6.3 Bonds: supply, demand and price

seen for an irredeemable bond. We simply rearrange eqn 6.5 so that the rate of

interest appears on the left-hand side. Thus, if the current price of an irredeemable

1

bond with a 2/2% coupon is £60, the rate of interest received by the holder is:

i C/P

(6.8)

In this case, £2.50 £60 4.17 per cent.

However, as we saw earlier, the return on bonds can be expressed in at least two

forms. Firstly, we can calculate the ‘running’ or ‘interest’ yield. This is what we have

just calculated using eqn 6.8. Alternatively, we can calculate the ‘redemption’ yield

or ‘yield to maturity’. This takes account of the fact that most bonds trade at a price

which is different from their maturity value. Thus, if we hold them to maturity, we

shall make a capital gain (or loss) and this has to be added to the return which we earn

from the coupon payments. In Box 6.2, for example, if market interest rates were 6 per

cent, we would have paid £105.30 for a bond maturing in three years. If we calculated

the interest yield, this would give us 8 105.30 7.6 per cent. But this takes no

account of the fact that if we hold the bond to maturity we shall make a capital loss

of £5.30 or approximately £1.77 per year. In most cases we should wish to take this

into account by calculating the redemption yield. (Notice that since irredeemable

bonds have no redemption date, we can onlycalculate an interest yield. Equation 6.8

is the only expression we ever need for calculating the return on undated bonds.)

Unfortunately, calculating the redemption yield is no simple task. It has to be

done by iteration or ‘trial and error’. It can be done quickly by computer, but only

then because a computer can perform hundreds of iterations per second.

To understand how we nd the redemption yield, look again at eqn 6.7. We

know P, the market price, and C, the coupon. We also know n, the term to maturity

(and thus the number of coupon payments) and Mthe maturity value. Finding the

redemption yield involves nding a value for iwhich makes the present value of

the stream of coupon payments and the maturity value equal to the current market

price. The technique involves four steps:

1.Choose a rate of interest which is bound to give a value (PV) which is less than

1

the market price (i.e. choose a value of ithat is too high).

2.Choose a rate of interest which is bound to give a value (PV) which is greater

2

than the market price (i.e. choose a value of ithat is too low).

3.See where the current market price falls, between the two calculated values PV

1

and PV.

2

4.Choose a new interest rate which falls between the two previous rates in the same

position as the market price falls between PVand PV.

12

Box 6.3 provides an example of how it is done.

In practice, when we talk about bond yields it is the redemption yield that we

are interested in. Bonds of similar risk and similar residual maturity will usually have

redemption yields which are very close together; furthermore, these redemption yields

will be equal (or very close) to the rate of return on all other assets of similar risk

and maturity. In other words, bond redemption yields (and therefore prices) must

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Chapter 6 • The capital markets

Box 6.3

Finding redemption yields

A 6% bond, with three years to maturity, is trading at £92.40. What is its redemption

yield? (Assume that a coupon has just been paid: there are three coupon payments left.)

Step 1

Notice that the bond is trading at a discount to its redemption value. We know from our

earlier discussion that this means the rate we are looking for is greater than the coupon

rate. If we want to be sure that our rst trial redemption rate is ‘too high’, we might start

with 10 per cent. If we follow the procedures we adopted in Box 6.2, we shall nd that a

trial rate of 10 per cent gives us a present value for the coupon payments of £14.93, and

a PVfor the maturity value of £75.13. The present value of both (PV) is thus £90.01.

1

Step 2

£90.01 is fairly close to the market price of £92.40, suggesting that 10 per cent is not

far from the true yield to redemption. In order to get a present value which is above the

market price, we shall not need to pitch our second trial rate very far below the rst.

We might try 8 per cent. This gives a PVfor the coupon payments of £15.43 and a PV

for the maturity value of £79.38. Thus PV£94.81.

2

Step 3

PVPV£94.81 £90.01 £4.80. If we now look at the market price of £92.40, we

21

can see that it is £2.39 more than PV. £2.39 is very close to one half of £4.80, i.e. it is

1

half-way between the two trial PVs. (Our calculations have involved a very small amount

of rounding, which a computer would avoid.) This suggests that we should try a gure

for redemption yield half-way between our two trial rates.

Step 4

If we do the calculations once more, using an interest rate of 9 per cent, we nd that

the present value of the coupon payments is £15.18, while the PVof the maturity value

is £77.22. A redemption yield of 9 per cent makes the present value of the coupon and

redemption payments just equal to the market price of £92.40.

reect market conditions. This need not be true of the interest or running yields on

bonds. These can show signicant divergence across individual bonds and between

individual bonds and other assets. We shall notice this when we look at bond price

data in section 6.6.

As we saw in Chapter 4, the major holders of government bonds are long-term

insurance funds, followed closely by pension funds and more distantly by build-

ing societies and general insurance companies. Discount houses are also signicant

holders of bonds. As a general rule the attractiveness of such assets lies in their

guaranteed rate of return if held to redemption. For intermediaries with long-term

liabilities, holding to redemption is invariably the rule. The short-term liabilities of

building societies and discount houses, however, mean that they might in certain

circumstances be forced into the sale of some gilt holdings. The effect of this is shown

in their preference for short-dated bonds whose prices, as we have just seen, are less

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