7.7 The structure of interest rates

to ensure that their future incomes match those future liabilities. They may then

be income risk-averse and prefer to lend long rather than short. Box 7.5 treats both

risk-aversion cases formally.

Box 7.5

The expectations view of the term structure of interest ratesassuming risk aversion

A. Capital risk aversion

Assume that the market is dominated by capital risk averters. Then if if, investors

2

will be deterred from shifting from short to long bonds as in the risk-neutral case dis-

cussed in Box 7.4 because of their fear of capital loss (downside risk). This means that

in equilibrium, iwill be below f. That is, investors will accept a lower return on short

2

bonds because going short reduces capital risk. It follows that even when no rise in short

rates is expected, fwill be greater than iand iwill therefore be less than i*. The yield

2ss

curve will slope upwards because of the risk premium attached to long bonds. This is

accepted as the ‘normal’ case.

B. Income risk aversion

Assume that the market is dominated by income risk averters. Now if if, investors

2

will be deterred from shifting from long to short because of their fear of loss of income

should interest rates fall. In equilibrium, iwill be greater than fand, even with no change

2

in interest rates expected, fwill be lower than iand iwill be greater than i*. The yield

2ss

curve will slope downwards as a result of the dominance of income risk aversion. This is

known as the ‘reverse’ yield curve.

The existence of ination complicates things further. We have said above that

people who intend to hold bonds until maturity know they will be paid the face

value of the bond at maturity and thus face no capital risk. However, they know

only the nominal sum they will receive, not what the purchasing power (or real

value) of that sum will be. Short-term bonds have an advantage under ination since

their holders have greater exibility to shift into real assets to maintain the real

value of their wealth. Thus, if ination rates are expected to be high in the future,

even those who are capital risk-averse may prefer short to long bonds. It follows that

the existence of inationary expectations should make it more likely that borrowers

will have to pay a term premium to enable them to borrow long.

Nonetheless, we can still say that if there are sufcient income risk-averse lenders

in the market, it is possible that borrowers may not have to pay such a term premium.

Indeed, it is possible that the usual situation may be reversed and that savers wish to

lend longer than borrowers wish to borrow. In such a case, the term premium would

be negative. Lenders would accept a lower rate of interest on long-term securities

than that suggested by the average of expected future short-term rates of interest.

It has been suggested that the attitude to different types of risk varies in different

parts of the market – for instance, that income risk averters dominate in long-dated

bonds and capital risk averters in short-dated ones. This produced what Bank of

England researchers have called the ‘walking stick’ hypothesis: a yield curve initially

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Chapter 7 • Interest rates

sloping upwards as capital risk-averting lenders demand a term premium, but then

turning down as income risk-averting lenders accept a negative risk premium.

The term premium approach to the term structure of interest rates proposes, then,

that the shape of the yield curve at any time is determined by two factors: (a) expecta-

tions regarding future short-term interest rates, and (b) the extent and nature of risk

aversion in the market.