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A bond is an IOU. Bond issuers borrow a sum of money and issue bonds promising to pay back the bond-holder at a given date, or in installments. Here we are talking about 'long term' borrowing - greater than one year. For short term borrowing see MoneyMarkets.

'Treasuries' or 'Gilts' (in UK) are bonds issued by governments. Other common bond-issuing entities are banks and corporates. AssetBackedSecurities are a type of bonds. Unlike equities, bonds do not give ownership rights. Although they may be 'secured' or 'backed' in some way - eg. mortgage backed bonds in which bondholders have the right to demand that the issuer sells property in order to repay. Thus some types of bonds may give bond investors some form of effective control over borrowers' business decisions. Indeed bond investors can be in a strong position of influence on a (troubled) firm - they generally have the first claim on a firm's assets, before short-term lenders and before shareholders.

The 'par value' (or 'face value') of the bond = the amount of debt represented by this IOU, the amount to be paid back. The par value of an individual bond is normalised at 100 (currency units), investors buy multiples of these.

The maturity (or 'tenor') of the bond is the timescale for repayment. In the simplest case, full repayment is made on one future date - eg jan 1st in ten years. Such bonds are sometimes called 'bullets'. Other bonds 'pay down' in installments - this process of gradual repayment is called 'amortisation'. In this case the 'legal maturity' is the date when the very last installment is made. Some bonds, called 'perpetuities', never mature - the lender gets a perpetual stream of coupon payments, but never gets back the par value. Many bonds give the issuer an option to 'call' - i.e., pay early, maybe at given points or after a given period.

As well as an eventual repayment of the par value, most bonds also pay a regular 'coupon' - eg. twice yearly. This is basically the 'interest' payment on the debt. Some bonds pay a fixed coupon - eg. 5% per year. Many bonds are 'floating rate bonds', which usually meand the coupon payment is linked to a government-backed interest rate. For example, a bond may pay '3 month euribor plus 25 basis points'. Three month euribor is the european central bank interest rate for three-month money market lending; a basis point is 1/100th of one percent. (There are also bonds called 'zeroes' which do not pay any coupon.)

In general bond holders have a first call on an issuer's income - the borrower must pay bondholders before other creditors, and before allocating investment funds and dividends to shareholders. However some bondholders may come before others - these are said to be 'senior', whilst bonds further down the queue are 'subordinated'. Sometimes a bond is issued in 'tranches', levels of seniority.

Fair Value

The market price of a bond should then be quite straightforward to work out. It depends on the par value (though here normalised to 100 for all bonds), the coupon payment, and the remaining lifespan of the debt.

The basic equation is for a (bullet) bond price B0 at time t=0 is:

B0 = P/(1+i)T) + sum (c/(1+i)t) (summed over t=0 to t=T)

Here P = par value; c = coupon payment; i = market interest rate; T is the maturity period of the bond.

So the first term P/ (1+i)T is the present discounted value of the final repayment of the par value at time T. The second term is the sum of the present discounted values of the coupon payments in all time periods from now (time 0) to maturity (time T).

B0 represents what is sometimes called the 'fair value' or 'fair price' of the bond. However, the market may have other ideas.

Market Price

Let's call M the actual price at which a bond trades in the market. When the bond is first issued, in general it is sold at par: M = P (though this is not the case for 'zeroes' which are initially sold below par). If the (bullet) bond is just about to be paid back, then we should expect M = P. At any point in between, M = P will not generally be true.

If M > P the bond is trading above par, or 'at a premium'.

If M < P the bond is trading below par, or 'at a discount'.

Suppose you have a choice between buying a bond of par value P with a coupon c or investing P in money for the same period, receiving an interest rate i. If i = c then there is no difference in the return on these two investments. Assuming a liquid bond market, you should then be able to sell on the bond for a sum of money equal to its par value at any point. If: bond markets are as liquid as money markets; there is no greater risk to holding bonds then money; and i = c; then bonds should always trade at their par value, M = P.

In general this is not true, and the major factor is risk. Above all, there is always a risk that the bond-issuer will not repay ('default risk').

If the bond is to sell at its par value, it must be that the coupon payments are sufficiently greater than the risk-free interest rate (c > i) to compensate bond-buyers for the risk they are taking on. The differential c - i is primarily a market assessment of the riskiness of a bond - a 'risk premium'.

In general, then, a bond will initially be sold at par with a coupon set to compensate buyers for risk as assessed at that time.

After that, bonds can be traded on in the secondary market. But market assessments of risk can change. If the market comes to take a more cautious view of a bond's riskiness, then it will trade at a discount to par (M < P). Or if the market becomes more confident, then it could trade at a premium (M > P).

More 'subordinated' bonds are obviously more risky, and so come with higher coupons.

prices, yields, interest rates

The bond's 'yield' is the actual return on the bond given the price the investor paid for it. There are three common measures of yield:

The 'current yield', defined as y = c/M (where M is expressed as a percentage of P), is effectively the actual 'interest rate' for the bond.

Current yield is thus a measure of the return over one period. 'Yield to maturity' (YTM) is a measure of the return you would get from holding the bond to maturity. It is defined as y that satisfies this familiar looking equation:

M = P/(1+y)T) + sum (c/(1+y)t)

I.e., YTM is the discount rate which would make the market price the 'fair value'.

'Yield to call' is the same but calculated to the date that a call option becomes available, rather than to maturity.

For all measures: the higher the coupon, the higher the yield; the lower the price, the higher the yield.


A major question is plainly: how do market participants assess risks?

For most of them the answer is - they get someone else to do most of the work for them. RatingsAgencies are key agents who specialise in assessing the riskiness of securities. The rating agencies' assessments are encoded in 'ratings' grades. For all ratings agencies, the highest grade is AAA. A rating of BBB (triple B) or above indicates what is called an 'investment grade' security. Riskier bonds are called 'sub-investment grade' or sometimes 'junk bonds'.

The higher the bond's rating, the lower the risk premium (c - i) investors need to buy the bond. Ratings agencies are thus key players in setting coupons (the initial 'pricing' of the bond on issue). They continue to be important in the secondary markets by doing ongoing monitoring developments on bonds they have rated. Eg., if they think that risks associated with a bond have increased, they may 'downgrade' the rating. This will then have a negative impact on the bond's market price.

Ratings are not the only factors in setting coupons and secondary prices. A lot will depend on the size of the market (demand) for a particular (type of security). This is plainly related to risk considerations captured by ratings, but other major factors might be, eg: concentration - eg. if large numbers of investors have historically accumulated very large holdings in certain kinds of bonds, a desire to reduce concentration in these bonds may reduce demand; on the other hand, with newer types of securities, even when they get good ratings investors' lack of familiarity with the market may make them feel uncomfortable about buying. These kind of market dynamics may be sheep-like, and not particularly based on rational assessments.

Of course, the ratings agencies don't always get it right. If you are eg. investor who has a better grasp of risk in a market than ratings imply, you can do well. Opportunities to profit from out-thinking rating agency-led prices in a market are sometimes referred to as 'rating agency arbitrage'. (I.e. - there is a discrepancy between your internal assessment of the correct bond price and the rating agencies' - though this may be pushing the use of the term 'arbitrage' a bit).

Yield curves

A yield curve is a line drawn through yields of bonds that are the same (eg. a particular sovereign's treasurues) apart from their maturities.

In general, a longer-maturity bond is seen by the market as riskier - the closer you are to pay-back, the less riskj that something will go wrong before you cash in. They will therefore have higher coupons, and higher yields.

However, another factor is the market's expectations of future movements in bond markets. If investors believe that coupons rates will be increasing in future, they don't want to be tied up buying long-term bonds that will become relatively unrewarding against what will become available. They thus demand even higher yields for longer-term holdings. The yield curve is thus steeper when expectations of growth are higher.

On the other hand, if investors think rates are going to go down in future then they rush to lock in today's coupon rates by buying long tenor bonds. When markets fear imminent recession there may be an 'inverted' yield curve.

See also :

  • US Bond Market Association site, more info and price data:

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