# Standard bond

The fixed rate bond (also: coupon bond , straight bond ; English Fixed Rate Notes, straight bonds, plain vanilla bonds ) is a bond whose bond conditions a firm usually annual arrears paid nominal interest rate and a full repayment at their maturity provide.

## General

The bonds with the world's largest issuance volume are standard bonds . According to their issuers or purpose they are specifically mortgage bonds , municipal bonds , mortgage bonds , government bonds or corporate bonds called. Not to standard bonds are Annuitätenanleihen , draw bonds , dual currency bonds , perpetual bonds , floaters , foreign currency bonds , hybrid bonds , inflation-linked bonds , junk bonds , catastrophe bonds , lottery loans , zero coupon bonds , bonds with warrants , amortization bonds , convertible bonds or forced loans . Other bonds that do not belong to the standard bonds are, for example, bonds for which the bond conditions provide for a right of termination for creditors or debtors .

The nominal interest rate (“ coupon ”) on standard bonds is usually not the same as the market interest rate . This may be because the market interest that since issuance of the bonds has changed, the market rate of round was a different and therefore the market interest in the interest of a round nominal interest rate has been selected. For example, if the market interest rate is 2.85%, the issuer chooses a nominal interest rate of 3%, which affects the issue price ( over-par issue ). Another reason can be seen in the fact that these are deep discount bonds that were deliberately issued below par .

## rating

Assuming a flat interest structure , a standard bond is valued according to the following formula:

${\ displaystyle P_ {0} = {\ frac {K} {r}} + {\ frac {N - {\ frac {K} {r}}} {(1 + r) ^ {n}}}}$

in which

• ${\ displaystyle P_ {0}}$= Present value ( stock exchange price of the bond),
• ${\ displaystyle K}$ = Coupon,
• ${\ displaystyle r}$ = (term-independent) market interest rate,
• ${\ displaystyle n}$ = Term in years,
• ${\ displaystyle N}$= Face value of the bond.

## Yield to Maturity (effective interest rate)

The effective interest rate ( English yield to maturity, YTM ) is calculated by discounting the future cash flows (coupon and nominal amount) with a uniform discount rate. The result of the discounting is today's rate.

### Problems

The effective interest rate is only suitable to a limited extent for comparing bonds.

• For many bonds, the effective rate of return cannot even be calculated.
• Additional problems arise with regard to the remaining term :
• With a free remaining term , the reinvestment premise is necessary in order to be able to compare two bond options at all, otherwise the bond with the longest remaining term automatically has the highest effective interest rate.
• With a given remaining term , relative overvaluations and undervaluations in the market do not depend on a comparison variable. By linear combination of different instruments can u. U. a higher effective interest rate can be achieved.
• Theoretical coupon effect : With a normal interest rate structure , for bonds with the same residual term, the lower the effective interest rate , the higher the coupon. In the case of an inverse interest rate structure, the reverse applies, which results from the reinvestment premise.

## Valuation with interest payments during the year

If the coupon is not paid annually, but z. B. takes place every six months or quarterly, the interest periods and market interest rates must be adjusted accordingly, because a compound interest effect must be taken into account for the coupons paid out during the year. Alternatively, you can adjust the annual coupon so that the compound interest effect is included in the interest.

Version 1:

For the interest r z paid during the year :
${\ displaystyle r_ {z} = (1 + r) ^ {\ frac {1} {z}} - 1}$,
where represents the number of annual interest payments.${\ displaystyle z}$
The valuation formula for the standard bond with interest payments during the year is then adjusted as follows:
${\ displaystyle P_ {0} = {\ frac {\ frac {K} {z}} {r_ {z}}} + {\ frac {N - {\ frac {\ frac {K} {z}} {r_ {z}}}} {(1 + r_ {z}) ^ {zn}}}}$.

Variant 2:

The annual coupon is corrected taking into account the compound interest effect, e.g. B. for half-yearly interest payments:${\ displaystyle K_ {J}}$
${\ displaystyle K_ {J} = {\ frac {\ frac {K} {2}} {(1 + r) ^ {\ frac {1} {2}} + {\ frac {K} {2}}} }}$,
or in general:
${\ displaystyle K_ {J} = \ sum _ {n = 1} ^ {z} {\ frac {K} {z}} q ^ {\ frac {zu} {z}}}$.

## Asset and risk class

Even if standard bonds with the nominal interest paid in arrears and the full repayment share common characteristics, they do not belong to a single asset class . With regard to the price risk, there are government bonds from relatively risk-free debtor states (such as federal bonds ) and highly volatile government bonds with a high financial risk (such as Argentina bonds). In the risk class , investors are divided into risk-averse to risk-averse investors according to their risk tolerance , so that the corresponding asset class can also be assigned to the associated risk class within the framework of the asset allocation .