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2024/2/27
Chapter Two
Determinants of
Interest Rates
1
Interest Rate Fundamentals

Nominal interest rates: the interest rates
actually observed in financial markets

Directly affect the value (price) of most
securities traded in the money and capital
markets.

Changes in interest rates influence the
performance and decision making for
individual investors, businesses, and
governmental units.
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Key U.S. Interest Rates, 1972 to 2019
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Loanable Funds Theory



Loanable funds theory explains interest rates
and interest rate movements
The interaction of supply and demand of funds
sets the basic opportunity cost rate (real
interest rate) in the economy.
The central bank estimates supply and demand
of funds from households, business,
government and foreign sources through its flow
of funds accounts.
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Supply and Demand
of Loanable Funds
Interest
Rate
Demand
Supply
r*
Quantity of Loanable Funds
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Supply and Demand
of Loanable Funds



Other factors held constant; more funds are
supplied as interest rates increase. (The reward
of supplying funds is higher.)
More funds are demanded as interest rates
decrease. (The cost of borrowing funds is lower.)
The interaction of supply and demand of funds
sets the basic opportunity cost rate (real interest
rate) in the economy.
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Supply and Demand
of Loanable Funds



The central bank estimates supply and demand of
funds from households, business, government and
foreign sources through its flow of funds accounts.
The largest suppliers of loanable funds are
households. Household savings rates have
increased since the financial crisis.
The second largest net supplier of funds is the
foreign sector. The U.S. remains highly reliant on
foreign sources of funds to meet its funds’
demands.
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Net Supply of Funds
in U.S. in 2019
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Determinants of Household
Savings
1.
2.
3.
4.
Interest rates
Income and wealth: the greater the wealth or
income, the greater the amount saved,
Risk of securities investments: the greater the
perceived risk of securities investments, the less
households are willing to invest at each interest
rate.
Near-term spending needs: they will reduce the
supply of funds from a given household.
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Determinants of Business
Invested domestically.
Business sector often has excess cash or working
capital, that it can invest for short period of time in
financial assets.
1.
Interest rates on financial assets
2.
Expected risk on financial securities
3.
Businesses’ future investment needs
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Determinants of Governments
Invested in the U.S.

When some governments temporarily generate
more cash inflows than they have budgeted to
spend. These fund can be loaned out to financial
market fund users until needed.

During the financial crisis, the federal
government significantly increased the funds it
supplied to business and consumers as it
attempted to rescue the U.S. economy.
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Determinants of Foreign Funds
Invested in the U.S.
1.
Relative interest rates and returns on global
investments
2.
Expected exchange rate changes
3.
Financial conditions in foreign investors’ home
countries change relative to the U.S. economy
4.
Foreign central bank investments in the U.S.
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Demand for Loanable Funds

Other factors held constant, more funds are
demanded as interest rates decrease (the cost
of borrowing funds is lower).

Demand by Households

Financing purchase of homes (mortgage loans)

Durable good (car loans, appliance loans)

Nondurable goods (education loans, medical loans)
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Demand for Loanable Funds

Demand by Businesses

Financing investment in long-term (fixed) assets (plant
and equipment)

Financing short-term working capital needs (inventory
and accounts receivable)

By issuing debt and other financial instruments

The greater the number of profitable projects
available to businesses, or the better the overall
economic conditions, the greater the demand for
loanable funds.
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Demand for Loanable Funds

Demand by Governments

State and local government issue debt instrument to
finance temporary imbalances between operating
revenues (e.g. taxes) and budged expenditures.

The central government finance current budget deficit
(expenditures greater than taxes) and partly to finance
past deficit.
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Demand for Loanable Funds

Demand by Foreign participants (households,
businesses, and governments)

Foreign borrowers look for the cheapest source of
dollar funds globally.

In addition to interest costs, foreign borrowers consider
non-price terms on loanable funds as well as economic
conditions in their home country and the general
attractiveness of the U.S. dollar relative to their
domestic currency.
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Equilibrium Interest Rates
Excess supply
Excess demand
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Equilibrium Interest Rates



As long as competitive forces are allowed to
operate freely in a financial system, the interest
rate that equates the aggregate supply of loanable
funds with the aggregate demand, Q*, is the
equilibrium interest rate, i*.
When the interest rate is iH, a surplus of loanable
funds in the financial system will result in a lower
interest rate.
In contrast, when the interest rate is iL, a shortage
of loanable funds in the financial system will result
in a higher interest rate.
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Shifts in Supply and Demand Curves
change Equilibrium Interest Rates
Increased supply of loanable funds Increased demand for loanable funds
Interest
Rate
Interest
Rate
SS
DD
SS*
DD
DD*
i**
i*
E
i*
E*
i**
Q* Q**
Quantity of
Funds
SS
E*
E
Q* Q**
Quantity of
Funds
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Factors that Cause Supply and
Demand Curves to Shift
Increase in
Affect on Supply
Affect on Demand
Wealth & income
Increase
N/A
As wealth and income increase, funds suppliers are more willing to supply funds
to markets. Result: lower interest rates
Risk
Decrease
Decrease
As the risk of an investment decreases,
funds
suppliers
are
less
willing
to
increases
purchase the claim. All else equal, demanders of funds would be less willing to
borrow as well. Result: higher interest rates
Near term spending needs
Decrease
N/A
As current spending needs increase, funds suppliers are less willing to invest.
Result: higher interest rates
Monetary expansion
Increase
N/A
As the central bank increases the supply of money in the economy, this directly
increases the supply of funds available for lending. Result: lower interest rates
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Factors that Cause Supply and
Demand Curves to Shift
Increase in
Affect on Supply
Affect on Demand
Economic growth
Increase
Increase
With stronger economic growth, wealth and incomes rise, increasing the supply of funds
available. As U.S. economic strength improves relative to the rest of the world, foreign
supply of funds is also increased. Business demand for funds increases as more projects
are profitable. Result: indeterminate effect on interest rates, but at more rapid growth
rates interest rates tend to rise.
Utility derived from assets
Decrease
Increase
As utility from owning assets increases, funds suppliers are less willing to invest and
postpone consumption whereas funds demanders are more willing to borrow. Result:
higher interest rates
Restrictive covenants
Increase
Decrease
As loan or bond covenants become more restrictive, borrowers reduce their demand for
funds. Result: lower interest rates
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Factors that Cause Supply and
Demand Curves to Shift
Factor
Impact on Supply of Funds
Impact on Equilibrium Interest Rate*
Interest rate
Movement along the supply curve
Direct
Total wealth
Shift supply curve
Inverse
Risk of financial security
Shift supply curve
Direct
Near-term spending needs
Shift supply curve
Direct
Monetary expansion
Shift supply curve
Inverse
Economic conditions
Shift supply curve
Inverse
Factor
Impact on Demand of Funds
Impact on Equilibrium Interest Rate
Interest rate
Movement along the demand
curve
Direct
Utility derived from asset
purchased with borrowed
funds
Shift demand curve
Direct
Restrictiveness of nonprice
conditions
Shift demand curve
Inverse
Economic conditions
Shift demand curve
Direct
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Interest Rate Fundamentals

The components of the nominal
interest rate:



The real riskless rate of interest that is
compensation for the pure time value of
money,
An expected inflation premium that is time
dependent
A risk premium for liquidity, default and
interest rate risk.
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Determinants of Interest Rates
for Individual Securities

𝒊∗𝒋 = 𝒇 𝑹𝑰𝑹, 𝑰𝑷, 𝑫𝑹𝑷𝒋 , 𝑳𝑹𝑷𝒋 , 𝑺𝑪𝑷𝒋 , 𝑴𝑷𝒋
where
𝑹𝑰𝑹 = 𝒓𝒆𝒂𝒍 𝒊𝒏𝒕𝒆𝒓𝒆𝒔𝒕 𝒓𝒂𝒕𝒆
𝑰𝑷 = 𝒊𝒏𝒇𝒍𝒂𝒕𝒊𝒐𝒏 𝒓𝒂𝒕𝒆
𝑫𝑹𝑷𝒋 = 𝒅𝒆𝒇𝒂𝒖𝒍𝒕 𝒓𝒊𝒔𝒌 𝒑𝒓𝒆𝒎𝒊𝒖𝒎
𝑳𝑹𝑷𝒋 = 𝒍𝒊𝒒𝒖𝒊𝒅𝒊𝒕𝒚 𝒓𝒊𝒔𝒌 𝒑𝒓𝒆𝒎𝒊𝒖𝒎
𝑺𝑪𝑷𝒋 = special provisions
𝑴𝑷𝒋 = 𝒎𝒂𝒕𝒖𝒓𝒊𝒕𝒚 𝒑𝒓𝒆𝒎𝒊𝒖𝒎
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Determinants of Interest Rates
for Individual Securities: Inflation
 Inflation is the continual increase in the price level of a
basket of goods and services
 In a lot of countries, inflation is measured using indexes.
• Consumer price index (CPI).
• Producer price index (PPI).
 Annual inflation rate using the CPI index between years t and t + 1
would be equal to:
Inflation (IP ) 
CPI t 1  CPI t
100
CPI t
© McGraw Hill
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Determinants of Interest Rates for
Individual Securities: Real Risk-Free
Rate

A real risk-free rate is the interest rate that would exist
on a risk-free security if no inflation were expected over
the holding period of a security.

The higher society’s preference to consume today, the
higher the real risk-free rate (𝑹𝑭𝑹).

Relationship among the real risk-free rate (𝑹𝑭𝑹), the
expected rate of inflation (𝑬 𝑰𝑷 ), and the nominal
interest rate (i) is referred to as the Fisher effect.
• The Fisher effect is often written as the following:
𝒊 = 𝑹𝑭𝑹 + 𝑬(𝑰𝑷)
© McGraw Hill
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Example 2-1 Calculations of Real Interest Rates (r)
The one-year T-bill rate in 2018 averaged 2.25% and
inflation for the year was 1.90%. If investors had
expected the same inflation rate as that actually
realized (i.e., 1.90%), then according to the Fisher
effect the real interest rate for 2018 was:
r (RIR) =
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Determinants of Interest Rates
for Individual Securities (cont’d)

Default Risk Premium (DRP)(Credit Risk)
DRPj = ijt – iTt
ijt = interest rate on security j at time t
iTt = interest rate on similar maturity U.S. Treasury
security at time t (risk-free rate)
the risk that a security issuer will fail to make its

promised interest and principal payments to the
buyer of a security.
The default risk on many corporate bonds is

evaluated and categorized by various bond rating
agencies such as Moody’s and Standard & Poor’s..
The default risk premium tend to increase when the

economy is contracting.
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Moody’s Rating
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Determinants of Interest Rates
for Individual Securities (cont’d)
Financial
Crisis
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Determinants of Interest Rates
for Individual Securities (cont’d)
Liquidity risk
 the risk that a security can be sold at a predictable price with
low transaction costs on short notice.
 A highly liquid asset is one that can be sold at a predictable
price with low transaction costs, and thus can be converted into
its full market value at short notice.
 If a security is illiquid, investors add a liquidity risk premium
(𝑳𝑹𝑷) to the interest rate on the security that reflects its relative
liquidity.
• L R P might also be thought of as an “illiquidity” premium.
 L R P may also exist if investors dislike long-term securities
because their prices (present values) are more sensitive to
interest rate changes than short-term securities.
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Determinants of Interest Rates
for Individual Securities (cont’d)

Special Provisions (SCP)


Written into the contracts underlying the issuance
of a security.
Taxability:


Convertibility


Ex. Interest payments on municipal bonds are free of
federal, state, and local taxes.
Security holders have the opportunity to exchange one
security for another type of the issuer’s securities at a
preset price.
Callability

An issuer has the option to call a security prior to
maturity at a preset price.
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Determinants of Interest Rates
for Individual Securities (cont’d)

Term to Maturity

Term structure of interest rates (yield curve)


a comparison of market yields on securities, assuming
all characteristics except maturity are the same.
Maturity premium (MP)

The difference between the required yield on longand short-term securities of the same characteristics
except maturity.
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Term Structure of Interest Rates
Relationship between a security’s interest rate and its
remaining term to maturity (that is, the term structure
of interest rates) can take a number of different
shapes.
Explanations for the shape of the yield curve fall
predominately into three theories:
1. Unbiased expectations theory.
2. Liquidity premium theory.
3. Market segmentation theory.
© McGraw Hill
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Explanations for the Shape of the
Term Structure of Interest Rates
Unbiased expectations theory—at any given point in time, the yield
curve reflects the market’s current expectations of future short-term rates.
According to the unbiased expectations theory, the return for holding a
four-year bond to maturity should equal the expected return for investing in
four successive one-year bonds (as long as the market is in equilibrium).
Liquidity premium theory—long-term rates are equal to geometric
averages of current and expected short-term rates, plus liquidity risk
premiums that increase with the security’s maturity. Longer maturities on
securities mean greater market and liquidity risk. So, investors will hold
long-term maturities only when they are offered at a premium to
compensate for future uncertainty in the security’s value. The liquidity
premium increases as maturity increases.
Market segmentation theory—assumes that investors do not consider
securities with different maturities as perfect substitutes. Rather, individual
investors and FIs have preferred investment horizons (habitats) dictated by
the nature of the liabilities they hold. Thus, interest rates are determined by
distinct supply and demand conditions within a particular maturity segment
(for example, the short end and long end of the bond market).
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Term Structure of Interest Rates:
the Yield Curve
Yield to
Maturity
3 most common sharps:
(a) Upward sloping
(b) Inverted (or downward)
sloping
(a)
(c) Flat
(c)
(b)
Time to Maturity
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Unbiased Expectations Theory

Long-term interest rates are geometric averages
of current and expected future short-term
interest rates
0
RN  [(1 0 R1 )(1  E (1 r1 ))...(1  E ( N 1 r1 ))]1/ N  1
0RN
= actual N-period rate today
N = term to maturity, N = 1, 2, …
0R1 = actual current one-year rate today
E(ir1) = expected one-year rates for starting years, i =0, 1 to
N-1
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Unbiased Expectations Theory

Example: construction of a yield curve using the
unbiased expectation theory
 0R1=1.3%,
E(1r1)=1.5%, E(2r1)=1.7%, E(3r1)=1.9%
 0R2=?
 0R3=?
 0R4=?
 Yield curve
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Liquidity Premium Theory

Long-term interest rates are geometric averages
of current and expected future short-term
interest rates plus liquidity risk premiums that
increase with maturity
0
RN  [(1 0 R1 )(1  E (1 R 1 )  L2 )...(1  E ( N 1 R 1 )  LN )]1/ N  1
Lt = liquidity premium for period t
L2 < L3 < …<LN
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Liquidity Premium Theory

Example: construction of a yield curve using the liquidity
premium theory
 0R1=1.3%,

E(1r1)=1.5%, E(2r1)=1.7%, E(3r1)=1.9%
L2= 0.1%, L3= 0.2%, L4= 0.3%
 0R2=?
 0R3=?
 0R4=?
 Yield curve
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Market Segmentation Theory




Individual investors and FIs have specific maturity
preferences
Interest rates are determined by distinct supply and
demand conditions within many maturity segments
Investors and borrowers deviate from their preferred
maturity segment only when adequately
compensated to do so
Figure 2-10: As the supply of securities decreases in
the short-term market and increases in the long-term
market, the slope of the yield curve becomes
steeper.
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Market Segmentation Theory
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Implied Forward Rates


A forward rate (f) is an expected rate on a shortterm security that is to be originated at some
point in the future
The one-year forward rate for any year N in the
future is:
f  [(1 0 RN ) N /(1 0 RN 1 ) N 1 ]  1
N 1 1
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Forecasting interest Rates

Example: construction of implied forward rates using the
unbiased expectation theory
 0R1=1.3%, 0R2=1.4%, 0R3=1.5%, 0R4=1.6%,
 1f1=?
 2f1 =?
 3f1 =?
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