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Unformatted text preview: Lecture 3 Understanding
Interest Rates Present Value Four Types of Credit Instruments
1 . Simple loan 2. Fixedpayment loan 3.Coupon bond 4. Discount (zero coupon) bond Concept of Present Value Simple loan of $1 at 10% interest Year 1 2 3 n
$1.10 $1.21 $1.33 $1x(1 +1)" PV of future $1 = Yield to Maturity: Loans Yield to maturity = interest rate that equates today’s
value with present value of all future payments 1. Simple Loan (1': 10%)
$100 = $110/(1 +1):>
_$110—$100 $10 =—= 0.10 = 10%
$100 $100 2. Fixed Payment Loan (i = 12%) $126 $126 $126
$1000 = + + + +
(1+1) (1+1)2 (1+i)3 PP PP FP FP
+ + + + (1+0 (1+1? (1+03 1' Yield to Maturity: Bonds 3. Coupon Bond (Coupon rate = 10% = OF) P: $100 + $100 + $100 + + $100 +$1000 (1+?) (1+1? (H03 0+0") 0+0” C C C C F
+ + + + + (1+0 (1+02 (1+5? UH)" (1+I')” Consol: Fixed coupon payments of SC forever C P
4. Discount Bond (P = $900, F = $1000), one year _ $1000
$900— “+0 3 51000—0900
'= ————— =.111=11.10
‘ $900 0 /° j: Relationship Between Price
and Yield to Maturity Table 1 Yields to Maturity an a 1 liii—CaupmtRate Bond Maturing in Ten
Years (Face Value : $1,000) Price of Bond ($) Yield to Maturity {96)
1,200 7.13
1,100 8.48
1,000 10.00
900 l 1.75
800 13.8} V'Three interacting Facts In Table} _ __ _ 11.‘ . When bond is at par, yield equate coupon rate _ '2. ' Price and yield are negatively related _ _ _ _  _ _
23. Yield greater than coupon rate When bend price is below par value Current Yield Two Characteristics I. Is better approximation to yield to maturity, nearer price is to par and longer is maturity
of bond 2. Change in current yield always signals change in same direction as yield to maturity Yield on a Discount Basis I (F— P) 360
= x —........._._
Idb F (number of days to maturity) One year bill, P = $900, F= $1000 $1000 — $900 360
idb = — x = 0.099 = 9.9%
$1000 365
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 Bond Page
of the
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Rates and Returns = current yield = capital gain Rate of Return C+Pt+1—Pt RET= Key Facts about Relationship
Between Interest Rates and Returns Table 2 OneYear Returns on Diﬁerentvlt'iaturity leisCouponRate
Semis When Interest Rates Rise from 16% to 20% (1)
Years to (2} (5)
Maturity Initial ' Rate of
When Current Captiai
Bond Is Yield ' Gain
Purchased (‘36) (96) to ~49}
it} —48_4
to —40.3
10 —25.9
to ~83
in 0.0 'Cslculnled using Equation 3. Maturity and the Volatility
of Bond Returns Key Findings from Table 2
. Only bond whose return = yield is one with maturity = holding period
. For bonds with maturity > holding period, iT Pi implying capital loss . Longer is maturity, greater is % price change associated with
interest rate change . Longer is maturity, more return changes with change in interest rate
. Bond with high initial interest rate can still have negative return if i T Conclusion from Table 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
penod and Nominal Interest Rates
Real Interest Rate Interest rate that is adjusted for expected changes in the
price level i,=i—Ic9 1. Real interest rate more accurately reflects true cost of
borrowing ‘ 2. When real rate is low, greater incentives to borrow and
less to lend if i = 5% and 1:9 = 3% then:
i, = 5% — 3% = 2% if i = 8% and at” = 10% then
i,= 8% — 10% = —2% US. Real and Nominal Interest
Rates interest Rate (as)
13 1965 1970 1975 1980 1985 1990 1995 2000 Determinants of Asset Demand  S‘i‘mfmﬂh'fi Tabie 1 Response of the Quantity of an Asset ﬂenlanded to Changes in Wealth.
Expected Returns, Risk. and Liquidity Change in
Variable Change in Variable Quantity Demanded V‘L’wllh Expected return relative to other assets
Risk relative to other was [.iquidiLy relative to other (ISSCIS MW: Only incrmscs in Ihc rariahlrs an‘ shown Tha' «ﬂan ofdccruscs in [he mnabks on the change in demand would be 1hr opposite
{II (host: indicated in {IN Iighlmusl calunm, Derivation of Bond Demand Curve i=RET° =(F—;P) Point A:
P = $950 I. é$1000  $950) = 0.053 = . 0
$950 5 3" B" = $100 billion Derivation of Bond Demand Curve
Point B: P = $900 .=($1000 — $900) : : 0
I $900 0.111 11.1/0 Bd = $200 billion Point c: P = $850, i= 17.6% Bd = $300 billion
Point D: P = $800, i= 25.0% 8" = $400 billion
Point E: P = $750, i= 33.0% 8" = $500 billion Demand Curve is Ed in Figure 1 which connects points Derivation of Bond Supply Curve
Point F:P = $750, i= 33.0%, BS = $100 billion
Point G: P = $800, i= 25.0%, 18S = $200 billion
Point c: P = $850, i= 17.6%, BS = $300 billion
Point H: P = $900, i= 11.1%, 83 = $400 billion
Point I: P = $950, i= 5.3%, B8 = $500 billion Supply Curve is 85 that connects points F, G, C, H, i,
and has upward slope PﬁoaoledetS) Intaresi Rala.i(%)
Demand (Plncteaaes‘n (Jlncmaseal) Analysis of I ' ‘
the Bond
Market  Market Equilibrium ' . I ' :
:..10ccurs'when 3‘ = 3’, at 3* =1 _  $850.1" =_17.6°_/o  _ '2. “gm P'= $950; r'"= 5.3%. B.’ 2
B {excess supply): P Jr to P‘, i
1m [6 ' . . . I 3. WhenP= $150, i= 330,33 ' B’ (Excessdsmand): PI tel”,
u to .2 . :  . ___..'...... 200300400500 Quantity 01 Bonds, 5
(t billions) Loanable Funds Terminology Interase Rate. use) Demand to: Bonds. 3"
(Ilnuroases‘n (Supply of Loanable Funds. If) 33.0 1. Demand for.bo_nds
21=supplyof' .
3j_'lo'anableifunds j ' '  '= s IfBond.B"
' : Of_  _ (DemangpfgrngamblesFunds, 1.")
demand. for  loanable'funds ' “309400500800 Quantity of Bonds. 5
(Loanabia Funds. L)
(s billions) Shifts in the Bond Demand Curve Price at Bonds, P interest Rate. i‘ (VG)
(P lncreasesT) (i increases“ 1.000 0.0
950 5.3 900 100 200 300 400 500 600 Quantity 0! Bonds, 8
(s biliions) Demand Curve 1. Wealth
A. Economy grows, wealth T, B” T, Bti shifts out to right 2. Expected Return
A. ii in future, R9 for longterm bonds T, 3" shifts out to right
B. n9 i, Relative R9 T, B" shifts out to right C. Expected return of other assests T, B‘i T, Bd shifts out to
right
3. Risk
A. Risk of bonds i, B“ T, Bd shifts out to right B. Risk of other assets T. Bd T, B“ shifts out to right
4. Liquidity
A. Liquidity of Bonds T, B” T, B“ shifts out to right
B. Liquidity of other assets i, B” T, 3d shifts out to right 10 1:1th 2 Human Thin! Slt‘tlt. thr: Demand Cuer tar Bumls Change. in
change in Quantity stun In 
Vlrlablc Demlndrd Dun11d. Curv: 1T.“ Facﬁors
that Shift Demand
Curve for Expected innnuou Bonds mm” Hisktnrss of hands f
rclatlv: m mhcr asst.15 "mun" D Liquidity ul'bnnds .'
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13¢ m: (“we plum Indian9d m m ramming ueinmue. Shifts in the Bond Supply Curve rmmtab'"? °f'  Price of Bonds. P (5) Interest Rate. my.)
. “V95 m9"  (Plncraases‘r) (1' Increases 1,)
Opportunities mm 0.0 _ j_ Business cycle
I‘e'xpanslon'. '
j'._inve_Stmant ._ ..jopportuni_tles ' ff, 53311.33 900
j} _sh1ﬁs out to I . 3*ﬁght ' 1: = 350 _2. Expected2' ji _ Inflation _ _ ;. Boo
.ﬁtmtmr
j .shlﬁs outta ;' 3._ Government '  A i ' 
Guy" as 100 200 300 400 500 600 700 " 'jDeﬁ'citsT, as .
  T. B“ shifts out Quanttustiggrids, B toright'_. . .j 950 750 lianlms Timl Shift lhl: Supply uf Balms S h Chm in 3:31: . Shlﬂ in anlahlu I Variable Supplled Supply Curve
supply T T
Curve for Bonds Expeued inflation . Gm'lmmcm deﬁcit Mir: Fatd Elmman :noﬁma'xr llama1m Pun Ihc 2d: wrlrdaw annexes aswa p1 “print was While Ion the ng'hl Wkll axis In. um
nswr go down the “Elm, laxmam Ihl‘ rumblrs am slum 11w mm m rimma; in da urablﬁou Hm ﬂungc m wp‘ﬂy laugh!
in 1h: uppmil: nfllwstmdxllul \n Ihrnnmmng Doll:an Chanes in 7:9: the Fisher Effect Price a! Bonds, P Interest Rate. I
(P increases T) (i increases l) we? . _
1. Relative
' RETB ~L, Bushifts ; in to left . BST,BS
jj shiftsout
' I to right .' 'P Jail: I Quanllly of Bonds. 8 12 Evidence on the Fisher Effect
in the United States Annual Rate (5%)
 20 Expeoled inﬂation Interest Rate i980 1965 1970 1975 1980 1985 1990 1995 2WD Business Cycle Expansion Price 0! Bonds. P Interest Flats, i
(P increases T) (I Increases.” 1. Wealth .T. ad
'':T'..B”'shiﬁs.
 'o_'utto right 2.Investm_ent 1‘, 
.: 83.1" B; .. .
 _. snifts outta right _ 3 . If B3 shifts _
more than. a BathenPL
_. .m. .. Quantity 0! Bonds. 8 13 Evidence on Business Cycles
and Interest Rates Interest Rate (‘18)
18 1B 14 Interest Rate

\ 1975 1980 i985 1990 1995 2000 Does
Higher
Money
Growth Lower
Interest
Rates? 14 Evidence on Money Growth
and Interest Rates Money
Growth Rate
($3 annual rate] 14 12 1950 1955 1960 1965 1970 1975 1960 19m 1995 2000 15 ...
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This note was uploaded on 02/29/2012 for the course ECONOMICS EC 3332 taught by Professor Shandre during the Spring '12 term at National University of Singapore.
 Spring '12
 Shandre

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