Transcript FINANCIAL MARKETS AND INSTITIUTIONS: A Modern Perspective

Chapter Two
Determinants of
Interest Rates
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Interest Rate Fundamentals
• Nominal interest rates - the interest
rate actually observed in financial
markets
– directly affect the value (price) of most
securities traded in the market
– affect the relationship between spot and
forward FX rates
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Time Value of Money and Interest Rates
• Assumes the basic notion that a dollar
received today is worth more than a dollar
received at some future date
• Compound interest
– interest earned on an investment is reinvested
• Simple interest
– interest earned on an investment is not
reinvested
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Calculation of Simple Interest
Value = Principal + Interest (year 1) + Interest (year 2)
Example:
$1,000 to invest for a period of two years at 12 percent
Value = $1,000 + $1,000(.12) + $1,000(.12)
= $1,000 + $1,000(.12)(2)
= $1,240
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Value of Compound Interest
Value = Principal + Interest + Compounded interest
Value = $1,000 + $1,000(.12) + $1,000(.12) + $1,000(.12)
= $1,000[1 + 2(.12) + (.12)2]
= $1,000(1.12)2
= $1,254.40
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Present Value of a Lump Sum
• PV function converts cash flows received over a future
investment horizon into an equivalent (present) value
by discounting future cash flows back to present using
current market interest rate
– lump sum payment
• a single cash payment received at the end of some
investment horizon
– annuity
• a series of equal cash payments received at fixed
intervals over the investment horizon
• PVs decrease as interest rates increase
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Calculating Present Value (PV) of a Lump
Sum
PV = FVn(1/(1 + i/m))nm = FVn(PVIFi/m,nm)
where:
PV = present value
FV = future value (lump sum) received in n years
i = simple annual interest rate earned
n = number of years in investment horizon
m = number of compounding periods in a year
i/m = periodic rate earned on investments
nm = total number of compounding periods
PVIF = present value interest factor of a lump sum
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Calculating Present Value of a Lump Sum
• You are offered a security investment that pays $10,000 at
the end of 6 years in exchange for a fixed payment today.
•
PV = FV(PVIFi/m,nm)
•
at 8% interest - = $10,000(0.630170) = $6,301.70
•
at 12% interest - = $10,000(0.506631) = $5,066.31
•
at 16% interest - = $10,000(0.410442) = $4,104.42
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Calculation of Present Value (PV) of an
Annuity
nm
PV = PMT  (1/(1 + i/m))t = PMT(PVIFA i/m,nm)
t=1
where:
PV = present value
PMT = periodic annuity payment received
during investment horizon
i/m = periodic rate earned on investments
nm = total number of compounding periods
PVIFA = present value interest factor of an annuity
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Calculation of Present Value of an Annuity
You are offered a security investment that pays $10,000 on
the last day of every year for the next 6 years in exchange
for a fixed payment today.
PV = PMT(PVIFAi/m,nm)
at 8% interest - = $10,000(4.622880) = $46,228.80
If the investment pays on the last day of every quarter for
the next six years
at 8% interest - = $10,000(18.913926) = $189,139.26
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Future Values
• Translate cash flows received during an
investment period to a terminal (future)
value at the end of an investment horizon
• FV increases with both the time horizon and
the interest rate
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Future Values Equations
FV of lump sum equation
FVn = PV(1 + i/m)nm = PV(FVIF i/m, nm)
FV of annuity payment equation
(nm-1)
FVn = PMT

(1 + i/m)t = PMT(FVIFAi/m, mn)
(t = 0)
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Calculation of Future Value of a Lump Sum
• You invest $10,000 today in exchange for a fixed
payment at the end of six years
–
–
–
–
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at 8% interest = $10,000(1.586874) = $15,868.74
at 12% interest = $10,000(1.973823) = $19,738.23
at 16% interest = $10,000(2.436396) = $24,363.96
at 16% interest compounded semiannually
• = $10,000(2.518170) = $25,181.70
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Calculation of the Future Value of an Annuity
• You invest $10,000 on the last day of every year
for the next six years,
– at 8% interest = $10,000(7.335929) = $73,359.29
• If the investment pays you $10,000 on the last day
of every quarter for the next six years,
– FV = $10,000(30.421862) = $304,218.62
• If the annuity is paid on the first day of each
quarter,
– FV = $10,000(31.030300) = $310,303.00
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Relation between Interest Rates and
Present and Future Values
Present
Value
(PV)
Future
Value
(FV)
Interest Rate
Interest Rate
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Equivalent Annual Return (EAR)
If you invest in a security that matures in 75 days and
offers a 7% annual interest rate:
EAR = (1 + i/(365/h))365/h - 1
=(1 + (.07)/(365/75))365/75 - 1 = 7.20%
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Discount Yields
Money market instruments (e.g., Treasury
bills and commercial paper) that are bought
and sold on a discount basis
idy = [(Pf - Po)/Pf](360/h)
Where:
Pf = Face value
Po = Discount price of security
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Single Payment Yields
Money market securities (e.g., jumbo CDs,
fed funds) that pay interest only once during
their lives: at maturity
ibey = ispy(365/360)
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Loanable Funds Theory
• A theory of interest rate determination that
views equilibrium interest rates in financial
markets as a result of the supply and demand
for loanable funds
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Supply of Loanable Funds
Demand
Supply
Interest
Rate
Quantity of Loanable Funds
Supplied and Demanded
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Funds Supplied and Demanded by Various
Groups (in billions of dollars)
Funds Supplied Funds Demanded
Households
Business - nonfinancial
Business - financial
Government units
Foreign participants
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$30,857.3
9,892.5
29,508.9
10,072.9
8,193.8
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$12,849.2
28,229.9
39,484.7
4,873.7
3,081.9
Net
$18,002.1
-18,337.4
-9,975.8
5,199.2
5,111.9
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Determination of Equilibrium Interest Rates
D
S
Interest
Rate
IH
i
E
IL
Q
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Quantity of Loanable Funds
Supplied and Demanded
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Effect on Interest rates from a Shift in the
Demand Curve for or Supply curve of
Loanable Funds
Increased supply of loanable funds
Interest
Rate
Increased demand for loanable funds
SS
DD
DD
SS*
DD*
i**
i*
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i*
E*
Q* Q**
E*
E
E
i**
SS
Quantity of
Funds Supplied
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Q* Q**
Quantity of
Funds Demanded
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Factors Affecting Nominal Interest
Rates
• Inflation
– continual increase in price of goods/services
• Real Interest Rate
– nominal interest rate in the absence of inflation
• Default Risk
– risk that issuer will fail to make promised payment
(continued)
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• Liquidity Risk
– risk that a security can not be sold at a
predictable price with low transaction cost on
short notice
• Special Provisions
– taxability
– convertibility
– callability
• Term to Maturity
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Inflation and Interest Rates: The
Fisher Effect
The interest rate should compensate an investor
for both expected inflation and the opportunity
cost of foregone consumption
(the real rate component)
or
i = RIR + Expected(IP)
RIR = i – Expected(IP)
Example: 3.49% - 1.60% = 1.89%
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Default Risk and Interest Rates
The risk that a security’s issuer will default
on that security by being late on or missing
an interest or principal payment
DRPj = ijt - iTt
Example: DRPAaa = 6.61% - 5.48% = 1.13%
DRPBaa = 7.92% - 5.48% = 2.44%
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Tax Effects: The Tax Exemption of Interest
on Municipal Bonds
Interest payments on municipal securities are
exempt from federal taxes and possibly state and
local taxes. Therefore, yields on “munis” are
generally lower than on equivalent taxable bonds
such as corporate bonds.
im = ic(1 - ts - tF)
Where:
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ic =
im =
ts =
tF =
Interest rate on a corporate bond
Interest rate on a municipal bond
State plus local tax rate
Federal tax rate
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Term to Maturity and Interest Rates:
Yield Curve
(a) Upward sloping
(b) Inverted or downward
sloping
(c) Flat
Yield to
Maturity
(a)
(c)
(b)
Time to Maturity
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Term Structure of Interest Rates
• Unbiased Expectations Theory
– at a given point in time, the yield curve reflects the
market’s current expectations of future short-term
rates
• Liquidity Premium Theory
– investors will only hold long-term maturities if they
are offered a premium to compensate for future
uncertainty in a security’s value
• Market Segmentation Theory
– investors have specific maturity preferences and will
generally demand a higher maturity premium
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Forecasting Interest Rates
Forward rate is an expected or “implied” rate
on a security that is to be originated at some
point in the future using the unbiased
expectations theory
_
_
1/2 - 1
R
=
[(1
+
R
)(1
+
(
f
))]
1 2
1 1
2 1
where
2 f1
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= expected one-year rate for year 2, or the implied
forward one-year rate for next year
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