340 chapter 4
TRANSCRIPT
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Chapter 4. UnderstandingChapter 4. Understanding
Interest RatesInterest Rates Present ValuePresent Value
Yield to MaturityYield to Maturity
Other YieldsOther Yields Other Measurement IssuesOther Measurement Issues
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I. Measuring Interest RatesI. Measuring Interest Rates
A. Credit Market InstrumentsA. Credit Market Instruments
simple loansimple loan
borrower pays back loan and interest inborrower pays back loan and interest inone lump sumone lump sum
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fixedfixed--payment loanpayment loan
loan is repaid with equal (monthly)loan is repaid with equal (monthly)paymentspayments
each payment is combination ofeach payment is combination of
principal and interestprincipal and interest
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coupon bondcoupon bond
purchase price (P)purchase price (P)
interest payments (6 months)interest payments (6 months)
face value at maturity (F)face value at maturity (F)
size of interest paymentssize of interest payments
---- coupon ratecoupon rate
---- face valueface value
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discount bonddiscount bond
zero coupon bondzero coupon bond
purchased price less than face valuepurchased price less than face value
---- F > PF > P
face value at maturityface value at maturity no interest paymentsno interest payments
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B. Present & Future ValueB. Present & Future Value
time value ofmoneytime value ofmoney
$100 today vs. $100 in 1 year$100 today vs. $100 in 1 year
not indifferent!not indifferent! money earns interest over time,money earns interest over time,
and we prefer consuming todayand we prefer consuming today
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example: future valueexample: future value
$100 today$100 today
interest rate 5% annuallyinterest rate 5% annually
at end of 1 year:at end of 1 year:100 + (100 x .05)100 + (100 x .05)
= 100(1.05) = $105= 100(1.05) = $105
at end of 2 years:at end of 2 years:100 + (1.05)100 + (1.05)22 = $110.25= $110.25
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future valuefuture value
of$100 inof$100 in nn years if interest rate isyears if interest rate is ii::
= $100(1 + i)= $100(1 + i)nn
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present valuepresent value
work backwardswork backwards
if get $100 inif get $100 in nn years,years,
what is that worth today?what is that worth today?
PV =$100
(1+ i)n
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exampleexample
receive $100 in 3 yearsreceive $100 in 3 years
i = 5%i = 5%
what is PV?what is PV?
PV =$100
(1+ .05)3
= $86.36
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n
i
PV
PV
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C. Yield to Maturity (YTM)C. Yield to Maturity (YTM)
a measure of interest ratea measure of interest rate
interest rate whereinterest rate where
P = PV of cash flows
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example 1: simple loanexample 1: simple loan
loan = $1500, 1 year, 6%loan = $1500, 1 year, 6%
future paymentfuture payment
= $1500(1+.06) = $1590= $1500(1+.06) = $1590 yield to maturity, iyield to maturity, i
$1500 =$1590
(1+ i)i = 6%
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example 2: fixed pmt. loanexample 2: fixed pmt. loan
$15,000 car loan, 5 years$15,000 car loan, 5 years
monthly pmt. = $300monthly pmt. = $300
so $15,000 is price todayso $15,000 is price today cash flow is 60 pmts. of $300cash flow is 60 pmts. of $300
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YTM solvesYTM solves
i/12 is monthly discount ratei/12 is monthly discount rate
i is yield to maturityi is yield to maturity
i/12 is monthly discount ratei/12 is monthly discount rate
i is yield to maturityi is yield to maturity
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how to solve for i?how to solve for i?
trialtrial--andand--errorerror
bond table*bond table*
financial calculatorfinancial calculator
spreadsheetspreadsheet
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payment between $297.02 &payment between $297.02 &
$300.57$300.57 YTM is between 7% and 7.5%YTM is between 7% and 7.5%
(7.42%)(7.42%)
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Example 3: Coupon BondExample 3: Coupon Bond
2 year T2 year T--Note, F = $10,000Note, F = $10,000
coupon rate 6%coupon rate 6%
price of $9750price of $9750 what are interest payments?what are interest payments?
(.06)($10,000)(.5) = $300(.06)($10,000)(.5) = $300
every 6 mos.every 6 mos.
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YTM solves the equationYTM solves the equation
i/2 is 6i/2 is 6--month discount ratemonth discount rate
i is yield to maturityi is yield to maturity
i/2 is 6i/2 is 6--month discount ratemonth discount rate
i is yield to maturityi is yield to maturity
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price between $9816 & $9726price between $9816 & $9726
YTM is between 7% and 7.5%YTM is between 7% and 7.5%(7.37%)(7.37%)
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P, F and YTMP, F and YTM
P = F then YTM = coupon rateP = F then YTM = coupon rate
P < F then YTM > coupon rateP < F then YTM > coupon rate
bond sells at a discountbond sells at a discount P > F then YTM < coupon rateP > F then YTM < coupon rate
bond sells at a premiumbond sells at a premium
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P and YTM move in oppositeP and YTM move in opposite
directionsdirections interest rates and value of debtinterest rates and value of debt
securities move in oppositesecurities move in opposite
directionsdirections if rates rise, bond prices fallif rates rise, bond prices fall
if rates fall, bond prices riseif rates fall, bond prices rise
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example 4: discount bondexample 4: discount bond
90 day Tbill,90 day Tbill,
P = $9850, F = $10,000P = $9850, F = $10,000
YTM solvesYTM solves
!
365901
000109850
i
,$$
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9850
00010
365
901
$
,$i !
19850
00010
365
90!
$
,$i
9850985000010
36590
$,$i
!
90365
9850985000010 v
! $,$i = 6.18%
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in general,in general,
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D. Current YieldD. Current Yield
approximation of YTM for couponapproximation of YTM for couponbondsbonds
ic =annual coupon payment
bond price
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better approximation whenbetter approximation when
maturity is longermaturity is longer
P is close to FP is close to F
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example 5example 5
2 year Tnotes, F = $10,0002 year Tnotes, F = $10,000
P = $9750, coupon rate = 6%P = $9750, coupon rate = 6%
current yieldcurrent yield
ic =600
9750= 6.15%
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current yield = 6.15%current yield = 6.15%
true YTM = 7.37%true YTM = 7.37% lousy approximationlousy approximation
only 2 years to maturityonly 2 years to maturity
selling 25% below Fselling 25% below F
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E. Discount YieldE. Discount Yield
yield on a discount basisyield on a discount basis
approximation of YTMapproximation of YTM
idb =F - P
Fx
360
d
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compare w/ YTMcompare w/ YTM
idb =F - P
Fx
360
d
iytm =F - P
Px
365
d
iytm > idb
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example 6:example 6:
9090--day Tday T--bill, price $9850bill, price $9850
idb = 10,000 - 985010,000
x 36090
= 6%true YTM is 6.18%
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II. Other measurement issuesII. Other measurement issues
A. Interest rates vs. returnA. Interest rates vs. return
YTM assumes bond is held untilYTM assumes bond is held until
maturitymaturity if not, resale price is importantif not, resale price is important
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B. Maturity & bond priceB. Maturity & bond price
volatilityvolatility
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YTM rises from 6 to 8%YTM rises from 6 to 8%
bond prices fallbond prices fall but 10but 10--year bond price falls the mostyear bond price falls the most
Prices are more volatile for longerPrices are more volatile for longer
maturitiesmaturities longlong--term bonds have greater interestterm bonds have greater interest
rate riskrate risk
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Why?Why?
longlong--term bonds lock in a coupon rateterm bonds lock in a coupon ratefor a longer timefor a longer time
if interest rates riseif interest rates rise
---- stuck with a belowstuck with a below--market couponmarket coupon
raterate
if interest rates fallif interest rates fall
---- receiving an abovereceiving an above--market couponmarket coupon
raterate
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C. Real vs. Nominal InterestC. Real vs. Nominal Interest
RatesRates Thus far we have calculated nominalThus far we have calculated nominal
interest ratesinterest rates
ignores effects of rising inflationignores effects of rising inflation
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Real Interest Rate, iReal Interest Rate, irr
nominal interest rate = inominal interest rate = i
expected inflation rate =expected inflation rate = ee
approximately:approximately:i = ii = irr ++
ee
The Fisher equationThe Fisher equation
oror iirr= i= i -- ee
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real interest rates measure true cost ofreal interest rates measure true cost of
borrowingborrowing
why?why?
as inflation rises, real value of loanas inflation rises, real value of loan
payments falls,payments falls, so real cost of borrowing fallsso real cost of borrowing falls
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