CHAPTER 4 THE LEVEL OF INTEREST RATES. Learning Objectives Define the concept of an interest rate and explain the role of interest rates in the economy

CHAPTER 4

THE LEVEL OF INTEREST RATES

Learning Objectives

• Define the concept of an interest rate and explain the role of interest rates in the economy.

• Define the concept of real interest rates and explain what causes the real interest rate to change.

• Explain how inflation affects interest rates.

• Calculate the realized real rate of return.Copyright© 2006 John Wiley &

Sons, Inc. 2

What are Interest Rates?• The cost of borrowing money for the use of its

purchasing power (rental price for money).

• To a borrower, it is penalty for consuming before earning.

• To a lender, it is reward for postponing consumption.

• Expressed in terms of annual rates.

• As with any price, interest rates serve to allocate resources allocative function.

• SSU wants to buy financial claims with the highest returns ,whereas DSUs want to sell financial claims at the lowest possible interest rates.

3

The Real Rate of Interest

• The main determinants of interest rate are:

1.Production opportunities. 2.Time preferences for consumption.

Copyright© 2006 John Wiley & Sons, Inc. 4

The Real Rate of Interest• Production opportunities: Producers (investors in capital

projects) seek financing for real assets. Expected ROI is upper limit on interest rate producers can pay for financing.

• Time preferences for consumption: Most people prefer to consume today rather than tomorrow (positive time preference for consumption). Savers require compensation for deferring consumption. Time value of consumption is lower limit on interest rate at which savers will provide financing.

• Real interest rate occurs at equilibrium between desired real investment (demand for funds) and desired saving (supply of funds).


The Real Rate of Interest• The determination of market interest rates occurs in demand

and supply framework.

• The supply side is saving curve. At low rates, most people postpone very little consumption for the sake of saving(i.e. they save less) and at high rates, consumers tend to save more. Hence, the supply curve is upward sloped.


The Real Rate of Interest

• The demand is the Investment curve. At high rates, fewer businesses can earn an expected return high enough to cover this high interest costs. Therefore, they borrow less. On the other hand, at low rates, they tend to borrow more. Hence, the demand curve is downward sloped.

• The equilibrium rate of interest is called the real rate of interest(r*).


Determinants of the Real Rate of Interest


Economic Forces change interest rates• Factors that shift the investment curve either to the right or to the

left:1. Productivity 2. Technology 3. taxes, 4. expected risk 5. expected sales

Factor that shift the saving curve either to the right or to the left:1. Consumer attitude (propensity to save)2. personal Income, 3. personal income tax


Loanable Funds Theory• It is difficult to use the desired savings and investment

framework to explain short-run changes in the interest rate. Therefore, in the short run, interest rate depends on the supply of and the demand for loanable funds.

• Supply of loanable funds—– All sources of funds available to invest in

(purchase) financial claims

• Demand for loanable funds—– All uses of funds raised from issuing

financial claims


Supply of loanable funds• All sources of funds available to invest in

financial claims:– Consumer savings– Business savings– Government budget surpluses– Central Bank Action


Demand for Loanable Funds

• All uses of funds raised from issuing financial claims:– Consumer credit purchases– Business investment– Government budget deficits


Loanable Funds Theory


Equilibrium Interest Rate

• Equilibrium interest rate occurs when supply of loanable funds = demand for loanable funds

• Equilibrium is temporary or dynamic: Any force that shifts supply or demand will tend to change interest rates.



Factors effect on Supply of Loanable Funds

1. Change in GOV. Budget (from Deficit to Surplus Position)2. Change in Consumer Saving3. Change in Business Savings



Factors effect on Demand for Loanable Funds

1. Change in Business investment2. Change in GOV. Budget (from surplus to deficit position)3. Change in consumer credit purchases


Price Expectations and Interest Rates

• Unanticipated inflation benefits borrowers at expense of lenders during the life of a loan contract, because the borrower pay the lender money with less purchasing power.

• Therefore, lenders charge additional interest to offset anticipated decreases in purchasing power.

• Expected inflation is embodied in nominal interest rates: The Fisher Effect. The Fisher Effect Theory states that the nominal interest rate includes real interest rate (interest rate without inflation) and expected annual inflation rate.


Fisher Effect

The exact Fisher equation is:


inflation. of rate annual expected the

interest, of rate real ther

interest, of rate nominal observed the i

where

111

e

e

P

Pri

Fisher Effect, cont.

From the Fisher equation, we derive the nominal (contract) rate:

We see that a lender gets compensated for:rental of purchasing poweranticipated loss of purchasing power on the principalanticipated loss of purchasing power on the interest


ee PrPri *

Fisher Effect: Example

• 1-year $1000 loan • Parties agree on 3% rental rate for money and• 5% expected rate of inflation.

– Items to pay Calculation Amount– Principal $1,000.00– Rent on money $1,000 x 3% 30.00– PP loss on principal $1,000 x 5% 50.00– PP loss on interest $1,000 x 3% x 5% 1.50

– Total Compensation $1,081.50


Simplified Fisher Equation

The third term in the Fisher equation is negligible, so it is commonly dropped. The resulting equation is


ePri

Fisher Equation

• Example 1:If real interest rate is 5%, actual inflation last year was 7%, and

expected inflation for the coming year is 9%. What is the current level of nominal interest rate?

• Example 2:What is the total compensation required by an investor for

lending a U.S. Treasury $1000 for 1 year if the real rate of interest is 4%, actual inflation last year was 6%, and expected inflation for the coming year is 7%?


The Realized Real Rate• The Fisher equation is based on expected inflation rate.

• The actual rate of inflation may be different from the anticipated rate.

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

• The realized (actual) real rate is calculated as : r = i - ΔPa,

• Where; r = is the realized real rate of return, i = the nominal interest rate, and ΔPa = is the actual rate of inflation


The Realized Real Rate-continued

• If the actual inflation turns out to be higher than the expected inflation, then the lender will have a lower realized real rate of return i.e. there was an unintended transfer of purchasing power to borrower from lender.

• If the actual inflation turns out to be less than the expected inflation, then the lender will have a higher realized real rate of return i.e. there was an unintended transfer of purchasing power to lender from borrower.



The realized real rate may be Positive, Zero or Negative.

1. If nominal interest rate (i) > actual inflation, then realized real rate is positive

2. If nominal interest rate (i) = actual inflation then realized real rate is zero

3. if nominal interest rate (i) ˂ actual inflation then realized real rate is negative



• Example:An investor buys a 1 –year Treasury security with a promised

yield of 10%. The investor expected the annual rate of inflation to be 6%; however, the actual rate turned out to be 10%. What were the expected and the realized real rates of return for the investor?

• The expected real rate =

• The realized real rate =


Interest Rate Movements and Inflation

• Historically, interest rates tend to change with changes in the rate of inflation, substantiating the Fisher equation.

• Short-term rates are more responsive to changes in inflation than long-term rates.


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CHAPTER 4 THE LEVEL OF INTEREST RATES. Learning Objectives Define the concept of an interest rate and explain the role of interest rates in the economy