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Chapter Two
Determination of
Interest Rates
2-1
Interest Rate Fundamentals
• Nominal interest rates: the interest rates
actually observed in financial markets
– Reflect the rate of exchange between monetary
assets goods across time
– Affect the values (prices) of securities traded in
money and capital markets
• Real interest rates
– Reflect the rate of exchange between real goods
across time
2-2
Loanable Funds Theory
• Loanable funds theory explains interest rates
and interest rate movements
• Views level of interest rates in financial
markets as a result of the supply and demand
for loanable funds
• Domestic and foreign households, businesses,
and governments all supply and demand
loanable funds
2-3
Supply and Demand of Loanable Funds
Demand
Supply
Interest
Rate
Quantity of Loanable Funds
Supplied and Demanded
2-4
Shifts in Supply and Demand Curves
change Equilibrium Interest Rates
Increased supply of loanable funds
Interest
Rate
Interest
Rate
SS
DD
Increased demand for loanable funds
SS*
DD
DD*
i**
i*
i*
E*
Q* Q**
E*
E
E
i**
SS
Quantity of
Funds Supplied
2-5
Q* Q**
Quantity of
Funds Demanded
Supply and Demand for Funds
Source Text
Table 2-2
August 07 data
Funds
Supplied
Trill $
Demanded
Trill $
Households
$42.52
$13.43
$ 29.09
25.4%
37.1%
11.7%
Business
Nonfinancial
14.62
33.44
(18.82)
-16.4%
12.8%
29.2%
Financial
Intermediary
40.71
54.76
(14.05)
-12.3%
35.5%
47.8%
Government
3.80
7.51
( 3.71)
-3.2%
3.3%
6.6%
12.93
5.44
7.49
6.5%
11.3%
4.7%
$114.58
$114.58
$ 0.00
0.0%
100.0%
100.0%
Foreign
Totals
2-6
Net $
Net %*
Supply
%
Demand
%
Shift in Supply and Demand Curves for Loanable Funds
Increase in
Affect on
Supply
Affect on
Demand
Wealth & income
Increase
N/A
Risk
Decrease
Decrease
Near term spending needs
Decrease
N/A
Monetary expansion
Increase
N/A
Economic growth
Increase
Increase
Utility derived from assets
Decrease
Increase
Expected inflation
Decrease
Increase
Taxes
Decrease
Currency Value
Increase
Restrictive covenants
Decrease
2-7
Determinants of Interest Rates
for Individual Securities
• Real Interest Rate (RIR) and the Fisher
effect
RIR = i – Expected (IP)
• The actual Fisher Effect is given as
(1+i) = (1+RIR)*(1+Expected(IP))
• Inflation (IP)
IP = [(CPIt+1) – (CPIt)]/(CPIt) x (100/1)
2-8
Determinants of Interest Rates
for Individual Securities (cont’d)
• Default Risk Premium (DRP)
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
• Liquidity Risk (LRP)
• Special Provisions (SCP)
• Term to Maturity (MP)
2-9
Nominal Rate of Interest
ij* = f(RIR, IP, DRPj, LRPj,MPj,, SCPj)
•
•
•
•
•
•
Riskless real rate +
Expected inflation +
Default risk premium +
Liquidity risk premium +
Maturity risk premium) +
Special covenant premium
2-10
Term Structure of Interest Rates:
the Yield Curve
(a) Upward sloping
(b) Inverted or downward
sloping
(c) Flat
Yield to
Maturity
(a)
(c)
(b)
Time to Maturity
2-11
http://finance.yahoo.com/bonds
The Living Yield Curve
2-12
Unbiased Expectations Theory
• Long-term interest rates are geometric
averages of current and expected future shortterm interest rates
RN  [(11 R1 )(1  E ( 2 r1 ))...(1  E ( N r1 ))]
1/ N
1
1RN
1
= actual N-period rate today
N = term to maturity, N = 1, 2, …, 4, …
1R1 = actual current one-year rate today
E(ir1) = expected one-year rates for years, i = 1 to N
2-13
UET Arbitrage Proof
• If the expected one year rates are 6%, 7% and 8% for the next three
years respectively, and the three year rate is 5%, how could one make
money on this relationship?
• Using the text’s terminology: 1R1 = 6%, 2R1=7% and 3R1 = 8% but
1R3=5%
1R1
t=0
2R1=7%
= 6%,
3R1
2
1
= 8%
3
1R3=5%
3
t=0
2-14
UET Arbitrage Proof
• The average of the short term one year rates is 7%,
but the three year rate is only 5%.
• One could borrow any given amount such as
$1000 for the full three years and invest that
money one year at a time and rolling over the
investment for three years.
• The borrowing cost per year is 5% and the average
rate of return is 7%. This is a riskless arbitrage.
• It would force the three year rate and the average
of the one year rates to converge.
2-15
Liquidity Premium Theory
• Long-term interest rates are geometric
averages of current and expected future shortterm interest rates plus liquidity risk premiums
that increase with maturity
1/ N
R

[(
1

R
)(
1

E
(
r
)

L
)...(
1

E
(
r
)

L
)]
1
1
N
1 1
2 1
2
N 1
N
Lt = liquidity premium for period t
L2 < L3 < …<LN
2-16
Yield to
Maturity
Liquidity Premium Theory
Observed YC
Liquidity Premium
Actual YC
Maturity
2-17
Market Segmentation Theory
• Individual investors and FIs have specific
maturity preferences
• Interest rates are determined by distinct supply
and demand conditions within many maturity
segments
• Investors and borrowers deviate from their
preferred maturity segment only when
adequately compensated to do so
2-18
Market Segmentation
Yield to
Maturity
Short
Intermediate
2-19
Long
Maturity
Implied Forward Rates
• A forward rate (f) is an expected rate on a
short-term security that is to be originated at
some point in the future
• The one-year forward rate for any year N in
the future is:
N
f1  [(11 RN ) N /(11 RN 1 ) N 1 ]  1
2-20
Forecasting Interest Rates
•
•
•
•
•
A forward rate is a rate that can be imputed
from the existing term structure.
Given a set of long term spot rates one can find
the individual one year forward rates. For
instance, one year spot rate = 4% and two year
spot rate = 5%
(1+1R2)2 = (1+1R1)*(1+2F1)
(1.05)2 = (1.04)(1+2F1)
2 / (1.04) -1 = 6.01%
F
=
(1.05)
2 1
2-21
Net Supply of Funds in U.S. in 2010
Sector
Households & NPOs
Business Nonfinancial
State & Local Govt.
Federal Government
Financial Sector
Foreign
Totals (Discrepancy)
Net Supply
($ Billions)
$ 786.9
75.3
-19.3
-1378.6
-178.3
324.3
-$389.7
Source Federal Reserve Flow of Funds Matrix Year 2010 data
Source: Federal Reserve Bank of St.
Louis
Determinants of Household Savings
1. Interest rates and tax policy
2. Income and wealth: the greater the wealth or income,
the greater the amount saved,
3. Attitudes about saving versus borrowing,
4. Credit availability, the greater the amount of easily
obtainable consumer credit the lower the need to
save,
5. Job security and belief in soundness of entitlements,
Determinants of Foreign Funds Invested in
the U.S.
1. Relative interest rates and returns on global
investments
2. Expected exchange rate changes
3. Safe haven status of U.S. investments
4. Foreign central bank investments in the U.S.
Determinants of Foreign Funds Invested in
the U.S.
Country
China
Saudi Arabia
Russia
Taiwan
S. Korea
Source: Economist, February 2011
Foreign Currency Reserves
(all $ in billions)
$2,847
456
444
382
292
Federal Government Demand for Funds
Source: CBO 2011 report
• Source: CBO 2011 report, http://www.cbo.gov/ftpdocs/74xx/doc7492/08-17BudgetUpdate.pdf
Federal Government Demand for Funds
• Federal debt held by the public was at $9.0 trillion at
end of 2010 (62% GDP) and is projected to grow to
$17.4 trillion by 2020 (76% of projected 2020 GDP,
120% of current GDP)
 Large potential for crowding out and/or
dependence on foreign investment
Federal Government Demand for Funds
• Total Federal Debt is currently $14.1 trillion (97%
GDP) and is projected to grow to $23.1 trillion by
2020 (64% increase)
o Interest expense is projected to grow to 3.5%
of GDP by 2020