Advanced finance

Lesson 4: Bond markets

Earning money
Bonds: introduction
Types of bonds
Basic properties of bonds
Further discussion of bonds

  • Russia's economy: smoke and mirrors
  • Can't grasp credit crisis? Join the club
  • Hedge funds in difficulty
  • Bear Stearns
  • "The financial system must be saved"
  • The story of pepper

  • Go to lesson:

    Colonial Finance Corporation, Delaware, USA, 1920s




    Enterprise, borrowing, finance, time and risk
    The concept of enterprise encompasses the idea of time: some event will take place at the initial time t0, and some other events will happen in the future, at times t1, t2, t3, etc. Borrowing encompasses time. And finance too. The concept of enterprise, borrowing, finance and time are closely linked. To these four concepts we shall add a fifth one: risk.

    Financing a physical investment
    The basic situation, which interests us, is this: an entrepreneur foresees the possibility to create an enterprise which requires the acquisition of various assets at its inception and then will be able to produce value over a long period of time. If the entrepreneur does not have funds he can borrow them and then repay them later, according to a schedule, with the forthcoming proceeds from his enterprise, also called project, or venture.

    Three agents
    Notice that this involves already three agents at time t0: the entrepreneur E, the lender of funds I, and the seller of initial assets A.


    Why not sell directly to A the financial contract?
    The entrepreneur E could actually make simply a single transaction with the seller of assets A: he would buy the assets and pay with the financial contract. But the financial contract represents only a promise of E to pay. It has a risk. While money represents value with no risk.

    Separating risky and non risky operations
    So the two operations, of bearing a risk and of buying assets, are separated and handled by E with two different agents:

    • A, the seller of assets, receives riskless value (money from the entrepreneur), and
    • I, the investor, (which provides money to the entrepreneur) receives a financial contract signed by E.



    1. The entrepreneur E and the seller of assets A deal with real goods and services, whereas the investor I only deals with signs.
    2. Conventional explanations say that the investor will get his remuneration for two services:
      1. he "postpones", to a later time, the use of his money for consumption
      2. he takes a risk (which is reduced to zero, say conventional explanations, only if he buys short term government bills)
    3. The financial contract is a contract specifying a schedule of payments in the future. It is a sign of sorts.
    4. The risk, here, is the risk of the enterprise, or, equivalently, of the entrepreneur.
    5. We reviewed the history of money: it is no longer tangible value, it is pure signs. And modern money is legal tender, "guaranteed" by the state (not as well as one could wish, as we know)
    6. Indeed, this money does not have to be tangible as long as it is trustworthy (fiduciary money). This is what is meant when we say that "commerce needs money, and [that] this money can be created according to the needs of commerce". And it is what John Law and others began to understand as early as the late XVIIth century.
    7. Conventional explanations view the money lent by the investor as something "equivalent to tangible value", in the sense that he could use it, instead, to buy and consume goods and services. This is the support for the age-old perception of money as value and as a purely quantitative notion. Yet this money can be created at will (we saw how central banks, and even commercial banks create official money). And indeed when there is a dearth of liquidities the economy suffers, money must then be created; and when there is too much liquidities economic dysfunctionings appear too, like lending to insolvent borrowers.
    8. The somewhat disturbing relationship between money and tangible goods lead some economists in the XIXth century to declare that "money is only a veil", an irrelevant algebraic measuring convention to equate various goods. Nothing could be farther from a good model (i.e. from "the truth")!
    9. The reason why John Law failed is that he did not manage his created money correctly, not because he created money.
    10. It is a moot question whether modern central banks and in particular the Fed manage money correctly. Is the injection of $660 billion in the American and European financial systems, which was made in the last few months (and it is not finished),
      1. a normal event in the course of business of central banks?
      2. an exceptional event in response to an exceptional situation? (But what makes the beginning of the XXIst century exceptional?)
      3. a bail out of rich reckless people by thrifty reasonable people?
      4. an advance indication of forthcoming bigger events?
    11. Does it behoove central banks to take steps to prevent reckless lending, or is it not their business but the business of governments?
    12. In the 1920's and 1930's financial crises were cured with tight monetary policy "to purge" the system. It was followed by a blaze of bankruptcies, huge unemployment and social distress, but it was deemed necessary. Nowadays, however, central banks medicine is giant scale money creation and injection.
    13. When central banks are less and less reliable, there will come a point when entrepreneurs and/or large private companies will be able to issue debt instruments less risky than official currencies. It has already begun. But since it undermines the power of nation states it is fought by official authorities. eBay, when it bought paypal, was forced to make it a simple electronic bank reporting in detail to national authorities and under their strict control, like any other bank. Google has been looking at a money for a long time, but is still pondering...
    14. The entrepreneur is able to start a firm without money (or only his small personal funds, the role of which is just to prove that he is willing to take himself substantial risks; it is an additional guarantee for the investor)


    The above picture and explanations do not specify explicitly whether the investor invests in equity or in debt. We already know, from our introductory course in finance, the difference:

    • Equity gives "a stake" in the enterprise to the investor. He buys stocks issued by the enterprise at an agreed upon price, which gives him ownership over a percentage of the firm. Usually the rest of the firm is the property of the entrepreneur. The investor will be paid with dividends and with the resale, someday, of his stocks to another investor, or, theoretically, with the possible liquidation of the firm.
    • Debt does not give any title of ownership over the firm. The investor, in that case, will be paid back his initial money, plus interests, according to a schedule and conditions specified in the financial contract. In the case of liquidation of the firm, the investor into debt has priority over the investor in equity to get his money back.


    In this course we shall use the concept of money in its conventional sense: means of payment, of an official nature, which extinguish debts. Then the study of the exchange of money now, for streams of money in the future, under various conditions, will be reasonably straightforward.

    But we begin to see that money is some sort of nonquantitative concept (it is a more complex factor, measuring the state of a social system, than conventional wisdom perceives) which sets or does not set the economy in movement. (It has been compared, in turn, to grease, to temperature, to entropy, but all these miss the point: a new description is called for.) It is a paradox that the creators of money can use it right away for consumption and yet it is useful because it sets the economy moving. This was for example a privilege of the Spanish empire during the XVIth century, but for a complex set of reasons it did not profit Spain. It is the privilege of any official issuer of money (it bears the name of seigneurage). It is also the gist of the debate on America's "exorbitant privilege" to print dollars (or T-bills) to pay for its consumption. Modern banks do create money but it is with the double mechanism of receiving a loan and opening a credit, which must be refunded, and this money is not just consumed.

    So we shall keep in mind that the relationship between the entrepreneur E and the investor I (i.e. the right half of the above picture) embodies deeper phenomena than is immediately apparent in the lending/borrowing of money.

    The study of equity markets will be the subject of a later lesson. The present present one is debt markets, and, more specifically, the simplest and most important of them: the bond markets.



    Earning money

    In a society, an individual who does not live in autarky has two ways of earning money:

    1. Selling the resource he/she produces naturally, that is his/her work
    2. Profit from the variation in value of assets he/she possesses or (equivalently) can acquire. This takes us back to the two fundamental types of investments:
      1. physical investment: we will be able to exploit advantages we are alone to enjoy in the vicinity,
      2. financial investment: Modern Financial Theory says NPV is zero.

    To sell one's work, there are again two possibilities: either work in a firm owned and run by other people, it is the situation of most salaried people; or create a firm and work in it, this is the situation of the above entrepreneur E.

    Entrepreneur E starts a firm by acquiring initial assets necessary for operations. And, if he doesn't have the necessary initial funds, we saw that he can borrow them (with ou without collateral guarantees), and pay them later, according to a schedule, with the earnings of his firm. If on top of this his firm makes good money, he can pay himself a salary, that is, sell his work to his own firm. As we know, in France, revenues from labor are highly taxed (yet the nation's income statement is in deep deficit, of the order of 100 billion euros a year), and our entrepreneur's only real perspective of getting rich is that his firm become very successful and at some point he sell it to other people.

    The real economy being full of paradoxes, it is sometimes possible to start the equivalent of a firm which will be able to repay the initial loan and turn a profit, without the entrepreneur doing anything! This is the case when someone E buys an appartment A, say in the Bastille district of Paris, finances 100% of it with a mortgage loan from I, and then rents it to tenants. We have known many situations where the rent covered the repayment of the loan (interest and capital), and after 10 or 15 years, the "entrepreneur" became the full owner of a flat without having put any work in the venture.

    In certain circumtances, a Leverage Buy Out (LBO) is not much different. A special holding firm H is set up, financed mostly by debt (i.e. with a "high leverage"). The cash raised is then used to buy an existing firm F (often a subsidiary which a group wants to divest). Finally the existing firm F is somewhat reorganised, "turned around" to produce high cash flows, and these are used to pay quickly back the debt of the holding H. In several countries, tax laws facilitate LBO's by taxing lightly the dividends funneled from F to H.

    The second way to earn money is to profit, we said, from a variation in the value of assets. A simple illustrative example of a pure speculation is given by the father of an acquaintance of mine, who, at the end of WWII, bought all the stamps and bank notes that AMGOT had planned to introduce in France, but that De Gaulle refused, and which turned out to be useless. In fact they turned out to become "collectors items". My friend's father was careful not to resell them too quickly. Over the course of two decades, he made a fortune, and his son enjoys a large wealth that leaves him time to do high level mathematics (a notoriously inadequate activity to become rich).

    Amgot (Allied Military Government for Occupied Territories) money planned for France in 1944 (source: Wikipedia)

    Of course, when one is able to control the variation in value of the acquired assets, like buying farm land, and then buying municipal agents to reclassify it as constructible land, it is all the better, although it is discouraged in courses in business ethics. (Whether courses in business ethics are of any use is questionable, but it employs people.)

    These are final introductory comments on money and value before we turn to the mechanisms of bonds.


    Bonds: introduction

    Bonds are nothing more than plain loans split among many lenders. They appeared in the XIIth century when some princes found that their bankers were reluctant to (or just could not) lend them more than a certain sum. By splitting the money needed among several investors, the borrower could raise more money, while each investor limited its exposure. The first recorded bond was issued in Venice in 1157 and served to finance a war with Constantinople (Levinson, p 58).

    The simplest bond, also called "plain vanilla" bond, has the following structure (we take the example of a 7 year 5% bond):

    • At date y0, today, the lender-investor-buyer gives 1000 euros to the borrower-issuer-seller, and receives a signed contract from the seller. This contract is the bond tying the borrower to the lender (bond means tie). The initial sum of 1000 euros is called the principal or the face value of the bond.
    • One year later, at date y1 (or just called date 1) the borrower pays to the lender an interest (also called a coupon) of 50 euros, i.e. 5% of the initial value.
    • After one more year, at date y2, the same coupon payment takes place from the issuer to the holder of the bond. The bond holder is the initial investor, unless the initial investor has sold the bond to somebody else who becomes the bond holder.
    • ...
    • After 7 years, at date y7, the borrower pays to the bond holder a final interest of 50 euros and repays the principal of 1000 euros.

    the arrow pointing downward represent money from investor to issuer, and the arrows pointing upward represent money from the issuer to the bond holder.


    Bonds used to be thought of as dull financial products, good for safe investments to keep wealth for the next generation. But since the 1980's this has changed. We shall see in a moment the large variety of bonds, beyond the plain vanilla bond described above, and aside from all the so-called "exotic", "derivative" or "structured" financial products.


    Size of markets

    Giving a numerical figure to measure the bond markets (or market) is difficult. For one thing, contrary to stocks which are all handled through stock markets and are reasonably easy to monitor, most bonds are issued and traded over-the-counter (in French, "de gré à gré"), that is in a private transaction between an issuer and an investor. It is not mandatory that an official authority record the bond. An estimated figure, however, is that the total size of the bond market worldwide (the outstanding bonds) at the end of 2004 was approximately $50 trillion, of which roughly $37 trillion traded on domestic markets, and another $13 trillion traded outside the issuer's country of residence.

    In the United States, the largest single market, over $400 billion worth of bonds change hands on an average day, and the value of outstanding bonds at March 2005 exceeded $13 trillion (Levinson).


    Why issue bonds?

    1. Cost: financing via bonds, when it is possible, is usually cheaper than via bank loans
    2. Matching revenues and expenses: the regular schedule of future payments, required by a bond issue, from the borrower is well suited to finance projects where the future cash inflows are likely to be reliable and steady. This is the case for instance of a new freeway with a toll, or a bridge like the Millau bridge. There are also financial institutions which have steady cash inflows: insurance companies. It is advisable for them to issue bonds when they need financing to pay for damages, or simply enough, to invest into sure assets (like apartment and commercial buildings).
    3. Inter-generational equity: it is natural to finance with long term bonds the construction of a public project that will be beneficial to society over several generations. This way the costs will be supported, via taxes or tolls, by all the generations using the works. Notice that the actual flows of resources and money must be analyzed carefully (as for pensions): the project will still be constructed with the labor and other resources of people at time t0 (today, or "the present"), but some people (the investors into the financing bonds) will relinquish possible present consumption for a stream of future payments, that will even accrue to their heirs.
      This "inter-generational equity" means nothing more than "some future people will owe money to some other future people as a consequence of the lending by their ancestors, which took place today". For example, since the early 1970's, the 5 million Norwegians, who were able in the early 1960's to convince the international community that they own about 1/3 of the oil reserves in the North sea, have been extracting and selling this oil, in exchange for money and financial securities (bonds and stocks - in "ethical" businesses they require, giving lessons of moral to the rest of the world). At present the financial securities of the Norway oil fund are mostly denominated in dollars and represent approximately $380 billion. Current Norwegians expect future generations of Norwegians to be able to sell back these securities to the rest of the world in exchange for consumption which they are "relinquishing" today.
    4. Controlling risk: the obligation to repay a bond can be tied to a specific project or a particular government agency. This can insulate the parent corporation or government from responsibility if the bond payments are not made as required. We shall even see this mechanism at work in the process of "securitization" - in French "titrisation" - where a lender can resell bundled securities as a new one, the payments of which are tied to the initial ones. More on this in the next lesson.
    5. Avoiding short-term financial constraints: governments and firms may turn to the bond markets to avoid painful steps, such as tax increases, redundancies ("mise au chômage") or wage reductions, that might otherwise be necessary owing to a lack of cash.

    This last point simply says "if you don't have the money, you may borrow it". Beyond its mundane looking appearance, it actually touches on the deep nature of money and credit. In a certain modelling approach, money and credit are the same: if you don't have money, but have credit (i.e. people are willing to lend you money), "for all practical purposes" it is as if you had money. And conversely, to have money is useless if you can neither consume it nor lend it to somebody else whom you trust. For example, landing on a desert island with a trunk full of euro bills, or even gold, is useless.


    Who issues bonds?

    Four basic types of entities issue bonds (from Levinson).

    National governments

    Bonds backed by the full faith and credit of national governments are called sovereigns. These are generally considered the most secure type of bond. A national government has strong incentives to pay on time in order to retain access to credit markets, and it has extraordinary powers, including the ability to print money and to take control of foreign- currency reserves, that can be employed to make payments. Notice that, for a government, printing savings bonds or printing money are not that much different.

    US debt to foreign countries in the form of US treasury bonds


    The best-known sovereigns are those issued by the governments of large, wealthy countries. US Treasury bonds, known as Treasuries, are the most widely held securities in the world, with $5.3 trillion in private ownership as of early March 2008 (the above table shows the part owned by foreign countries). Other popular sovereigns include Japanese government bonds, called JGBs; the German government's Bundesanleihen, or Bunds; the gilt-edged shares issued by the British government, known as gilts', and OATs, the French government's Obligations assimilables du trésor. Governments of so-called emerging economies, such as Brazil, Argentina and Russia, also issue large amounts of bonds.

    Another category of sovereigns includes bonds issued by entities, such as a province or an enterprise, for which a national government has agreed to take responsibility. Investors' enthusiasm for such bonds will depend, among other things, on whether the government has made a legally binding commitment to repay or has only an unenforceable moral obligation. In many countries the amount of debt for which the national government is potentially responsible is extremely high. In the United States, for example, federally sponsored agencies had $2.7 trillion in bonds outstanding as of 2005. Although much of this does not represent legal obligations of the US government, the government would come under heavy pressure to pay if one of the issuing agencies were to default.

    Lower levels government

    Bonds issued by a government at the subnational level, such as a city, a province or a state, are called semi-sovereigns. Semi-sovereigns are generally riskier than sovereigns because a city, unlike a national government, has no power to print money or to take control of foreign exchange.

    The best-known semi-sovereigns are the municipal bonds issued by state and local governments in the United States, which are favoured by some investors because the interest is exempt from US federal income taxes and income taxes in the issuer's state. About $2.1 trillion worth were outstanding in 2005. Canadian provincial bonds, Italian local government bonds and the bonds of Japanese regions and municipalities are also widely traded. Many countries, however, deliberately seek to keep sub- sovereign entities away from the bond markets. This serves to limit their indebtedness, but also has the less noble goal of providing a steady flow of loan business to balks. Germany's states, or Länder, have emerged as significant issuers, with €170 billion of bonds outstanding at the end of 2004 - a leap from only €59 billion of bond indebtedness in 1999. German local governments, however, had almost no bonds outstanding.

    There are many categories of semi-sovereigns, depending on the way in which repayment is assured. A general-obligation bond gives the bondholder a priority claim on the issuer's tax revenue in the event of default. A revenue bond finances a particular project and gives bondholders a claim only on the revenue the project generates; in the case of a revenue bond issued to build a municipal car park, for example, bondholders cannot rely on the city government to make payments if the car park fails to generate sufficient revenue. Special-purpose bonds provide for repayment from a particular revenue source, such as a tax on hotel stays dedicated to service the bonds for a convention centre, but usually are not backed by the issuer's general fund.

    Public-sector debt, including sovereign and semi-sovereign issues, accounts for about 60% of all domestic debt worldwide. The total amount of public-sector debt outstanding at June 2005 was almost $24 trillion, of which $22 trillion was issued by governments within their domestic bond markets and $1.4 trillion was issued internationally.


    Corporate bonds are issued by a business enterprise, whether owned by private investors or by a government. Large firms may have many debt issues outstanding at a given time. In issuing a secured obligation, the firm must pledge specific assets to bondholders. In the case of an electric utility that sells secured bonds to finance a generating plant, for example, the bondholders might be entitled to take possession of and sell the plant if the company defaults on its bonds, but they would have no claim on other generating plants or the revenue they earn. The holders of general-purpose debt have first claim on the company's revenue and assets if the firm defaults, save those pledged to secured bondholders.

    The holders of subordinated debt have no claim on assets or income until all other bondholders have been paid. A big firm may have several classes of subordinated debt. Mezzanine debt is a bond issue that has less security than the issuer's other bonds, but more than its shares.

    Securitization vehicles

    An asset-backed security is a type of bond on which the required payments will be made out of the income generated by specific assets, such as mortgage loans or future sales. Some asset-backed securities are initiated by government agencies, others by private-sector entities. These sorts of securities are assembled by an investment bank, and often do not represent the obligations of a particular issuer. (Asset-backed securities are discussed in the next lesson.)



    Illustration of the securitization process: Fannie Mae lends money in exchange for mortgage-loans (right part of the picture), and then "securitizes" them into a new bond (left part of the picture) the payments of which are not guaranteed by Fannie Mae, but rest only on the payments from the home owners.

    (Technically Fannie Mae does not deal directly, on the right, with home owners, but with local institutions lending to home owners.)


    The distinctions among the various categories of bonds are often blurred. Government agencies, for example, frequently issue bonds to assist private companies, although investors may have no legal claim against the government if the issuer fails to pay. National governments may lend their moral support, but not necessarily their full faith and credit, to bond issues by state-owned enterprises or even by private enterprises. Corporations in one country may arrange for bonds to be issued by subsidiaries in other countries, eliminating the parent's liability in the event of default but making payment dependent upon the policies of the foreign government.


    National markets

    Table 4.2  Outstanding private-sector domestic debt securities ($billion)  
    1993 1998 2000 2002 2004
    United States 3 419 5 984 6 504 11 761 13 661
    Japan 1 325 1 453 1 543 1 829 2 030
    Germany 738 1 140 956 966 1 033
    France 541 477 432 645 959
    Italy 300 364 296 544 877
    United Kingdom 134 388 470 290 367
    Others 46 1 496 1 628 2 204 3 419
    Total 6 503 11 302 11 829 18 239 22 346
    Source : Banque des réglements internationaux      


    Read Levinson (chapter 4) on:

    Issuing bonds

    • Underwriters and dealers
    • Swaps
    • Setting the interest rate
    • Selling direct

    No more coupons

    The changing nature of the market

    • Secondary dealing
    • Electronic trading
    • Settlement


    Types of bonds

    A bond is a financial contract between an investor (lending money) and an issuer of bond (borrowing money) specifying how the issuer will remunerate and pay back the investor. All sorts of refinements can be imagined.

    Before the 1980's, as we saw, bonds were mostly simple mundane products, and were usually kept by their intial buyer on the primary market. Since then things have changed. Many variations on the basic contract have been introduced. When the financial contract stays within certain limits of sophistication, we are still in the realm of bonds; while if the level of sophistication of the contract becomes high (with payments, for instance, depending upon the happenstance of certain future events) we enter the realm of structured financial products, exotic products and derivatives.

    Here is a list of financial products still qualifying as bonds:

    • Straight bonds (also called "plain vanilla" bonds): those described at the beginning to the previous section
    • Callable bonds: the issuer may reserve the right to call the bonds at particular dates. A call obliges the owner to sell the bonds to the issuer for a price, specified when the bond was issued, that usually exceeds the current market price. The difference between the call price and the current market price is called the premium. A bond that is callable is worth less than an identical bond that is non-callable, to compensate the investor for the risk that it will not receive all of the anticipated interest payments.
    • Non-refundable bonds: these may be called only if the issuer is able to generate the funds internally, from sales or taxes. This prohibits an issuer from selling new bonds at a lower interest rate and using the proceeds to call bonds that bear a higher interest rate.
    • Putable bonds: they give the investor the right to sell the bonds back to the issuer at par value (= face value) on designated dates.
    • Perpetuities: bonds with no maturity date (i.e. they pay coupons forever unless the holder agrees to sell them back to the issuer).
    • Zero-coupon bonds: no coupons between issuance and maturity date when they are paid back at face value. The investors make money because the bonds are sold initially below their face value.
    • STRIPS (Separately Registered Interest and Principal of Securities): a type of securitization, where the holder of an initial bond, say a 10 year 5% treasury bond from a government, sells 11 zero coupon bonds the payments of which will be the payments (10 interest payments, and one final capital payment) of the initial bond. These were introduced in the United States in 1982, and in Europe (by France, where they are called "Felin") in 1991. Aside from their exotic look, they contribute to the liquidity of the market.
    • Convertible bonds: under specified conditions, and strictly at the bondholder's option, convertible bonds may be exchanged for another security, usually the issuer's common shares. The prospectus for a convertible issue specifies the conversion ratio, the number of shares for which each bond may be exchanged. A convertible bond has a conversion value, which is simply the price of the common share for which it may be traded. The buyer must usually pay a premium over conversion value, to reflect the fact that the bond pays interest until and unless it is converted. Convertibles often come with hard call protection, which prohibits the issuer from calling the bonds before the conversion date.
    • Adjustable bonds: various bonds with floating-rate adjustable according to specifications set at issuance.

    Bonds that have options attached to them are called structured securities. Technically, callables, putables and convertibles are simple examples of structured securities.


    Basic properties of bonds

    We review briefly, below, the basic properties of bonds. For an more complete elementary discussion, students may go to the teacher's first year course in accounting and finance.

    When studying bonds, one must distinguish clearly between the primary market and the secondary market. On the primary market, bonds are new financial products issued by borrowers (also called issuers, or sellers). The money paid by their buyer (also called investor, lender, or bondholder) goes into the pocket of the issuer, usually to finance a physical project. On the secondary market, bonds are financial products issued some times ago and which are traded between two bondholders. The money going from the buyer to the seller does not end up in the till of the initial issuer. The price at which the bond is sold and bought on the secondary market does not have to be and is usually not its face value.

    To review the properties of bonds, let's concentrate once again on a 7 year 5% "plain vanilla" bond of face value 1000 euros.

    Maturity: the term is used alternatively for the date at which the bond will be paid back, and for the number of years to go until that date.


    Interest rate: it is the yearly payment from the issuer to the buyer until maturity, expressed as a percentage of face value. It is also called the coupon rate, because when bonds were paper securities, they had coupons which the holder would have to tear off and take to the bank managing the bond for the issuer. The coupon would then be exchanged for the interest payment.

    There are plenty of variations on this simple structure. Some bonds have quarterly payments or semi-annual payments.

    Some bonds are "to the bearer" (whoever holds them is their owner) and other bonds have a "registered buyer" (their buyer is recorded in the books of the bank managing the bond for the issuer).

    Buying a bond is an investment with all the standard characteristics of any other investment. Remember that for any investment (physical of financial) there are two fundamental rates:

    1. a rate relating to the market environment, called the opportunity cost of capital of the investment: it is the rate of one year securities in the same class of risk as the investment under consideration.
    2. an internal rate, called the internal rate of return: it is a generalization of the concept of profitability, which we are familiar with for a one year security.

    The opportunity cost of capital of an investment is used to compute the present values of the future cash flows and therefore its NPV.

    For a new bond, the opportunity cost of capital and the IRR are equal, and they are both equal to the coupon rate. For the IRR it is a simple algebraic calculation to check this. For the opportunity cost of capital, it requires a full-fledged model of the randomness of securities under study, which we shall not get into.

    Suffices to say that the randomness of the future cash flows, for the investor, comes from the risk that seller defaults on some of its payments. In the case of a "sure borrower" (the government of a large prosperous nation), there is still randomness related to future purchasing power of the issuer currency: that is the risk of future inflation in the issuer country or of future exchange rate decline between the currency in which the bond is denominated and other currencies. For instance, this is exactly what's happening to foreign holders of US bonds: over the past few years, as of 2008, the dollar has lost ground compared to the euro, the yen, and to a lesser extent the yuan. And this trend seems likely to continue.

    (Technical note: for bonds the framework of discounting is somewhat different from that for shares, because we use the "max cash flows" and not the "expected cash flows" that would take into account the default risk each year. But this point can be technically cleared, and the two methods are equivalent to compute the new price of old bonds see below calculation of prices of old bonds.)

    So, for an investment into a new bond, like for any financial investment, NPV = 0.

    We shall see in a minute that this is also true of old bonds and that it is precisely how one computes the price of an old bond.


    On the secondary market, for an old bond we define several concepts.

    Current yield: it is the annual coupon divided by the current price. For instance, if after two years, the current price today of the above bond is 1065 euros, its current yield will be 50/1065 = 4,69%. This yield does not bear much significance.


    Yield to maturity: (this one is not new, but is important) it is the IRR of the investment into the second hand bond. Let's consider the 7 year 5% bond which is traded after two years:

    There are now 5 years to go, and, for the investor, the stream of cash flows during these five years is [-price today, 50, 50, 50, 50, 1050].

    If the price today is 1065€, then we can compute the IRR for the investor: it is, as you remember, the value of the discounting factor r such that NPV = 0. The general equation to solve for the unknown r is:

    General discounting formula : NPV(Investment, r) = -price today + C1/(1+r) + C2/(1+r)2 + ... + Cn-1/(1+r)n-1 + Cn/(1+r)n = 0


    The calculations using Excel, first of all using a discounting factor of 10%, give this (you may make a note of the formula to compute the present value of each future cash flow):


    And then, with the "goal seek" tool of Excel,


    we obtain IRR = 3,56%

    This "yield to maturity" of 3,56% is a more significant financial figure than the current yield computed above.


    Duration: practitioners in the bond market use the concept of duration of a bond. We quote Levinson: "It is a number expressing how quickly the investor will receive half of the total payment due over the bond's remaining life, with an adjustment for the fact that payments in the distant future are worth less than payments due soon. This complicated concept can be grasped by looking at two extremes. A zero-coupon bond offers payments only at maturity, so its duration is precisely equal to its term. A hypothetical ten-year bond yielding, say, 70% annually lets the owner collect a great deal of money in the early years of ownership, so its duration is much shorter than its term. Most bonds fall in between. If two bonds have identical terms, the one with the higher yield will have the shorter duration, because the holder is receiving more money sooner."

    The concept of duration does not add any substance to the general concepts of discounting future cash flows, NPV and IRR, but it is in use.


    Rate structure: at any given time t, the interest rate offered by bonds depends on two factors:

    1. the maturity of the bond (i.e. the number of years still to go)
    2. the financial reliability of the issuer

    For a given level of reliability of issuers, the curve of rate as a function of maturity is called the rate structure (in French "courbe de rendement"). Here is the example of US government bonds in 2002:


    Pricing of a second hand bond: we already said that the price of a second hand bond does not have to be and usually is not its face value. It all depends on the rate structure at the time of change of hands of the second hand bond.

    In short, if at the time of change of hands of our original 7 year 5% bond with 5 years to go (i.e. two years after its issue) the going rate for new 5 year bonds, of the same class of risk, is say 4%, then this 4% is the opportunity cost of capital of the second hand bond. Therefore we can compute, discounting the remaining future cash flows, its price today. Not surprisingly we shall find a price higher than the original face value:


    The going price of the second hand bond with 5 years to go, and "competing" with new 5 year 4% bonds, is 1044 euros.

    Similarly, if the going rate is 3,56%, then, as we saw, the price of the second hand bond is 1065€. These are just plays around the above general discounting formula.


    Impact of rate and maturity on the price of a second hand bond. You should remember from your first year course in finance, the important relationship between the price, the rate and the maturity of a second hand bond. It is summarized in the following formula:

    When rates decrease, the value of second hand bonds increase.
    And the effect is stronger on longer term bonds.


    Here is an illustration. We start with three bonds, all of them with initial rate 5%, and initial value 100 euros. The first one has maturity 1 year (grey line), the second one has maturity 5 years (dotted line), and the third one has maturity 10 year (black line). We look at the impact of a change in interest rate (abscissa), immediately after issue, on the price (ordinate):

    When rates decrease, the value of second hand bonds increase. And the effect is stronger on longer term bonds.


    Further discussion of bonds

    Read Levinson to learn more on the following topics:

    Rating agencies

    Interpreting the price of a bond

    Exchange rates and bond prices and returns

    Interpretation of the yield curve


    Enhancing security


    Junk bonds

    International markets:

    • Foreign bonds
    • Eurobonds

    Bond indexes



  • Russia's economy: smoke and mirrors (The Economist, March 1st, 2008)
  • Can't grasp credit crisis? Join the club (New York Times, March 19, 2008)
  • Hedge funds in difficulty (Le Monde, 11 March, 2008, in French)
  • Bear Stearns (Le Monde, March 15, 2008, in French)
  • "The financial system must be saved" (Le Monde, March 18, 2008, in French)
  • The story of pepper & Oeuvres complètes de Pierre Poivre, both in French.

  • Go to lesson 5