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Copyright © 2004 by Thomson Southwestern All rights reserved.
8-1
Interest Rates, Exchange Rates and Inflation Theories and Forecasting
Chapter 8
Copyright © 2004 by Thomson Southwestern All rights reserved.
8-2
Part A: Theories of Interest Rates
Interest Rates • A change causes an automatic market repricing
of all fixed interest obligations• Are altered as a major instrument of monetary
policy by central banks to direct the economy• Can be very volatile
Foreign Exchange Rates• A change alters international flows of both
goods and capital• Can be very volatile
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8-3
Theories Are Important to Managers
Many decisions made on the basis of forecasts
Need to understand assumptions underlying forecasts and data
Need to understand the reasons why the assumptions are made
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8-4
A Historical Look at Interest Rates
See Figures 8.1 and 8.2, pages 268-269Interest Rates Are Constantly Changing and
Have Been Particularly Volatile in Recent Decades.
Interest Rates Generally Fall During Recessions
Interest Rates Incorporate the Real Rate of Interest
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8-5
The General Level of Interest Rates
Standard conventions1. Models focus on the determination of the
equilibrium interest rate◦ Economy is rarely in equilibrium◦ Assumption is made that economy is always
moving toward equilibrium2. Models use simplifying assumptions and hope
that critical factors are not omitted3. Focus is on the rate of interest not differences
in rates among various securities
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8-6
Loanable Funds TheoryInterest rates are determined by supply and
demand of funds for investmentAssumes open and competitive money and
capital marketsUseful for forecastingMarket participant are borrowers and lenders
• Households or Consumers• Businesses• Governments• The Central Bank• The Foreign Sector
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8-7
Households as Suppliers
Time preference for consumptionReward for saving is necessaryCash balances may be held due to
• Transactions demand• Precautionary demand• Speculative demand
Savings necessary due to future needs(e.g. illness, college fund, retirement)
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8-8
Business as Suppliers
More often demandersSupply from business affected by
• Available funds◦ Depreciation◦ Retained earnings
• Investment options (real and financial)• Nature of the business• Management philosophy
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8-9
Other Supply Factors
The Money Supply• Changed by Federal Reserve System policy• An increase in the money supply increases
funds available for investmentThe Foreign Sector
• Funds are also supplied from participants in other countries
• Supply is affected by interest rates & economic growth in the two countries and other factors
Governments
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8-10
The Demand for Loanable Funds
Businesses and households will demand less funds at higher interest rates
Demand by governments is inelastic with respect to interest rates and due to budget deficits
Demand by the foreign sector is due to• Same factors affecting domestic units• Differences in U.S. rates and rates abroad
Copyright © 2004 by Thomson Southwestern All rights reserved.
8-11
Loanable Funds ($)
Inte
rest
Rat
e (%
)
0
(Household + Business +M + Foreign)
SLF
Loanable Funds ($)
SUPPLY OF LOANABLE FUNDS
The supply of loanable funds increases as the expected interest rate increases.
0
(Business +Government + Foreign)
DLFIn
tere
st R
ate
(%)
DEMAND FOR LOANABLE FUNDS
The demand for loanable funds decreases as the expected interest rate increases.
Copyright © 2004 by Thomson Southwestern All rights reserved.
8-12
I*
SLF
DLF
Q*
Loanable Funds ($)
Inte
rest
Rat
e (%
)
0
EQUILIBRIUM RATE OF INTERESTThe equilibrium level of interest rates is the rate at which the quantity of loanable funds demanded equals the quantity of loanable funds supplied.
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8-13
Loanable Funds Theory and Interest Rate Forecasting
Changes in Supply or Demand can be caused by• Government Fiscal Policy (determined by
Congress)◦ Federal Budget Deficit◦ Taxation
• Government Monetary Policy (determined by the Federal Reserve System
Supply and demand determine the equilibrium interest rate (price) and equilibrium loanable funds (quantity)
Copyright © 2004 by Thomson Southwestern All rights reserved.
8-14
I'
Inte
rest
Rat
e (%
)
I*
Loanable Funds ($)0
SLF
DLF
DLF'
Higher DLF
0
Inte
rest
Rat
e (%
)
I*
I'
Loanable Funds ($)
SLF
DLF
DLF'
Lower DLF
SHIFTS IN THE DEMAND CURVE AND CHANGES IN THE EQUILIBRIUM RATE OF INTEREST
If the demand for loanable funds increases, the equilibrium interest rate will increase.If the demand for loanable funds decreases, the equilibrium interest rate will fall.
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8-15
Inflation and New Financial Innovations Due to Inflation
Variable rate loansVariable rate depositsAdjustable-rate bonds and mortgagesZero-coupon bondsInterest rate swapsInflation-adjusted Treasury securitiesInflation futures contractsOther derivatives
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8-16
The Fisher Effect
Explains the relationship between • The nominal interest rate,• The real interest rate, and • Expected inflation
Inflation affects real purchasing power.Investors will demand a higher interest rate
(an inflation premium) for expected lost purchasing power over the period of an investment.
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8-17
The Fisher Effect(1 + iN) = (1 + iR)(1 + Expected Inflation Rate)
iN = [(1+iR) )(1 + Expected Inflation Rate)] – 1
where iN is the nominal interest rate demanded
iR is the real rate of return desired
If the real rate of return desired is 2% and expected inflation is 12%, then the nominal rate demanded is:
(1.02)(1.12) - 1 = .1424 or 14.24%
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8-18
The real ex post return that investors actually get is given by:
iR = [( + iN)/(1 + Actual Inflation Rate)] – 1
If inflation turned out to be 12%, and the nominal rate was 14.2%, the real ex post return would be:
(1.142)/(1.12) - 1 = .02 or 2%
Real Ex Post Return
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8-19
The Fisher effect approximation formula eliminates the cross-products.
iN = iR + Expected Inflation
iR = iN – Expected Inflation
or iN = 2% + 12% = 14%The Fisher effect assumes that the iR remains unchanged.Changes in nominal interest rates are driven by changes in expected inflation.
Expected Inflation Drives Changes in Nominal Interest Rates
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8-20
Expected Inflation and the Loanable Funds Theory
Loanable Funds ($)Q*0
iR
iN
Interest Rate (%)
E(INFL)
SLF
SLF”
DLF”
DLF”
Panel B: Inflationary Expectations and the Real Rate of Interest Panel A: Inflation and the
Equilibrium Rate of Interest
Q0
iR’
iR
Interest Rate (%)
SLF
SLF”
DLF”
Q’Loanable Funds ($)
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8-21
Evaluation of the Fisher EffectThe theory is based on
• ex ante real rates• ex ante expected inflation
These are not observable, resulting in measurement problems in testing the theory.
Ex post real rates are not stable which suggests that inflationary expectations by investors were consistently incorrect.
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8-22
Further Evaluation of the Fisher Theory
Historical RelationshipsMeasurement Problems
• Historical Ex Post Analysis• Interest Rate Behavior Adjustments for
Deflation?Adjusting for the Tax EffectAccuracy of Interest Rate ForecastingProfessional Forecasts Based on the Loanable
Funds Theory
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8-23
Adjusting for the Tax EffectIncome taxes are levied on nominal rather than on
real returns. • This suggests that changes in nominal yields will
actually be greater than that predicted by Fisher to compensate for the tax on the inflation premiums.
The nominal rate adjusting for tax effects isiN = [(1 + iR)(1 + Before-Tax Inflation Premium)] – 1where iN= the nominal return before taxes
iR = the real rate expected before taxes
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8-24
Calculating Effective Annual Yields on Money Market Securities
Money Market Securities• Maturity less than one year• Generally sold at a discount• Maximum maturity is 360 days• If the yield is calculated in a 365 day year (to
compare yields with capital market securities, it is the coupon equivalent yield
• If the yield is calculated in a 360 day year, it is the bank discount yield
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8-25
Coupon Equivalent Yield on Money Market Securities
n
y 365P
P - )(Por Par 0
01
where:P0 = the initial amount investedPar = the par value at maturityP1 = price received if sold before maturityn = the number of days until maturity or sold
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8-26
Effective Annual Yield
The equation implicitly assumes that any money received will be reinvested at the given annual rate during the year, resulting in a higher effective rate of return at the end of the year. Hence, y* will be greater than y.
3651*
0
Par (or P ) 1P
ny
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8-27
Bank Discount Yield
The yield on money market securities is quoted as a percentage of par. Thus, discount yield (d) will always be lower than the annual yield (y) or the effective annual rate (y*).
0
0
Par - P 360P
dn
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8-28
The purchase price of money market securities is found by:
01- (d n)P Par
360
Purchase Price of Money Market Securities
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8-29
Find the price, the coupon equivalent yield and the effective annual yield for a 91-day T-bill with a discount yield of 4.425%.
Purchase price of the T-bill
3601)(.04425)(91100% P0 98.8% of par
The price that must be paid for the T-bill with a par value of $10,000 would be $9,888.10.
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8-30
Coupon equivalent (annual) yield for the T-bill
91
365%881.98
%881.98%100y 0.04539 or 4.539%
The effective annual yield for the T-bill
1
%881.98%100 91
365
*y .04618 or 4.618%
Yield Calculations
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8-31
Differences in Yields for Money Market Securities
Calculating Yields for Negotiable CDs and Fed Funds
1d nP Amount Invested 1360
where:P1 = the amount received at maturity, equal to interest earned at the quoted rate plus the principal or amount investedd = the quoted rate
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8-32
Find the effective annual yield on a 180-day CD with a face value of $1 million and a coupon rate of 3.5%.
Amount received at maturity
360)180)(035(.1 million 1$P1 $1.0175 million
The effective annual yield on the CD
180
365*
10175.1y .03581 or 3.581%
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8-33
Differences in Yields for Money Market Securities
Default riskLiquidity
Influenced by the size of the secondary market for the particular security.
Denomination sizeMaturity
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8-34
Part B: Currency Exchange RatesCompanies doing business in more than one
country face exchange rate riskThe risk that money will be lost solely through
variations in the exchange rate of the two currencies
Direct exchange rate – U.S. dollars per unit of foreign currency
Indirect exchange rate – units of foreign currency per U.S. dollar
Spot rate – rate for immediate currency exchange
Forward rate – rate for an exchange on a future date agreed upon today
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8-35
Theories of Exchange Rate Determination
Supply and Demand for Goods and ServicesFloating Exchange Rates as Adjusters for
International Monetary Surpluses and Deficits
Relative Inflation RatesPurchasing Power Parity Theorem
Relative Interest RatesInterest Rate Parity Theorem
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8-36
Theories of Exchange Rate Determination
Controlling Inflation for the Euro• Politics Changing the Fiscal Rules
Underpinning the Euro• A Complex Puzzle• The Role of Expectations