6.3 Bonds: supply, demand and price

Exercise 6.2

Using the approach adopted in Box 6.2, calculate the price of an 8% bond with ve yearsto maturity when interest rates are 6 per cent and again when they are 9 per cent.Compare the results carefully with those in Box 6.2. Answers at end of chapter

The results in Box 6.2 (and in Exercise 6.2) lead us to three important conclusions.

All three are concerned with the relationship between interest rates and bond prices.

The rst we have met before. It is that:

A rise in interest rates causes a fall in bond prices and vice versa.

Box 6.2

Interest rates and bond prices

Imagine an 8% bond which matures for £100 in three years’ time. Interest rates are

currently 6 per cent. We assume that a coupon payment has just been made, so that

an investor holding the bond to redemption receives three coupon payments and the

maturity value. Using eqn 6.7 we can write:

	3 8100
P	∑ (1 + 0.06)t(1 + 0.06)3 t1

However, in Appendix I we show that the rst part of this expression, the value of any

series of regular payments, could be found using:

AA1D
PV1	(A1.5)
CnF
i(1 i)

Substituting values, we have:

8A1D100

P1 

C³F³

0.06(1 0.06)(1 + 0.06)

which gives us:

A1D100

P133.33 1 

CF

1.1911.191

(133.33 0.16) 83.963

21.33 83.96 £105.30

If we repeat the last stage of this calculation, but setting the interest rate to 9 per cent,

we have:

8A1D100

P1 

C³F³

0.09(1 0.09)(1 + 0.09)

and the result is:

A1D100

P88.88 1 

CF

1.2951.295

(88.88 0.228) 77.22

20.264 77.22 £97.48

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Chapter 6 • The capital markets

The second is that:

When the rate of interest exceeds the coupon rate, the price of the bond stands at a

‘discount’ to its maturity value; when the rate of interest is below the coupon rate, the

price stands at a premium.

If we continue with our assumption that the maturity or redemption value is

£100, and if we let cstand for the coupon rate, we can summarise this particular rule

as follows:

i c, P 100

i c, P 100

The third is that:

The longer the residual maturity of a bond, other things being equal, the greater is the

sensitivity of its price to changes in interest rates.

In each of our cases above, the level of interest rates changed by three percentage

points. The price change for the three-year bond was about £8, while the price

change for the ve-year bond was over £12.

The extent of this sensitivity to interest rate changes is expressed by the concept

of ‘duration’. The duration of a bond can be calculated, though the mathematics are

beyond the scope of a book like this (see Howells and Bain, 2005, ch. 16; or Pilbeam,

2005, ch. 6). Duration is dened as the weighted average maturity of a bond. The

logic behind the idea of ‘weighted average maturity’ is that for bonds which pay

regular coupons, the total cash ow from that bond is spread over a period (from

now to the date of maturity). Depending upon the characteristics of the bond, this

cash ow could be heavily weighted towards the immediate future or towards the

more distant future. (The ‘strips’ we mentioned earlier in this chapter have just one

payment at the end of their life, which gives them a longer duration than the bond

from which they were created.) Since changes in the discount rate always have a

larger effect upon distant payments than upon short ones, a bond where the weight

of payments is soon should be less interest-sensitive than a bond where the weight

of payments lies further away. Duration, therefore, is trying to capture the average

time that it takes to receive the cashow.

Duration is mainly determined by the residual maturity of a bond. However,

other things being equal, duration increases with lower coupons and, again other

things being equal, it is higher for lower redemption yields. It follows that if you

wish to hold bonds whose price has the maximum exposure to interest changes

(because you expect interest rates to fall, for example), you should concentrate on

long-dated, low-coupon stock and buy the bonds with the lowest redemption yield

in that group!

What we have just seen is that if we know the appropriate market rate of interest,

that is to say the rate of interest on assets of similar maturity and risk, we can nd

the price of a bond. Equally, of course, it follows that if we know the price at which

a bond is trading, we can calculate the rate of return on that bond. This is very easily

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