What is the zero coupon bond

Easily calculate the yield on the zero coupon bond

Zero coupon bonds are also called zero bonds and are a special form of interest-bearing securities. In contrast to traditional bonds, however, zero coupon bonds do not have a coupon. This means that there are no fixed interest payments during the term. What sounds disadvantageous at first, however, also has positive sides.

Of course, an investor also receives a corresponding return with a zero coupon bond. This is even easier to calculate than with many other types of loan. The reason is that only a few factors need to be taken into account in the calculation. Since these are known, the calculation method is comparatively simple.

Zero Coupon Bond Yield: Important Data to Calculate

In the case of classic bonds, the main reason why the calculation of the return is difficult is that there are annual interest payments. This is precisely what is not the case with zero coupon bonds. Bonds are usually issued "at par", i.e. 100%.

Zero coupon bonds, on the other hand, are issued at a high discount. This means: At the beginning of the term, the zero coupon bonds are issued at a much lower value than they are redeemed at the end of the term. Disadvantage for the issuer: he receives less money. Advantage for the issuer: he does not have to make any interest payments during the term.

The yield on the zero coupon bond is calculated from the difference between the purchase price (or the current market price and the redemption price (nominal value) taking into account the remaining term. In financial mathematics, the current price corresponds exactly to the present value of the bond.

The nominal value is fixed from the start, usually 100%. The present value can change during the term because zero coupon bonds are traded on the market like all other bonds. The respective price is determined by supply and demand and is dependent on the respective creditworthiness of the debtor and the general interest rate level on the market

Formula for calculating the yield on a zero coupon bond

Due to the structure of this type of bond, the profit for the investor results from the difference between the buying and selling price. In order to calculate the annual return, the remaining term must also be taken into account. The best way to calculate the return is to use a formula. This is:

However, since the investor knows the purchase price, this formula has to be rearranged so that the solution is the interest rate. The yield on the zero coupon bond is obtained by taking the x-th root from the redemption price / purchase price (x = term) and subtracting the value 1.

Calculating the yield on zero coupon bonds - sample calculation

A zero coupon bond with a term of 10 years is used as an example. It has a cash value of € 550 and a repayment rate of € 1,000. If you are now based on the formula, you must first divide the repayment rate by the present value (values ​​are rounded):

1.000 / 550 = 1,82

Since the remaining term is 10 years, the 10th root is taken from the calculated value. The result is 1.062. The value 1 is now subtracted from this, so that you get 0.062, which corresponds to an annual return of 6.2%.

In this way, you can quickly find out whether an offered zero-coupon bond can generate an attractive return compared to other (fixed-income) bonds.

There are yield calculators that can be used to carry out such a calculation. As a control, however, it is advisable to understand the calculation method and to be able to calculate yourself in the event of inconsistencies.

May 2021: The 3 largest investments by top investor Bill NygrenTop investor Bill Nygren is sticking to tech giants and doing well with them: Top position Alphabet pulverizes analyst expectations. Share is scratching its all-time high ›read more

© Verlag für die Deutsche Wirtschaft AG, all rights reserved