Transcript The Loanable Funds Model of Interest Rates

FNCE 3020
Financial Markets and Institutions
Fall Semester 2005
Lecture 3
The Behavior of Interest Rates
How Might We Examine How Interest
Rates Behave?

Examine interest rates in two stages:
 First, through the Bond Market Model: i.e.,
demand and supply analysis of bonds in the
bond market!


What happens to the quantity demand and quantity
supplied of bonds as we varying the price!
Second, from the Bond Market Model to
Loanable Funds Model, where:


The Demand for bonds = supply of loanable funds
The Supply of bonds = demand for loanable funds
Determinants of Financial Asset
Demand

When anyone is faced with the question of whether to
buy and hold an asset or whether to buy one asset
rather than another, the following factors are likely to
enter into the decision:

Wealth, i.e., the total resources currently owned by the
individual, including all financial assets held

Expected return, i.e., the return expected over the next
investment period on an asset relative to alternative assets.

Risk, i.e., the degree of uncertainty associated with the return
on an asset relative to alternative assets.

Liquidity, i.e., the ease and speed with which an asset can be
turned into cash relative to alternative assets.
What Changes the Quantity of an
Asset Demanded

The (quantity) demanded of a particular financial asset
varies according to:




Wealth: An increase in wealth raises the quantity demanded of
an asset.
Expected return: An increase in an asset’s expected return,
relative to that of alternative assets, raises the quantity
demanded of the asset.
Risk: An increase in an asset’s risk, rises relative to that of
alternative assets, reduces the quantity demanded of the asset.
Liquidity: The more liquid an asset, relative to alternative
assets, the more desirable it is, and thus the greater will be the
quantity demanded of the asset.
Summary Table: Response of
Demand to Changes in Four Factors
The Derivation of the Economy’s
Demand Curve for Bonds

Bond Demand Curve: Plots the relationship
between the quantity demanded for bonds
and the price of a bond, when all other
factors are held constant.


Thus, we are only looking at the relationship
between prices and quantity demanded.
This is important!!!
Conceptualizing the Demand for
Bonds


Begin, by examining the demand for a 1 year
discount bond.
Question: What is the expected return on this
bond?






We can calculate the expected return as the investment
yield on a 1 year discount bond as follows (see
investment yield formula, Lecture 2):
Where:
i = investment yield
FV  PP
Re = “expected return”
e
iR 
F = face value
PP
P = market price


Plotting Appropriate Points Along the
Bond Demand Curve

Demand for 1 year bond, for a given price of $950.



Demand for the 1 year bond at a given price of $900



i = Re = (1,000-950/950) = 5.3%
Assume at this price (and yield) 100 bonds will be demanded.
 this will be point A on the demand schedule (see second
slide).
i = Re = (1,000-900/900) = 11.1%
Assume at this price (and yield) 200 bonds will be demanded
 This will be point B on the demand schedule (see second
slide).
Important: We assume the market will hold more (demand
more) of the bond as its price decreases.

Why: At a lower price, the expected yield increases.
Determining Additional Points Along
the Bond Demand Curve

Point C: P = $850
i = 17.6%
Bd = 300

Point D: P = $800
i = 25.0%
Bd = 400

Point E: P = $750
i = 33.0%
Bd = 500

Demand Curve is Bd in Figure 1 which connects
points A, B, C, D, E

Demand Curve has a downward slope!

As the price of the bond decreases, demand for the bond
will increase (see movement along the x axis; next slide).

Why: As the price decreases, the yield (expected return)
increases!
Figure 1: Demand Curve (Bd)
Demand Curve is Bd
connecting points A,
B, C, D, E.
Demand Curve has a
downward slope.
As the price of the
bond decreases (and
the yield increases),
the demand for bonds
will increase (along
the x axis).
Reason: The
expected yield has
increased.
Derivation of the Supply Curve

Supply Curve: shows the relationship between the
quantity of a bond supplied and its price, when all other
factors are held constant.



Again, we are only looking at the relationship between price and
quality supplied
Assume the following supply conditions:
Point F:
P = $750
i = 33.0%
Bs = 100
Point G:
P = $800
i = 25.0%
Bs = 200
Point C:
P = $850
i = 17.6%
Bs = 300
Point H:
P = $900
i = 11.1%
Bs = 400
Point I:
P = $950
i = 5.3%
Bs = 500
Important: As the price of the bond increases, supply will
increase.

Why: The cost to borrow funds decreases and thus more bonds
will be supplied by borrowers (e.g., corporations).
Figure 2: Supply Curve (Bs)
Supply Curve is Bs
connecting points F,
G, C, H, and I.
Supply Curve has
upward slope.
As the price of the
bond increases (and
the yield decreases),
the supply of bonds
will increase (along
the x axis).
Reason: The cost of
borrowing has
decreased.
Point of Bond Market Equilibrium

Bond Market Equilibrium: This occurs when
the amount of bonds an economy is willing to
buy (i.e., demand) equals the amount of
bonds an economy is willing to sell (i.e.,
supply).



This point is called the “market-clearing price.”
In the previous slide, this is point C.
Any Bond Market disequilibrium (i.e., excess
demand or excess supply) is corrected
through price changes!
Restoring Market Equilibrium
Equilibrium occurs when
Bd = Bs, or at P* = 850,
i* = 17.6% (Point C)
However, when P =
$950, i = 5.3%, Bs > Bd
There is excess supply,
To restore equilibrium:
P  to P*, i  to i*
And, when P = $750, i =
33.0, Bd > Bs
There is excess demand,
to restore equilibrium:
P  to P*, i  to i*
Shifts in the Bond Demand and Supply
Schedules

Up to this point, we have examined what will cause
a movement along (up or down) a bond demand
and bond supply curve.


Now we need to examine, what will cause either
schedule to shift (inward or outward)


There is only one factor: Changes in the price of the bond.
These will occur in response to all factors other than a
change in the price of the bond.
Important: When one of the schedules changes, this
produces a change in the economy’s equilibrium
(i.e., market) interest rate.
Shifts in the Demand and Supply Curves

The analysis of interest rate behavior (i.e., changes in the market
equilibrium interest rate) needs to explore why the curves shift in or
out!
Factors Causing the Demand Schedule
to Shift Outward

Wealth: When the economy grows, wealth
increases. Increased wealth will result in a higher
demand for bonds (in investor portfolios).


During a business expansion, as incomes (and wealth)
increase, the demand for bonds will also increase.
Risk: As prices in the bond market become less
volatile (i.e., as the risk decreases), bonds will
become more attractive and thus the demand for
bonds will rise.

Additionally, as alternative financial assets (e.g., on stocks)
become more risky, the demand for bonds will rise.
Factors Causing the Demand Schedule
to Shift Outward

Expected Future Returns on Bonds: If the
interest rate is “expected” to be lower in the
future than it is now, the demand for bonds
will increase now:

Why: Because if interest rates do fall in the
future, the prices of currently held bonds will rise.


Recall the inverse relationship between bond prices and
yield.
Additionally, if expected returns on alternative
financial assets falls (e.g., on stocks), the demand
for bonds will increase
Factors Causing the Demand Schedule
to Shift

Liquidity: Increases in the liquidity of bonds (i.e.,
their marketability in secondary markets) will cause
bonds to be more attractive, and increase their
demand.


Additionally, decreases in the liquidity of alternative
financial assets (e.g., stocks), causes the demand for
bonds to increase
Expected Rate of Inflation: Decreases in the
expected rate of inflation, will result in an increase in
the real return on bonds, and cause the demand for
bonds to increase.

The real return is the interest rate minus the rate of
inflation.
Summary of Demand Factors
1.
Wealth

2.
Expected Return

3.

Risk of bonds , Bd shifts out to right
Risk of other assets , Bd shifts out to right
Liquidity


5.
Re for bonds (in the future) , Bd shifts out to the right.
Risk

4.
Wealth , Bd shifts out to right
Liquidity of bonds , Bd shifts out to right
Liquidity of other assets , Bd shifts out to right
Expected Inflation

πe , real return , Bd shifts out to right
Factors that Cause the Supply
Schedule to Shift Outward

Expected Profitability of Business Investment
Opportunities: As businesses anticipate
higher profits on their potential investments,
they will be more willing to borrow to fund
those investments.


Increase business borrowing results in an
increase in the supply of bonds in the market.
This generally occurs during a business
expansion as demand for products increases and
businesses become more optimistic about the
future.
Factors that Cause the Supply
Schedule to Shift Outward

Expected Inflation: When expected inflation
increases, the real cost of borrowing decreases.



As the real cost of borrowing falls, businesses increase
their borrowing.
Increase borrowing results in an increase in the supply of
bonds in the market.
Government Policies: Higher government deficits
increases the need for government borrowing.


Deficits result from a shortfall of tax receipts over spending.
Increase government borrowing results in an increase in
the supply of bonds in the market.
Summary of Supply Factors
1.
Expected Profitability of Business Investment

2.
Profitability, Bs shifts out to right
Expected Inflation
πe , real cost of borrowing , Bs shifts out to right
3.
Government Policies

Government deficits , Bs shifts out to right
Adding the Rest of the World to the
Model.


Foreign sector activity can result in shifts in another
country’s demand and supply curves.
Assume the U.S. financial market:



Inward investment from overseas investors will shift the
demand schedule (for bonds) out.
Inward borrowing from overseas businesses will shift the
supply schedule (for bonds) out.
Thus, we need to consider the impact of a global
financial market on changes in a country’s
equilibrium (i.e., market) interest rate.

This is important…
And What About the Central Bank?

We can introduce the central bank into this model
through its impact on actions on the debt markets.

One of the major policy instruments used by the Federal
Reserve is open market operations.


As the central bank buys securities, this will increase the
demand.


Buying and selling government securities to influence the
amount of reserves in the banking system.
Push up the price and bring down the interest rate.
As the central bank sells securities, this will increase
supply.

Lower the price, and increase the interest rate.
The Loanable Funds Model of Interest
Rates



Now that we have developed the bond market
model, we need to move to the loanable funds
model of interest rates.
Loanable Funds Model Defined: Changes in the
quantity of “loans” demanded and supplied in an
economy explains interest rate changes.
Loans refers to the amount of funds supplied or
demanded in an economy.


Thus, the demand for bonds is equal to the supply of
loanable funds (Bd = Ls on the next slide).
And the supply of bonds is equal to the demand for
loanable funds (Bs = Ld on the next slide)
The Loanable Fund Model Illustrated

Note: The model has as the price the interest rate on the Y-axis.
Changes in the Market’s Equilibrium
Interest Rate

Decreasing interest rate results from either:



Increase in the demand for bonds (increase in the
supply of loanable funds)
Decrease in the supply of bonds (decrease in the
demand for loanable funds)
Increasing interest rate results from either:


Decrease in the demand for bonds (decrease in
the supply of loanable funds)
Increase in the supply of bonds (increase in the
demand for loanable funds)
Decreasing Interest Rate Illustrated
Increasing Interest Rate Illustrated
Additional Interest Rate Considerations:
The Fisher Interest Rate Effect


This is another possible explanation of the market
rate of interest.
Fisher Effect states that the market rate of interest is
the sum of (1) the real interest rate plus (2) the
market’s expected rate of inflation.



The real rate of interest reflects the rate of real economic
growth (i.e., the amount of reward that should accrue to
the lender for lending to a productive economy).
Then, an inflation premium is added to the real rate, to
produce a market interest rates that protects investors
against this loss of purchasing power.
So: interest rate = real rate + inflation expectations.
Changes in Market Interest Rates with
the Fisher Model

According to the Fisher Model, over time, changes
in market interest rates may be attributed to
changes either in




the real interest rate, or
to changes in inflationary expectations.
Changes in the real rate reflects the behavior in the
market for loanable funds in response to changing
long term economic activity (real economic activity).
Explaining changes in inflationary expectations
tends to be a more complicated matter.

One hypotheses is that current inflationary expectations are
based on the history of past actual rates of inflation.

Called Adaptive Expectations model.
Evidence on the Fisher Effect in the
United States: 1953-2004
Expected Inflation and Interest Rates (Three-Month Treasury Bills), 1953–2004
Additional Consideration in Using the
Fisher Interest Rate Model


At the time the debt contract (i.e., bond) is priced the
inflation premium is based on expected rates of
future inflation.
If these expectations differ from actual inflation rates
during the life of the debt instrument (i.e., bond)
either the lender (investor) or borrower can be
adversely affected.


For example, the lender (investor) can end up with a
negative return if actual inflation is greater than yield on the
purchased debt instrument.
Or the borrower can end up paying much more in real
terms if the actual rate of inflation falls short of the
expected at the time the bond was issued.
Final Consideration: Impact of the
Business Cycle on Interest Rates



Historically, interest rates have moved in a “pro-cyclical” manner.
Generally we have observed that:
 Rates moving down during a business recession.
 Rates moving up in during a business expansion.
Why?
 Business cycle impacts, especially business demand for funds.
 Central bank impacts, i.e., the central bank responding to
changes in economic activity.
However, the inflationary environment can affect (and offset or
dominate) this cyclical move.
 1970s: High and rising inflationary expectations in economy.
 1990 - present: Falling and eventually low inflationary
expectations in the economy.
Business Cycles and Short Term Rates
Business Cycles and Long Term Rates
Central Bank Impacts Over the
Business Cycle
Pro Active Federal Reserve