Obligation (finance)

A obligation (in English: jump ) is a evidence of indebtedness (transferable security or financial Immobilization) representative of a loan. As such, the obligation is transferable and can thus be the subject of a quotation on a Bourse. In practice, exchanged volumes are negotiated mainly Private.

Principal characteristics

This title is a contract between the transmitter and the successive holders of the title, whose two principal elements are the bill book of financial flows and their way of calculating.

The transmitting (borrowers) are as well private organizations as communities (in particular Treasuries).

An obligation is emitted originally with short, average or long run, even without date of expiry (perpetual obligations). However one often holds the name of obligation under lasted higher than 5 or 7 years. For the lower durations, the " terms; bon" (of the Treasury…) or " billet" (of treasury…) are generally preferred.

Example

The assimilable Obligation of the Treasury 4.75% 4/25/2035, whose unit detention (one also says: Face value) is of a Euro, is a contract by which the French Republic is committed pouring with the holder of the known as contract:

each year on April 25th 0,0475 euro, between now and on April 25th, 2035 included,
more 1,00 euro on April 25th, 2035.

The price to which this contract is currently negotiated is the Current value of the obligation.

A second way of presenting the things is to say that the holder of the obligation:

ready with the French Republic (which it, borrows)
the current value (the price) of the obligation, for the face value of one euro,
which will be refunded to him at the 100% ( face value ) on April 25th, 2035
and will give place to a payment of annual interest of 4,75% (of the face value ) each April 25th between now and 2035 included.

Transmitters

An obligation can be emitted by:

a State in its clean currency - one speaks then about Emprunt of State;
a State in another currency that his - one then speaks about sovereign Obligation;
a company of the public sector, an public agency, an local government agency - one speaks then about obligation of the public sector ;
a private company, an association, or any other moral person, of which the Pools of credits, and one speaks then about obligation corporate .

Transactions and detention

The detention of the obligations by the private individuals became primarily indirect: it is carried out very largely via OPCVM and the contracts of Assurance-vie.

Nevertheless, the obligations can always theoretically be held directly by the private individuals and are the subject thus in the regular manner of an official quotation - though often without transactions, therefore fictitious , or theoretical - on a Bourse.

The near total, in volume, of the transactions are carried out Private, except purse , between financial institutions: banks of investment, insurers, administrative of OPCVM, deposit banks, etc

Exchanged volumes are considerable, several thousands of billion euros each day, particularly in and Government loans derivative products of those, which constitute the directing market of the Interest rate in the medium and long term.

The negotiable evidences of indebtedness are instruments very close to the obligations but which, them, are not intended to be held on line by private individuals, only by managers of OPCVM and other professionals of the financial markets. Their regulation is thus slightly different.

Current value

detailed Articles: Actualization, Discount coefficient, Annual percentage rate, Rate zero-coupon, Curve of rate, Spread of credit and the general article Interest rate

An obligation is a whole of flows shifted in time. These flows are thus not directly comparable between them. One euro on a date $d_ {1} \, \!$ does not have the same value as the same euro on a date $d_ {2} \, \!$ , would be this only because of the Inflation.

Let us note

Flux (d_ {I}) \, \!

with

{i=1,…, N} \, \!

the whole of flow falling at the dates $d_ {I} \, \!$ and constituting the obligation.

To bring back these flows to a common base, their equivalent on a single date $d_ {0} \, \!$ , one multiplies them each one by their Discount coefficient $CA (d_ {I}) \, \!$ . This discount coefficient is obtained by calculation starting from interest rate that one chooses to apply to this particular obligation to bring up to date between the dates $d_ {0} \, \!$ and $d_ {I} \, \!$ .

The current value (the correct term is rather brought up to date value but current value is the usual expression) of the obligation is thus the sum of the current values of each flow:

VA (d_ {0}) = \ sum_ {i=1,…, N} CA (d_ {I}) \ times Flow (d_ {I}) \, \!

There exists a simplified formula of actualization, with only one rate, the Annual percentage rate, which although vague, is very much used and is useful in a first approximation.

A tool for evaluation: the output at the limit

Actualization consists in returning equivalent a price of the year X + 1 at a price of year X. Each year the prices increase X % and thus consequently occasion the value of the money also (1 € in 1945 was not worth 1 today €). To return to the obligations, those will pour each year the same interest.

Definition: the output at the limit is the rate which returns equivalent the current price of the obligation to the actualization of the future incomes.

(let us suppose 1 000 €). One knows that to receive 1 000 today or in 10 years does not return to same: therefore one will bring up to date these interests and especially the capital which will be refunded at the end to know the value of the obligation.

Example: an obligation over 3 years of €: 100000 which gives interests of 10% is with dimensions to 98%. Which is the output at the limit?

the future incomes are:

2002 : : 10000 (interests)
2003: : 10000 (interests)
2004: : 110000 (interests + refunding of the capital

To know the output at the limit, should be solved the following equation:

0,98 \ times {} 100000 = \ frac {10000} {1+t} + \ frac {10000} {\ left (1+t \ right) ^2} + \ frac {110000} {\ left (1+t \ right) ^3}

The output at the limit is the rate (T) which makes it possible to solve this formula. Here, 10,82% are found

Definition: the annual percentage rate is the real output of the obligation at the limit, which has nothing to do with nominal interest rate.

Example: by approximation:

To determine the annual percentage rate by approximation, it is enough to determine the overcost and to distribute it over the duration. The overcost is the issue price of 2%, that is to say per annum 0,2% that one deduces from the nominal rate (7% - 0,2% = 6,8%).

Conclusion: The longer the lifespan of the obligation is, the more the cost of the extra premium will be spread out and thus its weaker impact.

Example: by approximate formula:

(Refunding - Course)/Many years Interest + ______________________________________ (Refunding + Course)/2

Course of the obligation: 103%
Lifespan: 4 years
nominal Interest rate: 6%
Refunding: 100%

6+ \ frac {\ frac {100-103} {4}} {\ frac {100 +103} {2}} = 5,995 \ %

Legal methods

The legal methods of an obligation can be very diverse. In the case of a private placement (obligations not - dimensioned), the methods of the titles are defined in a contract of emission (or contract of subscription ). In the case of an emission carried out by public call to the saving or when the admission of the obligations to the negotiation on a regulated market was required (obligations with dimensions), the methods of the titles are generally defined in a leaflet controlled by the controlling authority of the market (for a quotation on Euronext Paris, Authority of the financial markets, for a quotation on Luxembourg Stock Exchange, Commission of monitoring of the financial sector).

Principal parameters

Flows of an obligation are defined by:

the currency in which it is emitted;
the face value of the obligation, called the even ;
its date of expiry (also called maturity);
the mode of refunding (one also says “damping”):

in only once at the limit ( in fine )
or by sections ,
or never (perpetual obligations);

the price of refunding , i.e. the amount, expressed as a percentage of the par, which will be refunded at the limit;
the interest rate of the obligation and the way of calculating of this one;
the periodicity (often annual) of the payments of interest, called coupons .

Fixed, variable or null rate

The rate of interest can be:

fixes - Voir the principal article: Obligation atrate fixes
or variable (even “revisable”) - Voir the principal article Obligation atfluctuating rate
or no one - Voir the principal article Obligation zero-coupon .

Possible options

Moreover, certain obligations are equipped with option S , such as for example the advance payment on certain dates with the liking of the English transmitter (: callable jumps ) or contrary to extension at the limit, or of exchange against another title, with or without Good of subscription separate.

Some are equipped with an option of exchange against actions - Voir the principal article: Convertible bond.

General case

The majority of the obligations are traditional annual obligations (which one calls in English: lime pit vanilla jumps , “obligations with vanilla”), i.e.:

refunded

in fine (in English, one speaks about bullet jumps )
with the par

paying a rate fixes , known as “nominal rate”
via a annual coupon .

Example: the assimilable Obligation of the Treasury 4,75% 4/25/2035, already taken for example above in introduction, is a traditional obligation atfixed rate of expiry 4/25/2035 and nominal rate 4,75%.

Cours and run coupon

See principal article: Coupon run .

It is of use to arbitrarily separate the current value from an obligation in:

course , also known as course foot of coupon , expressed in % of the nominal one;
Coupon run , also expressed in % of nominal, generally with three decimals.

This practice comes from one time - the 19th century - where neither the computers nor the calculators existed. It was thus important to be able to post a apparent price obligations (the course ) making it possible to compare them between them without having to make complex calculations. The development of the means of electronic computation made that less necessary, but the use remained.

Indeed, as one can note it on the graph opposite, more one approaches a date of payment coupon, and more the price of the obligation (blue line), mechanically, integrates the amount of the known as coupon. It reperd, also mechanically, but abruptly, once the aforementioned versed coupon. While withdrawing, proportion temporis , from the price of an obligation the effect of the next coupon, the “run coupon”, one obtains a curve (in red, on the graph) much more regular and easy to interpolate in time: the “course”.

Two English terms are regularly used to evaluate an obligation:

Clean Price : the course of the obligation is mentioned without taking account of the receivable interests not fallen
Dirty Price : the course includes/understands the receivable interests not fallen

Credit risk and premium of liquidity

See the principal articles: Spread of credit, Credit risk, Premium of liquidity and financial Notation

In the event of defect of transmitter (bankruptcy, voluntary liquidation, etc) the holder of an obligation supports the risk not to find his capital (ex: Enron, Worldcom, Parmalat…). Admittedly, the inherent risk with an obligation is weaker than that presented by a action, owing to the fact that the holders of obligations occupy a row much higher in the order of the creditors than the shareholders. Nevertheless, this risk is quite real.

If the only appropriations which are really without risk are… those which were refunded, there exists a good approximation of one credit at the same time without risk and non-encore fallen. It is consisted the most liquid Government loans emitted by the least involved in debt large developed countries, i.e. negotiable obligations

constantly for significant amounts
and emitted in the currency where the transmitter lays out at the same time

of good additional credit-worthinesses
and of the full engine rating.

The rates derived from these loans thus correspond, for each currency where they exist, with the Taux without risk. The other obligations, less liquid, involve a risk, whose measurement by the bond market is given by the difference in rate between their yield and the rates without risk. This variation of rate, or Spread of credit, corresponds in theory to the sum:

of a Premium of liquidity, i.e. the cost of negotiation of the obligation
and, especially, expectation of the risk of defect of the transmitter multiplied by the rate of recovery of the debts awaited in the event of defect.

The obligations often make - although that is not obligatory - the object of a financial Notation which normally makes it possible to better evaluate the credit risk presented by the title.

Cours des obligations and interest rate

See principal articles: Curve of rate and Spread of credit

As one saw, an obligation is a loan which serves a Interest rate, expressed in the form of a sequence of coupon S over a given period, then of a final refunding, generally with the face value . To evaluate an obligation, one calculates the Current value of all the payments to come ( coupons and face value ) while bringing up to date the sums with a Interest rate corresponding to the risk from the obligation. Also, when the Interest rate S increase, one will bring up to date ata higher rate, and thus that will reduce the Current value incomes of the obligation. One from of deduced that:

when the rates go up, the current value (= the price) of the obligations lowers , and conversely;
more one obligation has an expiry moved away, plus the Actualisation of the incomes will have an significant impact on the value. In short, when the rates go up, an obligation at 30 years will drop more than one obligation at 2 years. One speaks about sensitivity of the obligation.

See too

Financial market, Bond market
Discount coefficient, Annual percentage rate, Face value, Interest rate
Risk of rates, Sensitivity, Duration
Repo
swap, Future, Derived
Government loan, OAT, Bund, OLO, T-Jump, BTP
Curve of rate, Rate zero-coupon, Obligation zero-coupon, Obligation atrate fixes, Strip, Dismemberment
negotiable Evidence of indebtedness
Credit risk, financial Notation, Credit default swap, Spread of credit, Premium of liquidity, Flight to quality
Subordination, Securitization

External bonds

The specialized agencies (Bloomberg, Reuters, Dow Jones, etc) as well as the platforms of trading of instrument of interest rate (MTS, Cantor Fitzgerald, BrokerTec, etc) draw an important part of their incomes from the sale of quantitative information to the participants in the financial markets. The information on the markets of interest rate free, or even more generally at an accessible price for a private individual, is thus strong not very available on Internet .

Euro

Daily statements at Paris 11:00, time

Euribor
Annual percentage rate of the swaps, 1 to 30 years, against Euribor 3 months
Rate of Government loans and certain obligations of the public sector, on Euro-MTS, including in '' asset swap '' against Euribor
TEC10: annual percentage rate of a theoretical OAT of expiry 10ans

Spreads of credit

Rate of '' Credit default swaps ''
Rate D ''' asset swap '' against Euribor on Euro-MTS

US Dollar

Database of the Federal fund of the United States - Attention, conventions heterogeneous.

Complementary references

Mathematical Dalbarade J-M., of the financial markets , 2005, Eska.
Of Bruslerie H., bond Management. Volume 1, Marchés, interest rate and financial credits , 2002, Economica.
Of Bruslerie H., bond Management. Volume 2, Rentabilité, strategies and control , 2006, Economica.
Kolifrath G. and T. Journel, Market money and bond , 2003, the essential ones of the Review Banks.
Quittard-Pinon F. and T. Rollando, Risk management of interest rate , 2000, Economica.

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