# bond

A bond (also fixed income security , bond paper , bond or bond , English bond or debenture bond ) is an interest- bearing securities . It is a security that grants the obligee the right to repayment as well as to payment of agreed interest . Additional rights can also be agreed (see section Forms ). Typically, bonds are used by the debtor for - mostly long-term - debt financing and the creditor for capital investment . The securities class of bonds include government bonds (including municipal bonds ), corporate bonds and Pfandbriefe ; does not include loans such as personal loans and borrower's note loans .

US \$ 5,000 loan from the New York Central and Hudson River Railroad Company dated October 29, 1894
Loan from the German Reich or bond dated August 1, 1922, shortly before the start of hyperinflation

## etymology

The word pension paper can be traced back to the old French rendre for “income”, which first appeared in Germany in 1340 as “pension”. In German, the word pension was initially used for the - regularly payable - interest , so that an annuity paper represented an "interest paper".

The word bond appeared for the first time in 1585 in a document book of the state of Dithmarschen ("Princely mandate regarding bonds and pawns and usurious contracts"), according to which a bond had to be recorded in the presence of scribes and witnesses. The Romance scholar Matthias Kramer translated the German word Schuldverschreibung in 1679 into Italian ( Italian prestito obbligazionario ), the linguist Kaspar von Stieler listed the term under the heading “prescribing” in 1691. In 1741, the linguist Johann Leonhard Frisch explained the bond by stating that the debtor was writing his goods to someone else, which the creditor could hold onto. The General Prussian Land Law raised the word debt security to a legal term in June 1794 .

The word bond as a synonym for bond appeared for the first time on September 16, 1789 on a poster for borrowing from the duchies of Schleswig and Holstein. It is derived from the Old High German analёhan (around 800), which was used in German for a loan ( Latin mutuum ).

## history

The bond came up in the Middle Ages as "Rentenbrief" ( French brevet de rente ), when cities used it to finance their debts . The forerunners of today's government bonds were the medieval war bonds ( Italian "Prestiti" or "Prestanze" , "loan") in Venice or Florence . In Venice, the Doge Vitale Michiel II took out a 4% loan from his Venetian citizens in 1156 - the first early form of government loan. In Florence, Philipp Tuskhan and 2 brothers have run the local pawnshop since 1287 ( Italian "casanam prestiti" ). These were compulsory interest-bearing bonds from the small and city-states of northern Italy, which were often not repaid. In the English domestic trade one used since the late 12th century, the owner - promissory note similar negotiable instruments ( Latin littera obligatoria , also known as Latin scripta obligatoria or French Escript obligatoire ). They are considered the forerunners of modern debt securities. Edward III von England needed money for the Hundred Years War with France in November 1338 , which the banker Bonifacio di Tommaso, among others , lent him to the Peruzzi , but never got it back.

The city of Ulm pledged by a mortgage in 1378 their revenue from gate tariffs of 1,800 florins to a Jew, from whom she had lent money. In addition to the pledging of income, assets were also loaned . In Austria, for example, the dukes Albrecht and Leopold pledged their Hainburg Castle to Johann von Lichtenstein in 1379, for which a Pfandbrief was issued in November 1388. Around 1400, in addition to the Pfandbrief, the bond had emerged in Germany in which the amount owed and the interest as well as - in the event of default in payment - a right of immission ( lien ) were specified. A term or maturity was usually not provided; they were also perpetual annuities . The city of Cologne issued annuities that could be removed from the city in 1416.

On April 12, 1519, the Spanish King Charles V signed a bond issued for Anton Fugger . On January 29, 1512, the city ​​of Antwerp took out a city loan from Antwerp merchants, the Antwerp stock exchange began regular trading in bonds in 1532, including Dutch court letters (government bonds), private bonds from Dutch state officials and magnates (for the account of the government) , Bonds of the Dutch provincial estates, city bonds, rentier's letters and bonds of the English crown and the king of Portugal. An imperial mandate in 1537 equated the bearer obligation with a change . In 1568 Philip II financed the Eighty Years' War of the Netherlands against Spain with a government loan of 3 million guilders. The Bank of England was founded in July 1694 by an English government loan by William III. at the rate of 8%. In 1751, the English "Consols bond" was the first government bond based on perpetual annuity. The state only committed itself to paying the interest (“pension”) and did not assume any repayment obligation, at most it granted itself a repayment right. The constant and ongoing interest payments have earned her the name "eternal annuity" on the bond market. This form was only allowed for government papers.

With the exception of Antwerp, the existing stock exchanges ( Amsterdam stock exchange founded in 1611, Königsberg 1613, Lübeck 1614, Frankfurt am Main 1615 or Leipzig 1635) traded exclusively in bills of exchange and sorts . It was not until 1830 that bonds were listed on the Frankfurt stock exchange , namely Bavarian, Austrian, Dutch, Neapolitan and Spanish bonds. In 1854 Frankfurt-listed 81 railway bonds, 6 US Treasuries, 24 US states bonds 20 US city bonds and 5 of US bonds counties . The investments of the early years brought the industry not only stocks around 1860 but also corporate bonds as a financing instrument , which were placed on stock exchanges. 41% of the overseas bonds traded on the London Stock Exchange between 1865 and 1914 came from railroad companies .

The beginning of the global economic crisis in 1929 put a massive strain on the short-term bond markets in Germany and the USA. The state interventionism of the capital market policy of the National Socialist German Reich from 1933 to 1945 led to German government bonds being traded in Swiss francs on the Swiss stock exchange during this period . After the annexation of Austria , the bonds of the then non-existent Alpine state were added. The pension indices showed an opposite trend and portrayed the war in opposite directions. German bonds lost 38.7% of their market value in Swiss trade when war broke out (September 1, 1939) and 6.5% during the Russian Stalingrad offensive. The Yalta conference resulted in losses of 34%. Austrian securities lost massive amounts due to the dissolution of the state, but were able to break away from the trend towards German securities from 1943 onwards , because market participants expected Austria to be re-established after the defeat of the German Reich. So these bonds benefited from the military and political events.

The emerging after the Second World War economic boom also boosted the German bond market , because in 1960 listed German stock markets over 260 different industrial bonds. The worldwide increasing national debt led to the dominance of government bonds on the international bond markets from 1980 onwards, so that the rating agencies decided in 1982 to assess the increasing country risks with a national rating. In June 1991 the German bond index REX was created, which summarizes the market development of the bond market in an index number for federal bonds, the basis of which is the current yield . The national debt first reached excessive levels from March 1997 in Asia ( Asian crisis ), then from May 1998 during the Russian crisis and finally from April 2010 in Europe. It thereby increased the financial risks on the bond markets and conjured up the risk of financial crises . The Frankfurt Stock Exchange introduced the “ Entry Standard ” in April 2011 and the “ Prime Standard ” for bonds in October 2012 .

## term

A fixed-rate capacity title ( English fixed income product ) is a fault legal claim on two things:

In contrast to shares , the buyer of a corporate bond does not acquire a share of the company's equity , but grants it credit , i.e. debt .

The term fixed-income securities does not refer to the type of interest, but to the legal status of the financial title holder. Fixed income securities include income bonds , Asset Backed Securities (ABS), convertible bonds and bonds with warrants . They also include zero coupon bonds , floaters and certificates (including index bonds ), although they do not offer a fixed regular interest rate.

### Certificate

Nonvaleur bond

The certificate consists of a coat and bow . The coat securitized the receivables of the creditor . The sheet consists of coupons , which are used to assert income claims (e.g. interest) and, if applicable, a renewal coupon ( talon ). The coat and bow must be presented together to the issuer of the certificate in order to receive the performance promised in the certificate.

Bonds are traded on the bond market , a segment of the capital market. They can be bought and sold there at the current rate . New issues take place in the stock exchange segment of the primary market , bonds already in circulation are traded on the secondary market.

In most countries, however, bonds do not have to be traded on the stock exchange, which means that they do not have to be listed on the stock exchange. Trading on stock exchanges is relatively insignificant for price determination in these countries, as the majority of the volumes are traded over the counter .

In recent years, electronic trading systems have become more prevalent for more and more types of bonds . Today, the vast majority of sales in liquid European government bonds are no longer processed by telephone, but rather via electronic trading platforms such as Bondvision , Tradeweb , Eurex Bonds and Bloomberg Bond Trading .

The bond is considered to be a rather low-risk form of investment, as it has defined interest claims and a fixed repayment, and is secured depending on the structure . Institutional investors (e.g. insurance companies ) are required to invest a large proportion of the funds under management in securities with a high credit rating , with fixed-income securities often being the choice. If the debtor has a bad credit rating, the bond carries a high credit risk, which the investor is usually rewarded with a correspondingly high interest rate, which is then referred to as high-yield bonds .

Bonds are generally considered bearer instrument issued (see bearer bond ) because the improved tradability is. The owner of the bond is thus also the creditor. However, there is also the design as name, order or recta paper .

The quotation of individual bonds is different. Some bonds are traded according to yield (e.g. Swedish government bonds SGB, Australian government bonds or Japanese government bonds JGB), others are traded at prices (e.g. German government bonds DBR, Austrian government bonds RAGB, British government bonds Gilts). In the United States, Treasuries are quoted at 32nds (1/32) (e.g. "101-16" equals 101 16/32 = 101.50).

The standard value date for European government bonds is normally T + 3, for US government bonds T + 1, depending on the settlement system in Japan T + 2 (Furukai - Furiketsu) or T + 4 (Toruku).

## Functions

By dividing the fixed-interest title - often amounts of several million currency units (e.g. US dollars or euros ) - into a large number of bonds with nominal amounts of, for example, 50, 100, 1000 or 10,000 currency units, a lot size transformation takes place . This also makes the bonds attractive for small investors. Bonds fulfill a mobilization function .

By standardizing the bonds, a higher level of fungibility can be achieved. In this way, the different commitment periods of the issuer and the creditors can be harmonized. This temporal transformation function is due to liquid secondary markets .

## Issuers and Issues

### Issuers

Possible issuers of bonds are:

In Austria and Germany, most of the bonds are issued by banks and the public sector , while in the United States many companies issue bonds. The reason for this is to be seen in the fact that companies in Europe raise capital more frequently through self-financing or obtain loans from commercial banks.

### Issuing procedure

The issue of bonds can be carried out as a self- issue or as a third-party issue . A bank or a placement consortium acts as an intermediary in the case of third-party issuance .

The issue can be carried out as a private placement or a public placement. The following forms are common for the public placement of bonds:

• Private sale : The sale takes place at a fixed price until the proceedings are discontinued or until the sale (example: federal treasury notes )
• Launch for public subscription : The investors bindingly declare within a period what amount of the bond they are willing to accept. However, you are not entitled to the subscribed securities. If the demand exceeds the supply (oversubscription), the issuer can allocate (repartition) at its own discretion.
• Tender procedure : Similar to an auction; however, the subscribers indicate what amount they are willing to purchase at what rate. The issuer then serves all bids that do not fall below a minimum price (selected by the issuer). The issue volume is not fixed from the start, but is adjusted depending on the size of the bids. A distinction is made between the American (where each bidder pays his own bid) and the Dutch method (where everyone pays the same price). This procedure is used for federal securities .
• Continuous issue : ongoing further issue under the same conditions.

Bonds are issued at an issue price that may differ from their face value . Depending on the ratio of the issue price to the nominal value, one speaks of the issue below par , par or above par . The discount at below par is called a disagio , the surcharge for above par is called a premium or premium.

### Markets

#### National

A domestic bond is placed on the national bond market. It is the issue of a bond from a domestic issuer. It is issued in the local currency and with the use of a domestic consortium, whereby the regulations of the country of residence must be complied with. An example of this is a federal bond . The German Rentenindex measures their performance .

#### International

“International” means that the issue takes place outside the home country of the issuer. A distinction is made between euro markets and foreign bond markets.

A Eurobond is issued by an international banking consortium. The international placement takes place in an internationally recognized foreign currency ( US dollar , euro , yen ). A foreign bond is a domestic currency bond issued by a foreign issuer relative to the currency or a foreign currency bond. It is placed by a domestic banking consortium in the currency country. The domestic regulations apply.

## Bond terms

For investors who are loan terms of interest, which shall be negotiated between the obligor and the issuing bank consortium. As a rule, this is based on the bond standards of the International Capital Markets Association (ICMA). These begin with the choice of law , which can be decided between the law of the issuing state or the law of major financial market jurisdictions. Since 1992, states that submit their bonds to US law and denominate them in US dollars can be sued in the US.

### Clauses

Clauses such as the pari passu clause , negative declaration , cross-default clause and the collective action clause must be observed because they can have serious effects on the investor in the event of a crisis in the bond debtor.

• The pari passu clause assures the bondholders of absolute equality of their unsecured claims , in which the policy is realized that no type of claims is given an implicit priority. This does not put the creditors of later bond tranches at a disadvantage.
• This principle of formal equality is through the negative pledge expanded ( "negative pledge") to the collateral level by the clause assuring the unsecured bondholders collateralisation of their claims, the obligor other creditors should provide collateral.
• With the cross-default clause , the bondholders have a special right of termination if the debtor pays off their bond but falls behind with another payment obligation. As a result, all creditors should be affected by the debtor's payment difficulties at the same time.
• The Collective Action Clause makes a change to individual bond terms dependent on the approval of the majority of the creditors and is binding for all bond creditors in the event of a majority approval. As a result, minorities can be outvoted and are forced, for example, to support debt relief .

### running time

The distinction between bonds according to their term is of a purely formal nature and, in the case of corporate bonds, is usually based on the term regulations of Section 285 No. 1a HGB :

• short and medium term (up to 5 years),
• long-term (5 to 8 years)
• long term (more than 8 years)
• Government bonds have the longest maturities with maturities between 10 and 30 years .

Bonds with a longer term, in particular those without a fixed repayment period ("perpetual bonds", also called consols ), are not common in Germany.

The relationship between the (remaining) term and the interest rate of a bond is reflected in the yield curve .

### Collateral

Bonds can be differentiated according to the type and scope of collateral:

• Government bonds are usually unsecured.
• Pfandbriefe are secured by land and land rights ( mortgage Pfandbriefe ) or claims on the public sector ( municipal loans : public Pfandbriefe, formerly municipal bonds ) and are subject to the requirements of the Pfandbrief Act .
• Ship Pfandbriefe and Airplane Pfandbriefe are secured by mortgages on ships or aircraft and represent a special form of Pfandbrief.
• Mortgage bonds are also secured by land, but are not subject to the strict requirements of the Pfandbrief Act.
• Covered bonds are also similar to Pfandbriefe.
• Brady bonds are a special feature of collateralization. These government bonds from emerging countries are collateralized by zero coupon bonds from borrowers with high credit ratings.
• Backed securities ( English asset-backed securities , ABS) consist Here, the payment claims against a solely for the purpose of the transaction, the asset-security serving SPV ( English Special Purpose Vehicle ). The payment claims are covered by a stock of claims ( English assets ).
• Catastrophe Bonds: This special type of bond allows insurance companies to sellthe risk of natural disasters in capital markets. Similar to asset-backed securities, a special purpose vehicle is set up that invests its capital in default-risk-free bonds. If the natural disaster does not occur, the investors receive interest and repayment in accordance with the contract. If, on the other hand, the natural disaster occurs, the damage is paid to the insurance companyfirst.

By contrast, government bonds - for example federal bonds - are unsecured bonds. Local authorities in Germany are not capable of bankruptcy . In the USA are municipalities in insolvency insolvent in accordance with the special provisions of Chapter 9 of the United States Bankruptcy Code . Since Argentina's insolvency (see also Argentina crisis ), however, there has been a discussion about bankruptcy law for nation states. Federal bonds are still considered safe, as tax revenues and state assets (e.g. forest areas , real estate , equity investments ) are considered solid sources of income; At least in theory, the state can always make available the means necessary to service the liabilities by changing tax legislation .

In practice, however, the case of Argentina and the Greek crisis with their partial debt relief show that this alone is not enough. The Soviet Union, as the legal successor to Tsarist Russia, had also refused to service loans from this period. As a result, the Soviet Union was unable to borrow money for a long time. Russia had to partially service the tsarist bonds in the early 1990s in order to be able to raise money on the capital market with new bonds.

## Stripping

With bond stripping or coupon stripping , the bond is broken down into individual securities for the nominal value (security shell) and for each individual coupon payment. The resulting securities are all zero coupon bonds and can be traded individually. The separation is carried out for the owner of the bond by the respective custodian, the credit institution or the federal securities administration. The English verb "to strip" means "to take away"; In this context, however, "STRIPS" as an acronym for is english separate trading of registered interest and principal of securities ( "separate trading of interest and the nominal value of securities") referred to as an explanation.

Stripping in this form has existed in the USA since 1985, in France since 1991 and in Belgium and the Netherlands since 1993. Since July 1997, stripping has been possible on certain federal bonds with a minimum amount of € 50,000.

## to form

Bonds come in many different forms. The financial market has produced a variety of innovative financial instruments over the past two decades, with bonds having played a significant role. Many of these financial instruments have disappeared from the market, while others hold up longer or have been added to the standard repertoire of financial institutions.

The main forms are:

• Standard bond or fixed-rate bond (English straight bond or plain vanilla bond ): This has a fixed interest rate (coupon) over the entire term (example: 5% of the nominal value pa). It is the most common form of loan.
• Zero coupon bond (also zero bond called): This is a loan without interest coupons. The creditor's income consists exclusively of the difference between the redemption price and the issue price. Usually, zero coupon bonds are issued at a discount, i.e. below par, and are repaid at 100% (par) when they mature.
• Redemption bondor draw bond: This bond has a fixed coupon; However, their nominal value is not repaid in full on the due date, as is the case with the fixed-rate bond, but in partial installments over a certain period of time. As a rule, a grace period has been agreed, after which a raffle is made regularly to determine which of the bond subscribers should receive their money back.
• Annuity bond: With this bond, the repayment is made in equal amounts until the end of the term. These amounts include both the coupon and part of the redemption.
• Perpetual annuity or Konsolbond (English perpetual or perpetuity ): Such a bond never has to be redeemed by the issuer. The investor only benefits from the interest or the coupon, provided the issuer does not prematurely terminate and redeem the bond in accordance with the respective bond conditions.
• Zero-Perpetual: This bond is never redeemed and also has no coupon. The investor is effectively giving away the purchase price. This special form of bond is both a zero coupon bond and a perpetual annuity. Zero perpetuals are used for fundraising campaigns. It makes sense that a posting line is retained in the balance sheet (of the fund, the bank, etc.).
• Floating rate note or floating-rate bond (English floating rate note or short floater ): The interest of such a bond is adjusted during the term. This interest rate is usually based on a reference interest ratesuch as the EURIBOR (European Interbank Offered Rate) or the LIBOR (London Interbank Offered Rate). The interest rate can also be linked to the respective returns on short-term debt securities (e.g. treasury bills, T-bills) or to indicators such as the inflation rate. Market interest papers are a special form of these bonds.
• Auction Rate Security : This is a special form common in the USA; their interest rate is set in regular auctions.
• Special forms with interest rate caps: The floor floater has a lower interest limit, the cap floater has an upper limit. With the mini-max floater , the interest rate is capped , both upwards and downwards.
• Reverse floater : With this special form, the amount of the coupon payments increases when the agreed reference interest rate falls, and vice versa.
• Step-by-step interest rate bond: The interest rate changes during the term, with the interest rate step being determined at the time of issue. A distinction is made between the forms “up” (English “step up”) and “downward” (English “step down”), depending on whether the coupon rises or falls over time. Example: Federal Treasury Bills
• Bonds with step-up coupons : Here, the amount of the interest payment is often based on the credit ratings of rating agencies such as Moody's and Standard & Poor's . If the credit rating of the bond is downgraded, the interest rate rises, and vice versa. The English term step-up bond is ambiguous, as step-up interest bonds are also called this internationally.
• Inflation-linked bonds or inflation-linked bond (English inflation-linked bond ): This type of bond provides protection against the risk of inflation. Typically, the nominal isadjustedwithin a predefined period according to inflation . In most countries, the consumer price index or a corresponding index is used for this.
• Forced loan : This is a (government) loan that must be compulsorily subscribed by law. A historical example were the bonds of the Kingdom of Westphalia .
• Dual currency bond: With this bond, the coupon payments are made in a different currency than the repayment.

### Bonds with option rights

• Convertible bond or convertible bond : In this case, the creditor has the right to exchange the bond for shares in the issuer; The time and number of shares are determined at the time of issue. Technically, it is a bond that is linked to a call option.
• Warrant bond : In contrast to the convertible bond, the right to purchase the shares of the issuer is separate from the bond. This means that the option can also be traded and exercised separately.
• Reverse Convertible (English reverse convertible or equity bond ): This bond has issuer the right, upon maturity of the nominal value rather than an agreed upon issue number of shares to provide the issuer. In addition to the interest, the coupons also contain a fee for assuming the risk of writing a put option. There is also the variant in which the issuer does not actually have to deliver the shares, but pays the amount of money determined at the price on the redemption date. In this variant, other values ​​or indices can be used instead of stocks, as in the following examples:
• Index bond : special types of reverse convertible bonds in which the repayment depends on the price of an index.
• Commodity bond : Here the repayment depends on the price of a commodity index .
• Basket-bond (English basket bond ): This special form of repayment depends on the price of a basket of different stocks, stock or Commodity. The weightings of the stocks / indices in the basket and the influence of their performance can vary widely.
• Callable bond : A bond with a right of cancellation by the issuer or the creditor.
• BOLO bond (English BOLO bond, abbreviation for borrowers option, lenders option ): With this bond, the issuer has the right to set the coupon at will after a period of time; the owner then has the right to terminate. Features are the coupon, the term, the redemption rate and the issue price.
• Bunny bond (English bunny bond or multiplier bond ): The holder of such a bond has the right to choose between paying out or investing the coupon amount in a bond of the same type for each intended coupon payment. If the coupon is lower than the current interest rate , he will choose to pay out the coupon. Conversely, a bond of the same type, purchased at face value, offers a higher rate of return. There is thus a hedge against reinvestment risk if the holder makes the right decision for each coupon payment date. In this respect, these bonds are in the middle between standard bonds (full reinvestment risk) and zero coupon bonds (no reinvestment risk). The reinvestment and the interest rate risk shift to the issuer.
• Lottery loan : In the case of a lottery loan, the amount of the interest payment or the repayment of individual tranches is subject to the drawing.

### Other special forms

• Hybrid bond : This is an equity-like, subordinated corporate bond with no term limit.
• Other exotic structured products: The repayment amount and / or the interest payment are not firmly agreed, but are linked , for example, to the status of a certain variable such as a price index or stock index .

### Special terms

In the technical language of the stock exchange, different groups of securities have their own names. Examples are:

• Samurai bonds : interest-bearing securities of foreign issuers on the Japanese capital market in yen
• Uridashi bonds : Interest- bearing securities issued by foreign issuers on the Japanese capital market in a currency other than the yen
• Yankee bonds : interest-bearing securities from non-US issuers on the US capital market in US dollars.

## Accrued interest

When buying a bond, the buyer pays the previous owner his share of the coupon. This is called accrued interest or accrued interest .

Example: Investor A has a bond from X AG with an annual interest rate of 6% in his custody account. The next interest payment would be on July 1st. However, he already sells the paper on June 1 to B. In this case, in addition to the actual market value, the buyer B has the interest of 5.5% (330 days / 360 days times 6%) accrued since the last interest payment to A. to pay. On the interest date, B then receives the full 6% from X AG, even though he was only invested for one month.

## Market price and valuation

### rating

With a bond, the investor can generate two types of income :

• In the form of interest ( pension ) (ordinary income)
• In the form of price increases (extraordinary income)

Most bonds are quoted as a percentage of their nominal value. A rate of 101.25 means that the buyer has to pay 101.25% of the nominal value of the bond when buying it (plus any accrued interest ). There are, however, a few exceptions that are not quoted in the nominal currency (e.g. French convertible bonds).

The value of a bond is the present value of all payments expected in the future (i.e. coupon payments and repayment of nominal value). This means that the yield on bonds with the same credit rating and remaining term is always the same regardless of the coupon, namely the market yield plus a credit rating premium.

The general formula for calculating the value of a bond with a constant interest rate r is :

${\ displaystyle P_ {0} = {\ frac {C} {1 + r}} + {\ frac {C} {(1 + r) ^ {2}}} + \ dotsb + {\ frac {C} { (1 + r) ^ {n}}} + {\ frac {N} {(1 + r) ^ {n}}}}$

or.

${\ displaystyle P_ {0} = {\ frac {N} {(1 + r) ^ {n}}} + \ sum _ {t = 1} ^ {n} {\ frac {C} {(1 + r ) ^ {t}}}}$

in which

• P 0 = present value (= price),
• C = coupon payment,
• N = nominal (payment on final maturity),
• n = number of periods,
• r = currently valid interest rate

However, it should be noted critically with the above formula that

• Coupon payments for "partial" periods are not correctly recorded (see accrued interest ),
• Payment flows would have to be precisely forecast (but: floaters sometimes have uncertain cash flows),
• the discounting would have to be carried out with an interest rate appropriate to the term.

### Evaluation example

The X AG bond has the following features:

A prospective buyer can therefore safely expect the following cash flows over the next three years:

• in 1 year: 5 € coupon
• in 2 years: 5 € coupon
• in 3 years: € 5 coupon + € 100 repayment = € 105

The present value of the paper is determined using the risk-free market interest rate, which we have equated to the coupon of 5% in the above assumption:

${\ displaystyle P_ {0} = {\ frac {5} {1 {,} 05}} + {\ frac {5} {1 {,} 05 ^ {2}}} + {\ frac {105} {1 {,} 05 ^ {3}}} = 100}$

Now let's assume that shortly after buying the above-mentioned bond, the risk-free market interest rate rises to 8%. The investor is still entitled to the agreed payments, but the price (cash value) of his bond changes:

${\ displaystyle P_ {0} = {\ frac {5} {1 {,} 08}} + {\ frac {5} {1 {1 {,} 08 ^ {2}}} + {\ frac {105} {1 {,} 08 ^ {3}}} = 92 {,} 27}$

The price of the bond falls because potential buyers take into account that they receive a risk-free interest rate of 8% on an alternative form of investment. As a result, it is uneconomical to buy the bond for € 100 from the investor and only use a five percent interest rate. The only way to be able to sell the security after all is usually to accept a lower selling price.

When it comes to the prices of exchange-traded bonds, the risk of default is also a factor that determines the price and coupon. The default risk is determined by the expected solvency (creditworthiness) of the bond debtor. The coupon of a bond at the time the bond is issued, the higher the risk-free market interest rate, the lower the credit rating. If the creditworthiness of a bond debtor deteriorates, the increasing risk of default leads to a larger discount on the bond value (higher discount rate) and the price drops.

### Calculation of the yield (effective interest rate, yield to maturity, yield to maturity)

Often it is not interesting to know what value a bond has today, but what return one can achieve by buying a bond at a price known today. The return will usually differ from the interest rate on the market and also from the coupon of the bond, depending on the creditworthiness of the debtor, etc. The following approximation formula is used for the assessment:

${\ displaystyle r_ {e} = {\ frac {K + {\ frac {100-P_ {M}} {n}}} {P_ {M}}} \ cdot 100}$

With

• K = coupon
• P M = market price
• n = remaining term in years
• Face value assumed to be 100

It is more precise to use one iteration to insert interest rates in the valuation formula for the respective bond type until the calculated value matches the purchase price.

Return calculators are special programs for calculating the return as precisely as possible. Some of these are available on the Internet as online calculators.

In addition to the more common yield on final maturity ( effective interest rate ), there is also the current yield. This also differs from the interest rate. It is simply calculated as “interest multiplied by 100 divided by rate”.

${\ displaystyle {\ text {Current interest}} = {\ frac {K \ cdot 100} {P_ {M}}}}$

The current return is not a benchmark in bond trading. However, the current return shows the percentage interest based on the respective exchange rate. It is gaining in importance for bonds from issuers with a low credit rating and where the price deviates significantly from the nominal value.

Another way of comparing different bonds is the so-called "Doppler effect". To determine how quickly the value of a bond investment doubles, investors sometimes use a rule of thumb: the number 70 is divided by the yield to maturity. With a return of seven percent z. B. the capital doubles in 10 years (70: 7 = 10). If, on the other hand, the return is five percent, it takes 14 years. Precondition for the calculation: The interest due is regularly reinvested at constant conditions (compound interest effect).

### arbitrage

In the case of bonds, mispricing can be arbitrated. For example, an arbitrage strategy is conceivable if a coupon bond is valued too low. Then you buy them (stock exchange jargon: you go “long”) and at the same time sell (“short sell”) zero coupon bonds in the amount of the interest payments. The arbitrage profit is then (in this model example) today, with all positions resulting in zero in the future.

However, different evaluations can also result from differences in creditworthiness and market frictions.

## Risks

The bond risks can be divided as follows:

Spread, credit and liquidity risk are combined to form the credit spread . Depending on the level and extent of the risk, the bonds are divided into risk classes.

### Failure risk

The failure or creditworthiness risk is that risk, which arises from the fact that the debtor is in default of payment may come or even insolvent. The worse the credit rating, the higher the risk of default on the bond. Debtors with poor credit ratings must therefore offer a higher interest rate in order to remain attractive despite the risk of default. In December 2008, for example, it became clear that even government bonds harbor risks with bonds from the Republic of Ecuador , which suspended interest payments.

The default risk of bonds can be partially diversified by dividing the investor's capital between bonds from different issuers. As a result, the default of a single bond in the portfolio results in a less severe loss. However, it can be observed that bond defaults can accumulate in a certain time interval . This means that significantly more bonds can default in a certain period of time than one would expect in the case of stochastically independent defaults.

International, independent rating agencies use a rating to measure the creditworthiness of individual companies and bonds from their point of view . The best-known rating agencies are Moody’s , Standard & Poor’s and Fitch . Bonds issued by borrowers with poor credit ratings are also known as high-yield bonds , junk bonds and junk bonds ( English junk bonds or high yield bonds ), respectively.

In order to reduce the risk of default for investors, bond insurers assume this risk for a fee.

The repayment of a bond can also be wholly or partially omitted against the will of an individual creditor, provided that a corresponding collective action clause is stored in the bond conditions and a majority of the creditors consent to the cancellation ( Section 5 of the German Debt Securities Act).

### Interest rate risk

The interest rate risk is the risk that arises from the possibility of a change in the market interest rate . While a bond is always repaid at face value, the market interest rate has an impact on the price of the bond, which is important if the bond is sold again before it matures.

The market interest rate is the most important, but at the same time also the most volatile parameter for valuing a bond. A change in the interest rate has the following effects for the holder of a bond:

• The value of the bond goes down when the market rate rises. This effect depends on the price sensitivity, which can be measured using duration and convexity .
• The redemption amounts (coupon and redemption) are invested at the new interest rate. If the interest rate rises, the amount resulting from the reinvestment of the repayment amounts also rises (the compound interest ).
• The interest income from the coupons on the bond remains unchanged.

The rate change and the compound interest effect are opposite. The concept of duration was developed to answer the question of what overall effect a change in interest rates has on the price of a bond.

### Termination risk, draw risk, conversion risk

These are three types of uncertainties that only arise with certain bonds where the right to call the debtor or a draw for redemption has been agreed, or when it comes to convertible bonds.

### Currency / Exchange Rate Risk

The nominal currency is the currency in which the bond will be repaid by the issuer when it matures. The coupon currency is the currency in which the interest is paid out. Almost all bonds have the same coupon and nominal currency.

Due to changes in exchange rates, the purchase of a foreign currency bond involves an exchange rate risk. If the nominal currency falls against the buyer's home currency, he suffers losses; if the nominal currency rises against the home currency, he can realize profits.

The currency risk can be minimized through currency options , currency forwards or currency futures .

### Inflation risk

The inflation risk describes the uncertainty about the real amount of future payments. Since the Fisher effect can only be empirically proven in the long term, the inflation risk must be assessed separately from the interest rate risk. The risk of inflation can be eliminated by purchasing inflation-linked bonds .

### Liquidity risk

It is possible that by the time the bond is about to be sold, this cannot be done without large price discounts. This risk is usually negligible in markets with a large market volume; it can exist in small markets or in exotic bonds. See also: Market Liquidity Risk

## Development of the course over time

Since the nominal value of the bonds is repaid at the end of the term , there is a convergence of nominal values , so the prices of the bonds move towards the end of the term in the direction of the nominal value. The effect of price changes resulting from the passage of time - without taking the yield curve changes - is called Rolling down the yield curve refers effect. Assuming a constant yield curve over time (this does not mean a flat yield curve), this effect can be represented using the bond price at any point in time during the term. The price will first rise above the issue price and then fall back to the nominal value.

### Causes rolling down the yield curve effect

The same payments are discounted at lower interest rates given a normal yield curve. The discounting also takes place over a shorter period of time. This explains an increase in the price. The opposite effect, that the coupon for the previous dates is no longer available, dominates at the end of the term. The movement in the price of a bond towards par at maturity is known as the pull-to-par effect.

## literature

• Rolf Beike, Johannes Schlütz: Read, understand, use financial news. A guide through quotes and market reports. 4th edition. Schäffer-Poeschel, Stuttgart 2005, ISBN 3-7910-2354-3 .
• Frank J. Fabozzi, Michael G. Ferri, Frank Jones, Franco G. Modigliani: Foundations of Financial Markets and Institutions. 3. Edition. Prentice Hall, Upper Saddle River NJ 2002, ISBN 0-13-018079-3 .
• Peter Steiner, Helmut Uhlir: Securities Analysis. 4th edition. Physica-Verlag, Heidelberg 2001, ISBN 3-7908-1302-8 .
• Jutta MD Siebers, Alfred BJ Siebers: Bonds. Earn money with fixed-income securities (= dtv 5824 Beck-Wirtschaftsberater ). 2nd Edition. Deutscher Taschenbuch-Verlag, Munich 2004, ISBN 3-423-05824-2 .
• Manfred Steiner , Christoph Bruns: Securities Management. Professional securities analysis and portfolio structuring. 9th edition. Schäffer-Poeschel, Stuttgart 2007, ISBN 978-3-7910-2677-0 .

Wiktionary: Loan  - explanations of meanings, word origins, synonyms, translations

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36. ^ Ecuador officially defaulted on part of its foreign debt