Download The Real Rate of Interest

CHAPTER 5
THE LEVEL OF INTEREST RATES
What are Interest Rates?
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Rental price for money.
The time value of consumption.
Opportunity cost.
Expressed in terms of annual rates.
As with any price, interest rates serve to allocate funds to
alternative uses.
The Real Rate of Interest
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There is a preference for "real" applications for savings such as
consumption or real investment.
– Real interest rate compensates for delayed consumption.
– The higher the desire for consumption, the higher the real
rate of interest.
The real rate of interest is determined by the demand and
supply for savings at a given point in time.
– The real rate is the price needed to delay consumption of
funds demanded for real investment.
– Upward shifts to the right (increases) in demand for desired
real investment cause the real rate of interest to increase.
– If the supply of desired savings shifts upward (increases) to
the right, the real rate of interest declines.
Determinants of the
Real Rate of Interest
Loanable Funds Theory of Interest
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The level of interest rates is determined by the supply and
demand for loanable funds.
– The real rate of interest is the long-term base rate of interest.
– Short-run supply/demand factors and financial market risks
affect nominal interest rates.
– The quantity demanded of loanable funds, DL, is inversely
related to the level of interest rates; the quantity supplied is
directly related to interest rates.
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DSUs demand loanable funds for home building,
plant/equipment, and inventory financing.
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The supply of loanable funds available for financial investment
may come from decreasing money balances or past savings.
Sources of Supply of and
Demand for Loanable Funds
Notice that households, businesses, and governmental units are both suppliers and
demanders of loanable funds. During most periods, households are net suppliers of
funds, whereas the federal government is almost always a net demander of funds.
Supply of Loanable Funds (SSU)
Consumer savings
Business savings (depreciation and retained earnings)
State and local government budget surpluses
Federal government budget surplus (if any)
Federal Reserve increases the money supply (M)
Demand for Loanable Funds (DSU)
Consumer credit purchases
Business investment
Federal government budget deficits
State and local government budget deficits
Loanable Funds Theory of
Interest Rate Determination
Loanable Funds Theory of
Interest Rate Determination
Price Expectations and
Interest Rates
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Expected inflation, ex ante, is embodied in
nominal interest rates -- The Fisher Effect.
– Investors want compensation for expected
decreases in the purchasing power of their wealth.
– If investors feel the prices of real goods will
increase (inflation), it will take increased interest
rates to encourage them to place their funds in
financial assets.
Fisher Effect
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The formula for the Fisher equation is:
1  i   1  r 1  Pe 
where
i  the observed nominal rate of interest,
r  the real rate of interest,
Pe  the expected annual rate of inflation.
Fisher Effect (continued)
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From the Fisher equation, with a little algebra, we
see that the nominal (contract) rate is:
i  r  Pe  r * Pe 
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From this equation we see that a lender gets
compensated for:
– rent on money loaned,
– compensation for loss of purchasing power on the
principal,
– compensation for loss of purchasing power on the
interest.
Fisher Effect (continued)
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Contract rate example for: 1-year $1000 loan
when the loan parties agree on a 3% rental rate
for money and a 5% expected rate of inflation.
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Items to pay
Principal
Rent on money
PP loss on principal
PP loss on interest
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Calculation
Amount
$1,000.00
$1,000 x 3%
30.00
$1,000 x 5%
50.00
$1,000 x 3% x 5%
1.50
Total Compensation
$1,081.50
Fisher Effect (concluded)
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The third term in the Fisher equation is
approximately equal to zero, so it is dropped in
many applications. The resulting equation is
referred to as the approximate Fisher equation
and is the following:
i  r  Pe
Price Expectations and
Interest Rates
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Actual realized ex-post rates of return reflect the
impact of inflation on past investments or on
investors.
– r = i - Pa, where the annual "realized" rate of
return from past securities purchases, r, equals the
annual nominal rate minus the actual annual rate
of inflation.
– With ever-increasing rates of inflation, investors'
inflation premiums, Pe, may lag actual rates of
inflation, Pa, yielding low or even negative actual
real rates of return.
Three-Month Treasury Bill Rates
Annual Percentage Rate
20
15
10
5
0
-5
-10
May-96
Aug-93
Nov-90
Mar-88
Jun-85
Sep-82
Dec-79
Mar-77
Jun-74
Sep-71
Jan-69
Month-Year
Nominal Rates
Realized Real Rates
Impact of Inflation on Loanable
Funds Theory of Interest
Interest Rate Changes and
Changes in Inflation
15
10
5
)
0
Month-Year
Three-Month Treasury Bills
Ten-Year Treasury Notes
Rate of Inflation (CPI)
May-96
Aug-93
Nov-90
Mar-88
Jun-85
Sep-82
Dec-79
Mar-77
Jun-74
Sep-71
-5
Jan-69
Annual Percentage Rate
20
Interest Rate Changes and
Changes in Inflation (concluded)
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What do we learn from the previous slide?
– Interest rates change with changes in inflation.
– Short-term interest rates change more than longterm interest rates for a given change in inflation.