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Key Concepts and Skills
Know the important bond features andbond types
Understand:
Bond values and why they fluctuate
Bond ratings and what they mean
The impact of inflation on interest rates
The term structure of interest rates andthe shape of the yield curve
determinants of bond yields
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Chapter Outline
6.1 Bonds and Bond Valuation
6.2 More on Bond Features
6.3 Bond Ratings6.4 Some Different Types of Bonds
6.5 Bond Markets
6.6 Inflation and Interest Rates6.7 Determinants of Bond Yields
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Bond Definitions
Bond
Debt contract
Normally a interest-only loan
Par value (face value) ~ $1,000 (repaid at end)
Coupon payment =(interest payment on bond)
Coupon rate =(annual coupon / face value) Maturity date =(time until face value repaid)
Yield to maturity= (market interest rate required on bond)
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Key Features of a Bond
Par value: Face amount
Re-paid at maturity
Assume $1,000 for corporate bonds
Coupon interest rate: Stated interest rate
Usually = YTM at issue YTM = Yield to Maturity
Multiply by par value to get coupon payment
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Bond Calculations
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Coupon Payment = Coupon Rate Par Value
Coupon Rate = Coupon Payment / Par Value
Par Value = Coupon Payment / Coupon Rate
CP = CR * PRV
CR =
PRV =
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Key Features of a Bond
Maturity:
Years until bond must be repaid
Yield to maturity (YTM):
The market required rate of return for bonds of
similarriskand maturity
The discount rate used to value a bond
Return if bond held to maturity
Usually = coupon rate at issue
Quoted as an APR
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Bond Value
Bond Value = PV(coupons) + PV(par)
Bond Value = PV(annuity) + PV(lump sum)
Remember:As interest rates increase present values
decrease ( r PV )
As interest rates increase, bond pricesdecrease and vice versa
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The Bond-Pricing Equation
t
t
YTM)(1
F
YTM
YTM)(1
1
1-CValueBond
PV(Annuity) PV(lump sum)
C = Coupon payment; F = Face value
Return
to Quiz
What is the relationship between bond prices and yields?
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Spreadsheet Formulas
=FV(Rate,Nper,Pmt,PV,0/1)
=PV(Rate,Nper,Pmt,FV,0/1)
=RATE(Nper,Pmt,PV,FV,0/1)
=NPER(Rate,Pmt,PV,FV,0/1)
=PMT(Rate,Nper,PV,FV,0/1)
Inside parens: (RATE,NPER,PMT,PV,FV,0/1) 0/1Ordinary annuity = 0 (default)
Annuity Due = 1 (must be entered)
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Pricing Specific Bonds in Excel=PRICE(Settlement,Maturity,Rate,Yld,Redemption,
Frequency,Basis)=YIELD(Settlement,Maturity,Rate,Pr,Redemption,
Frequency,Basis)
Settlement = actual date as a serial number; date
settled after security issued. Maturity = actual date as a serial number; maturity date
of bond.
Redemption and Pr(ice) = % of par value
Rate (coupon) and Yld = annual rates as decimals Frequency = # of coupons per year
Basis = day count convention (enter 2 for ACT/360)
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Basis: Type of day count basis to use.
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Bond Cash Flows
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What is the present value of the face (par) value?
What is the present value of the annual coupon payments?
What is the total bond value?
Using Excel: =PV(0.08, 10, 80, 0, 0) = 536.81
Using Excel: =PV(0.08, 10, 0, 1000, 0) = 463.19
TV = PV Par + PV Coupons = 463.19 + 536.81 = 1,000
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NOTE: Coupon Rate andMarket Rate are Equal
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The amount lost due to rising rates.
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The amount gained due to falling rates.
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Valuing a New Bond with AnnualCoupons Issued at Market
Coupon rate = 10% Annual coupons
Par = $1,000
Maturity = 5 years
YTM = 10%
5
5
101
1000
100
101
11
100
).(.
).(
B
Using the formula:B = PV(annuity) + PV(lump sum)
B = 379.08 + 620.92 = 1000
Using Excel: =PV(0.10, 5, 100, 1000, 0) = $1000
Note: When YTM = Coupon rate Price = Par Value
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Valuing a Discount Bond withAnnual Coupons
Coupon rate = 10% Annual coupons
Par = $1,000
Maturity = 5 years
YTM = 11%
5
5
)11.1(
1000
11.0
)11.1(
11
100B
Using the formula:B = PV(annuity) + PV(lump sum)
B = 369.59 + 593.45 = 963.04
Note: When YTM > Coupon rate Price < Par = Discount Bond
Using Excel: =PV(0.11, 5, 100, 1000, 0) = $963.04
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Valuing a Premium Bond withAnnual Coupons
Coupon rate = 10%
Annual coupons
Par = $1,000
Maturity = 20 years YTM = 8%
20
20
)08.1(
1000
08.0
)08.1(
11
100
B
Using the formula:B = PV(annuity) + PV(lump sum)
B = 981.81 + 214.55 = 1196.36
Note: When YTM < Coupon rate Price > Par = Premium Bond
Using Excel: =PV(0.08, 20, 100, 1000, 0) = $1,196.36
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Graphical Relationship Between Priceand Yield-to-maturity
600
700
800
900
1000
1100
1200
1300
1400
1500
0% 2% 4% 6% 8% 10% 12% 14%
Bond
Pr
ice
Yield-to-maturity
What is par value of the bond and what is the coupon rate?
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Bond Prices:Relationship Between Coupon and Yield
Coupon rate = YTM Price = Par
Coupon rate < YTM Price < Par
Discount bond Why? Because the bond pays less than the market rate of interest.
Coupon rate > YTM Price > Par
Premium bond Why? Because the bond pays more than the market rate of interest.
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M
Premium
1,000
Discount
30 25 20 15 10 5 0
CR>YTM
CR
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The Bond-Pricing EquationAdjusted for Semi-annualCoupons
2t
2t
YTM/2)(1
F
YTM/2
YTM/2)(1
1-1
2
CValueBond
C = Annual coupon payment C/2 = Semi-annual coupon
YTM = Annual YTM (as an APR) YTM/2 = Semi-annualYTM
t = Years to maturity 2t = Number of 6-monthperiods to maturity
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Semiannual BondsExample 6.1
Coupon rate = 14% - Semiannual
YTM = 16% (APR)
Maturity = 7 years Number of coupon payments? (t)
14 = 2 x 7 years
Semiannual coupon payment? (C)
$70 = (14% x Face Value)/2 Semiannual yield? (YTM)
8% = 16%/2
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Example 6.1
Semiannual coupon = $70
Semiannual YTM = 8%
Periods to maturity = 14
Bond value =
70[11/(1.08)14] / .08 +1000 / (1.08)14= 917.56
t
t
YTM)(1F
YTMYTM)(1
11-
CValueBond
14
14
)08.1(1000
08.0)08.1(
11
70
B
Using Excel: =PV(0.08, 14, 70, 1000, 0)
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Bond Prices: 3
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Using Excel: =PV(0.08, 9, 60, 1000, 0) = $875.06
Using Excel: =10*PRICE(settlement,maturity,0.06,0.08,100,1) = $875.06
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Bond Yields: 4
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Using Excel: =RATE(9,70,-1038.5,1000,0) = 6.42%
Using Excel: =YIELD(settlement,maturity,0.7,103.85,100,1) = 6.42%
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Coupon Rates: 5
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Using Excel: =PMT(0.075,12,-963,1000,0) = $70.22
7.022%.,
. 070220
0001
2270
PRV
CPCR
Using Excel: =RATE(12,70.22,-963,1000,0) = 7.50%
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Interest Rate Risk
Price Risk
Change in price due to changes in interestrates
Long-term bonds have more price risk thanshort-term bonds
Low coupon rate bonds have more pricerisk than high coupon rate bonds
Bonds with a higher coupon has a larger cash flow early in its life,
so its value is less sensitive to changes in the discount rate.
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Interest Rate Risk
Reinvestment Rate Risk Uncertainty concerning rates at which cash
flows coupons can be reinvested at same rate
Short-term bonds have more reinvestment raterisk than long-term bonds
High coupon rate bonds have morereinvestment rate risk than low coupon rate
bonds
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Figure 6.2
The longer the time to maturity, the greater
the interest rate risk; ceteris paribus. Smallchanges in interest rates can lead to largechanges in the bonds value.
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Computing Yield-to-Maturity YTM
Yield-to-maturity (YTM) = the marketrequired rate of return implied by thecurrent bond price
With a financial calculator or Excel,
Enter ,/,.and0
Remember the sign convention
/
and0
need to have the same sign (+)
.the opposite sign (-)
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YTM with Annual Coupons
Consider a bond with a 10% annualcoupon rate, 15 years to maturity and apar value of $1000. The current price is$928.09. Will the yield be more or less than 10%?
Using Excel: =RATE(15, 100, -928.09, 1000, 0) = 11% = YTM
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YTM with Semiannual Coupons
Suppose a bond with a 10% coupon rateand semiannual coupons, has a face value
of $1000, 20 years to maturity and is
selling for $1,197.93. Is the YTM more or less than 10%?
The bond is trading at a premium, YTM < CR
What is the semiannual coupon payment? CP = 10% * $1,000 = $100 / 2 = $50
How many periods are there?
T*2 = 20 * 2 = 40
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YTM with Semiannual Coupons
Suppose a bond with a 10% coupon rate andsemiannual coupons, has a face value of $1,000,20 years to maturity and is selling for $1,197.93.
NOTE: Solving a semi-annual payer
for YTM results in a 6-month YTM.
Excel will solve what you enter.
Using Excel: =RATE(40, 50, -1197.93, 1000, 0) = 4%4% or YTM * 2 = 8% YTM
Using Excel: =RATE(40, 50, -1197.93, 1000, 0)*2 = 8%
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Table 6.1
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Debt versus Equity
Debt Notan ownership interest No voting rights
Interest is tax-deductible(issuer, sometimes by holder)
Creditors have legal recourseif interest or principalpayments are missed
Debt can result in higherreturns to the firm (taxbenefits to debt), but
Excess debt can lead tofinancial distress andbankruptcy
Equity Ownership interest
Common stockholdersvote to elect the board ofdirectors and on otherissues
Dividends are not taxdeductible (by firm orstockholder)
Dividends are not aliability of the firm untildeclared. Stockholders
have no legal recourse ifdividends are not declared
Equity holders are paidafter debt holders, but notrequired
An all-equity firm cannotgo bankrupt
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The Bond IndentureDeed of Trust
Contract between issuing company andbondholders includes:
Basic terms of the bonds
Total amount of bonds issued Secured versus Unsecured
Sinking fund provisions
Call provisions Deferred call
Call premium
Details of protective covenantsReturn
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Bond Classifications
Registered vs. Bearer Bonds Registered: company records ownership, payments made to
and information sent to owner.
Bearer: Issued without record of owner name, payments madeto holder after receipt of detachable coupon. May be difficult torecover if lost or stolen, bondholders cannot be notified ofimportant event.
Security Collateral: secured by financial securities (bonds and stocks)
Mortgage: secured by real property, normally land or buildings
Debentures: unsecured
Notes: unsecured debt with original maturity less than 10 years
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Bond Classifications
Seniority Senior versus Junior, Subordinated
Debt cannot be subordinated to equity.
Repayment Can be repaid at maturity, or sinking fund
established to retire or repurchase bonds
Call Provision
Repurchase or call part or all of bond issueat a specific price prior to maturity, usually ata premium, the call may be deferred and thebondholder protected during the prohibition
period.
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Bond Classifications
Protective Covenants Indenture provision that limit certain actions
that might be taken during the term of theloan, usually to protect the lender.
Negative Covenants: Thou Shalt Not Limit amount of dividends to prescribed formula
No pledging of any assets to other lenders
No merger with another firm
No issuance of additional long-term debt Positive Covenants: Thou Shalt
Maintain working capital at or above a certain level
Furnish financial statements to lender
Maintain collateral in good condition
B d Ch t i ti d
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Bond Characteristics andRequired Returns
Coupon rate
(risk characteristics of the bond when issued)
Usually yield at issue
Which bonds will have the higher coupon,all else equal? Secured debt versus a debenture
Subordinated debenture versus senior debtA bond with a sinking fund versus one without
Sinking funds can retire a portion of the debt or call some bonds
A callable bond versus a non-callable bond
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Bond Ratings
Bond ratings are concerned onlywith thepossibility of default.
Bond ratings do not address interest rate risk,
the risk of a change in the value (i.e. price) of abond resulting from a change in interest rates.
The price of a highly rated bond can still be quitevolatile given interest rate risk.
Return
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Investment-grade bonds are bonds rated at least BBB by S&P or Baa byMoodys.
A bonds credit rating can change as the issuers financial strength improves
or deteriorates. Credit ratings are important because defaults really do occur, and if they do,
investors can lose heavily.
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Bond RatingsInvestment Quality
High Grade MoodysAaa and S&P AAAcapacity to pay is
extremely strong
MoodysAa and S&P AAcapacity to pay is verystrong
Medium Grade
Moodys A and S&P A capacity to pay is strong,
but more susceptible to changes in circumstances Moodys Baa and S&P BBB capacity to pay is
adequate, adverse conditions will have moreimpact on the firms ability to pay
Return
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Bond Ratings - Speculative
Low Grade Moodys Ba, B, Caa and Ca
S&P BB, B, CCC, CC
Considered speculative with respect to capacityto pay. The B ratings are the lowest degree
of speculation.
Very Low Grade
Moodys C and S&P C income bonds with nointerest being paid
Moodys D and S&P D in default withprincipal and interest in arrears
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Government Bonds
Treasury Securities = Federal government debt Treasury Bills (T-bills)
Pure discount bonds
Original maturity of one year or less
Treasury notes Coupon debt
Original maturity between one and ten years
Treasury bonds Coupon debt Original maturity greaterthan ten years
Exempt from state but not federal taxation.
G t B d
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Government Bonds
Municipal Securities Debt of state and local governments
Varying degrees of default risk, rated similar to
corporate debt Interest received is tax-exempt at the federal
level
Interest usually exempt from state tax in
issuing state
Yields usually lower than treasury or corporatebonds since advantage of not being taxed.
Example 6 4
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Example 6.4
A taxable bond has a yield of 8% and a
municipal bond has a yield of 6% If you are in a 40% tax bracket, which bond do you prefer?
What is the after tax return on a taxable bond?
8%(1 - .4) = 4.8%
The after-tax return on the corporate bond is 4.8%, compared to a 6%return on the municipal
At what tax rate would you be indifferent between the twobonds?
8%(1T) = 6%
T = 25%
At what municipal yield would you be indifferent to a taxablebond?
8%(1-0.40)=M
M=4.8
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Zero Coupon Bonds
Make no periodic interest payments (coupon rate = 0%)
Entire yield-to-maturity comes from the differencebetween the purchase price and the par value (capital
gains) Cannot sell for more than par value
Sometimes called zeroes, or deep discount bonds
Treasury Bills and U.S. Savings bonds are goodexamples of zeroes
Z C B d I t t
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Zero Coupon Bond Interest
EIN Company issues a $1,000 face value, five-year zero
coupon bond. What should the bond sell for at issue, assuminga 14 percent yield to maturity using semiannual periods?
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Using Excel: =PV(0.07, 10, 0, 1000, 0) = $508.35
What is the amount of interest paid over the life of the bond?
$1000 - $508.35 = $491.65
What is the annual interest deduction calculated on a
straight-line basis?
$491.65 / 5 = $98.33
NOTE: The issuer of a zero must deduct interest every year even though no interest is actually paid. Also,the owner must pay taxes on interest accrued every year even though no interest is received. Current tax
law requires interest to be determined by amortizing the loan as opposed to straight line.
Z C I li it B d I t t
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Zero Coupon Implicit Bond Interest
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Floating Rate Bonds
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Floating Rate Bonds
Coupon rate floats depending on some indexvalue
Examplesadjustable rate mortgages andinflation-linked Treasuries (TIPS)
Less price risk with floating rate bonds Coupon floats, so is less likely to differ
substantially from the yield-to-maturity
Coupons may have a collar the ratecannot go above a specified ceiling orbelow a specified floor
Other Bond Types
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Other Bond Types
Income bonds Coupon dependent on company income
Convertible bonds Convertible to shares of stock
Put bonds Holder forces issues to buy back at stated price, the
reverse of a call provision
Many types of provisions can be added to a bond Important to recognize how these provisions affect
required returns
Who does the provision benefit?
B d M k
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Bond Markets
Primarily over-the-counter transactions withdealers connected electronically
Extremely large number of bond issues(compared to equity), but generally low daily
volume in single issues and little transparency Getting up-to-date prices difficult, particularly
on small company or municipal issues
Treasury securities are an exception What is the largest securities market in the
world?
U.S. Treasury Market not the NYSE.
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Work the Web Example
Bond information is available online One good site:
http://cxa.marketwatch.com/finra/BondCenter
Click on the web surfer to go to the site Use Quick Bond Search to observe the
yields for various bond types, and theshape of the yield curve.
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Bond Yields: 7
2-61
Using Excel: =RATE(26, 34.50, -940, 1000, 0) = 3.82%
3.82% or YTM * 2 = 7.64% YTMUsing Excel: =2*RATE(21, 34.50, -945, 1000, 0) = 7.64%
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Coupon Rates: 8
2-62
Using Excel: =PMT(0.042, 21, -945, 1000, 0) = $38.01
$38.01*2 = $76.02; $76.02 / $1,000 = 7.60%
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Bond Yields: 19
2-63
Using Excel: =2*RATE(40, 39, -1125, 1000, 0) = 6.66%
Treasury Quotations
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Treasury Quotations
Treasury Quotations
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Treasury Quotations Highlighted quote in Figure 6.3
5/15/2030 6.250 150.7188 150.7500 .8906 2.713
When does the bond mature?
What is the coupon rate on the bond?
What is the bid price? What does this mean?
May 15, 2030
6.25% per year on semiannual basis, $62.50/2 = $31.25 on a $1,000face value bond
Bidamount dealer offers to buy from you, 150.7188% (i.e.,1.507188) of the par or face value, therefore the bid is $1,570.188 =(1, 000 * 1.507188)
Treasury Quotations
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Treasury Quotations Highlighted quote in Figure 6.3
5/15/2030 6.250 150.7188 150.7500 .8906 2.713
What is the ask price? What does this mean?
How much did the price change from the previous day?
What is the YTM based on Ask price and why?
Askamount dealer is willing to sell to you, 150.7500% of the par orface value (i.e., 1.507500), therefore the ask is = $1,507.50 = ($1,000* 1.507500)
Asked price up by 0.890% from the previous day
Asked yield is 2.713%, lower than coupon rate since this is a premium
bond and sells for more than the face value.
Treasury Quotations
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Treasury Quotations Highlighted quote in Figure 6.3
5/15/2030 6.250 150.7188 150.7500 .8906 2.713
What is bid-ask spread, what does this represent?AskBid = $1,507.500 - $1,507.188 - = $0.312 and represents thedealers profit.
Q t d P i I i P i
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Quoted Price vs. Invoice Price
Quoted bond prices = clean price
Net of accrued interest
Invoice Price = dirty or full price
Price actually paid
Includes accrued interest
Accrued Interest
Interest earned since last coupon payment isowed to bond seller at time of sale
The Bellwether Bond
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The very lastbond, usuallyquoted on theevening news as
to the direction oflong-term interestrates. If bondyield went up(down), bondprice went down(up). This isknown as thebellwether bond.
I fl ti d I t t R t
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Inflation and Interest Rates
Real rate of interest=Change in purchasing power
Nominal rate of interest
= Quoted rate of interest,= Change in purchasing power and inflation
The ex ante nominal rate of interest
includes our desired real rate of returnplus an adjustment for expected inflation
The Fisher Effect
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The Fisher EffectThe Fisher Effect defines the relationship between real rates, nominal rates
and inflation
(1 + R) = (1 + r)(1 + h)
R= nominal rate (Quoted rate)
r= real rate
h= expectedinflation rate
R = r + h + rh= real + inflation + compounding
Approximation: R = r + h
only if r or h not high Return
to Quiz
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The Fisher Effect
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The Fisher EffectThe Fisher Effect defines the relationship between real rates, nominal rates
and inflation
(1 + R) = (1 + r)(1 + h)
R= nominal rate (Quoted rate)
r= real rate
h= expectedinflation rate
Return
to Quiz
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The Fisher EffectThe Fisher Effect defines the relationship between real rates, nominal rates
and inflation
(1 + R) = (1 + r)(1 + h)
R= nominal rate (Quoted rate)
r= real rate
h= expectedinflation rate
Return
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Calculating The Fisher Effect
If the nominal interest rate is 15.50% and theinflation rate is 5%, what is the real rate?
(1 + R) = (1 + r)(1 + h)
(1 + 0.1550) = (1+ r)(1 + 0.05)
(1 + r) = 1.1550 / 1.05 = 1.10
r = 1.101 = 0.10 or 10%
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Example 6.6
If we require a 10% real return and weexpect inflation to be 8%, what is the
nominal rate?
R = (1.1)(1.08)1 = .188 = 18.8%
Approximation: R = 10% + 8% = 18%
Because the real return and expected inflation are
relatively high, there is significant difference between
the actual Fisher Effect and the approximation.
C l l ti R l R t f R t 9
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Calculating Real Rates of Return: 9
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Inflation and Nominal Returns: 10
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Nominal and Real Returns: 11
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Term Structure of Interest Rates
Term structure: The relationship betweentime to maturity and yields, all else equal(Ceteris Paribus):
The effect of default risk, different coupons,etc. has been removed.
Shape of term structure determined by:
Real Rate of Interest
Inflation Premium Interest Rate Risk Premium
Increases with maturity length
Returnto Quiz
Term Structure of Interest Rates
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Term Structure of Interest Rates
Yield cu rve: Graphical representation ofthe term structure
Normal = upward-sloping L/T > S/T
Inverted = downward-sloping L/T < S/T
Returnto Quiz
Figure 6.5 A Upward-Sloping
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Figure 6.5 A Upward SlopingYield Curve
RISING
CONSTANT
RISING
Inflation Premium higher in long than short run.
Figure 6.5 B Downward-
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Figure 6.5 B DownwardSloping Yield Curve
FALLING
CONSTANT
RISING
Inflation Premium higher in short than long run.
Figure 6 6 Treasury Yield Curve
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Figure 6.6Treasury Yield Curve
Based on datain Figure 6.3
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Factors Affecting Required Return
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Factors Affecting Required Return
Default risk premiumbond ratings
Taxability premiummunicipal versus taxable
Liquidity premiumbonds that have more
frequent trading will generally have lowerrequired returns
Maturity premiumlonger term bonds will tendto have higher required returns.
Anything else that affects the r isk o f the cash f lows to
the bondho lders w i l l affect the required returns
Returnto Quiz
Interest Rate Risk: 17
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Interest Rate Risk: 17
2-86
Using Excel: =PV(0.04, 20, 20, 1000, 0) = $728.19
Using Excel: =PV(0.05, 20, 20, 1000, 0) = $626.13
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Quick Quiz
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Quick Quiz How do you find the value of a bond and why
do bond prices change? (Slide 6.8) What is a bond indenture and what are someof the important features? (Slide 6.30)
What are bond ratings and why are they
important?(Slide 6.33)
How does inflation affect interest rates?(Slide 6.48)
What is the term structure of interest rates?(Slide 6.50)
What factors determine the required return onbonds? (Slide 6.54)
E d f Ch t Q ti t R i
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End of Chapter Questions to Review
Question Topic
1 Interpreting Bond Yields
2 Interpreting Bond Yields
3 Bond Prices
4 Bond Yields5 Coupon Rates
6 Bond Prices
7 Bond Yields
8 Coupon Rates
9 Calculating Real Rates of Return
10 Inflation and Nominal Returns
11 Nominal and Real Returns
5-88
E d f Ch t Q ti t R i
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End of Chapter Questions to Review
Question Topic
12 Nominal versus Real Returns
13 Using Treasury Quotes
17 Interest Rate Risk
18 Bond Yields19 Bond Yields
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Chapter 6
END
Previous Treasury Quotations
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y Highlighted quote in Figure 6.3
2020 Feb 15 8.5 145.12 145.15 +64 3.4730
When does the bond mature?
What is the coupon rate on the bond?
What is the bid price? What does this mean?
February 15, 2020
8.5% per year on semiannual basis, $85/2 = $42.50 on a $1,000 facevalue bond
Bidamount dealer offers to buy from you, quoted in 32nds, 145 and12/32 % of par = 145.375% (i.e., 1.45375) of the face value, thereforethe bid is $1,453.75 = (1, 000 * 1.45375)
Treasury prices werepreviously quoted in
32nds.
Previous Treasury Quotations
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y Highlighted quote in Figure 6.3
2020 Feb 15 8.5 145.12 145.15 +64 3.4730
What is the ask price? What does this mean?
How much did the price change from the previous day?
What is the YTM based on Ask price and why?
Askamount dealer is willing to sell to you, quoted in 32nds, 145 and15/32 % of par cent = 145.46875 % (i.e., 1.4546875) of the facevalue, therefore the ask is = $1,454.69 = ($1,000 * 1.4546875)
+64/32 of 1 percent or 2 percent; a tick size = 1/32
Asked yield is 3.4730%, lower than coupon rate since this is apremium bond and sells for more than the face value.
Treasury prices were previouslyquoted in 32nds.
Previous Treasury Quotations
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y Highlighted quote in Figure 6.3
2020 Feb 15 8.5 145.12 145.15 +64 3.4730
What is bid-ask spread, what does this represent?AskBid = $1,454.69 - 1,453.75 - = $0.94 and represents thedealers profit.
Treasury prices were previouslyquoted in 32nds.