2012 Pearson Prentice Hall. All rights reserved. 2-1 2012 Pearson Prentice Hall. All rights reserved. 2-1 Chapter 1THEORY O !"TERE#T RATE 2012 Pearson Prentice Hall. All rights reserved. 2-2 2012 Pearson Prentice Hall. All rights reserved. 2-2 !ntrod$ctionTheactsofsavingandlending,and borrowing and investing, are significantly influencedbyandtiedtogetherbythe interest rate.Theinterestrateisthepriceaborrower mustpaytosecurescarceloanable fundsfromalenderforanagreed-upon time period. 2012 Pearson Prentice Hall. All rights reserved. 2-% 2012 Pearson Prentice Hall. All rights reserved. 2-% $nctions o& the !nterest Rate in the Econo'(Theinterestratehelpsguaranteethatcurrent savingswillflowintoinvestmenttopromote economic growth.Itrationstheavailablesupplyofcredit, generallyprovidingloanablefundstothose investment projects with the highest return.It brings the supply of money into balance with the publics demand for money. 2012 Pearson Prentice Hall. All rights reserved. 2-) 2012 Pearson Prentice Hall. All rights reserved. 2-) $nctions o& the !nterest Rate in the Econo'(The interest rate serves as an important tool for government policy through its influence on the volume of savings and investment. 2012 Pearson Prentice Hall. All rights reserved. 2-* 2012 Pearson Prentice Hall. All rights reserved. 2-* Ris+ #tr$ct$re o& !nterest RatesDefault riskoccurs when the issuer of the bond is unable or unwilling to make interest payments or pay off the face value!.". T-bonds are considered default free#isk premiumthe spread between the interest rates on bonds with default risk and the interest rates on T-bonds $i%uiditythe ease with which an asset can be converted into cashIncome ta& considerations 2012 Pearson Prentice Hall. All rights reserved. 2-, 2012 Pearson Prentice Hall. All rights reserved. 2-, E-pected ret$rn and ris+Risk-return tradeof.Then the 'average of return, i.e. expected return is measured by 'mean of R:risk is measured by variance or standard deviation1 1 2 2( ) ...N N N NNER R R R R = = + + +( ) ( ) R VarR =22 2 21 1 2 2( ) ( ( ))( ( )) ( ( )) ... ( ( ))N NNN NVarR R ERR ER R ER R ER = = + + + 2012 Pearson Prentice Hall. All rights reserved. 2-. 2012 Pearson Prentice Hall. All rights reserved. 2-. Ris+ str$ct$re o& interest rate 2012 Pearson Prentice Hall. All rights reserved. 2-/ 2012 Pearson Prentice Hall. All rights reserved. 2-/ Ter' str$ct$re o& interest rate 2012 Pearson Prentice Hall. All rights reserved. 2-0 2012 Pearson Prentice Hall. All rights reserved. 2-0 2012 Pearson Prentice Hall. All rights reserved. 2-10 2012 Pearson Prentice Hall. All rights reserved. 2-10 Ter' #tr$ct$re o& !nterest Rates(onds with identical risk, li%uidity, and ta& characteristics mayhavedifferentinterestratesbecausethetime remaining to maturity is different)ieldcurveaplotoftheyieldonbondswithdiffering termstomaturitybutthesamerisk,li%uidityandta& considerations!pward-slopinglong-termratesareabove short-term rates*lat short- and long-term rates are the sameInverted long-term rates are below short-term rates 2012 Pearson Prentice Hall. All rights reserved. 2-11 2012 Pearson Prentice Hall. All rights reserved. 2-11 $p1ard slopingmaturityyield 2012 Pearson Prentice Hall. All rights reserved. 2-12 2012 Pearson Prentice Hall. All rights reserved. 2-12 do1n1ard sloping 2inverted3maturityyield 2012 Pearson Prentice Hall. All rights reserved. 2-1% 2012 Pearson Prentice Hall. All rights reserved. 2-1% &latmaturityyield 2012 Pearson Prentice Hall. All rights reserved. 2-1) 2012 Pearson Prentice Hall. All rights reserved. 2-1) acts Theor( o& the Ter' #tr$ct$re o& !nterest Rates 4$st E-plain+. Interest rates on bonds of different maturities move together over time,. -hen short-term interest rates are low, yield curvesaremorelikelytohaveanupward slope.whenshort-termratesarehigh,yield curvesaremorelikelytoslopedownward and be inverted/. )ieldcurvesalmostalways slope upward 2012 Pearson Prentice Hall. All rights reserved. 2-1* 2012 Pearson Prentice Hall. All rights reserved. 2-1* Three Theories to E-plain the Three acts+. 0&pectations theory e&plains the first two facts but not the third,. "egmented markets theory e&plains fact three but not the first two/. $i%uidity premium theory combines the two theories to e&plain all three facts 2012 Pearson Prentice Hall. All rights reserved. 2-1, 2012 Pearson Prentice Hall. All rights reserved. 2-1, 2012 Pearson Prentice Hall. All rights reserved. 2-1. 2012 Pearson Prentice Hall. All rights reserved. 2-1. E-pectations Theor(Theinterestrateonalong-termbondwill e%ualanaverageoftheshort-terminterest ratesthatpeoplee&pecttooccuroverthelife of the long-term bond(uyersofbondsdonotpreferbondsofone maturityoveranother.theywillnothold any%uantityofabondifitse&pectedreturn islessthanthatofanotherbondwitha different maturity(ondslikethesearesaidtobeperfect substitutes 2012 Pearson Prentice Hall. All rights reserved. 2-1/ 2012 Pearson Prentice Hall. All rights reserved. 2-1/ E-pectations Theor(5E-a'ple$et the current rate on one-year bond be 12.)ou e&pect the interest rate on a one-year bond to be 32 ne&t year.Then the e&pected return for buying two one-year bonds averages 412 5 3267, 8 92.The interest rate on a two-year bond must be 92 for you to be willing to purchase it. 2012 Pearson Prentice Hall. All rights reserved. 2-10 2012 Pearson Prentice Hall. All rights reserved. 2-10 E-pectations Theor(5!n 6eneral12For an investment of $1= today's interest rate on a one-period bond= interest rate on a one-period bond expected for next period= today's interest rate on the to-period bondtettiii+ 2012 Pearson Prentice Hall. All rights reserved. 2-20 2012 Pearson Prentice Hall. All rights reserved. 2-20 E-pectations Theor(5!n 6eneral 2cont7d32 222 222 222!xpected return over the to periods from investin" $1 in theto-period bond and holdin" it for the to periods(1 #)(1 #) 11 2 ( ) 12 ( )$ince ( )is very smallthe expected ret tt tt tti ii ii ii= + + = +2turn for holdin" the to-period bond for to periods is2ti 2012 Pearson Prentice Hall. All rights reserved. 2-21 2012 Pearson Prentice Hall. All rights reserved. 2-21 E-pectations Theor(5!n 6eneral 2cont7d311 11 111%f to one-period bonds are bou"ht ith the $1 investment(1 )(1 ) 11 ( ) 1( )( ) is extremely small$implifyin" e "etet te et t t te et t t tet tet ti ii i i ii i i ii ii i++ ++ ++++ + + + + + ++ 2012 Pearson Prentice Hall. All rights reserved. 2-22 2012 Pearson Prentice Hall. All rights reserved. 2-22 E-pectations Theor(5!n 6eneral 2cont7d32 112&oth bonds ill be held only if the expected returns are e'ual22(he to-period rate must e'ual the avera"e of the to one-period ratesFor bonds ith lon"er maturitieset t tet ttt tnti i ii iii ii+++= ++=+=1 2 ( 1)...(he-period interest rate e'uals the avera"e of the one-periodinterest rates expected to occur over the-period life of the bonde e et t ni innn+ + + + + 2012 Pearson Prentice Hall. All rights reserved. 2-2% 2012 Pearson Prentice Hall. All rights reserved. 2-2% E-pectations Theor(0&plainswhythetermstructureofinterestrates changes at different times0&plainswhyinterestratesonbondswith different maturities move together over time 4fact +60&plains why yield curves tend to slope up when short-termratesarelowandslopedownwhen short-term rates are high 4fact ,6:annote&plainwhyyieldcurvesusuallyslope upward 4fact /6 2012 Pearson Prentice Hall. All rights reserved. 2-2) 2012 Pearson Prentice Hall. All rights reserved. 2-2) #eg'ented 4ar+ets Theor((onds of different maturities are not substitutes at allTheinterestrateforeachbondwithadifferentmaturity is determined by the demand for and supply of that bondInvestorshavepreferencesforbondsofonematurity over anotherIfinvestorshaveshortdesiredholdingperiodsand generallypreferbondswithshortermaturitiesthathave less interest-rate risk, then this e&plains why yield curves usually slope upward 4fact /6 2012 Pearson Prentice Hall. All rights reserved. 2-2* 2012 Pearson Prentice Hall. All rights reserved. 2-2* assumption is too strictso implication is not %uite correct 2012 Pearson Prentice Hall. All rights reserved. 2-2, 2012 Pearson Prentice Hall. All rights reserved. 2-2, 8i9$idit( Pre'i$' : Pre&erred Ha;itat TheoriesTheinterestrateonalong-termbondwill e%ualanaverageofshort-terminterest rates e&pected to occur over the life of the long-termbondplusali%uiditypremium thatrespondstosupplyanddemand conditions for that bond(ondsofdifferentmaturitiesare substitutes but not perfect substitutes 2012 Pearson Prentice Hall. All rights reserved. 2-2. 2012 Pearson Prentice Hall. All rights reserved. 2-2. 8i9$idit( Pre'i$' Theor( int = it + it +1e+ it +2e+... + it +( n1)en+ lnthere lnt is the li'uidity premium for the n-period bond at time tlnt is alays positive)ises ith the term to maturity 2012 Pearson Prentice Hall. All rights reserved. 2-2/ 2012 Pearson Prentice Hall. All rights reserved. 2-2/ Pro;le';ow do we interpret yield curve