Week2.ppt - ECF2331 Tepic 2 Interest Rates and the Bend...

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Unformatted text preview: ECF2331 Tepic 2 Interest Rates and the Bend Market [I] Discounting and Present Value [II] Measuring Interest Rates [III] The Band Market Disceunting Future Payments Principal = $1DD I: [1.11] =1D% In one year $1DDs{1+D.1D} = $11IC]| 9' In two years $11Ds{1+fl.1fl}= $121 = $1ss:i;{1+i:r.1i:iiE in three years $121 s{1+fl.1fl}= $133 = 1131131131-1'{1+[lh1fl]3 In N years $1DD s {1+D.1D}“ — Each dellar receiyedrpaid in the future is iess yaiuahie than a deliar receiyedrpaid new — The payment receiyed in the future needs te he disceunted hack ta teday’s yaiue fer a meaningful cemparisen Present Value i‘r Present Value [PU] c-f a future amc-unt c-f payment is the current wc-rth c-f future cash fic-ws {CF} given a specified rate pf interest if}. CF PV=— (1+.i)fl 3% After cc-nyerting each stream c-f future payment tc- its present yaiue. we can cpmpare payments scheduied at different times. $10G $110 $121 CF Year 0 1 2 n W 100 11D!{1+i) 121,I"(1+i}2 GFI(1+i]“ YTM an A Simple Lean 5-“- The lender prdyides the ladrrewer with a given amdunt effunds called the principal; 5-“- The funds. aldng with an additidnal payment fer the interest. must be repaid tn the lender in a single payment at the maturity date. PM“ = amdunt borrowed = $1131] CF = cash flow in one year = $111] a: number dfyears = 1 $1113 {1+ i)‘ n+n$1aa=$11a 1+l = 1.1 $100 = i=fl.1=1fl% Interest Rate = VTM = 10% YTM an A Fixed-Payment Lean 3-“- The lender prdyides the bdrrdwer 1with a giyen amdunt effunds called the principal; i=- The same cash flew payment, censiating at part dfthe principal and interest, needs td he made eyery peridd thrdughdut the life dfthe lean. P9 = Lean Value = $19,999 Fixed yearly payment = $9,439.29 :1 = number pfyeara until maturity = 29 $9,439.29 $9,439.29 $9,439.29 $9,439.29 mean = —_+—_+—_+..._‘ $ 1 +1 (1 +11)2 [1 + 1113 (1 +1)“ i=?% Interest Rate = VTM = 7% YTM on a 10%-coupon-rate bond maturing in 10 years (face value = $1,000) 1L‘E'ielilis to Maturity an a lflfi-EnupuII-Rate Bend Hatuting in Ten Years [Face Value = $1,000) Price of Bond ($11 Yield to 11".laltllrilj.Ir (‘11:) 1,200 T.13 1,100 0.40 1,000 10.00 900 11.?5 800 1131 3* Price of the pond is negative re iated to WM 3* If coupon pond price = face wraiue, ‘r‘TM equais the coupon rate. 3* If coupon pond price is beiow its face vaiue, ‘r‘TM is greater than the coupon rate; If coupon bond price is above its face vaiue, ‘r‘TM is iess than the coupon rate. Other Bonds is A discount bond is bought at a price below its face value {at the discount) and the face value is re paid at maturity date. No coupons — also called zero-coupon bond. Face Value = $1 .flflfl [to be repaid in one yea r} Current Price = $9DD $1,ooo _ $soo= 1+, —r WM=I=11.1% i 3* A consol or perpetuity has no maturity date and does to repay the principal, but instead proyides fixed coupon payment foreyer. P = Price of the consol {i.e. today's yalue} E: fixed coupon payment i: ”field to maturity of the consol For long—term bonds. matu rlty date is far a way. Hence. i=CrF' can be used to approximate WM. Thls approximation ls called the current yield. Rate ef Return vs. Interest Rate Irv Rate of return an a hand measures hc-w well eff an inyestc-r is lay awning the hand. Irv Rate of return equals the payments tcu the hc-lder at the hand [e.g. $1DD} plus the change in value dfthe lacund [e.g. $2DD}. expressed as a fractic-n c-f its initial purchase price. FHCE 1I.I"E:ilUIl'-i = $1.UDD Rate _ $113.] + ($1’2flfl _ $1,0flfl] Yearly cc-upc-n payment = $1DD 01” $1.0flfl Return = sass Selling price in cmeyear’s time = $1.33!? Irv Rate of return _ + frc-m ttc- t+I Rate at Cprrent Capital "field Gain :rr Rate of return dues n_et necessarily equal the ‘I'TM. Irv A rise in interest rates means a fall in hand prices. which can result in capital less and therelay a lewer rate c-f return. Irv The risk cufinterest rate changes is called interest rate risk. Trading Icing-term hands inyc-lyes mere risk than trading shcurt—term hands. Nominal vs. Real Interest Rates Nominal interest rate is not adjusted for inflation. Real interest rate is adjusted for inflation so it more accurately reflects the true cost of borrowing. Fisher Equation f = nominal interest rate fr = real interest rate a” = expected inflation rate Ex ante real interest rate is adjusted for expected changes in the aggregate price level. Ex post real interest rate is adjusted for actual changes in the aggregate price level. 1,0013 {mafia} 95D ii= 5.3%} 900 {i=11.1%} {FF-1:33;; Equiiihrium am [i = 25.0%} THEE if: 33.D%] "-"n-"I'l-"I L::-:.-: :-.-'=..-=.~.-_. |'.‘-'I'.'"H'|-H."|I'.1. ii'I-S—j- tilt—MW! :':-'I-:T.'&.': FIE-1'." .'-_'-. 11:: f1" 1m 2m 3m 4m 5m Eiuan‘lity uf Bands. 5 iii billinns} Shift in Demand Curve fer Bends “Uhatfacters Price of Bonds. P shift D-cu FVE tetheright? An increase in the demand fer bends E-HIHE the. bend demand curve rightward. Expected Interest Expected I Return on Hands Expected lnflafien Quantity of Bonds, 3 Price cf Bends. P Shift in Supply Curve fer Bends Quantity cf Bends, B What factors shift S-curve tn the right ? of Prefitahility Investments I Arr rncreese in the supc-Iy' c-f trends shlfis the b-fll'ld Supflly‘ c: L] we rig h 1. we r cl. Expected lnflatiun Government Budget Deficit Response to A Change in Expected Inflation Price Di 3mm1 p Step 2. end ehiite the bend eueelyr eurue ngt'itwerd . . _ Step ii- eeueing P the price ei bends. te tell and the equilibrium Step 1. A rise in interest rate te nee. P2 expected inlletien ehihe the trend demand cu we leftward . _ _ Quantity of Bonds. 5 Fisher Effect: when expected infietien rises. interest rates will rise [e.g. prices will fall} Response to A Business Cycle Expansion Price of Bands, F Step 2. and shifts- the bend Eierhenrj curve rigiwhmard. hut _ 5 by a lesser arr'leuh‘t . . . E 1 Ste; 1 . A business cycle e:—;pensten shifts. the bend supply curve rightward . . . I BE _- .--. .- , -_ _._ :JEE'E: :3. Eu the grim: hf t:::‘.-:='!~’_1:E. fats and the eel_1§!éb:+'=-s_ih"- “IE-"EST r‘EiE' H1393. Quantity of Bonds, 5 ...
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