Chapter 13

An introduction to interest rate determination and forecasting

Learning objective 1: describe the macroeconomic context of interest rate determination, in

particular the liquidity effect, the income effect and the inflation effect on interest rates

In forming a view on the future direction of interest rates, it is necessary to recognise that

changes in monetary policy settings are likely to affect the state of the economy, which in turn

affects interest rates generally.

For example, when a monetary-policy-induced increase in interest rates causes a reduction in the

pace of economic growth, the demand for funds begins to decline and the rate of interest begins

to ease. Furthermore, there is likely to be an accompanying reduction in the rate of inflation, thus

causing interest rates to fall further.

Within the macroeconomic context, these progressive changes are referred to as the liquidity

effect, the income effect and the inflation effect on interest rates.

Therefore, in trying to forecast the state of an economy and future interest rates, policy makers,

economists and financial market participants often consider a range of economic indicators.

Indicators may be described as leading, coincident and lagging indicators of future economic

activity.

Learning objective 2: explain the loanable funds approach to interest rate determination,

including demand and supply variables for loanable funds, equilibrium and the effect of changes

in variables on interest rates

A more disciplined approach to forming a view on the future of interest rates is provided by the

loanable funds approach.

The demand for funds originates from the business sector and the government sector.

The supply of loanable funds is identified as being determined by the savings of the household

sector, changes in the money supply, and the hoarding or dishoarding that takes place in response

to changes in the rate of interest.

The prevailing rate of interest is the rate that equates to the demand for and the supply of

loanable funds.

Factors that cause the demand or supply to change will result in a change in the rate of interest.

While the framework is useful in identifying impacts on interest rates, its major shortcoming is

that the supply and demand curves are interdependent. As a result, it is not possible to determine

a unique equilibrium interest rate.

Another shortcoming of the loanable funds approach is that it addresses interest rate

determination as if only one interest rate exists at a particular time. This is clearly not the case in

reality. At any point there are many rates of interest.

The differences in rates reflect the different terms to maturity of instruments and the credit risk

of a borrower. Differences between the interest rates on instruments of similar risk, but with

different terms to maturity, are explained by theories of the term structure of interest rates.

Learning objective 3: understand yields and the shape of various yield curves within the context of

the term structure of interest rates, and apply the expectations theory, the segmented markets

theory and the liquidity premium theory

The term structure of interest rates is represented by a yield curve.

The yield is the rate of return on debt instruments and a yield curve graphs the relationship

between interest rates and the term to maturity of debt instruments in the same risk class.

The shape of the yield curve may be normal, inverse or humped.

A normal yield curve is an upward-sloping curve where there is an expectation that short-term

interest rates in the future will rise. A steeper normal curve indicates an expectation that there

will be larger interest rate increases.

An inverse yield curve is a downward-sloping curve, typically induced through a tightening of

monetary policy by a central bank. It indicates that current short-term interest rates are high, but

that there is an expectation that in the future there will be an easing of monetary policy and

short-term interest rates will begin to fall.

The expectations theory argues that, in an efficient market, interest rates on longer-term

instruments are determined by two factors: the current short-term interest rate and the short-term

rates that are expected to prevail over the longer term.

The segmented markets theory provides a further explanation of the shape of the yield curve.

It contends that investors do not view bonds of different maturities as being close substitutes. It

is argued that investors will have a preference to accumulate a majority of securities in an

investment portfolio that have predominantly short-term, medium-term or long-term maturities.

The implication is that the shape of the yield curve is explained by the demand and supply

conditions that are evident in the various maturity segments of the yield curve.

However, the arguments of the segmented markets theory ignore the role of market arbitrage and

speculation in ensuring that the yield curve over the maturity spectrum remains in equilibrium.

Also, in a modern financial market, risk managers are able to hedge such risk using synthetic risk

management products such as derivatives. As a result, the forecasts derived from the segmented

markets approach must be treated with caution.

An extension to the theory is obtained by the inclusion of a liquidity premium. The liquidity

premium theory contends that investors need to be compensated for a loss of liquidity and the

higher risk levels that may exist in long-term investments; that is, investors will require a

borrower to pay a liquidity premium before they are willing to give up their preference for short-

term assets. Therefore, the liquidity premium will change the slope of a yield curve.

Learning objective 4: explain the risk structure of interest rates, the risk-free rate and explore the

effects of default risk on interest rates

The other element that has to be considered in explaining the range of interest rates that are

available at any one moment in time is the default or credit risk of the borrower. Higher-risk

borrowers must pay a higher rate of return than would be required of lower-risk borrowers.

The risk-free rate of interest is defined as the yield on government Treasury bonds. All other

borrowers will pay a risk premium above the risk-free rate.

The risk structure of interest rates incorporates the level of credit risk, over time, attached to a

particular debt issue.

A corporation with an AA credit rating will pay a lower yield than a corporation with a BBB

credit rating, but both will pay a margin above the risk-free rate of the government Treasury

bond.

The yield curve evident within the financial markets for a particular security will change in its

shape and slope from time to time, in particular as business and economic conditions change.

True/False questions

1. T The liquidity effect of a tight monetary policy is likely to see interest rates rise in the first

place, but as the pace of economic activity slows down the income effect is likely to result in some

easing of the interest rates in the market.

2. F Economic indicators provide market participants with clear and unambiguous messages as

to the future direction of economic activity and growth.

3. F A lagging indicator is one that might be used to indicate the direction in which the

economy is headed.

4. T In the loanable funds approach to interest rates, the demand for funds originates from the

business sector and the government sector.

5. T The supply of loanable funds is derived from the savings of the household sector, changes

in the money supply and dishoarding.

6. F An increase in the money supply would permanently shift the supply curve of loanable

funds to the right.

7. F An increase in interest rates is likely to result in a permanently higher level of dishoarding.

8. F The government sector demand curve in the loanable funds approach is downward sloping,

with the slope changing in response to the size of government expenditures.

9. T One of the key inadequacies of the loanable funds approach to interest rate determination

is that, because the demand and supply curves are not independent of each other, it is impossible to

determine a unique equilibrium interest rate.

10. F Applying the loanable funds approach, an increase in inflationary expectations will result

in an increase in interest rates equal to the increase in inflationary expectations.

11. F The yield curve is a single curve at a point in time that shows the rates of return on all

fixed-interest and discount instruments, which have different terms to maturity and which are issued

by governments and corporations.

12. F A normal yield curve is one in which short-term interest rates are higher than longer-term

interest rates.

13. F When a central bank implements an expansionary monetary policy, an inverse yield curve

will eventuate.

14. T Under the expectations theory of the yield curve, longer-term interest rates are a function

of the current short-term interest rate and forecast future short-term interest rates that will exist over

the longer term.

15. T Using the expectations approach, if the one-year interest rate is currently 6.00 per cent per

annum, and the current two-year rate is 8.00 per cent per annum, there is an expectation that in 12

months’ time the one-year interest rate will have increased to 10.00 per cent per annum.

16. T Under the segmented markets approach to explaining the yield curve, an increase in the

supply of short-term instruments and an equal reduction in the supply of long-term instruments

would cause the short end of the yield curve to rise and the long end to fall.

17. T The liquidity premium theory suggests that investors will demand a higher rate of interest

to induce them to buy long-term instruments so that they will be compensated for increased risk and

loss of liquidity.

18. F The existence of an inverse yield curve indicates that investors are not demanding a

liquidity premium in periods of tight monetary policy.

19. F The risk structure of interest rates includes a premium to compensate the holders of

instruments for the risk that interest rates, and thus the prices of instruments, may change.

20. F The risk-free rate of interest is the yield paid on longer-term securities issued by corporate

borrowers that have an investment-grade credit rating.

Essay questions

The following suggested answers incorporate the main points that should be recognised by a student.

An instructor should advise students of the depth of analysis and discussion that is required for a

particular question. For example, an undergraduate student may only be required to briefly introduce

points, explain in their own words and provide an example. On the other hand, a post-graduate

student may be required to provide much greater depth of analysis and discussion.

1. Within Australia the Reserve Bank is responsible for the implementation of monetary

policy. The central banks of other developed economies also have similar responsibilities.

Briefly identify and discuss a range of issues that a central bank would consider when

monitoring its current monetary policy settings. (LO 13.1)

Current monetary policy is principally directed towards containing inflation within a target range of

2 to 3 per cent over the business cycle. In directing its policy decisions to achieve this objective, the

central bank will consider:

the underlying rate of inflation over the business cycle

the rate of employment / unemployment / employment growth

the stability of the currency – in particular relative to major trading partners

the welfare of the people

the current economic environment / business cycle

current monetary policy settings

the direction of economic growth

the impact on past monetary policy settings on current and future economic growth

time delays between a change in monetary policy settings and a change in economic growth

economic fundamentals in major trading partner countries

forecast changes in international economic growth

a wide range of economic indicators (discussed in question 3).

2. The open market transactions of the central bank impact interest rates within an economy.

The macroeconomic context of interest rate determination attempts to explain the interactions

of a change in monetary policy settings. The macroeconomic context of interest rate

determination identifies three distinct effects of a change in monetary policy. List, explain and

give examples of each of the three effects. (LO 13.1)

(i) Liquidity effect:

The monetary policy actions of the central bank that impact upon interest rates, particularly the

overnight cash rate

Central bank buys or sell government securities in order to affect the money supply and the level

of liquidity in the financial system

If the central bank buys securities from the financial system then there will be more cash in the

system and interest rates will fall; an easing of liquidity

If the central bank sells securities into the financial system there will be less cash in the system

as the investors pay cash to buy the securities and interest rates will rise; a tightening of liquidity.

(ii) Income effect:

Refers to the flow-on effect from the initial liquidity impact on interest rates

Using the example of the central bank tightening liquidity and increasing interest rates in order to

reduce the levels of spending in the economy

Reduced levels of spending will result in lower incomes in all sectors of the economy: the

household sector, the business sector and the government sector

This occurs as employment growth contracts, demand for goods and services eases, and taxation

revenues to government decline

As the rate of growth in economic activity slows, the demand for loans also slows

The slowing in the demand for funds results in an easing in interest rates.

(iii) Inflation effect:

In so far as the economy was previously experiencing inflationary pressures due to high levels of

demand, now the slowing of the pace of economic activity will cause the rate of inflation to ease

This easing allows rates of interest to ease as well

The nominal rate of interest is said to comprise two components, being the real rate of return

plus compensation for the expected rate of inflation

If the rate of inflation is expected to fall, then market interest rates should fall.

3. A central bank will typically implement monetary policy settings in order to achieve certain

economic outcomes over a business cycle. In order to forecast future economic conditions and

business activity, business managers therefore need to understand the business cycle.

(a) Draw a diagram and explain the structure of a business cycle over time.

The business cycle is a measure of changes in the level of economic activity in an economy over

time

It tends to move in changing cycles of peaks and troughs

The business cycle peak—the highest level of economic activity during a cycle

The business cycle trough—the lowest level of economic activity during a cycle.

(b) Discuss and give examples of different economic indicators that may give an insight into

the stage of a business cycle. (LO 13.1)

Economic indicators are constructed from a set of historic data that provide some insight into

possible future economic growth

Leading indicators—economic variables that change before there is a change in the business

cycle

Coincident indicators—economic variables that change at the same time as the business cycle

changes

Lagging indicators—economic variables that change after there is a change in the business cycle.

There is a wide range of economic indicators. Governments, central banks, corporations and analysts

will select a number of indicators that best inform them, including:

the rate of inflation over the business cycle

the rate of growth in gross domestic product

the balance of payments

credit growth and associated debt levels

the exchange rate relative to major trading partner currencies

the rate of unemployment, job vacancies and ratio of full-time and part-time employment

the balance of payments, imports and exports growth

finance for housing, residential and non-residential building approvals

economic activity and capacity utilisation

wages growth and overtime worked

retail sales

share price movements.

4. The financial markets often use the loanable funds approach when forecasting interest rates.

Describe the concept of the loanable funds approach to interest rate determination. In your

answer identify and explain the elements that comprise the supply of, and the demand for,

loanable funds. Note: you may find it convenient to draw diagrams showing the demand curve,

the supply curve and the equilibrium interest rate. (LO 13.2)

Loanable funds approach—the rate of interest is determined by the supply of and the demand for

loanable funds

Loanable funds are the flows of funds into the market for securities.

Demand for loanable funds:

There are two principal components:

business demand for funds—to finance its liquidity and capital investment requirements. The

lower the rate of interest, all else being constant, the greater will be the volume of funds

demanded. This is represented by the downward-sloping curve (labelled B). Any factors that

cause an increase (decrease) by business in its demand for funds would be represented by a shift

to the right (left) in the B curve. The curve shown represents the net business demand for funds.

government sector demand for funds—the total public sector borrowing requirement; includes

the Commonwealth, States and local governments and their instrumentalities. It is normally

proposed that the PSBR is independent of the rate of interest, and this is represented by the

vertical curve labelled G. With a smaller (larger) borrowing requirement, the G curve would be

located further to the left (right) in the diagram. The two demand curves are combined to give

the total demand for loanable funds (labelled G + B).

Q Q Q

Loanable fundsLoanable fundsLoanable funds

Interest rates

Interest rates

Interest rates

B G G+B

Supply of loanable funds:

There are three principal sources:

savings of the household sector - the curve (S) is drawn with an upward slope on the basis of the

presumption that as interest rates increase people will save a larger proportion of their incomes.

The curve is steep because empirical evidence suggests increases in interest rates cause only

small increases in the quantity saved.

changes in the money supply (M) - Since the money supply is assumed to be independent of the

rate of interest, changes in the money supply are represented diagrammatically as a vertical line.

When M is added to the savings curve it simply changes the location of the curve (S + M). It

does not change the slope of the curve. If for example, the Reserve Bank increased the money

supply the S + M curve would be to the right of the S curve.

dishoarding (D) - as interest rates increase, there is an incentive to acquire more securities in

order to obtain the increased yields that are available. In attempting to buy more securities

money is given up (or dishoarded). Dishoarding is added to the S + M curve to give the total

supply of loanable funds curve.

Equilibrium in the loanable funds markets:

the equilibrium interest rate will be at the intersect of the demand and supply curves

Q Q Q

Loanable fundsLoanable fundsLoanable funds

Interest rates

Interest rates

Interest rates

S S S+M

S+M

S+M+D

5. A problem with the loanable funds approach to explaining interest rates is that since the

supply and demand curves are interdependent a unique equilibrium rate of interest cannot be

determined. Explain and illustrate this problem by reference to the effects of:

(a) an increase in inflationary expectations

The traditional approach to the analysis of the effects of inflation on interest rates can be seen in

the following diagram.

The initial equilibrium interest rate is i0, at the intersection of the original demand and supply

curves.

With an increase in inflationary expectations, the suppliers of funds will demand a higher rate of

interest in order to maintain the same real rate of return on their funds. Diagrammatically, the

supply curve will move vertically, by the extent of the inflationary expectation (pe), from supply0

to supply1.

The demand for funds will also change in response to the increased inflationary expectation. The

demand curve increases, by the extent of the inflationary expectations, from demand0 to demand1.

The demand for funds increases because businesses, in anticipating higher inflation, recognise

that they will require a greater quantity of funds merely to maintain their pre-inflation investment

plans.

The result of the increased inflationary expectations is that interest rates will rise to the full

extent of the anticipated inflation, and the quantity of loanable funds will remain unchanged at

Q0.

This is referred to as the Fisher effect.

QLoanable funds

Interest rates S+M

S+M+D

G+B

Equilibrium

It may be argued that non-Fisher effects will be evident which will lower the equilibrium interest

point; for example, increased inflation may reduce government demand for funds and the

demand curve will not move as far to the right.

The supply curve may in fact move to the right rather than the left as savings increase as a result

of higher wages and increased superannuation contributions.

(b) an expectation of a decrease in the level of economic activity. (LO 13.2)

An expectation of decreased economic activity may come from the business sector

This will result in a decrease in business demand for funds to finance investment projects due to

an anticipated fall in demand.

In a loanable funds demand and supply graph, the decrease in B would shift the demand curve to

the left, resulting in a decrease in the rate of interest.

As businesses decrease their investment in inventories and in capital equipment, they will reduce

their need to borrow and sell financial instruments to obtain funds.

As the supply of financial instruments on the market decreases, the prices of those instruments

will rise and their yields will decrease.

The higher prices on the securities (lower yields) will cause some savers to reallocate their

portfolios and sell securities; that is, hoarding will take place.

The forecast decrease in interest rates is only a temporary equilibrium.

There will be feedback mechanisms to consider in forecasting interest rate changes further into

the future.

Interest rate

Loanable funds Q

Supply1

Supply0

Demand1

Demand0Q0

Pe

i0

i1

For example, the hoarding that accompanied the initial decrease in interest rates will cease after

the desired portfolio re-allocations have been completed.

With no further hoarding, interest rates may have to fall further in order to prompt even more

hoarding.

The decrease in business investment adds to the expected decrease in economic activity, as

output levels fall, there will be a decrease in savings and this will relieve some of the downward

pressure on interest rates.

In addition, the decrease in output will see a worsening in the government budget position, with

an associated reduction in the government's borrowing requirement.

The depreciation of the currency that might be expected to accompany the decreased interest rate

is likely to result in increased demand for exports and a decrease in the demand for imports.

Businesses in the export-competing and import-competing sectors of the economy will increase

their investment, and thus increase their demand for funds. This will place some upward

pressures on interest rates.

6. Interest rates play an important role in monetary policy determinations, economic

performance and the business cycle, and the cost of funds. Financial market participants must

therefore understand the term structure of interest rates.

(a) Define the term ‘yield’ and explain how a yield curve is constructed.

Yield—the total return on an investment; comprising interest receipts and any capital gain or loss

Yield curve—a graph, at a single point in time, of yields on a particular security with different

terms to maturity; for example, it is possible to plot the yield, as at today, for bank bills that have

30 days, 60 days, 90 days and 180 days to maturity.

(b) Identify three different types of yield curves. Briefly describe each of these yield curves and

draw a fully labelled diagram of each curve. (LO 13.3)

Normal/positive/upward-sloping yield curve—reflects the preference for higher interest rates if

funds are invested longer-term. Short-term rates are lower than long-term rates.

Inverse/negative/downward sloping yield curve—illustrates that yield declines as maturity

lengthens. Short-term rates are higher than long-term rates.

Humped yield curve—combines the normal yield curve and the inverse yield curve and joined

by a period of a flat or horizontal yield curve.

Normal yield curve

Time

Yield

Inverse yield curve

Time

Yield

Humped yield curve

Time

Yield

7. A number of theories attempt to explain the term structure of interest rates. The

expectations theory provides a foundation for our understanding of interest rate

determination. Outline the expectations theory approach to the determination of interest rates.

In your answer, explain the relationships that the theory contends will exist between short-

term and longer-term interest rates. (LO13.3)

Expectations theory refers to the shape of a yield curve as a function of the current and future

short-term interest rates; that is, the return received on a continuous series of short-term

investments should be the same as that received for a longer-term investment.

An investor will therefore be indifferent as to whether they invest for a short period of a longer

period; for example, an investor has two options (1) invest today for a one-year period at 4% per

annum and reinvest the funds in twelve months time, or (2) invest the funds today for a two-year

period at 4.5% per annum. The expectation theory will contend that the one-year investment rate

in twelve months time should be 5% per annum (that is, 4.5% x 2 = 9% - 4% = 5%).

Assumptions of the expectations theory:

There are a large number of financial investors who hold reasonably homogeneous expectations

about the future values of short-term interest rates.

There are no transaction costs, and so investors can move into and out of instruments at no cost

as they change their expectations and as they see market rates that are inconsistent with their

expectations.

There are no impediments to market rates moving to their competitive equilibrium levels.

The goal of investors is to maximise their expected rate of return, that is, if all bonds as perfect

substitutes for each another, regardless of their term to maturity, then longer-term interest rates

paid on bonds will be equal to the average of the short-term interest rates expected to prevail

over the longer-term period.

8. Within the context of interest rate determination, the expectations theory attempts to

explain the various shapes of the yield curve. How is the existence of a normal yield curve and

an inverse yield curve explained by the theory? (LO 13.3)

Normal yield curve:

will result from expectations that future short-term rates will be higher than current short-term

rates

o the central bank may reduce short-term rates, but since the market believes that future short-

term rates will be higher than current short-term rates, longer-term rates will not fall as far as

the policy-induced cut in short-term rates; therefore, the yield curve will be upward-sloping

(that is, if E1i1 > 0i1, then the yield curve will be normal).

Inverse yield curve:

will result if the market expects future short-term rates to be lower than current short-term rates

o even though the central bank may increase rates at the short end of the yield curve to achieve

its monetary policy objectives, market participants expect that once those objectives have

been achieved, short-term rates will be lowered again; in this circumstance, long-term rates

will not rise to the same extent as the policy-induced change in short-term rates, and

therefore the yield curve will slope downwards.

9. The segmented markets theory challenges two of the assumptions of the expectations theory.

(a) Identify the two assumptions challenged, and explain the segmented markets approach.

The segmented markets theory rejects two expectation theory assumptions:

that all bonds are perfect substitutes for one another

that investors are indifferent between holding instruments with a short term to maturity and

holding instruments with a long term to maturity.

Segmented markets approach to explaining the yield curve:

Securities in different maturity ranges, for example a 1 to 3 year range versus a 9 to 10 year

range, are not viewed by various market participants as being perfect substitutes for one another.

Whereas bonds with a very short term to maturity may well be close substitutes for each other,

and likewise for bonds with long terms to maturity, a one-month-to-maturity bond is unlikely to

be seen as a close substitute for a 10-year bond.

Some market participants have a preference for short-dated securities, and others have a

preference for longer-term maturities; that is, different investors have preferences for different

segments of the market.

The particular preferences are motivated out of a desire by the various participants to reduce the

riskiness of their portfolios.

Investors will seek to minimise their exposure to fluctuations in the prices and yields associated

with their assets and liabilities by matching the cash flows and maturities of their assets and

liabilities; for example, life offices have mainly long-term liabilities and therefore tend to hold

more longer-term assets.

The implication of the segmented markets approach is that it is the relative demands for and

supplies of securities in the various maturity ranges that determine yields.

The shape and slope of the yield curve are determined by the relative demand and supply

conditions that exist along the maturity spectrum.

(b) It may be argued that the segmented markets approach is negated by modern risk

management practices, arbitrage and speculation. Explain what is meant by this assertion.

(LO 13.3)

The segmented markets approach emphasises the risk management motivation of market

participants; that is, the matching of cash flows and maturities of assets and liabilities in order to

minimise associated risk exposures. By implication, this approach would cause discontinuities in

a yield curve thus exposing significant speculation and arbitrage opportunities.

Arbitrageurs, who are indifferent about the maturity of the bonds they hold, will sell and buy to

take advantage of the discontinuities along the yield curve. Their actions will smooth out the

yield curve; that is, remove the segmentation distortions.

Therefore, it may be reasonable to argue that certain investors do have segment preferences

along a yield curve, but those preferences are balanced by investors with different preferences,

arbitrageurs and speculators.

10. If financial market participants considered that anticipated inflation would rise

significantly in the future, what effect would you expect this forecast to have on the slope of a

normal yield curve? Why? (LO 13.3)

A normal yield curve is upward sloping.

Yields on a particular security are higher as the term to maturity increases.

Yield %

Time

The nominal interest rate (yield) on an investment incorporates a component of real interest and

a component for anticipated inflation; therefore, all other impacts being equal, an anticipation of

an increase in inflation over time will push up nominal interest rates further out on the maturity

spectrum.

As indicated in the graph below, the slope of the yield curve will become steeper.

11. The liquidity premium theory seeks to extend our understanding of the expectations theory

and the determination of interest rates.

(a) Outline the principal contention of the liquidity premium theory.

A criticism of the pure expectations approach is its assumption that investors are indifferent as to

whether they hold long-term or short-term bonds.

There is one important characteristic that distinguishes short-term and longer-term securities that

may result in a violation of the assumption of indifference.

Longer-term-to-maturity bonds are susceptible to a greater risk of larger price fluctuations than

are shorter term instruments.

Given the greater price risk associated with longer term securities, it may be hypothesised that

investors require a premium if they are to be enticed away from the shorter end of the maturity

spectrum.

If this is the case, then the expectations hypothesis explanation of the level of longer term rates

may be presented as being approximately:

0i2 = (0i1 + E 1i1 ) + L

2

Where L is the liquidity premium that is demanded in order to hold the higher risk, longer-term

security.

The size of L is likely to increase the longer the term to maturity of the particular instrument.

The effect of the liquidity premium on the expectations hypothesis is shown below:

Yield %

Time

(b) How does the historic prevalence of a normal yield curve provide indirect evidence of the

existence of a liquidity premium?

Support for the addition of the liquidity premium to the expectations hypothesis is derived from

observations of the shape of the yield curve over time.

The positive or upward-sloping curve is labelled as the ‘normal’ yield curve.

The normal yield curve is typically the shape most frequently observed over the years.

The combination of the expectations theory and the liquidity premium explains the observed

dominance of the normal curve.

At times, even though the pure expectations outcome is an inverse curve, when the liquidity

premium is added to the curve it results in a positive or normal curve.

At other times, the slope of an inverse yield curve will become flatter as a result of the effect of

the liquidity premium; that is, the inverse curve will move upward.

The combined expectations and liquidity premium theories provide a useful framework for

understanding the behaviour of the yield curve.

(c) Does the existence of an inverse yield curve indicate a violation of the liquidity premium

contention? (LO 13.3)

No; an inverse yield curve is still possible.

In this instance, the downward slope of the inverse yield curve will be reduced by the liquidity

premium effect. That is, the yield curve will become flatter, but still retain an inverse slope.

Yield %

Time

observed yield curve

expectations yield curve

liquidity premium

12. The financial press is continually reporting changes in economic variables and seeking

informed opinion on the impact of changes in variables on the direction of future interest rate

changes. Market participants, including policy makers, regulators and corporate managers

also actively monitor interest rates. Within the context of market participants, what is the

importance of understanding the term structure of interest rates? Provide examples in your

response. (LO 13.3)

The term structure of interest rates represents the relationship of yield to the term to maturity on

a particular security such as Treasury bonds.

Yield is expressed at a given point in time where there is constant risk, the same security, but a

varying period to maturity.

Yield curves may be categorised as normal, inverse and flat. The shape and slope of each of

these types of curves provides information to the market.

Under the pure expectations theory, a normal yield curve implies that future short-term interest

rates are expected to be higher than current short-term rates. On the opposite side, an inverse

yield curve implies that future short-term interest rates are expected to be lower than current

short-term rates.

If the term structure of interest rates within the market are correct and in equilibrium, then the

shape and slope of the yield curve provides some very important indicators to market

participants:

o borrowers—assists borrowers to make informed decisions on the future direction of their

borrowing costs. The borrower may be able to restructure or reschedule their existing

funding arrangements to take advantage of expected movements in interest rates. New

borrowing issues may be brought forward, or alternatively delayed, depending on the

forecast future movement in interest rates. Decisions may also be made on the maturity

structure of existing and new funding arrangements.

Yield %

Time

observed yield curve

expectations yield curve

liquidity premium

o investors—will consider the term structure of interest rates in forecasting the future direction

of interest rates. This will influence their investment acquisition and disposal strategies; for

example, an investor with a portfolio of bonds may determine to sell the bonds if an interest

rate rise is forecast so as to avoid the price risk that prevails if yields increased

o financial institutions—are particularly concerned with current and future interest rates. The

price of most financial institution products is based on an interest rate. Therefore, any

movement in rates will have a direct impact on the institutions’ net interest margins.

Institutions will implement strategies to restructure their existing asset portfolios, together

with their liability commitments (gap management). Institutions will set the pricing of their

borrowing and lending products based on their interpretation of the future movement in

interest rates.

o government and Reserve Bank—government will analyse the term structure of interest rates

having regard to its economic, social and political objectives. These will be supported by the

determination and implementation of monetary policy by the Reserve Bank in order to

achieve its objectives of full employment, stability of the currency and maintenance of the

welfare of the people of Australia. To this end, monetary policy is currently directed towards

achieving an underlying inflation rate of 2 to 3 percent over a business cycle. The level of

anticipated inflation will affect the slope or steepness of the yield curve. If inflation is

expected to remain relatively low, then the slope of the yield curve should remain relatively

flat.

13. Explain the term ‘risk-free rate of interest’. Why is the existence of the risk-free rate of

interest important when examining the level of interest rates generally in the financial

markets? (LO 13.4)

The risk-free rate of interest is a return (yield) earned with certainty of payment; that is, there is

no risk of default by the issuer

Within the Australian markets, the Treasury bond, issued by the Commonwealth government, is

adopted as a proxy for the risk-free rate of return.

The Treasury bond is accepted as being risk-free in that it is presumed that the government is

able to meet its monetary commitments.

The importance of the risk-free rate of return is that it is the basis upon which other financial

assets are priced.

Securities which have a higher degree of risk attached to them are priced at a margin above the

risk-free rate; therefore, the Treasury bond becomes the benchmark upon which interest rates on

other securities with similar maturities are established.

The risk-free rate of interest is applied in a number of important pricing models, including the

options pricing model developed by Black & Scholes, and the Capital Asset Pricing Model.

The following graph demonstrates the role of the Treasury bond as the risk-free rate. Debentures

are priced above the Treasury bond rate, but unsecured notes are further priced above the

debenture rate. This reflects the relative risk of each of the securities.

14. As a finance researcher at a leading university you are interested in risk premiums applied

by the markets on corporate debt issues.

(a) Discuss the concept of a risk premium and the effect that a risk premium will have on the

yield curve for a corporate borrower.

Risk premiums will be applied to corporate borrowers relative to the risk free rate, being the

Treasury bond yield for the similar term to maturity.

Underlying the risk premium charged against a particular corporate borrower will be a range of

operational and financial variables, however, the basic measure will be the level of perceived

credit or default risk; that is, what is the probability that a borrower will be able to meet its future

on-going cash flow commitments when they are due.

The level of the risk premium will impact the cost of funds and the level of profitability of a

corporation.

A standard measure of risk used in the corporate bond market is the credit rating.

The higher the credit rating the lower is the risk premium and the cost of borrowing.

Yield %

Time (years)

Unsecured notes

DebenturesRisk premium

Treasury bonds

Risk premium

(b) Is it inevitable that the risk premium for a corporate borrower will be constant throughout

the maturity spectrum? Explain your response. (LO 13.4)

Whilst conceptually it is possible for a risk premium attached to a particular corporate borrower

to be constant over the maturity spectrum, it is more likely that the risk premium will change.

One set of conditions under which a widening risk premium gap may occur is if the corporate

borrower has been a highly successful corporation, but its future is somewhat uncertain; for

example, this could occur if the corporation's main products are towards the end of the product

life cycle, and the company has not devoted sufficient resources to the research and development

of a new product or production technique that will maintain its competitive advantage.

The increasing gap could also open up if the company has recently been involved in a takeover

or merger, the likely commercial success of which has not been clearly established by lenders.

In both cases, there is a low risk of default on the near-to-maturity instruments, but greater

uncertainty about the company's performance further into the future.

It is also possible that the yield curve for a higher-risk borrower may show a narrowing of the

risk premium gap as the term to maturity increases.

Such an outcome could result from a concern that, in the current business environment, the

company may have difficulty in redeeming the soon-to-mature instruments, but market

participants believe that if the company survives the near-term, then its prospects are relatively

good.

Another example may be a company that is involved in a reasonably speculative exploration

activity, or the development of a new technology, or an attempt to convert a laboratory discovery

into a commercial product. Near-term risk is high, but if successful the longer-term risk premium

will fall.

Extended learning question

15. This question requires calculations relating to the yield curve and the expectations theory.

(LO 13.5)

(a) If an investor possesses the following information, and expectations on Treasury bond

yields are:

0i1 = 7.50% p.a.

E1i1 = 8.80% p.a.

calculate the yield on a two-year bond (0i2) that would result in the investor being indifferent

between placing funds in a one-year bond now, to be followed by a one-year bond in a year’s

time, or placing the funds in a two-year bond now.

(1) Calculation using arithmetic average:

0i2 = (0i1 + E 1i1 )

2

= 7.5 + 8.8

2

= 8.15 %

(2) Calculation using geometric average:

0i2 = [( 1 + 0i1 ) ( 1 + E1i1 )] 0.5 - 1

= [( 1.075 ) ( 1.088 )] 0.5 - 1

= [ 1.1696 ] 0.5 - 1

= 8.148 %

(b) You are given the following data:

0i1 = 10.00% p.a.

E1i1 = 12.00% p.a.

E2i1 = 13.00% p.a.

E3i1 = 13.00% p.a.

On the basis of the expectations theory of the yield curve, complete the following.

Calculate the 0i2, 0i3 and 0i4 rates.

formula: 0in = [(1 + 0i1) (1 + E1i1) (1 + E2i1) ... (1 + En - 1i1)]1/n - 1

(i) 0i2 = [(1 + 0.10) (1 + 0.12)]1/2 - 1

= 11.00%

(ii) 0i3 = [(1 + 0.10) (1 + 0.12) (1 + 0.13]1/3 - 1

= 11.66%

(iii) 0i4 = [(1 + 0.10) (1 + 0.12) (1 + 0.13) (1 + 0.13]1/4 - 1

= 11.99%

Explain what is meant by implicit forward rates of interest.

On the basis of the expectations theory, a yield curve provides information on what the on-

balance expectations of market participants are concerning a large range of future interest

rates. That is, implicit in the yield curve there are indicators, or information, on a series of

expectations about future interest rates.

List the full range of one-year implicit rates of interest that could be calculated on the basis

of the yield curve data that provide the current rates on bonds with one, two and three

years to maturity.

Implicit interest rates that could be calculated on the basis of the above yield curve are 1i1 , 1i2 and 2i1.

Given the following yield curve data, calculate the 2i2, 1i2 and 3i1 implicit rates:

0i1 = 8.00% p.a.

0i2 = 9.00% p.a.

0i3 = 10.00% p.a.

0i4 = 11.00% p.a.

Yield %

1 2 30 Years

0i1

0i2

0i3

1i1

1i2

2i1

Actual rates

Implicit rates

formula: nik = [(1 + 0in+ k) n + k ] 1/k -1

[ (1 + 0in)n ]

(i) calculate 2i2 where: n = 2; k = 2

= [(1 + 0.11) 4 ]1/2 -1

[(1 + 0.09)2]

= 13.04%

(ii) calculate 1i2 where: n = 1; k = 2

= [(1 + 0.10) 3 ]1/2 -1

[(1 + 0.08)1]

= 11.01%

(iii) calculate 3i1 where: n = 3; k = 1

Yield %

1 2 30 Years

0i1

0i2

0i3

1i1

1i2

2i1

Actual rates

Implicit rates

4

0i4

1i3

2i1

3i1

8%

9%

10%

11%

= [(1 + 0.11) 4 ]1/1 –1

[ (1 + 0.10)3]

= 14.06%