1

1
Money and Banking The behavior of interest rates

• Spring 2007
• Martin Andreas Wurm
• University of Wisconsin - Milwaukee

2
The behavior of interest rates

• Required Reading Mishkin, Chapter 5

3
The behavior of interest rates

• 1. Overview
• So far we have developed some fundamental
  insights
• Financial markets are the place of exchange of
  funds between borrowers and lenders.
• Since a significant part of these funds are used
  by firms to invest, financial markets have a high
  significance for economic growth.
• The price borrowers have to pay and lenders
  receive for the provision of funds is measured by
  interest rates

4
The behavior of interest rates

• 1. Overview
• Because of this relation, macroeconomist are
  strongly concerned about interest rates
• Interest rates are not only a central determinant
  of investment and, thus, future economic growth,
  but also of households consumption and savings
• Interestingly enough, interest rates are not
  stable at all Figure 3.1. below displays the
  behavior of nominal interest rates on U.S.
  T-Bills from 1934 to 2006

5
The behavior of interest rates

• 1. Overview

6
The behavior of interest rates

• 1. Overview
• Interest rates until the middle of the 20th
  century were around 0-1, raised all the way up
  to 16 in the early 1980s and by 2002 were back
  to 1
• What causes these fluctuations in interest rates?
• We already discovered that asset prices and
  interest rates are negatively related.
• In order to explain interest rate fluctuations
  we, thus, will focus on the determinants of asset
  demand and supply

7
The behavior of interest rates

• 1. Overview
• Two theories are commonly used to discuss the
  behavior of interest rates
• The loanable funds framework
• The (Keynesian) liquidity preference framework
• In discussing these, we will focus our discussion
  mainly on bonds.

8
The behavior of interest rates

• 2. The demand for assets
• The price of bonds and, thus, the interest rate
  on bonds is determined by shifts in demand and
  supply of bonds
• Generally an individuals demand for assets is
  ceteris paribus - determined by four factors
• An individuals wealth, the expected returns to
  holding an asset, the assets risk and the
  liquidity of an asset
• Lets look at each of these four step by step

9
The behavior of interest rates

• 2. The demand for assets
• 1. Wealth
• Wealth indicates the total resources available to
  an individual (including all of her/his assets)
• Everything else the same an increase in an
  individuals wealth will raise her/his demand for
  (all forms of) assets, et vice versa.

10
The behavior of interest rates

• 2. The demand for assets
• 2. Expected Return
• We determined the return to a specific bond as
  its interest rate capital gains (/losses)
• Essentially all factors (other than the price)
  determining the return on a bond are unknown at
  the time of its purchase
• Potential future changes in asset prices, its
  interest rate and shifts in inflation are
  unknown.

11
The behavior of interest rates

• 2. The demand for assets
• 2. Expected Return
• The demand for a specific bond relative to
  another asset is, thus, determined by the
  expectations an individual forms about the return
  on this bond rather than by its actual return.
• A concept we use in economics to model
  expectations are so called expected values.
  Expected values of an outcome have an
  interpretation similar to an average outcome and
  are constructed in the following way.

12
The behavior of interest rates

• 2. The demand for assets
• 2. Expected Return
• To find the expected value on any action we first
  have to find all possible outcomes of that
  action.
• Then we have to assign a value or payoff to each
  of these outcomes and a probability of this
  outcome occuring
• Finally we sum up the products of the probability
  and the payoffs for each possible outcome.

13
The behavior of interest rates

• 2. The demand for assets
• 2. Expected Return An Example
• Assume you play roulette and put 100 on black.
• In American roulette, there are three possible
  outcomes The ball comes to rest on a red number,
  a green number or a black number.
• If the ball comes to a rest on a green or red
  number we receive nothing, if the ball comes to
  rest on a black number we receive 200.

14
The behavior of interest rates

• 2. The demand for assets
• 2. Expected Return An Example
• Finally, the probability that the ball comes to a
  rest on black is about 0.47
• The expected return E to playing black on a
  roulette table is, thus, given by
• So on average youre likely to win 94 on by
  putting 100 on black at a roulette-table.

15
The behavior of interest rates

• 2. The demand for assets
• 2. Expected Return An Example
• Similar to an expected payoff in the case of
  playing roulette, we can form an expectation on
  the return of a bond.
• For example if we suspect that a bond pays a
  return of 15 with a probability of 0.25 and a
  return of 5 with a probability of 0.75, the
  expected return on this bond is given by

16
The behavior of interest rates

• 2. The demand for assets
• 2. Expected Return
• Since individuals do not know ahead of time what
  the actual return on an asset is going to be,
  they act according to their expected returns
  instead.
• In practice these depend on expected changes in
  the relative price of an asset, in the interest
  rate and in particular on expected inflation,
  which will decrease the demand for a particular
  asset.

17
The behavior of interest rates

• 2. The demand for assets
• 2. Expected Return
• An increase in the expected return of one asset
  over another increases the demand for this asset
  and vice versa.
• Note that inflation does not affect the return to
  all assets identically. A bond which is denoted
  in nominal terms is stronger affected by high
  inflation than for example the rent produced by
  the ownership of real estate.

18
The behavior of interest rates

• 2. The demand for assets
• 3. Risk
• The expected return on an asset is not its only
  feature of interest Apart from the average
  return individuals also care about the risk of an
  asset.
• There are three types of agents according to
  their risk-behavior Risk-averse agents,
  risk-neutral agents and risk-lovers.

19
The behavior of interest rates

• 2. The demand for assets
• 3. Risk An Example
• To see the difference, consider the following
  example
• Assume you compare two bonds. The first one has a
  return of 100 with a probability of 25 and a
  return of 50 with a probability of 75. Its
  expected value is then given by 62.5. The
  second has a return of 200 with a probability of
  25 and a return of 16.67 with a probability of
  75. The expected value of this second bond is
  also equal to 62.5

20
The behavior of interest rates

• 2. The demand for assets
• 3. Risk An Example
• Clearly these two bonds are not the same!
• Bond 2 has a larger variation and, thus, a
  higher risk. A risk-neutral person would prefer
  bond 1, while a risk-lover would prefer bond 2. A
  risk-neutral person would be indifferent between
  the two.

Bond 1 25 of all cases 100 75 of all cases
50
Bond 2 25 of all cases 200 75 of all cases
16.67
21
The behavior of interest rates

• 2. The demand for assets
• 3. Risk
• The standard assumption in most economic models
  is that agents are risk-averse. Thus, an agents
  demand for an asset will decrease if the risk of
  this asset increases relative to others.
• Individuals are often inconsistent about their
  perception of risk For example Many people are
  afraid of terrorist threat, while they are
  perfectly fine with riding in a car. In 2001 the
  number of individuals in the U.S. killed in
  terrorist attacks were 2,986, while the number of
  deaths on the street was equal to 42,116.

22
The behavior of interest rates

• 2. The demand for assets
• 4. Liquidity
• We already discussed that agents prefer assets
  which are highly liquid since they have to
  satisfy uncertain transaction needs.
• An asset with higher liquidity will, thus, be
  demanded more than an asset with lower liquidity,
  everything else the same.

23
The behavior of interest rates

• 3. The supply of assets
• Again we will keep focusing on bonds (although
  most of the following holds for other assets as
  well). The supply of bonds depends mainly on
  three factors
• 1. The expected profitability of investment
  opportunities
• 2. Expected inflation
• 3. Government activities

24
The behavior of interest rates

• 3. The supply of assets
• 1. Expected profitability of investment
  opportunities
• If firms perceive a higher profitability in their
  investment options, their demand for funds will
  be higher. Thus, the supply of bonds (or stocks,
  etc.) will increase.
• During a business cycle expansion we, thus, see
  the supply of bonds increase, while during
  recessions, we see the supply of bonds decrease

25
The behavior of interest rates

• 3. The supply of assets
• 2. Expected inflation
• From the Fisher equation follows that high
  expected inflation reduces the real interest rate
  firms or governments have to pay on bonds.
• Thus, if firms or governments expect inflation to
  be high, their supply of bonds will increase,
  since the expected cost of borrowing c.p. becomes
  smaller in real terms.

26
The behavior of interest rates

• 3. The supply of assets
• 3. Government activities
• If a government decides to engage in any form of
  activity which increases the government deficit,
  it will turn to financial markets to obtain funds
  to finance this deficit.
• Thus an increase in the government deficit
  (through higher spending or lower taxation) leads
  to an increase in the supply of government bonds.

27
The behavior of interest rates

• 4. Equilibrium in the bonds market Loanable
  funds
• To model equilibrium in the bonds market lets
  assume for simplicity that there exists only one
  discount bond
• Let further Bd indicate the demand for this bond
  and Bs indicate supply of this bond.
• Let this discount bound have a face value of
  1,000 and a maturity of one year.

28
The behavior of interest rates

• 4. Equilibrium in the bonds market Loanable
  funds
• As usual, demand is a negative function of the
  price of this bond. The more costly a bond is
  today, the lower is its expected return tomorrow.
  The following graph indicates this relationship.
• Note that in this example demand for this bond
  for each level of price is arbitrary

29
The behavior of interest rates

• 4. Equilibrium in the bonds market Loanable
  funds

Price in
1900
1700
1500
1300
Bd
1100
900
Quantity of bonds in bil.
100
200
300
400
500
600
600
30
The behavior of interest rates

• 4. Equilibrium in the bonds market Loanable
  funds
• We further know that the price of a bond and the
  interest rate are negatively related.
• For a one period discount bond, the price is
  determined by its present discounted value
• Here

31
The behavior of interest rates

• 4. Equilibrium in the bonds market Loanable
  funds
• For different prices, we can, thus determine the
  bonds equilibrium interest rates, e.g.
• Pb 1,900
• Pb 1,700
• Pb1,500

32
The behavior of interest rates

• 4. Equilibrium in the bonds market Loanable
  funds
• Graphically we can illustrate this inverse
  relationship by adding a second vertical axis on
  the right side of our graph indicating the
  interest rate for each price
• In addition, we can add the supply curve of
  bonds, which is an upward-sloped function of the
  bond price, since a borrower obtains more funds,
  the higher the price he can sell a bond for c.p.

33
The behavior of interest rates

• 4. Equilibrium in the bonds market Loanable
  funds

Bs
Price in
Interest rate in
1900
5.26
E
17.65
1700
33.3
1500
1300
81.81
Bd
1100
900
Quantity of bonds in bil.
100
200
300
400
500
600
600
34
The behavior of interest rates

• 4. Equilibrium in the bonds market Loanable
  funds
• E indicates the equilibrium in the bonds market,
  since at E BdBs.
• From this diagram we can find the equilibrium
  price for this bonds (1,700), the equilibrium
  interest rate (17.65) and the equilibrium
  quantity (300 bill. worth of bonds).
• If any of the determinants of supply or demand of
  bonds changes, we can now easily analyze, how
  bond prices and interest rates are going to be
  affected.

35
The behavior of interest rates

• 4. Equilibrium in the bonds market Loanable
  funds
• Usually we do care more about interest rates than
  about bonds prices.
• Lets, thus, get rid of the bond prices in our
  diagram and flip around the vertical axis
  indicating the interest rate. The resulting graph
  is shown on the next slide

36
The behavior of interest rates

• 4. Equilibrium in the bonds market Loanable
  funds

Interest rate in
81.81
Bd
33.3
E
17.65
5.26
Bs
Quantity of bonds in bil.
100
200
300
400
500
600
600
37
The behavior of interest rates

• 4. Equilibrium in the bonds market Loanable
  funds
• This diagram allows us to directly determine how
  changes in the demand and supply of assets affect
  the interest rate, which is what we are
  ultimately interested in.
• It has one undesirable feature, however The
  demand curve in this graph is upward-sloping.
• We solve this problem with a trick

38
The behavior of interest rates

• 4. Equilibrium in the bonds market Loanable
  funds
• Remember that every bond is essentially a debt
  contract.
• While a bond can be viewed as supplied by the
  borrower and demanded by the lender, it can also
  be viewed as supply of funds by the lender and
  demand for these funds by the borrower.
• If we denote the supply of these loanable funds
  by Ls and their demand by Ld we can re-label our
  graph, such that we have a standard upward sloped
  supply and downward sloped demand curve

39
The behavior of interest rates

• 4. Equilibrium in the bonds market Loanable
  funds

Interest rate in
81.81
Ls
33.3
E
17.65
5.26
Ld
Loanable funds in bil.
100
200
300
400
500
600
600
40
The behavior of interest rates

• 4. Equilibrium in the bonds market Loanable
  funds
• This diagram is one of the most common
  instruments to analyze the causes in the changes
  of interest rates and is known as loanable funds
  framework
• An important feature is that supply and demand
  for loanable funds is given in stocks of funds,
  rather than in flows. This approach is called
  asset market approach.