Accrued interest

Accrued interest ( Swiss: accrued interest ) are in bonds , the interest rates between two interest payment dates, the buyer and seller have to divide among themselves.

General

Fixed-income securities carry coupons that are grouped into a sheet . These coupons represent the interest claim that the holder of the security has against the debtor of the bond on the coupon date . If the holder was the right holder of the bond for the entire interest period, he is entitled to the full interest. However, if the right holder of the bond has changed during the interest period, for example through sale, the interest is to be divided proportionally between seller and buyer as accrued interest. However, since the respective holder of the bond receives the interest for the entire interest period on the coupon date, he must reimburse the seller for the interest components from the start of the coupon term until the time of purchase. This happens immediately when buying this bond by adding the interest component to the market value , so that the buyer pays the accrued interest to the seller at the time of purchase and the buyer receives the full interest amount on the interest date.

ex coupon - cum coupon

Bonds can be listed on the stock exchange in two ways :

ex coupon - then the bond price does not contain a coupon component (also called “clean price”). Bonds are mostly quoted ex coupon in order to avoid unnecessary price fluctuations that only result from the problem of accrued interest.
cum coupon - the portion of the coupon that has accrued since the last coupon payment is then included in the price of the bond. On the day the coupon is paid out, there is then a discount (also known as the “dirty price”). This type is also known as "flat" quotation. Participation certificates (a hybrid of bonds and shares ) as well as shares and all other securities are listed with a coupon, provided they have a coupon at all. No coupon have e.g. B. Zero bonds (bonds without interest payment) or special derivatives (certificates, warrants, etc.).

calculation

When buying a bond, the previous owner not only has to pay the market value, but also his share of the coupon (the interest income of the security from the last interest payment to the value date of the purchase).

example

The bond will be bought on January 20, the value date on January 22. The last interest date was January 10th. Interest is calculated for 22-10 = 12 interest days .

The seller has already acquired this claim economically and legally, as he has already held the bond in the example for twelve days. However, the buyer of the bond will receive the full interest payment from the issuer on the next coupon date. By paying the accrued interest, the proportional interest claim of the seller is settled.

The following formula is used for the calculation:

{\ displaystyle {\ text {Accrued interest}} = {\ frac {{\ text {Nominal value}} \ cdot {\ text {Interest rate}} \ cdot {\ text {Interest days}}} {360}}}

Here, 360 is the approach for the days of the entire year; with the English interest calculation method , 365 or 366 days are used.

If, for example, a nominal EUR 10,000 bond is bought (sold) with a nominal interest rate of 3.5%, according to the above formula for the 12 interest days

10,000 × 3.5% × 12: 360 = € 11.67

calculated on accrued interest.

Special forms

There are also special forms of bonds that do not charge accrued interest. In addition, negative accrued interest is charged on some bonds shortly before an interest date because the seller still receives the next interest credit.

Accrued interest in the valuation of bonds

If you want to determine the fair price of a plain vanilla bond, the remaining term of which is not a full year, using the present value method, this must be taken into account when discounting :

{\ displaystyle P = \ sum _ {t = 1} ^ {n} {\ frac {K} {(1 + r) ^ {v} (1 + r) ^ {t-1}}} + {\ frac {M} {(1 + r) ^ {v} (1 + r) ^ {n-1}}} - S}

where the price of the bond in euros (cash value), the number of periods, the interest rate, the coupon, the payment on maturity (nominal value), the days until the next coupon payment / 360, the period in which the payment is received and the accrued interest are. ${\ displaystyle P}$ ${\ displaystyle n}$ ${\ displaystyle r}$ ${\ displaystyle K}$ ${\ displaystyle M}$ ${\ displaystyle v}$ ${\ displaystyle t}$ ${\ displaystyle S}$

Tax treatment of accrued interest

In Germany, accrued interest represents part of the sales proceeds in accordance with Section 20 (2) No. 7 EStG ; in Switzerland , the accrued interest is tax-free capital gain because it is not paid by the debtor of the bond but by a third party (Art. 16 para. 3 DBG ).

The accrued interest received or paid by a bank customer during a calendar year flows into an accrued interest pot , a sub-account of the securities account .

In Austria , according to Section 27a (3) No. 2a EStG, they are part of the income from capital assets for the seller and part of the acquisition costs for the buyer.

Individual evidence

^ Alpmann Brockhaus, Fachlexikon Recht , 2005, p. 1273 f.

[1] Alpmann Brockhaus, Fachlexikon Recht , 2005, p. 1273 f.