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CHAPTER
4
Determining Interest Rates
LEARNING OBJECTIVES
After studying this lesson, you should be able to:
4.1
Discuss the most important factors in building an investment portfolio
4.2
4.3
Use a model of demand and supply to determine market interest rates
for bonds
Use the bond market model to explain changes in interest rates
4.4
Use the loanable funds model to analyze the international capital market
CHAPTER
4
Determining Interest Rates
IF INFLATION INCREASES, ARE BONDS A GOOD INVESTMENT?
•Recently, interest rates on U.S. Treasury notes and corporate bonds
have been falling relative to their 30-year averages.
•If interest rates on these securities rose back to their historical
averages, holders of bonds would suffer losses.
•Not surprisingly, many financial advisers have warned investors that
buying bonds could be risky.
•In this lesson, we study how investors take into account
expectations of inflation, as well as other factors, such as risk and
information costs, when making investment decisions.
•An Inside Look at Policy on page 116 discusses movements in
interest rates during 2010.
Key Issue and Question
Issue: Federal Reserve policies to combat the recession of 2007–
2009 led some economists to predict that inflation would rise and
make long-term bonds a poor investment.
Question: How do investors take into account expected inflation and
other factors when making investment decisions?
4.1 Learning Objective
Discuss the most important factors in building an investment portfolio.
The Determinants of Portfolio Choice
The determinants of portfolio choice, sometimes referred to as determinants of asset
demand, are:
1.The saver’s wealth or total amount of savings to be allocated among investments
2. The expected rate of return from an investment compared with the expected rates
of return on other investments
3. The degree of risk in the investment compared with the degree of risk in other
investments
4. The liquidity of the investment compared with the liquidity of other investments
5. The cost of acquiring information about the investment compared with the cost of
acquiring information about other investments
How to Build an Investment Portfolio
Wealth
In general, when we view financial markets as a whole, we can assume that an
increase in wealth will increase the quantity demanded for most financial assets.
Expected Rate of Return
Expected return The return expected on an asset during a future period; also known
as expected rate of return.
We calculate the expected return on an investment using this formula:
Expected return = [(Probability of event 1 occurring) X (Value of event 1)]
+ [(Probability of event 2 occurring) X (Value of event 2)].
For example, with equal probability of a rate of return of 15% or a rate of return of 5%:
Expected return = (0.50)(15%) + (0.50)(5%) = 10%.
How to Build an Investment Portfolio
Risk
Risk The degree of uncertainty in the return on an asset.
• For example, if there is a probability of 50% that a bond will have a return of 12%
or a probability of 50% that the bond will have a return of 8%, then the expected
return on the bond is
(0.50)(12%) + (0.50)(8%) = 10%.
• Most investors are risk averse, which means that in choosing between two assets
with the same expected returns, they would choose the asset with the lower risk.
For this reason, there is a trade-off between risk and return.
• There are also risk-loving investors who prefer to hold risky assets with the
possibility of maximizing returns, and risk-neutral investors, who make their
decisions on the basis of expected returns, ignoring risk.
How to Build an Investment Portfolio
Making the Connection
Fear the Black Swan!
• The table below illustrates the trade-off between risk and return.
• Investors in stocks of small companies during these years experienced the highest
average returns but also accepted the most risk.
• Investors in U.S. Treasury bills experienced the lowest average returns but also the
least risk.
• The term black swan event refers to rare events that have a large impact on society
or the economy. Some economists see the financial crisis as a black swan event
because before it occurred, few believed it was possible.
How to Build an Investment Portfolio
Liquidity
• We saw in lesson 2 that liquidity is the ease with which an asset can be exchanged
for money.
• The greater an asset’s liquidity, the more desirable the asset is to investors.
The Cost of Acquiring Information
• All else being equal, investors will accept a lower return on an asset that has lower
costs of acquiring information.
We can summarize our discussion of the determinants of portfolio choice by noting
that desirable characteristics of a financial asset cause the quantity of the asset
demanded by investors to increase, and undesirable characteristics of a financial asset
cause the quantity of the asset demanded to decrease.
How to Build an Investment Portfolio
How to Build an Investment Portfolio
Diversification
Diversification Dividing wealth among many different assets to reduce risk.
Market (or systematic) risk Risk that is common to all assets of a certain type, such as
the increases and decreases in stocks resulting from the business cycle.
Idiosyncratic (or unsystematic) risk Risk that pertains to a particular asset rather than
to the market as a whole, as when the price of a particular firm’s stock fluctuates
because of the success or failure of a new product.
How to Build an Investment Portfolio
Making the Connection
How Much Risk Should You Tolerate in Your Portfolio?
One important factor in deciding on the degree of risk to accept is your time
horizon.
How to Build an Investment Portfolio
• In addition to your time horizon, you must consider the effects of inflation and
taxes in building a portfolio.
• We saw in lesson 3 the important difference between real and nominal interest
rates.
• Depending on the investment, your real, after-tax return may be considerably
different from your nominal pretax return.
• In lesson 5, we will look further at how differences in tax treatment can affect the
returns on certain investments.
• Understanding how risk, inflation, and taxation affect your investments will help
you reduce emotional reactions to market volatility and make better-informed
investment decisions.
How to Build an Investment Portfolio
4.2 Learning Objective
Use a model of demand and supply to determine market interest rates for bonds.
• The price of a bond, P, and its yield to maturity, i, are linked by the arithmetic of
the equation showing the price of a bond with coupon payments C that has a face
value FV and that matures in n years:
• Because the coupon payment and the face value do not change, once we have
determined the equilibrium price in the bond market, we have also determined the
equilibrium interest rate.
• In the analysis that follows, remember that the bond market approach is most
useful when considering how the factors affecting the demand and supply for
bonds affect the interest rate.
• The market for loanable funds approach, which treats the funds being traded as
the good, is most useful when considering how changes in the demand and supply
of funds affect the interest rate.
Market Interest Rates and the Demand and Supply for Bonds
A Demand and Supply Graph of the Bond Market
Figure 4.1
The Market for Bonds
The equilibrium price of bonds is
determined in the bond market.
By determining the price of
bonds, the bond market also
determines the interest rate on
bonds.
In this case, a one-year discount
bond with a face value of $1,000
has an equilibrium price of $960,
which means it has an interest
rate (i) of 4.2%.
The equilibrium quantity of bonds
is $500 billion.•
Market Interest Rates and the Demand and Supply for Bonds
Figure 4.2
Equilibrium in Markets for Bonds
At the equilibrium price of bonds of
$960, the quantity of bonds demanded
by investors equals the quantity of
bonds supplied by borrowers.
At any price above $960, there is an
excess supply of bonds, and the price
of bonds will fall.
At any price below $960, there is an
excess demand for bonds, and the
price of bonds will rise.
The behavior of bond buyers and
sellers pushes the price of bonds to
the equilibrium of $960.•
The interest rate on the bond is:
Market Interest Rates and the Demand and Supply for Bonds
Explaining Changes in Equilibrium Interest Rates
In drawing the demand and supply curves for bonds in Figure 4.1, we held constant
everything that could affect the willingness of investors to buy bonds—or firms and
investors to sell bonds—except for the price of bonds.
If the price of bonds changes, we move along the demand (or supply) curve, but the
curve does not shift, so we have a change in quantity demanded (or supplied).
If any other relevant variable—such as wealth or the expected rate of inflation—
changes, then the demand (or supply) curve shifts, and we have a change in demand
(or supply).
Market Interest Rates and the Demand and Supply for Bonds
Factors That Shift the Demand Curve for Bonds
Five factors cause the demand curve for bonds to shift:
1. Wealth
2. Expected return on bonds
3. Risk
4. Liquidity
5. Information costs
Market Interest Rates and the Demand and Supply for Bonds
Wealth
Figure 4.3 (1 of 2)
Shifts in the Demand
Curve for Bonds
An increase in wealth, holding
all other factors constant, will
shift the demand curve for
bonds to the right.
As the demand curve for bonds
shifts to the right, the
equilibrium price of bonds rises
from $960 to $980, and the
equilibrium quantity of bonds
increases from $500 billion to
$600 billion. •
Market Interest Rates and the Demand and Supply for Bonds
Wealth
Figure 4.3 (2 of 2)
Shifts in the Demand
Curve for Bonds (continued)
A decrease in wealth, holding
all other factors constant, will
shift the demand curve for
bonds to the left, reducing both
the equilibrium price and
equilibrium quantity.
As the demand curve for bonds
shifts to the left, the equilibrium
price falls from $960 to $940,
and the equilibrium quantity of
bonds decreases from $500
billion to $400 billion.•
Market Interest Rates and the Demand and Supply for Bonds
Expected return on bonds
If the expected return on bonds rises relative to expected returns on other assets,
investors will increase their demand for bonds, and the demand curve for
bonds will shift to the right.
Risk
A decrease in the riskiness of bonds relative to the riskiness of other assets
increases the willingness of investors to buy bonds and causes the demand
curve for bonds to shift to the right.
Liquidity
If the liquidity of bonds increases, investors demand more bonds at any given
price, and the demand curve for bonds shifts to the right.
Information costs
As a result of the lower information costs, the demand curve for bonds shifts to
the right.
Market Interest Rates and the Demand and Supply for Bonds
Table 4.2 (1 of 3)
Factors That Shift the Demand Curve for Bonds
Market Interest Rates and the Demand and Supply for Bonds
Table 4.2 (2 of 3)
Factors That Shift the Demand Curve for Bonds
Market Interest Rates and the Demand and Supply for Bonds
Table 4.2 (3 of 3)
Factors That Shift the Demand Curve for Bonds
Market Interest Rates and the Demand and Supply for Bonds
Factors That Shift the Supply Curve for Bonds
Four factors are most important in explaining shifts in the supply curve for bonds:
1. Expected pretax profitability of physical capital investments
2. Business taxes
3. Expected inflation
4. Government borrowing
Market Interest Rates and the Demand and Supply for Bonds
Expected pretax profitability of physical capital investments
Figure 4.4 (1 of 2)
Shifts in the Supply
Curve for Bonds
An increase in firms’
expectations of the profitability
of investments in physical
capital will, holding all other
factors constant, shift the
supply curve for bonds to the
right as firms issue more bonds
at any given price.
As the supply curve for bonds
shifts to the right, the
equilibrium price of bonds falls
from $960 to $940, and the
equilibrium quantity of bonds
increases from $500 billion to
$575 billion.•
Market Interest Rates and the Demand and Supply for Bonds
Expected pretax profitability of physical capital investments
Figure 4.4 (2 of 2)
Shifts in the Supply
Curve for Bonds (continued)
If firms become pessimistic
about the profits they could
earn from investing in physical
capital, then, holding all other
factors constant, the supply
curve for bonds will shift to the
left.
As the supply for bonds shifts
to the left, the equilibrium price
increases from $960 to $975,
and the equilibrium quantity of
bonds decreases from $500
billion to $400 billion.•
Market Interest Rates and the Demand and Supply for Bonds
Business taxes
When business taxes are raised, the profits firms earn on new investments in physical
capital decline, and firms issue fewer bonds. The result is that the supply curve for
bonds will shift to the left.
Expected inflation
An increase in the expected rate of inflation reduces investors’ demand for bonds by
reducing the expected real interest rate that investors receive for any given nominal
interest rate.
From the point of view of a firm issuing a bond, a lower expected real interest rate is
attractive because it means the firm pays less in real terms to borrow funds.
Market Interest Rates and the Demand and Supply for Bonds
Government borrowing
Figure 4.5
The Federal Budget
With the exception of a few years in the late 1990s, the federal government has typically
run a budget deficit. The recession of 2007–2009 led to record deficits that required the
federal government to borrow heavily by selling bonds.•
Market Interest Rates and the Demand and Supply for Bonds
Government borrowing
When the government runs a deficit, households may look ahead and conclude that at
some point the government will have to raise taxes to pay off the bonds issued to
finance the deficit.
To prepare for those future higher tax payments, households may begin to increase
their saving. This increased saving will shift the demand curve for bonds to the right at
the same time that the supply curve for bonds shifts to the right because of the
deficit.
If nothing else changes, an increase in government borrowing shifts the bond supply
curve to the right, reducing the price of bonds and increasing the interest rate. A fall in
government borrowing shifts the bond supply curve to the left, increasing the price of
bonds and decreasing the interest rate.
Market Interest Rates and the Demand and Supply for Bonds
Table 4.3 (1 of 2)
Factors That Shift the Supply Curve for Bonds
Market Interest Rates and the Demand and Supply for Bonds
Table 4.3 (2 of 2)
Factors That Shift the Supply Curve for Bonds
Market Interest Rates and the Demand and Supply for Bonds
4.3 Learning Objective
Use the bond market model to explain changes in interest rates.
In this section, we consider two examples of using the bond market model to explain
changes in interest rates:
(1) The movement of interest rates over the business cycle, which refers to the
alternating periods of economic expansion and economic recession experienced by
the United States and most other economies; and
(2) The Fisher effect, which describes the movement of interest rates in response to
changes in the rate of inflation.
The Bond Market Model and Changes in Interest Rates
Why Do Interest Rates Fall during Recessions?
Figure 4.6
Interest Rate Changes in an
Economic Downturn
The Bond Market Model and Changes in Interest Rates
1. From an initial equilibrium
at E1, an economic
downturn reduces
household wealth and
decreases the demand for
bonds at any bond price.
The bond demand curve
shifts to the left, from D1 to
D2.
2. The fall in expected
profitability reduces lenders’
supply of bonds at any
bond price. The bond
supply curve shifts to the
left, from S1 to S2.
3. In the new equilibrium, E2,
the bond price rises from P1
to P2.•
How Do Changes in Expected Inflation Affect Interest Rates?
The Fisher Effect
Fisher effect The assertion by Irving Fisher that the nominal interest rises or falls
point-for-point with changes in the expected inflation rate.
The discussion of the Fisher effect alerts us to two important facts about the bond
market:
1. Higher inflation rates result in higher nominal interest rates, and lower inflation
rates result in lower nominal interest rates.
2. Changes in expected inflation can lead to changes in nominal interest rates before a
change in actual inflation has occurred.
The Bond Market Model and Changes in Interest Rates
Figure 4.7
Expected Inflation and
Interest Rates
1. From an initial equilibrium at
E1, an increase in expected
inflation reduces investors’
expected real return,
reducing investors’
willingness to buy bonds at
any bond price. The demand
curve for bonds shifts to the
left, from D1 to D2.
2. The increase in expected
inflation increases firms’
willingness to issue bonds at
any bond price. The supply
curve for bonds shifts to the
right, from S1 to S2.
3. In the new equilibrium, E2,
the bond price falls from P1 to
P2.•
The Bond Market Model and Changes in Interest Rates
Solved Problem
4.3
Why Worry About Falling Bond Prices When the Inflation Rate Is Low?
The inflation rate in late 2009 was quite low, but financial advisor Bill Tedford forecast
that inflation would increase to 5% by 2011. He argued that this increase in inflation
made bonds a bad investment. Tedford was hardly alone in offering this advice. For
instance, in its March 2010 issue, Consumer Reports magazine advised its readers to
“steer clear of long-term Treasury bonds.”
a. Explain why an increase in expected inflation will make bonds a bad investment.
Include a demand and supply graph of the bond market.
b. If inflation was not expected to increase until 2011, should investors have waited
until then to sell their bonds? Briefly explain.
c. In its advice, Consumer Reports singles out “long-term bonds” as an investment for
its readers to avoid. Why would long-term bonds be a worse investment than shortterm bonds if expected inflation was increasing?
The Bond Market Model and Changes in Interest Rates
Solved Problem
4.3
Why Worry About Falling Bond Prices When the Inflation Rate Is Low?
Solving the Problem
Step 1 Review the lesson material.
Step 2 Answer part (a) by explaining
why an increase in expected
inflation may make bonds a
bad investment and illustrate
your response with a graph.
The Bond Market Model and Changes in Interest Rates
Solved Problem
4.3 (continued)
Why Worry About Falling Bond Prices When the Inflation Rate Is Low?
Solving the Problem
Step 3 Answer part (b) by discussing the difference in the effects of actual and
expected inflation on changes in bond prices.
Changes in bond prices result from changes in the expected rate of inflation. If Tedford
was correct that future inflation was going to be significantly higher, investors would be
wise to sell bonds right away. Waiting until the nominal interest rate had risen and
bond prices had fallen would be too late to avoid the capital losses from owning bonds.
Step 4 Explain why long-term bonds are a particularly bad investment if expected
inflation increases.
An increase in expected inflation will increase the nominal interest rate on both shortterm and long-term bonds. The longer the maturity of a bond, the greater the change
in price. So, the capital losses on long-term bonds will be greater than the ones on
short-term bonds.
The Bond Market Model and Changes in Interest Rates
4.4 Learning Objective
Use the loanable funds model to analyze the international capital market.
In the loanable funds approach, the borrower is the buyer because the borrower
purchases the use of the funds. The lender is the seller because the lender provides
the funds being borrowed.
Although the demand and supply of bonds approach and the loanable funds approach
are equivalent, the loanable funds approach is more useful when looking at the flow
of funds between the U.S. and foreign financial markets.
Table 4.4 summarizes the two views of the bond market.
The Loanable Funds Model and the International Capital Market
The Demand and Supply of Loanable Funds
Figure 4.8
The Demand for Bonds and the Supply of Loanable Funds
In panel (a), the bond demand curve, Bd, shows a negative relationship between the
quantity of bonds demanded by lenders and the price of bonds, all else being equal.
In panel (b), the supply curve for loanable funds, Ls, shows a positive relationship
between the quantity of loanable funds supplied by lenders and the interest rate, all else
being equal.•
The Loanable Funds Model and the International Capital Market
The Demand and Supply of Loanable Funds
Figure 4.9
The Supply of Bonds and the Demand for Loanable Funds
In panel (a), the bond supply curve, Bs, shows a positive relationship between the
quantity of bonds supplied by borrowers and the price of bonds, all else being equal.
In panel (b), the demand curve for loanable funds, Ld, shows a negative relationship
between the quantity of loanable funds demanded by borrowers and the interest rate, all
else being equal.•
The Loanable Funds Model and the International Capital Market
Equilibrium in the Bond Market from the Loanable Funds Perspective
Figure 4.10
Equilibrium in the Market for
Loanable Funds
At the equilibrium interest rate,
the quantity of loanable funds
supplied by lenders equals the
quantity of loanable funds
demanded by borrowers.
At any interest rate below the
equilibrium, there is an excess
demand for loanable funds.
At any interest rate above
equilibrium, there is an excess
supply of loanable funds.
The behavior of lenders and
borrowers pushes the interest
rate to 4.2%.•
The Loanable Funds Model and the International Capital Market
The International Capital Market and the Interest Rate
The foreign sector influences the domestic interest rate and the quantity of funds
available in the domestic economy.
The loanable funds approach provides a good framework for analyzing the interaction
between U.S. and foreign bond markets.
Closed economy An economy in which households, firms, and governments do not
borrow or lend internationally.
Open economy An economy in which households, firms, and governments borrow and
lend internationally.
The Loanable Funds Model and the International Capital Market
Small Open Economy
Small open economy An economy in which total saving is too small to affect the world
real interest rate.
The key ideas to remember about a small economy are as follows:
•The real interest rate in a small open economy is the same as the interest rate in the
international capital market.
•If the quantity of loanable funds supplied domestically exceeds the quantity of funds
demanded domestically at that interest rate, the country invests some of its loanable
funds abroad.
•If the quantity of loanable funds demanded domestically exceeds the quantity of
funds supplied domestically at that interest rate, the country finances some of its
domestic borrowing needs with funds from abroad.
The Loanable Funds Model and the International Capital Market
Small Open Economy
Figure 4.11
Determining the Real Interest
Rate in a Small Open
Economy
The domestic real interest rate
in a small open economy is the
world real interest rate, (rw),
which in this case is 3%.•
The Loanable Funds Model and the International Capital Market
Large Open Economy
Large open economy An economy in which shifts in domestic saving and investment
are large enough to affect the world real interest rate.
In the case of a large open economy, we cannot assume that the domestic real interest
rate is equal to the world real interest rate.
The Loanable Funds Model and the International Capital Market
Figure 4.12
Determining the Real Interest Rate in a Large Open Economy
Saving and investment shifts in a large open economy can affect the world real interest
rate. The world real interest rate adjusts to equalize desired international borrowing and
desired international lending.
At a world real interest rate of 4%, desired international lending by the domestic
economy equals desired international borrowing by the rest of the world.•
The Loanable Funds Model and the International Capital Market
Making the Connection
Did a Global “Saving Glut” Cause the U.S. Housing Boom?
Some economists have argued that the Fed persisted in a low-interest-rate policy for too
long a period, thereby fueling the housing boom.
Fed Chairman Ben Bernanke disagreed, arguing that “a significant increase in the global
supply of saving—a global saving glut— . . . helps to explain . . . the relatively low level
of long-term interest rates in the world today.”
The Loanable Funds Model and the International Capital Market
Answering the Key Question
At the beginning of this lesson, we asked the question:
“How do investors take into account expected inflation and other factors
when making investment decisions?”
We have seen in this lesson that investors increase or decrease their
demand for bonds as a result of changes in a number of factors.
When expected inflation increases, investors reduce their demand for
bonds because, for every nominal interest rate, the higher the inflation
rate, the lower the real interest rate investors will receive.
We have seen that increases in expected inflation lead to higher
nominal interest rates and capital losses for investors who hold bonds in
their portfolios.
AN INSIDE LOOK AT POLICY
Investors Forecast Lower Bond Prices, Higher Interest Rates
Wall Street Journal, Interest Rates Have Nowhere to Go but Up
Key Points in the Article
• As the U.S. economy recovered from recession in 2010, analysts forecast a period
of rising interest rates.
• Higher interest rates would damage the housing market, which had begun to
recover from the recession.
• Analysts expected interest rate increases because the federal government was
forced to sell more bonds to finance its budget deficits, and the rate of inflation
was likely to increase.
• Because low interest rates helped to fuel the growth of stock prices, higher interest
rates were likely to slow the growth of stock prices in the future.
• The figure in the next slide shows the impact of an increase in expected inflation on
the markets for bonds and loanable funds.
AN INSIDE LOOK AT POLICY