Lecture 3_EC3332[1] - Lecture 3 Understanding Interest...

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Unformatted text preview: Lecture 3 Understanding Interest Rates Present Value Four Types of Credit Instruments 1 . Simple loan 2. Fixed-payment 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—Caupmt-Rate 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 Newspaper nun-v lam. mu m SILL. JINIWZLEI‘JDJ Mamie auwwmuwmmdn “Mormon hm,” m. mum”. M “MW cm mmmqan-NMWWSM' 9111“! m‘fll VD. m1 wan;mmnwmwmu .y. mm: mllnflmai.flwflmwmfllfl=cflu Jl‘. Milo symm m Hun-ml“ mm mun mummy-.1 we'mmmm: “wawuwfimm ‘ g. . _ . n , m...“ .m. .mwmwm -u.u.mi,m law-nu new" 'whun'ulw-l. km awe-aw nugun d (A) Treasury bonds and nnlcs (b) treasury bills 2:38:233" flfififisssau {Ci Ncw York Slack Ir 'c hands . : v.2 La 5.3 an! mg.“ an a 35-25 :01 1% UL. “IIW "’1‘. I! (‘5 II DJ”. lunar. la“. &9 “Ill 9" lrI-nmw um mummy mu, can-o nun mevnw um» mm: 3991 mm. as 31:2 ml an... n. mm was axe-ms m. an aura mun-um sum “um awe-ell, up I Dewy an». inward Dune-gal npimswrm won: mum” romanc- pm to mum; raw ma Winn mu- mm u; ans '3: iu-n mum m. fill an! an m Mum m... n.- Inm- mm our mu: l'hlr. Mum-n sun msmm 3mm lumbar": MM Ym - 1.15M -- (MIMI Ylflé - l ".5556 can" Ynifl - in “3“ HOW ltliu ll can-n: held u 1,931; :3 ==3323i 23522232 “"33 H 8228: ====-:==r-m III? $233 “w ‘ “216 ha Malullw I 16896 male: 4n: lfll n” W 10‘ ‘16" A!!! 0‘ 2‘3 7‘5 ZSII 25 n [.3 w ’Jv'uu u. mm, H mm «we {\rd‘anr‘ Mme. 1x.u-..-‘..r pug-t a m-u .. r Distinction Between Interest 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 One-Year Returns on Difierentvlt'iaturity leis-Coupon-Rate 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 long-term bonds because have higher interest-rate risk 2. No interest-rate 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' . 3-j_'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 long-term 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 Dun-11d. 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 -.' relative to mllcr flsscts (Image-as 4) Nwr: ram 1 tum-m m appeal: dlmfiama: Pan mm tall “rum! fink inncmnai mgoup Ihe axia. whllr. n on It: right mm.“ m trk‘n‘fis n m- m down nu- :Ixts.l‘m1y m. am In lhc mumps one shown 11w .nnru ul Jaws.“ u. llu' van-Hrs mm: dung; in “mutual would 13¢ m: (“we plum Indian-9d 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 ._ ..-j-opportuni_tles ' ff, 53311.33 900 j} _sh1fis out to I . 3*fight ' 1-: = 350 _2. Expected-2' ji- _- Inflation _ _ ;.- Boo .fitmtmr j .shlfis outta ;' 3._ Government ' - A i ' - Guy" as 100 200 300 400 500 600 700 " 'j-Defi'cits-T, 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: Fat-d Elm-man :nofima'xr llama-1m- Pun Ihc 2d: wrlrdaw annexes aswa p1 “print was While Ion the ng'hl Wkll axis In. um nswr go down the “Elm,- lax-mam Ihl‘ rumblrs am slum 11w mm m rim-ma; 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 j-j 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.

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Lecture 3_EC3332[1] - Lecture 3 Understanding Interest...

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