UNIVERSITY OF DAR ES SALAAM
BUSINESS SCHOOL
DEPARTMENT OF FINANCE
FN201: Introduction to Financial Services
Topic 5: Interest rates
Godsaviour Christopher
(Bcom – Udsm, MA Economics – Udsm)
INTEREST RATES
 Overview of interest rates
 Time and value of assets
 Determinants of interest rate
 Structure of Interest rate
 Forecasting Interest rate.
 Relationship between Interest rate and Security Prices
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An overview on interest rates.
 Generally;
 Interest is that amount of funds paid to a lender by a borrower
as compensation for credit facility issued.
 In economics
 Interest is defined as price of using money or cost of capital,
cost of borrowing or price of a loan or price of credit issued
over a given period of time.
 In Finance
 Interest rate refers to a rate of return (expressed as percentage
of principal amount) an investor or lender earns on credit
facility over a specific time period
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An overview on interest rates.
 General reasons for charging interest rates
As payment for risk suffered.
Opportunity cost or the opportunity foregone.
Time value of money.
Interest are charged to cover the lending expenses, loan
management and evaluation costs the lending part has
incurred.
 Types of Interest rates
Nominal Interest rate
Real Interest rate
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THEORIES GOVERNING
DETERMINATION OF INTEREST RATES.
1. Loanable funds theory,
2. Fisher theory of interest rates and
3. Keynes Liquidity preference theory
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Loanable Funds Theory.
 by Knut Wickssell.
 According to the Loanable Funds Theory of Interest, the
rate of interest is determined on the basis of demand and
supply of loanable funds present in the capital market.
 The loanable funds theory suggests that the market
interest rate is determined by the factors that control the
supply and demand for loanable funds.
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Demand and supply of loanable funds
 Demand for loanable funds is composed of business firms,
government, foreign entities and households who demand
cash for financing investments, budget deficits and household
expenditures respectively .
 The supply for loanable funds are largely coming from
household though the government and business firms save
when their cash flows exceeds outflows. The foreign
corporations and governments supply funds by buying debt
securities.
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Equilibrium Interest Rate.
At the interaction of aggregate demand and supply of loanable
funds in the economy, the equilibrium interest rate is
determined.
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FISHER THEORY OF INTEREST RATE.
 Irving Fisher's theory of interest rates relates the nominal
interest rate i to the rate of inflation π and the real interest
rate r. the relation Fisher postulated between these three
rates is:
 (1+i) = (1+r) (1+π) = 1 + r + π + r π
This is equivalent to:
 i = r + π(1 + r)
Thus, according to this equation, if π increases by 1 percent the
nominal interest rate increases by more than 1 percent.
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KEYNES’ LIQUIDITY PREFERENCE
THEORY OF INTEREST.
By John Maynard Keynes in 1936,
 Keynes defines the rate of interest as the reward for parting
with liquidity for a specified period of time. According to
him, the rate of interest is determined by the demand for
(liquidity) and supply of money.
 Liquidity preference means the desire of the public to hold
cash. According to Keynes, there are three motives behind
the desire of the public to hold liquid cash:, the transaction
motive, the precautionary motive and the speculative
motive.
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According to Keynes….
 The rate of interest is determined at the level where the
demand for money equals the supply of money. In the
following figure, the vertical line QM represents the supply
of money and L the total demand for money curve. Both the
curves intersect at E2 where the equilibrium rate of interest
OR is established.
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IMPORTANCE OF THE THEORIES.
 All theories explained above do not give a concise view and
precise explanation on nature and the determination of
interest rates but they lay a basis/foundation from which we
discuss interest rates.
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MACRO ECONOMIC DETERMINANTS OF
INTEREST RATES.
 Impact of economic growth on interest rates.
 Impact of inflation on interest rates.
 Impact of money supply on interest rates.
 Impact of budget deficits on interest rates.
 Impact of foreign flows of funds on interest rates.
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MICRO ECONOMIC FACTORS
AFFECTING INTEREST RATE.
 Creditworthiness of the issuer,
 Liquidity of a debt security
 Nature of the business investment.
 Special provision of a debt security.
 Tax status of the security.
 Lending institutions policies and required returns
planned.
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TERM STRUCTURE OF INTEREST RATES
Definitions:
 The term structure of interest rates refers to the relationship
between the time to maturity and interest rates of default-free,
pure discount instruments.
 Yield curve is the graphical presentation of the relationship
between the financial securities of the same qualities but different
maturity dates.
 Spot rate is the interest rate paid on delivery of the financial
securities meanwhile Forward rate is the rate to be paid for
delivery of financial securities at some future date.
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Types of yield curves.
 Normal yield curve.
 Inverted yield curve.
 Flat yield curve.
 Market participants do observe the market tendencies
such as price levels and the security yield in the treasury
market so as to construct the yield curve.
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Normal yield curve
Annualized yield
yield curve
0
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maturity
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Flat yield curve.
Annualized yields
yield curve
o
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maturity
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Inverted yield curve.
 Annualized yield
yield curve
0
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maturity
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Theories explaining term structure of
interest rates
Theories explaining the relationship between maturity and
annualized yields of financial securities include the following;
 Pure/Unbiased expectations theory.
 Liquidity premium theory.
 Market segmentation theory.
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1. Unbiased Expectations Theory
 According to this theory, yield curve reflects the market’
s current expectations of future short term rates.
 Suppose an investor has a 4-year investment horizon
 Buy a 4-year bond and earn current yield on this bond, 1R4
 Invest in 4 sucessive one-year bonds.You know the 1-year spot
rate but form expectations on the future rates on 1-year bond
for 3 years, 1R1, E(2r1), E(3r1), E(4r1)
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 Example: Suppose that the current 1-year rate (spot rate),
1R1=1.94%.
 Expected one-year T-Bond rates over the following 3 years
are;
E(2r1)=3%, E(3r1)=3.74%, E(4r1)=4.10%
 Using the unbiased exp. theory current rates for two, three
and four year maturity T-Bonds should be;
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 1R2=[(1+0.0194)(1+0.03)]1/2-1=2.47%
 1R3=[(1+0.0194)(1+0.03)(1+0.0374)]1/3-1=2.89%
 1R4=[(1+0.0194)(1+0.03)(1+0.0374)(1+0.041]1/4-
1=3.19%
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2. Liquidity Premium Theory
 It is based on the idea that investors will hold L-T maturities
only if they are offered at a premium to compensate for
future uncertainity with security’s value.
 It states that L-T rates are equal to geometric average of
current and expected short term rates and liquidity risk
premium.
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 Example: Suppose that the current 1-year rate (spot rate),
1R1=1.94%.
Expected one-year T-Bond rates over the following 3 years
are;
E(2r1)=3%, E(3r1)=3.74%, E(4r1)=4.10%
In addition, investors charge a liquidity premium such that;
L2=0.10%, L3=0.20%, L4=0.30%,
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 Current rates for 1,2,3 and 4 year maturity Treasury




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securities;
1R1=1.94%
1/2-1 = 2.52%
R
=[(1+0.0194)(1+0.03+0.001)]
1 2
1/3
1R3=[(1+0.0194)(1+0.03+0.001)(1+0.0374+0.002)] 1=2.99%
1R4=[(1+0.0194)(1+0.03+0.001)(1+0.0374+0.002)(1+0.
041+0.003]1/4-1=3.34%
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Market Segmentation Theory
 Individual investors and FIs have spesific maturity
preferences, and to get them to hold maturities other
than their prefered requires a higher interest rate
(maturity premium).
 For example: banks might prefer to hold short term TBonds because short term nature of their deposits.
Insurance companies might prefer to hold L-T T-Bonds
because L-T nature of their liabilities (such as life
insurance policies)
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Forecasting Interest Rates
 Upward sloping yield curve suggests that the market
expects future short term interest rate to increase. So
that this theory can be used to forecast interest rates.
 “Forward rate” is the expected or implied rate on a short
term security. The market’s expectations of forward rates
can be derived directly from existing or actual rates on
securities currently traded in the spot market.
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 1R2=[(1+ 1R1)(1+ 2f1)]1/2-1
 2f1=[(1+ 1R2)2/(1+ 1R1)]-1
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 Example: The existing (current) one-year, two-year, three-
year and four-year zero coupon Treasury security rates;
 1R1=4.32%, 1R2=4.31%, 1R3=4.29%, 1R4=4.34%
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 Using the unbiased exp. theory, forward rates on zero
coupon T-Bonds for years 2, 3 and 4 are;
 2f1=[(1.0431)2/(1.0432)1]-1=4.30%
 3f1=[(1.0429)3/(1.0431)2]-1=4.25%
 4f1=[(1.0434)4/(1.0429)3]-1=4.49%
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Relationship between Interest rate and
Security Prices
 As suggested by discounting models, the price of the security
is equivalent to the present value of all future cash flows.
 For the case of stock, present value of all dividends to be paid
in the future is equivalent to its current market price.
 For the debt securities such as bond, PV of the coupon
(interest) received will represent the market price of the
security.
 PV has negative relationship with r, hence Price of securities
has negative relationship with interest rate.
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End of Topic 5
WISH YOU HAPPY MAULID, MERRY CHRISTMASS
AND HAPPY NEW YEAR 2016
TEST: SATURDAY 16TH JANUARY 2016
LASTLY…..
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SPECIAL QUIZ (Today)
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