1.

2 Determinants of
Interest Rates
Contents
1.2. Determinants of interest rates
1.2.1 Loanable funds theory
1.2.2 Determinants of interest rates for
individual securities
1.2.3 Term structure of interest rates
1.2.3.1 Unbiased expectations theory
1.2.3.2 Liquidity premium theory
1.2.3.3 Market segmentation theory
1.2.5 Forecasting interest rates
Interest Rate Fundamentals
•  Nominal interest rates: the interest rates
actually observed in financial markets
–  Used to determine fair present value and
prices of securities
–  Changes to it have impact on security values
–  Factors determining level of interest and
what causes movements is important
Key interest rates in the
Philippines
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
Supply and Demand of Loanable
Funds
Interest
Rate Demand Supply

i* E

Q*
Quantity of Loanable Funds
Supplied and Demanded
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.
 Business Demand for Funds

•  Level of interest rates:

–  When the cost of loanable funds is high
businesses finance internally,
•  Expected future profitability vs. risk:
–  The greater the number of profitable
projects available to businesses,
•  Expected economic growth
Shifts in Supply and Demand Curves
change Equilibrium Interest Rates
Increased supply of loanable funds Increased demand for loanable funds
Interest
Interest SS Rate DD* SS
Rate DD DD
SS*

i** E*
i* E
E i*
i** E*

Q* Q** Quantity of Q* Q** Quantity of

Funds Supplied Funds Demanded
Factors that Cause Supply and
Demand Curves to Shift
Factors that Cause Supply and
Demand Curves to Shift
Factors that Cause Supply and
Demand Curves to Shift
 Determinants of Interest
Rates for individual securities
•  Interest rates on each security is different
because securities have different
characteristics:
–  Default risk
–  Maturity
–  Liquidity risk
–  Payment terms
•  (1) Real risk-free rate of interest- nominal risk-free rate that
would exist if no inflation were expected
•  (2) Inflation- the continual increase in the price level of a basket
of goods and services
•  (3) Default risk- the risk that security issuer will default on that
security by being late on or missing an interest or principal
payment
•  (4) Liquidity risk- risk that a security cannot be sold at a
predictable price with low transaction costs at short notice
•  (5) Term to maturity- length of time a security has until maturity
•  (6) Special provisions- provisions that impact the security
holder beneficially or adversely and as such are reflected in the
interest rates on securities that contain such provisions
 Determinants of Interest Rates
for Individual Securities
General equation of interest rate on an
asset:
ij* = f(RFR, IP, DRPj, LRPj, SCPj, MPj)

RFR- Real risk-free rate

IP- inflation premium
DRP- Default risk premium
LRP- Liquidity risk premium
SCP- Special feature premium
MP- Maturity premium
 Real Risk-free Rate
ij* = f(RFR, IP, DRPj, LRPj, SCPj, MPj)
o Fisher effect model: relationship between the
nominal rate, the anticipated rate of inflation and
the real rate
o (1+nominal) = (1+real) (1+ expected inflation)
o Approximation: Nominal rate= Real rate +
Inflation rate
o Inflation premium (IP)= nominal rate – real rate
o Using approximation equation, compute for the
real rate of 2019 T-Bill of 3.32% if average
inflation was 2.50%.
o What is the approx. inflation premium?
 Inflation Premium (IP)
ij* = f(RFR, IP, DRPj, LRPj, SCPj, MPj)
–  Inflation premium is normally higher than the expected
inflation rate to compensate for (a) reduced purchasing
power of principal and (b) a premium for increased cost
of forgoing consumption today due to buying more
highly priced goods and services in the future
–  Measured using indexes such as Consumer price index
(CPI) or Producer price index (PPI)

•  Compute inflation premium for 2019 if

beginning and ending CPI is 118.9 and 121.9,
respectively.
CPI and Inflation rates in
the Philippines (2012=100)
Default or credit risk premium (DRP)
ij* = f(RFR, IP, DRPj, LRPj, SCPj, MPj)
–  Compensate investors for the perceived probability of
default and the potential recovery of the amount loaned
–  Computed using equation below
DRPj = ijt – iTt
ijt = interest rate on security j at time t
iTt = interest rate on similar maturity Treasury security
at time t
•  In Mar 2020, ABC Corp. and XYZ Inc.’s 10-year bond,
traded in the bond market, has interest rates of 8.99%
and 10.65%, respectively. At the same time, a 10-year
treasury bond interest have interest rate of 6.5%.
Compute for average DRPs.
Liquidity risk premium (LRP)
ij* = f(RFR, IP, DRPj, LRPj, SCPj, MPj)
–  Compensate investors for security’s lack of liquidity
and the potential price discount from selling it early

Special feature premium (SCP)

ij* = f(RFR, IP, DRPj, LRPj, SCPj, MPj)
–  Special provisions like taxability, convertability and
callability
–  Provide benefits to holder are associated with lower
interest rates and those that provide benefits to
issuer are associated with higher interest rate
Maturity premium (MP)
ij* = f(RFR, IP, DRPj, LRPj, SCPj, MPj)
–  Compensate investors for taking risk of holding
asset over a longer period of time
–  Relationship of interest rates and term to maturity is
called the Term structure of interest rates. Its
graphical depiction is called the yield curve.
 Term Structure of Interest Rates:
the Yield Curve
(a) Normal or upward sloping
yield curve- upward-sloping
yield curve indicates that
long-term interest rates are
Yield to generally higher than short-
Maturity term interest rates

(b) Inverted or downward

(a) sloping yield curve-
downward-sloping yield curve
(c) indicates that short-term
interest are generally higher
than long-term interest

(b) (c) Flat yield curve- A yield

curve that indicates that
Time to Maturity interest rates do not vary
much at different maturities
Yield curve (cont’d)

https://www.youtube.com/watch?v=xiiHjrewXNI&t=14s
Yield curve (cont’d)

o 
o  Unbiased Expectations Theory- yield curve reflects the market’s
current expectations of future short-term rates. At equilibrium,
investors should expect to earn the same return whether they invest
on LT bonds or a series of ST bonds;

o  Liquidity preference Theory- long-term rates are equal to geometric

averages of current and expected short-term rates, plus liquidity risk
premiums that increase with security’s maturity. Long-term rates are
generally higher than short-term because investor’s perceived short-
term investments to be more liquid.

o  Preferred habitat or market segmentation Theory- investors have

preferred investment horizons (habitats) dictated by the nature of
liabilities they hold; market is segmented on basis of maturity and that
supply and demand per segment determines interest rates.
 Unbiased Expectations Theory
•  Long-term interest rates are geometric averages of
current and expected future short-term interest
rates

Buy a four-year bond

(1 + 1R4 )4

0 1 2 3 4 Year
(1+1R1) 1+E(2r1) 1+E(3r1) 1+E(4r1)
Buy 4 one-year bond
 Unbiased Expectations Theory
•  Can be expressed in equation as follows:
(1+1RN)N=[(1+1R1)(1+E(2r1))…(1+E(Nr1))]

1R N = 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
 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
•  Unbiased expectations theory equation can be
rewritten to compute for the one-year forward rate of
any year N in the future is:

•  Formula for solving forward rates beyond the one year

maturity, K, is as follows:
o Example1: A one-year bond offers a yield of 5%
today and the same bond is expected to offer a yield
of 7.5% for next year. Under the expectations theory
what should be the yield on a two-year bond today?

o Example2: A one-year bond offers a yield of 4.5%

and a two year bond offers a yield of 8%. Under the
expectations theory what should be the yield on a
one year bond next year?
 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

Lt = liquidity premium for period t

L2 < L3 < …<LN

A one-year bond offers a yield of 7% today and the same bond is

expected to offer a yield of 11% for next year. Under the liquidity
premium theory what should be the yield on a two-year bond
today if liquidity premium for year 2 is 0.24%?
UET vs. Liquidity Premium Theory
Market Segmentation Theory
Conclusion from the three theories: slope of yield curve
is affected by (1) interest rates expectations; (2)
liquidity preferences; (3) comparative equilibrium of
supply and demand in the short- and long-term
market segments.

Upward sloping yield curve results from expectations of

rising interest rates, lenders preferences for shorter
maturity loans and greater supply of short-term than
long-term loans relative to demand
Contents
1.2. Determinants of interest rates
1.2.1 Loanable funds theory
1.2.2 Determinants of interest rates for
individual securities
1.2.3 Term structure of interest rates
1.2.3.1 Unbiased expectations theory
1.2.3.2 Liquidity premium theory
1.2.3.3 Market segmentation theory
1.2.5 Forecasting interest rates
End of Chapter 1.2

Questions?
Knowledge Check #1
A particular security’s equilibrium rate of
return is 8%. For all securities, the
inflation risk premium is 1.75% and the
real risk-free rate is 3.5%. The security’s
liquidity risk premium is 0.25% and
maturity risk premium is 0.85%. There is
no special covenants. Calculate the
security’s default risk premium.
Knowledge Check #2
•  Suppose that the current one-year rate (one-
year spot rate) and expected one-year T-bill
rates over the following three years (i.e., years
2, 3 and 4 respectively) are as follows:

1R1=6% E(2r1)=7% E(3r1)=7.5% E(4r1)=7.85%

•  Using unbiased expectations theory, calculate
the current (long-term rates ) for one-, two-
three- and four-year-maturity Treasury
securities.
Knowledge Check #3
The Wall Street Journal reports that the
rate on three-year Treasury securities is
5.25% and the rate on four-year Treasury
securities is 5.50%. The one-year interest
rate expected in three years, E(4r1), is
6.10%. According to liquidity premium
theory, what is the liquidity premium on
the four-year Treasury security, L4?
Knowledge Check #4
•  On March 11,20XX, the existing or current
(spot) one-year, two-year, three-year and
four-year zero-coupon Treasury security
rates were as follows:
1R1=4.75% 1R2=4.95% 1R3=5.25% 1R4=5.65%

•  Using unbiased expectations theory,

calculate the one-year forward rates on
zero-coupon Treasury bonds for years two,
three, and four as of March 11, 20XX.
Knowledge Check #5
•  Assume that as of today, the annualized
interest rate on a three-year security is 10
percent, while the annualized interest rate
on a two-year security is 7 percent. Use
this information to estimate the one-year
forward rate two years from now.
Knowledge Check #6
•  a. Assume that as of today, the
annualized two-year interest rate is 13
percent, while the one-year interest rate
is 12 percent. Use this information to
estimate the one-year forward rate.
•  b. Assume that the liquidity premium on a
two-year security is 0.3 percent. Use this
information to estimate the one-year
forward rate.