Description
Week 3: Interactive activity
3.1 Learning Outcomes:
Explain why the bond price must fall when the interest rate rises.
Explain why the real interest rate is a better measure of the tightness of credit market conditions than the nominal interest rate.
Explain why the between the return on a security and the interest rate as measured by the yield to maturity can differ substantially.
Explain the positive relationship between the duration of a security and its interestrate risk.
Explain the relationships between the quantity demanded of an asset and wealth, the expected return on the asset relative to alternative assets, the riskiness of the asset relative to alternative assets, and the liquidity of the asset relative to alternative assets.
Explain why diversification benefits investors.
Explain the theory of how interest rates are determined, as derived from the supply and demand analysis for bonds.
3.2 Action Required:
Revise the chapter 3 and 4
3.3 Test your Knowledge (Question):
Discuss few major factors for changing the Interest rates?

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Unformatted Attachment Preview
What Do Interest
Rates Mean and
What Is Their Role
in Valuation?
Copyright © 2012 Pearson Prentice Hall.
All rights reserved.
Chapter Preview
? Interest rates are among the most closely
watched variables in the economy. It is
imperative that what exactly is meant by
the phrase interest rates is understood.
In this chapter, we will see that a concept
known as yield to maturity (YTM) is the
most accurate measure of interest rates.
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31
Chapter Preview
? Any description of interest rates entails
an understanding certain vernacular and
definitions, most of which will not only
pertain directly to interest rates but will
also be vital to understanding many other
foundational concepts presented later in
the text.
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32
Chapter Preview
? So, in this chapter, we will develop a better
understanding of interest rates. We examine the
terminology and calculation of various rates, and
we show the importance of these rates in our
lives and the general economy. Topics include:
? Measuring Interest Rates
? The Distinction Between Real and Nominal
Interest Rates
? The Distinction Between Interest Rates and
Returns
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33
Present Value Introduction
? Different debt instruments have very different streams
of cash payments to the holder (known as cash
flows), with very different timing.
? All else being equal, debt instruments are evaluated
against one another based on the amount of each
cash flow and the timing of each cash flow.
? This evaluation, where the analysis of the amount and
timing of a debt instruments cash flows lead to its yield
to maturity or interest rate, is called present value
analysis.
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34
Present Value
? The concept of present value (or present discounted
value) is based on the commonsense notion that a
dollar of cash flow paid to you one year from now is
less valuable to you than a dollar paid to you today.
This notion is true because you could invest the dollar
in a savings account that earns interest and have more
than a dollar in one year.
? The term present value (PV) can be extended to mean
the PV of a single cash flow or the sum of a sequence
or group of cash flows.
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35
Present Value Applications
There are four basic types of credit
instruments which incorporate present
value concepts:
1. Simple Loan
2. Fixed Payment Loan
3. Coupon Bond
4. Discount Bond
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36
Present Value Concept:
Simple Loan Terms
? Loan Principal: the amount of funds the lender
provides to the borrower.
? Maturity Date: the date the loan must be repaid; the
Loan Term is from initiation to maturity date.
? Interest Payment: the cash amount that the borrower
must pay the lender for the use of the loan principal.
? Simple Interest Rate: the interest payment divided by
the loan principal; the percentage of principal that must
be paid as interest to the lender. Convention is to
express on an annual basis, irrespective of the loan
term.
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37
Present Value Concept:
Simple Loan
Simple loan of $100
Year: 0
1
$100
$110
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2
3
n
$121
$133
100?(1+i)n
38
Present Value Concept:
Simple Loan (cont.)
? The previous example reinforces the
concept that $100 today is preferable to
$100 a year from now since todays $100
could be lent out (or deposited) at 10%
interest to be worth $110 one year from
now, or $121 in two years or $133 in
three years.
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39
Yield to Maturity: Loans
Yield to maturity = interest rate that
equates todays value with present value
of all future payments
1. Simple Loan Interest Rate (i = 10%)
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310
Present Value of Cash Flows:
Example
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311
Present Value Concept:
FixedPayment Loan Terms
? Simple Loans require payment of one
amount which equals the loan principal
plus the interest.
? FixedPayment Loans are loans where
the loan principal and interest are repaid
in several payments, often monthly, in
equal dollar amounts over the loan term.
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312
Present Value Concept:
FixedPayment Loan Terms
? Installment Loans, such as auto loans
and home mortgages are frequently of
the fixedpayment type.
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313
Yield to Maturity: Loans
2. Fixed Payment Loan (i = 12%)
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314
Yield to Maturity: Bonds
3. Coupon Bond (Coupon rate = 10% = C/F)
Consol: Fixed coupon payments of $C
forever
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315
Yield to Maturity: Bonds
4. OneYear Discount Bond
(P = $900, F = $1000)
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316
Relationship Between Price
and Yield to Maturity
? Three interesting facts in Table 3.1
1. When bond is at par, yield equals coupon rate
2. Price and yield are negatively related
3. Yield greater than coupon rate when bond price is below par
value
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317
Relationship Between Price
and Yield to Maturity
? Its also straightforward to show that the
value of a bond (price) and yield to
maturity (YTM) are negatively related. If i
increases, the PV of any given cash flow
is lower; hence, the price of the bond
must be lower.
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318
Current Yield
? Current yield (CY) is just an approximation for
YTMeasier to calculate. However, we should
be aware of its properties:
1. If a bonds price is near par and has a long
maturity, then CY is a good approximation.
2. A change in the current yield always signals
change in same direction as yield to maturity
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319
Yield on a Discount Basis
? OneYear Bill (P = $900, F = $1000)
? Two Characteristics
1. Understates yield to maturity; longer the maturity,
greater is understatement
2. Change in discount yield always signals change
in same direction as yield to maturity
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320
Bond Page of the Newspaper
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321
Global perspective
? In November 1998, rates on Japanese
6month government bonds were negative!
Investors were willing to pay more than they
would receive in the future.
? Best explanation is that investors found the
convenience of the bills worth something
more convenient than cash. But that can only
go so farthe rate was only slightly negative.
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322
Distinction Between Real
and Nominal Interest Rates
? Real interest rate
1. Interest rate that is adjusted for expected
changes in the price level
ir = i pe
2. Real interest rate more accurately reflects
true cost of borrowing
3. When the real rate is low, there are greater
incentives to borrow and less to lend
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323
Distinction Between Real
and Nominal Interest Rates
? Real interest rate
ir = i pe
We usually refer to this rate as the ex ante real
rate of interest because it is adjusted for the
expected level of inflation. After the fact, we
can calculate the ex post real rate based on
the observed level of inflation.
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324
Distinction Between Real
and Nominal Interest Rates (cont.)
? If i = 5% and pe = 0% then
ir = 5%? 0%= 5%
? If i = 10% and pe = 20% then
ir = 10%? 20%= ?10%
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325
U.S. Real and Nominal
Interest Rates
Sample of current rates and indexes
http://www.martincapital.com/charts.htm
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326
Distinction Between Interest
Rates and Returns
? Rate of Return: we can decompose
returns into two pieces:
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327
Key Facts about the Relationship
Between Rates and Returns
Sample of current coupon rates and yields on government bonds
http://www.bloomberg.com/markets/iyc.html
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328
Maturity and the Volatility
of Bond Returns
? Key findings from Table 3.2
1. Only bond whose return = yield is one with
maturity = holding period
2. For bonds with maturity > holding period,
i ? P ? implying capital loss
3. Longer is maturity, greater is price change
associated with interest rate change
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329
Maturity and the Volatility
of Bond Returns (cont.)
? Key findings from Table 3.2 (continued)
4. Longer is maturity, more return changes
with change in interest rate
5. Bond with high initial interest rate can still
have negative return if i ?
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330
Maturity and the Volatility
of Bond Returns (cont.)
? Conclusion from Table 3.2 analysis
1. Prices and returns more volatile for longterm bonds because have higher interestrate risk
2. No interestrate risk for any bond whose
maturity equals holding period
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331
Reinvestment Risk
? Occurs if hold series of short bonds over
long holding period
? i at which reinvest uncertain
? Gain from i ?, lose when i ?
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332
Calculating Duration i =10%,
10Year 10% Coupon Bond
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333
Calculating Duration i = 20%,
10Year 10% Coupon Bond
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334
Formula for Duration
? Key facts about duration
1. All else equal, when the maturity of a bond
lengthens, the duration rises as well
2. All else equal, when interest rates rise, the
duration of a coupon bond fall
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335
Formula for Duration
1. The higher is the coupon rate on the bond,
the shorter is the duration of the bond
2. Duration is additive: the duration of a portfolio
of securities is the weightedaverage of the
durations of the individual securities, with the
weights equaling the proportion of the
portfolio invested in each
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336
Duration and InterestRate Risk
? i ? 10% to 11%:
? Table 3.4, ?10% coupon bond
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337
Duration and
InterestRate Risk (cont.)
? i ? 10% to 11%:
? 20% coupon bond, DUR = 5.72 years
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338
Duration and
InterestRate Risk (cont.)
? The greater is the duration of a security,
the greater is the percentage change in
the market value of the security for a
given change in interest rates
? Therefore, the greater is the duration of a
security, the greater is its interestrate
risk
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339
Chapter Summary
? Measuring Interest Rates: We examined
several techniques for measuring the
interest rate required on debt
instruments.
? The Distinction Between Real and
Nominal Interest Rates: We examined
the meaning of interest in the context of
price inflation.
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340
Chapter Summary (cont.)
? The Distinction Between Interest Rates
and Returns: We examined what each
means and how they should be viewed
for asset valuation.
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341
CHAPTER 4
Why Do Interest
Rates Change?
Copyright © 2012 Pearson Prentice Hall.
All rights reserved.
Chapter Preview
In the early 1950s, shortterm Treasury bills
were yielding about 1%. By 1981, the yields
rose to 15% and higher. But then dropped
back to 1% by 2003. In 2007, rates jumped
up to 5%, only to fall back to near zero in
2008.
What causes these changes?
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41
Chapter Preview
In this chapter, we examine the forces the
move interest rates and the theories behind
those movements. Topics include:
? Determining Asset Demand
? Supply and Demand in the Bond Market
? Changes in Equilibrium Interest Rates
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42
Determinants of Asset Demand
? An asset is a piece of property that is a store of value.
Facing the question of whether to buy and hold an asset
or whether to buy one asset rather than another, an
individual must consider the following factors:
1. Wealth, the total resources owned by the individual, including
all assets
2. Expected return (the return expected over the next period) on
one asset relative to alternative assets
3. Risk (the degree of uncertainty associated with the return) on
one asset relative to alternative assets
4. Liquidity (the ease and speed with which an asset can be
turned into cash) relative to alternative assets
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43
EXAMPLE 1: Expected Return
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44
EXAMPLE 2:
Standard Deviation (a)
Consider the following two companies and
their forecasted returns for the upcoming
year:
FlybyNight FeetontheGround
Probability
50%
100%
Outcome 1
Return
15%
10%
Probability
50%
Outcome 2
Return
5%
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45
EXAMPLE 2:
Standard Deviation (b)
What is the standard deviation of the returns
on the FlybyNight Airlines stock and FeetontheGround Bus Company, with the return
outcomes and probabilities described on the
previous slide? Of these two stocks, which is
riskier?
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46
EXAMPLE 2:
Standard Deviation (c)
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47
EXAMPLE 2:
Standard Deviation (d)
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48
EXAMPLE 2:
Standard Deviation (e)
? FlybyNight Airlines has a standard deviation of returns of 5%;
FeetontheGround Bus Company has a standard deviation of
returns of 0%.
? Clearly, FlybyNight Airlines is a riskier stock because its standard
deviation of returns of 5% is higher than the zero standard deviation of
returns for FeetontheGround Bus Company, which has a certain
return.
? A riskaverse person prefers stock in the FeetontheGround (the
sure thing) to FlybyNight stock (the riskier asset), even though the
stocks have the same expected return, 10%. By contrast, a person
who prefers risk is a risk preferrer or risk lover. We assume people are
riskaverse, especially in their financial decisions.
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49
Determinants of
Asset Demand (2)
The quantity demanded of an asset differs by factor.
1. Wealth: Holding everything else constant, an increase in wealth
raises the quantity demanded of an asset
2. Expected return: An increase in an assets expected return
relative to that of an alternative asset, holding everything else
unchanged, raises the quantity demanded of the asset
3. Risk: Holding everything else constant, if an assets risk rises
relative to that of alternative assets, its quantity demanded
will fall
4. Liquidity: The more liquid an asset is relative to alternative
assets, holding everything else unchanged, the more desirable
it is, and the greater will be the quantity demanded
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410
Determinants of
Asset Demand (3)
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411
Supply & Demand in the
Bond Market
We now turn our attention to the mechanics of
interest rates. That is, we are going to examine how
interest rates are determinedfrom a demand and
supply perspective. Keep in mind that these forces
act differently in different bond markets. That is,
current supply/demand conditions in the corporate
bond market are not necessarily the same as, say,
in the mortgage market. However, because rates
tend to move together, we will proceed as if there is
one interest rate for the entire economy.
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412
The Demand Curve
Lets start with the demand curve.
Lets consider a oneyear discount bond with
a face value of $1,000. In this case, the
return on this bond is entirely determined by
its price. The return is, then, the bonds yield
to maturity.
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413
Derivation of Demand Curve
? Point A: if the bond was selling for $950.
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414
Derivation of
Demand Curve (cont.)
? Point B: if the bond was selling for $900.
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415
Derivation of Demand Curve
How do we know the demand (Bd) at point A
is 100 and at point B is 200?
Well, we are just makingup those numbers.
But we are applying basic economicsmore
people will want (demand) the bonds if the
expected return is higher.
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416
Derivation of Demand Curve
To continue
? Point C: P = $850
i = 17.6% Bd = 300
? Point D: P = $800
i = 25.0% Bd = 400
? Point E: P = $750
i = 33.0% Bd = 500
? Demand Curve is Bd in Figure 4.1 which connects
points A, B, C, D, E.
? Has usual downward slope
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417
Supply and Demand for Bonds
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418
Derivation of Supply Curve
In the last figure, we snuck the supply curve
inthe line connecting points F, G, C, H, and
I. The derivation follows the same idea as
the demand curve.
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419
Derivation of Supply Curve
? Point F: P = $750
i = 33.0% Bs = 100
? Point G: P = $800
i = 25.0% Bs = 200
? Point C: P = $850
i = 17.6% Bs = 300
? Point H: P = $900
i = 11.1% Bs = 400
? Point I:
P = $950
i = 5.3%
Bs = 500
? Supply Curve is Bs that connects points F, G, C,
H, I, and has upward slope
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420
Derivation of Demand Curve
? How do we know the supply (Bs) at point P
is 100 and at point G is 200?
? Again, like the demand curve, we are just
makingup those numbers. But we are
applying basic economicsmore people
will offer (supply) the bonds if the expected
return is lower.
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421
Market Equilibrium
The equilibrium follows what we know from
supplydemand analysis:
? Occurs when Bd = Bs, at P* = 850, i* = 17.6%
? When P = $950, i = 5.3%, Bs > Bd
(excess supply): P ? to P*, i ? to i*
? When P = $750, i = 33.0, Bd > Bs
(excess demand): P ? to P*, i ? to i*
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422
Market Conditions
Market equilibrium occurs when the amount that people
are willing to buy (demand) equals the amount that people
are willing to sell (supply) at a given price
Excess supply occurs when the amount that people are
willing to sell (supply) is greater than the amount people are
willing to buy (demand) at a given price
Excess demand occurs when the amount that people are
willing to buy (demand) is greater than the amount that
people are willing to sell (supply) at a given price
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423
Supply & Demand Analysis
Notice in Figure 4.1 that we use two different vertical axes
one with price, which is hightolow starting from the top, and
one with interest rates, which is lowtohigh starting from the
top.
This just illustrates what we already know: bond prices and
interest rates are inversely related.
Also note that this analysis is an asset market approach
based on the stock of bonds. Another way to do this is to
examine the flows. However, the flows approach is tricky,
especially with inflation in the mix. So we will focus on the
stock approach.
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424
Changes in Equilibrium
Interest Rates
We now turn our attention to changes in interest
rate. We focus on actual shifts in the curves.
Remember: movements along the curve will be due
to price changes alone.
First, we examine shifts in the demand for bonds.
Then we will turn to the supply side.
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425
Factors
That Shift
Demand
Curve (a)
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426
Factors
That Shift
Demand
Curve (b)
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427
How Factors Shift
the Demand Curve
1. Wealth/saving
? Economy ?, wealth ?
? Bd ?, Bd shifts out to right
OR
? Economy ?, wealth ?
? Bd ?, Bd shifts out to right
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428
How Factors Shift
the Demand Curve
2. Expected Returns on bonds
? i ? in future, Re for longterm bonds ?
? Bd shifts out to right
OR
? pe ?, relative Re ?
? Bd shifts out to right
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429
How Factors Shift
the Demand Curve
and Expected Returns on other assets
? ER on other asset (stock) ?
? Re for longterm bonds ?
? Bd shifts out to left
These are closely tied to expected interest
rate and expected inflation from Table 4.2
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430
How Factors Shift
the Demand Curve
3. Risk
? Risk of bonds ?, Bd ?
? Bd shifts out to right
OR
? Risk of other assets ?, Bd ?
? Bd shifts out to right
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431
How Factors Shift
the Demand Curve
4. Liquidity
? Liquidity of bonds ?, Bd ?
? Bd shifts out to right
OR
? Liquidity of other assets ?, Bd ?
? Bd shifts out to right
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432
Shifts in the Demand Curve
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433
Summary of Shifts
in the Demand for Bonds
1. Wealth: in a business cycle expansion with
growing wealth, the demand for bonds rises,
conversely, in a recession, when income and
wealth are falling, the demand for bonds falls
2. Expected returns: higher expected interest
rates in the future decrease the demand for
longterm bonds, conversely, lower expected
interest rates in the future increase the demand
for longterm bonds
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434
Summary of Shifts
in the Demand for Bonds (2)
3. Risk: an increase in the riskiness of bonds
causes the demand for bonds to fall, conversely,
an increase in the riskiness of alternative assets
(like stocks) causes the demand for bonds
to rise
4. Liquidity: increased liquidity of the bond market
results in an increased demand for bonds,
conversely, increased liquidity of alternative
asset markets (like the stock market) lowers the
demand for bonds
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435
Factors That Shift Supply Curve
We now turn to
the supply curve.
We summarize
the effects in this
table:
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436
Shifts in the Supply Curve
1. Profitability of Investment Opportunities
? Business cycle expansion,
? investment opportunities ?, Bs ?,
? Bs shifts out to right
2. Expected Inflation
? pe ?, Bs ?
? Bs shifts out to right
3. Government Activities
?
?
Deficits ?, Bs ?
Bs shifts out to right
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437
Shifts in the Supply Curve
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438
Summary of Shifts
in the Supply of Bonds
1. Expected Profitability of Investment Opportunities: in
a business cycle expansion, the supply of bonds
increases, conversely, in a recession, when there are far
fewer expected profitable investment opportunities, the
supply of bonds falls
2. Expected Inflation: an increase in expected inflation
causes the supply of bonds to increase
3. Government Activities: higher government deficits
increase the supply of bonds, conversely, government
surpluses decrease the supply of bonds
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439
Case: Fisher Effect
Weve done the hard work. Now we turn to
some special cases. The first is the Fisher
Effect. Recall that rates are composed of
several components: a real rate, an inflation
premium, and various risk premiums.
What if there is only a change in expected
inflation?
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440
Changes in pe:
The Fisher Effect
If pe ?
1. Relative Re ?,
Bd shifts
in to left
2. Bs ?, Bs shifts
out to right
3. P ?, i ?
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441
Evidence on the Fisher Effect
in the United States
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442
Summary of the Fisher Effect
1. If expected inflation rises from 5% to 10%, the expected
return on bonds relative to real assets falls and, as a
result, the demand for bonds falls
2. The rise in expected inflation also means that the real
cost of borrowing has declined, causing the quantity of
bonds supplied to increase
3. When the demand for bonds falls and the quantity of
bonds supplied increases, the equilibrium bond
price falls
4. Since the bond price is negatively related to the interest
rate, this means that the interest rate will rise
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443
Case: Business Cycle
Expansion
Another good thing to examine is an
expansionary business cycle. Here, the
amount of goods and services for the country
is increasing, so national income is
increasing.
What is the expected effect on interest rates?
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444
Business Cycle Expansion
1.
Wealth ?, Bd ?,
Bd shifts out to
right
2.
Investment ?,
Bs ?, Bs shifts
right
3.
If Bs shifts
more than Bd
then P ?, i ?
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445
Evidence on Business Cycles
and Interest Rates
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446
Case: Low Japanese
Interest Rates
In November 1998, Japanese interest rates
on sixmonth Treasury bills turned slightly
negative. How can we explain that within the
framework discussed so far?
Its a little tricky, but we can do it!
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447
Case: Low Japanese
Interest Rates
1. Negative inflation lead to Bd ?
?Bd shifts out to right
2. Negative inflation lead to ? in real rates
?Bs shifts out to left
Net effect was an increase in bond prices
(falling interest rates).
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448
Case: Low Japanese
Interest Rates
3. Business cycle contraction lead to ? in
interest rates
? Bs shifts out to left
? Bd shifts out to left
But the shift in Bd is less significant than
the shift in Bs, so the net effect was also
an increase in bond prices.
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449
Case: WSJ Credit Markets
Everyday, the Wall Street Journal reports on
developments in the bond market in its
Credit Markets column.
Take a look at page 83 in your text. It
documents a surge in Treasury prices, noting
Euro Jitters as the root cause.
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450
Case: WSJ Credit Markets
What is this article telling us?
? Fear over debt problems in European
nations cause demand for Treasury
securities to rise. That follows what we
learned! Review Table 4.2. The perceived
riskiness of Treasury bonds fell relative to
Eurobonds.
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