6.3 Bonds: supply, demand and price

to a rise in price. However, before we leave this discussion of supply, we need to note

that there is one way in which price may have an effect upon the supply of bonds

but this can only happen in the medium or long term. In order to understand this,

we have to start thinking about some of the factors that underlie demand.

In Figure 6.2 we have a demand curve, D, intersecting the supply curve for a bond

at a price P. Notice that the demand curve slopes downward, in the normal way.

This is because bonds pay a xed income stream (see section 6.2.1) in the form of

a coupon. Clearly, the lower the price at which this xed income stream can be

purchased, the more attractive it will be and thus the greater the demand. More

precisely, the lower the price at which the income stream can be purchased, the

higher the rate of return the bond holder will receive. This amounts to saying that

for any individual bond, the price corresponds to a unique rate of return (expressed

as the running or interest yield) and that the price and rate of return vary inversely.

In Figure 6.2, therefore, we have assumed that we are looking at a bond with a 5 per

cent coupon whose current market price is £71.50. At this price the running yield is

7 per cent (5/71.50). We have marked this on the right-hand axis. Suppose something

happens to shift the demand curve to D′. The price rises to P′and the return falls.

If the price rises to £100, the running yield falls to 5 per cent. This increase in the

price of the bond indicates two related things to the issuer (or borrower): rstly, it

indicates that any new 5 per cent bond can be sold to raise £100 rather than £71.50;

secondly it shows that £100 can be raised for an interest rate of 5 per cent rather

than 7 per cent. Whichever way we look at it, the cost of borrowing by issuing new

bonds has fallen. Clearly, in these circumstances (and assuming nothing else has

changed) borrowers will be encouraged to issue more bonds. In these circumstances,

the stock of bonds increases (by the size of the new issue) and the supply curve moves

to S′. The increase in the supply may have the effect of lowering the price (to P″) and

raising the yield (the end result depends on the elasticity of the demand curve and

the scale of the new issue). The fact remains, however, that the borrower can borrow

more cheaply than otherwise would have been the case. Hence, an increase in price

could result in an increase in supply but this is shown by a shiftin the curve to S′,

and not, as more normally, by a movement alongan upward-sloping supply curve.

Figure 6.2 teaches us three very important lessons:

l	The rst is that (ceteris paribus) the return on a security varies inversely with itsprice.

l	Trading in an existing security determines the price at which new capital can beraised.

l	(If we ignore transaction costs) the yield on a security is simultaneously the rateof return to investors and the cost of capital for borrowers.

In Figure 6.2, we have seen that the price that investors are willing to pay for a

bond is mathematically linked to the rate of return that they receive. In fact, the

orthodox theory of asset pricing says that it is the required rate of return that deter-

minesthe price that people are willing to pay. Formally speaking, the price that people

are willing to pay is the value (more strictly, the present value) that they place upon

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Chapter 6 • The capital markets

the future payments. We look at how this is arrived at in the next few paragraphs.

The theory and techniques that we draw upon are explained more fully in Appendix I:

Portfolio theory.

In the calculation of a present value for the future stream of income owing

from a bond, the size of the coupon payments will obviously be crucial. Other things

being equal, a bond with a 15 per cent coupon will have a higher market price than

one with a 10 per cent coupon. As a rst attempt at a valuation we might be tempted

simply to sum the future payments. However, this overlooks a fundamental prin-

ciple of economics and nance, namely that a payment at some time in the future

is worth less than the same payment now. This is not because of ination (although

the presence of ination reinforces the point). Even in a zero-ination world the

principle would hold, as we explain in Appendix I: Portfolio theory. The reason

that £5, say, today is worth more than £5 in a year’s time is that the £5 today could

be put to some immediate use. Waiting for one year causes us a ‘loss’ equal to the

pleasure, satisfaction or whatever which could have been enjoyed by using the £5

in the intervening year.

The practice is therefore to discount future income payments by using a formula

which takes the current rate of interest to represent the cost of waiting and recognises

that the loss increases with the length of the wait. Notice that the rate of interest

here is the nominal rate. Notice also that since its function is to represent the cost to

us of not having the funds immediately available, it must be the rate of interest that

could be earned in the market now on other assets of similar risk and duration to

the bond. And this means that we can also think of it as the rate of return that we

would require (since we can get it elsewhere) to induce us to hold the bond. (These

equivalencies are discussed further in Appendix I: Portfolio theory.) Other things

being equal, we should expect nominal interest rates to rise and fall with increases and

decreases in the rate of ination (i.e. we should expect real rates to be fairly stable).

With high rates of ination, therefore, we should expect high nominal interest rates.

As we shall see, this will lower our present valuation of any future stream of income

and explains why bond prices are sensitive to, among other things, expectations of

ination.

The (discounted) present value of a payment in one year’s time is given by

	1
C		(6.1)
	1 i

where C is the coupon payment and i is the rate of interest. (Throughout our

examples, we assume that bonds pay a single coupon, annually. In practice, many

pay half the coupon at six-monthly intervals.) Take the case of the 15 per cent bond

mentioned earlier. Assume that the next coupon payment is exactly a year away,

and that interest rates are currently 10 per cent. The present value of the next

coupon payment would be £15/(1 + 0.10) or £13.63. The value of the same payment

in two years’ time is given by

	1
C		(6.2)
	(1 i)2

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