity.

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The U. Treasury Treasury securities are issued by the U.

### 1) What are Bonds?

Treasuries can be classified by their maturities as follows: Treasury bills — the maturity is one year or less; the currently available maturities are 4 weeks, 13 weeks, 26 weeks and 52 weeks Treasury notes — the maturity ranges between 1 and 10 years; the currently available maturities are 2, 3, 5, 7 and 10 years Treasury bonds — the maturity ranges between 20 and 30 years; the currently available maturity is 30 years Another key difference between these securities is that Treasury bills are sold at a discount from their face value and redeemed at face value; Treasury notes and bonds are sold and redeemed at face value and pay semi-annual coupons to investors.

These results show the following important relationship: The bond in the previous example can be priced using this alternate bond valuation formula as follows: The pricing formula for a zero coupon bond is: In order to be consistent with coupon-bearing bonds, where coupons are typically made on a semi-annual basis, the yield will be divided by 2, and the number of periods will be multiplied by 2: This equals the rate of return earned by a bond holder known as the holding period return if: The yield to call is computed as follows: The yield to call is: The current yield is computed as: Other articles in this series include: Strategies, Duration, Modified Duration, Convexity.