Financial Institution

Zaheer Swati 1

Unit 7

INTEREST RATE DETERMINATION

Interest rate depends on two things:

1- The rate of return on investment: the higher the return on investment, the more likely producers are to undertake

a particular investment project

2- The time preference between current and future consumption: most people prefer to consume goods today

rather than tomorrow. This is known as the positive time preference for consumption

Investment is negatively related to interest rate. That is, other things remaining equal, the higher the interest rate the

lower the investment (because cost of borrowing increase if interest rate increase)

Saving is positively related to the interest rate. That is, other things remaining equal, the higher the interest rate, the

higher the savings are.

This relationship gives:

Downward sloping demand curve for desired investment, and

Upward sloping supply curve of desired saving

The interaction of these two determines the rate if interest as shown in the figure below:

The two curves show that consumers will save more if producers offer higher interest rates on savings, and producers

will borrow more if consumers will accept lower return on their savings

The market equilibrium rate of interest (r*) is achieved when desired saving (s*) by savers equals desired investment

(I*) by producers across all economic units

This equilibrium rate of interest is called the real rate of interest. The real rate of interest is the fundamental long-run

interest rate in the economy. It is called the "real" rate of interest because it is determined by the real output of the

economy

Three theories on interest rate determination

S*=I*

r*

Interest rate Desired Savings (DS)

Desired Investments (DI)

Saving & investment

Financial Institution

Zaheer Swati 2

Unit 7

7.1 Loanable Funds Theory As noted above, the real interest rate is a long-run interest rate, so what determine interest rate in the short-run. The

loanable funds theory is a framework used to determine interest rate in the short-run

According to this the interest rate is determine by the demand for and supply of direct and indirect financial claims on

the primary and secondary markets during a given time period

The need to sell financial claims represents the demand for loanable funds (deficit spending unit)

Individuals and Households

Businesses

Governments

Foreign Demand

Buying of financial claims to earn interest represent the supply of loanable fund (surplus spending unit)

Individuals and Households – only net saver of funds

Businesses

Governments

Foreigners

In general:

Increases in interest rate will stimulate (motivate) more saving and increase supply of loanable funds

So, the loanable fund supply curve slopes upward. That is, there is a positive relationship between interest rate and

supply of loanable funds

Demand for loanable funds decreases as the interest rate increases (due to increase in cost of borrowing). That is, there

is a negative relationship between interest rate and demand for loanable funds. So that demand for loanable funds curve

slopes downward

The intersection of supply and demand for loanable funds determines the equilibrium interest rate and the equilibrium

quantity of loanable funds loaned out and demanded

Changes in interest rate, brings changes in quantity demanded and supplied of loanable funds, and is represented by a

movement along SL and DL curve

Q0

SL

DL

r1

r0

r2

Interest rate

Loanable funds

Financial Institution

Zaheer Swati 3

Unit 7

Therefore:

If interest rate is at r1 (below equilibrium), shortage of loanable funds exist, which force the interest up. And

If interest rate is at r2 (above equilibrium), surplus of loanable funds exist, which force the interest rate down

Changes in factors other than interest rate, changes the supply and demand for loanable funds. That is, SL and/or DL

curves shift upwards or downwards, and as a result a new equilibrium occurs.

What are the factors other than the interest rate?

7.1.1 Factors Affecting Supply of Loanable Funds

a. Changes in the quantity of money:

If quantity of money increases (Δ M is +), supply of loanable funds increases (people have more money to save), the SL

curve shifts to the right (or downwards), resulting in a new equilibrium with lower interest rate and higher equilibrium

quantity.

b. Change in the income tax:

A decrease in income tax increase saving. Thus, the supply of loanable funds increases, shifting the SL curve to the right,

decreasing r0 and increasing Q0.

c. Changes in government budget from deficit to surplus position:

Reduced government expenditure increases government savings, thus shifts the SL curve to the right.

d. Expected inflation:

If lower rates of inflation are expected in the future, saving increase (current consumption decreases waiting for the

expected reduction in prices), and supply of loanable fund will increases, which shift the SL curve to the right.

e. Change in saving rate or public desire to hold money balances:

An increase in saving rate (the percentage of income saved) will increase the supply of loanable funds, shifting the SL

curve shift to the right.

f. Changes in business saving:

An increase in business saving of course increases supply of loanable funds and SL curve shift to the right.

7.1.2 Factors Affecting Demand for Loanable Funds

a. Changes in future expected profits or business activities:

If business expected higher profit in the future demand for investment or investment demand increase, and so does

demand loanable funds, DL curve shifts to the right (or upwards), resulting in a new equilibrium with higher interest rate

and higher equilibrium quantity.

b. Changes in government budget from surplus to deficit position:

Increase in government expenditure, increases government borrowing to cover its deficit, therefore the demand for

loanable funds increases, and the DL curve shifts to the right.

c. changes in tax:

A decrease in tax, increase government deficit (since government revenue decreases), and thus increases the demand for

loanable funds, and DL curve will shift to the right.

In summary:

If SL only increases, Q0 will increase and r0 decreases

If DL only increases, Q0 will increase and r0 will increase

If both SL and DL increases, Q0 will increase r0 might increase, decrease, or remain unchanged

Financial Institution

Zaheer Swati 4

Unit 7

7.1.3 Sources of Demand and Supply of Loanable Funds

Source of supply loanable funds:

- Consumer savings

- Business savings

- Government savings

- Central bank, changing quantity of money

Source of Demand Loanable Funds:

- Business investment

- Consumer credit purchase

- Government budget deficit

7.1.4 Criticism

The theory is criticized on the following grounds

1. Unrealistic assumption: The theory assumes the level of national income to be constant. Actually the level of

income changes with the changes in the levels of investment in the country.

2. Unrealistic integration of monetary and ‘real factors: The theory has integrated the monetary and real factors

which affect the demand for and supply of loanable funds. Actually both these factors are to be studied separately and not

to be combined.

3. Assumption of full employment: The theory assumes full employment in the economy whereas less than full

employment is the general rule.

4. Interest-elastic factors. The theory assumes that saving, hoarding investment, etc. are related to the rate of interest.

Actually investment is not influenced by rate of interest alone. There are many other factors also which affect investment

in the country

7.2 Fisher’s Theory Market interest rates = real interest rate + inflation

Inflation is included through the fisher effect theory, which states that the nominal interest rate (contract rate)

includes real interest rate and expected annual inflation rate

The Fisher effect states that the real interest rate equals the nominal interest rate minus the expected inflation rate.

Therefore, real interest rates fall as inflation increases, unless nominal rates increase at the same rate as inflation

The contract rate is determined from the Fisher equation, which states that:

(1 + i) = (1+r)(1+ΔPe) ---------------(1)

Where

i = the nominal rate of interest (the contract, observed, or market rate)

r = real rate of interest in the absence of price level changes

ΔPe = expected annual change in commodity prices (expected inflation)

Financial Institution

Zaheer Swati 5

Unit 7

Solving the Fisher equation for i, we get the following equation:

i = r + ΔPe + (rΔPe) --------------- (2)

This equation shows the relationship between nominal (contract) rates and rates of expected inflation. The inflation

component of the equation (ΔPe + (rΔPe) is commonly referred to as to fisher effect.

The final term of the Fisher equation (rΔPe) is approximately equal to zero. So in many situations it is dropped from

the equation without creating a critical error. The equation without the final term is referred to as the approximate

Fisher equation and is stated as follows:

i = r + ΔPe ------------------------- (3)

Note that the equation can be used to calculate any of the unknowns if we know the other two:

Time period

Real rate

Expected price

change

Approximate

Nominal rate

Exact Nominal rate

0 5 0 5 5.00

1 5 7 12 12.35

2 5 7 12 12.35

3 5 9 14 14.45

4 5 3 8 8.15

5 5 -2 3 2.90

6 5 -7 0 0

However the nominal rate cannot decline below zero regardless of the rate of price decline. Lender would always

prefer to retain their money and purchase goods and services rather than to pay someone else (negative interest) to

do the same.

The nominal rate of interest is directly influenced by changes in the expected rate of inflation. That is the higher the

expected rate of inflation, the higher the nominal rate of interest

7.2.1 The Realized Real Rate

Actual inflation could be different from expected inflation rate

This may lead to the realized rate of return on a loan could be different from nominal interest rate agreed at the time

of the loan contract

Realized real rate is calculated using this formula:

rr = i - ΔPa

Where:

rr = is the realized real rate of return.

ΔPa = is the actual rate of inflation.

i = is nominal interest rate.

Financial Institution

Zaheer Swati 6

Unit 7

Example 7.1:

If real rate of interest (r) = 4%

Expected annual inflation rate (ΔPe) = 8%

So, nominal rate

If actual inflation rate (ΔPa) was 5%

Then the realized rate of return is:

If actual inflation rate was 2%

If actual inflation rate (Δpe) was 15% then,

So, realized rate of return can be negative

7.2.2 Inflation and Loanable Funds Model

o The loanable funds theory can be used to illustrate inflation’s effect on financial markets

o The higher the expected inflation rate, the higher is the demand for loanable funds (present consumption increase),

so the DL will shift upward (to the right) by the amount Δpe. The shift from DL0 to DL1 implies that borrowers are

willing to pay the inflation premium of Δpe

o Similarly, the higher the expected inflation rate, the lower is supply for loanable funds (saving decrease), so the SL

will shift upward (to the left) by the amount Δpe. The shift from SL0 to SL1 will be such that lenders are given a

higher nominal yield to compensate for their loss of purchasing power

o The net effect is that the market rate of interest will rise from r to i, where the different between i and r is the

expected inflation rate (Δpe)

o Even though the real rate of interest (r) remains unchanged, the nominal rate of interest (i) has adjusted fully for the

anticipated rate of inflation (Δpe), and the quantity of loanable funds in the market has remained the same at Q0.

i = r + ΔPa

4% + 8% = 12%

rr = i- ΔPa

r = 12% - 5% = 7%

rr = i- ΔPa

r = 12% - 2% = 10%

rr = i- ΔPa

r = 12% - 15% = -3%

Financial Institution

Zaheer Swati 7

Unit 7

7.2.3 Interest Rate Movements and Inflation

Interest rate vary directly with inflation rate, and directly with the level of economic activities, (recall that i= r + ΔPe

, so any change in r or ΔPe will change r directly)

Generally. short-term interest rates are more responsive to changes in expected inflation than long-term interest rate

Thus, a monthly change in the rate of inflation would have a large affect on the expectation across a three-month

contract while it would have a small effect across a ten-years contract

7.3 Determinants of Market Interest Rates

rd = Required rate of return on a debt security. It is also called quoted or nominal interest rate

irf = Real risk-free rate is the rate of interest on a security that is free of all risk: it is proxy by the T-bill rate or the T-

bond rate

IP = Inflation premium is the average expected inflation over the life of security. A premium equal to expected inflation

that investors add to the real risk free rate of return (higher inflation=higher IP).

DRP = Default risk premium is the risk that issuer will not pay interest or principal at stated times. Difference between

the interest rate of a U.S. Treasury bond and a corporate bond of equal maturity and marketability (reflects the likelihood

of default; higher likelihood = higher DRP)

LP = Liquidity (marketability) premium charged by lenders because some securities cannot be converted to cash in short

run at a reasonable notice. Liquidity risk premiums are increases in required or promised yields designed to offset the risk

of not being able to sell the asset in timely fashion at fair value (the longer it takes to get it to cash, the higher the LP)

IR

Pe

r

SL1

DL0

DL1

SL0 i

LF

rd = rrf + IP + DRP + LP + MRP

Financial Institution

Zaheer Swati 8

Unit 7

MRP = Maturity risk premium means that longer term security are exposed to significant risk of price declines due to

increases in inflation and interest rates. The longer the security must be held, the higher the MRP

Example 7.2: Fill in the following table by placing a check mark indicating which premiums are included in which of the

following securities.

Interest Premium Maturity Risk

Premium

Default Risk

Premium

Liquidity Premium

ST Treasury X

LT Treasury X X

ST Corporate X x

LT Corporate X X x x

Example 7.3: 30 day T-bills are currently yielding 5.5%. The following are current expected interest rate premiums

Inflation Premium= 3.45%

Liquidity Premium= 0.76%

Maturity Risk Premium= 1.65%

Default Risk Premium= 2.45%

What is the real risk free rate of return?

Solution:

Yield= r = 5.5%

T Bill Rate= r* + IP

5.5% = r* + 3.45

-3.45 - 3.45

2.05= r*

Example 7.4: A company’s 5 year bonds are yielding 7.85% each year. Treasury bonds with the same maturity are

yielding 4.82% per year, and the real risk free rate (rrf) is 2.3%. The average inflation premium is 2.5% and the maturity

risk premium is estimated to be 0.1 X (t-1) % where t= years to maturity. If the liquidity premium is .8%, what is the

default risk premium on the corporate bonds?

Solution:

r= r* + IP + DRP + LP + MRP

7.85= 2.3 + 2.5 + DRP + .8 + (.1) (5-1)

7.85= 2.3 + 2.5 + DRP + .8 + .4

7.85= 6 + DRP

-6 -6

1.85%= DRP

Financial Institution

Zaheer Swati 9

Unit 7

Example 7.5: The real risk free rate is 4%. Inflation is expected to be 2.5% in year one, 3.4% in year two and 5% each

year following. The maturity risk premium is 0.05 (t-1)%. (t= number of years to maturity) What is the yield on a 6 year

treasury note?

Solution: r= r* + IP + DRP + LP + MRP

r*= 4%

IP= (2.5 + 3.4 + 5(4))/ 6 = 4.31667 or about 4.32%

MRP= .05 (6-1) = .25%

DRP= 0

LP= 0

r= 4 + 4.32 + .25

= 8.57

Example 7.6: Suppose most investors expect the inflation rate to be 5 percent next year, 6 percent the following year,

and 8 percent thereafter. The real risk-free rate is 3 percent. The maturity risk premium is zero for securities that mature

in 1 year or less, 0.1 percent for 2-year securities, and then the MRP increases by 0.1 percent per year thereafter for 20

years, after which it is stable. What is the interest rate on 1-year, 10-year, and 20-year treasury securities? Draw a yield

curve with these data. What factors can explain why this constructed yield curve is upward sloping?

Solution:

Step 1: Find the average expected inflation rate over years 1 to 20:

Yr 1: IP = 5.0%.

Yr 10: IP = (5 + 6 + 8 + 8 + 8 + ... + 8)/10 = 7.5%.

Yr 20: IP = (5 + 6 + 8 + 8 + ... + 8)/20 = 7.75%.

Step 2: Find the maturity premium in each year:

Yr 1: MRP = 0.0%.

Yr 10: MRP = 0.1 9 = 0.9%.

Yr 20: MRP = 0.1 19 = 1.9%.

Step 3: Sum the IPS and MRPS, and add r* = 3%:

Yr 1: rRF = 3% + 5.0% + 0.0% = 8.0%.

Yr 10: rRF = 3% + 7.5% + 0.9% = 11.4%.

Yr 20: rRF = 3% + 7.75% + 1.9% = 12.65%.

Financial Institution

Zaheer Swati 10

Unit 7

The shape of the yield curve depends primarily on two factors:

(1) expectations about future inflation and (2) the relative riskiness of securities with different maturities.

The constructed yield curve is upward sloping. This is due to increasing expected inflation and an increasing maturity

risk premium.

13

12

11

10

9

8

Years to maturity0 1 5 10 15 20

Interestrate (%)