[资本市场和金融机构]2课件.ppt

1、1Interest RatesDefinitionFluctuation of interest ratesShifts on DemandShifts on SupplyTypes of interest ratesAnalysis of Bond ValuationRisk and Term Structure of Interest Rates(TSIR)5.1 Determinants of Risk Structure(RSIR)5.2 TSIR(Yield Curve).Theories:A)Pure Expectations Theory B)Market Segmentatio

2、n Theory C)Liquidity Theory Predictive Power of the Yield Curve 6.1 Future interest rates 6.2 Economic growthConclusions21.Interest Rate(i)i=Cost of borrowing or lending moneyIt plays a pivotal role in:the Investment and Financing of assets(real,financial)by individuals,companies,governments and FIt

3、he performance of the economyDetermined in the Debt Markets(supply and demand)and by government intervention.lCentral Bank Monetary policy(i,M)Is there an appropriate level of i?3Interest RatelHow the interest rates are determined?lWhat explains the fluctuation of interest rates?lMost accurate measu

4、re of interest rate:Yield to maturityExample applied to bond valuation4Determination of Interest Rate(i)Approaches1)Analysis of Demand of loanable funds and Supply of loanable funds2)Analysis of Demand for and supply of bondsSupply of loanable funds by households and firms.The higher the i the highe

5、r the quantity of loanable funds offeredDemand of loanable funds by households and firmsReasons for Consumer?For Firms?Total Demand=Demand by households and firmsDeterminants of the Demand and Supply5Supply and Demand for Loanable FundsInterest Rate(i)SupplyQuantity of loanable funds DemandQ*i*6 Wha

6、t determines the supply of loanable funds?The supply of loanable funds is determined by the interest rate offered to savers.A higher interest rate induces households to consume less today(save)in favor of greater consumption in the future.Firm also may have excess of cash that may be loaned(e.g.,pur

7、chase of other firms bond issue)instead of invested(real assets)because of the non availability of projects with+NPV.What determines the demand for loanable funds?It comes from:consumers who wish to consume more today than tomorrow,individuals,financial and non-financial firms to invest in financial

8、 assets financial and non-financial firms to invest in real assets Demand depends on the interest rate at which these three groups can borrow.The lower the interest rate the higher the demand and vice-versa.72.Fluctuation of interest rates What might cause the supply or demand for loanable funds to

9、shift,and how would that affect interest rates?Factors that shift the demand curve.a)Recession:It decreases demand at all interest rates,shifting the demand curve inwards and causing the equilibrium interest rate to fall.Quantity($)AB Interest Rate SDDiiQQ8b)An increase of the government deficit.C)R

10、ise in expected inflation shifts the demand curve to the right.Same as(b)Nominal Interest rate=real interest rate+rate of expected inflation D)increase on the growth rate of population.Same as(b)e)Business cycle expansion.Expected increase in economic growthSame as(b)iQ($)DD SAB9Examples that shift

11、the Supply curve to the right Increases in the money supply by the Central Bank,causing the interest rate to fall.b)Increases in real personal income make people more willing to make loans(e.g.deposits in banks accounts)c)Increase in tax exempt financial instruments.Note:if we assume that thecentral

12、 bank controls theamount of money supply at fixed quantity the Supply Curve for money S would be a vertical line.iQ($)SSAB103.Variety of Interest RatesT-bill rate(1year)Discount rate:Central Bank charges to banks In Canada is called the Overnight Bank Rate Commercial paper rate:Short term discount b

13、onds Prime rate:Short term Rate charged to largest firms(creditworthy)Corporate bond rate:Long term rate for debt issued by firmsLIBOR:Rate that largest creditworthy international banks dealing in Eurodollars charge each other for large loans.Fixed rates,floating rates,etc.They differ because of the

14、 differences in maturity,risk of lenders 11 4.Analysis of Bond ValuationIt sheds light on the concept of interest rate.Bond.Contract in which a borrower agrees to pay a bondholder(the lender)a specific amount of money in a period of time.Example:How much would you pay for a bond that promises a coup

15、on rate of$100 each year for a period of 10 years and the principal amount of$1,000(par value=nominal value=face value)at the end of the 10th year?Assume i=5%,i=10%,i=15%12Formula P=Coupon/(1+i)+Coupon/(1+i)2+Coupon/(1+i)10+Face Value/(1+i)10 C=$100C=$100C=$100P=?123 9 10C=$100$100+$1,000If i=5%P=$1

16、00/(1+0.05)+$100/(1+0.05)2+$100/(1+0.05)10+$1,000/(1+0.05)10=$1,386 i=10%P=$100/(1+0.10)+$100/(1+0.10)2+$100/(1+010)10+$1,000/(1+0.010)10=$1,000 i=15%P=$100/(1+0.15)+$100/(1+0.15)2+$100/(1+015)10+$1,000/(1+0.015)10=$749 Which i(discount rate or yield to maturity)from above makes the present value of

17、 a bonds payments equal to its current price P?A:?i=5%13YTM=Interest rate that equates the Present Value of payments received from a debt instrument(e.g.,bond)with its value today P.Alternatively,is the rate of interest earned on a bond if it is held to maturity.The YTM is the most important and acc

18、urate way of calculating interest rates.If P=$1,386 What is the YTM=i?$1,386=$100/(1+i)+$100/(1+i)2+$100/(1+i)10+$1,000/(1+i)10=$1,000 A:YTM=i=5%If P=$1,000 What is the YTM?YTM=10%If P=$749 What is the YTM?YTM=15%What is the relationship between the Bond price and the i?Why?Price of bond Fig.Yield t

19、o maturity of a bond=effective yield on a bond=i$1,00010%Interest Rate=i=YTM5%$1,386$74915%Scenarios:Assume you bought the bond in$1,000 and interest rates increased to 15%.Did you benefit?Assume you bought a corporate bond and the credit rating of the firm is downgraded to junk(default)1.What is th

20、e expected effect in the interest rate(YTM)?14PerpetuityBond paying out a fixed amount of money each year forever.Example The Canadian government issues a bond that will pay to perpetuity$50 a year.If the interest rate is 3%annual,a)what is the bond worth today?b)Would you buy the bond for$1,500?The

21、 present value of a perpetuity is easily obtained as PDV=perpetuity/RA:Effective Yield(YTM)on a Bond(perpetuity)Percentage return that one receives by investing in a bondAssume price of the perpetuity above is$1,666.67 and you receive a perpetual coupon rate of$50 per year.What is the effective yiel

22、d rate or rate or return?A:Now,suppose the current interest rate is 4%.Would you pay$1,666.67 for the bond?155.Risk and Term Structure of Interest RatesVariety of different interest rate=f(maturity,risk,liquidity,taxes).I I)Assuming various debt instruments(bonds)have same maturity,their is will dif

23、fer because of differences in risk.Risk Structure of Interest Rates(RSIR).RSIR expresses the relations of interest rates for various bond instruments whose determinants are(1)default risk,(2)liquidity,and(3)taxes (See Fig.1,p.110,Miskhin et al.-Long Term Bonds)II II)Assuming various bonds have same

24、risk their is may differ because of the differences in maturities.Term Structure of Interest Rates(TSIR).TSIR expresses the the relationship among is(YTMs)on zero coupon discount bonds with different maturities.165.15.1 Determinants of RISK STRUCTURE OF INTEREST RATES(RSIR)Interest rates on corporat

25、e bonds are higher than those on Canada bonds(See Figure 1)Reasons1.Higher Default Risk 2.Lower Liquidity 3.Tax considerations on is payments.Canadian(Cdn)bonds are default-free bonds Difference in is=Risk Premium 1.Effect of Default risk on interest rates Assume initially a corporate bonds with no

26、default risk,like Canada bonds(with same maturity).Possibility of a strong recession increases the possibility of default of corporate bonds.What will the effect be on interest rates of corporate bonds and Canada bonds?What will happen to the risk premium of corporate bonds?ii Price of bonds,PPQuant

27、ity of Corporate Bonds Quantity of Canada Bonds(a)Corporate bond market (b)Default-free Cdn bond marketic1Pc1Pc2ic2PT2PT1iT2iT1iT2 ic2RiskPremium=ic2-iT2Dc2Dc1ScDT1DT2STDecrease inInterest rate17Investment advisory firms providers of default risk information on bonds:Standards and Poors Canada,Domin

28、ion Bond Rating Service.Investment grade-bonds(AAA)vs.Junk bonds(D)(See Fig.3,p.113,Mishkin et al.)Risk premium on BBB corporate bond rates(Corporates-Canada Spread,1980-2019)182.Effect of Liquidity on interest ratesLiquidity.Ability to buy or sell an asset quickly and in large volume without substa

29、ntially affecting the assets price.Corporate bonds vs.Canada bondsWhich ones are more liquid?Spread?Assume initially corporate bonds and Canada bonds are equally liquid,ceteris paribus.a)Which event(s)would decrease the liquidity of corporate bonds?Why?b)What will the effect be on interest rates of

30、corporate bonds and Canada bonds?c)What will happen to the risk(liquidity)premium of corporate bonds?Draw their respective graphs(demand and supply curves of Corporates and Canada bonds).193.Tax ConsiderationsHow does taxation affect the interest rate(YTM)on bonds?Government bonds that pay no taxes

31、yield lower interest rates(e.g.,U.S.municipal bonds or munis).Munis are advantageous for high tax-bracket investors.Example:Suppose Charlie White(a US investor)has 2 alternatives to invest his savings(say$1,000)invest a$1,000 face value muni that sells for$,1000,with coupon payments of$80.2)invest a

32、$1,000 face value taxable bond that sells for$1,000 and has a coupon payment of$120.The tax-bracket is 35%.a)Which option should he choose?Why?b)Suppose Jane Red is faced with similar options but her tax-bracket is 30%.What option would be best for her?c)Does it matter to know the maturity of the bo

33、nds to obtain their YTM?205.25.2 Term Structure of Interest Rates(TSIR)The TSIR refers to the relationship between YTM and term to maturity for bonds of same risk class.The Yield Curve is the graphical representation of the TSIR.The Yield Curve shape can bea)Upward-sloping Long Term is Short Term is

34、b)Flat Long term is =Short Term isc)Downward-sloping(inverted yield curve)LT is Short Term is average of future ST rates is expected current short term rates Downward-sloping Long Term is Short Term is average of future ST rates is expected current short term rates Flat Long Term is =Short Term is a

35、verage of future ST rates is expected =current short term rates 25Expected holding-period yields(HPY)on bonds of all maturities(with same risk)ought to be about equal,that is:1.HPY(1-year bond)=HPY(2-year bond)=HPY(n-year bond)2.If we know the one-year HPY(commonly called yield)on two bonds of n-1,a

36、nd n maturities,we can obtain the market expectation of the future short-term interest rate on year n(also called forward rate).Implications of Expectations Theory26Example-If one-year bonds offer an 8%annual yield(return)and the principal and interest are reinvested at 10%at the end of first year w

37、hile-two-year bonds have an YTM(i,or annual yield,or commonly called yield*)of 8.995%,both bonds must have same holding period yield(HPY),that is:*In practice yield refers to one-year interest rate.1.Two-year HPY for both types of bonds Two-year HPY of 1-year bonds=(1+0.08)(1+0.1)-1=0.188 or 18.8%Tw

38、o-year HPY of 2-year bonds=(1.08995)(1.08995)-1=0.188 or 18.8%2.One-year HPY(commonly called yield)yield of 1-year bonds=(1+0.08)(1+0.1)1/2-1=(1.188)0.5 1=0.08995 or 8.995%yield of 2-year bonds=8.995%(given)If it is not given you can obtain it from Two-year HPY of 1-year bonds Yield of 2-year bonds=

39、(1+two-year HPY of 1-year bonds)1/2-1=(1.188)1/2 1=0.08995 or 8.995%.3.The expected year two interest rate,i2,(or forward rate)is obtained as follows (1+yield of one year bonds)1(1+i2)=(1+yield of two years bonds)2 (1+i2)=(1+yield of two years bonds)2/(1+yield of one year bonds)1=(1.08995)2/1.08-1 =

40、1.0999-1=9.999 10%27 1.One-year HPY(or yield)for 1-year bonds reinvested T periods(at t+1 rate)Yield of 1-year bonds=(1+i1)(1+i2)+(1+iT)1/T-1 Based on previous example T=2 HPY(1-year bonds)=(1+0.08)(1.1)1/2 1=0.08995 or 8.995 2.One-year HPY for n-year bonds(usually given)If it is not given,it can be

41、 obtained from the n-year HPY for 1-year bonds reinvested each year,as follows Yield of n-year bonds=(1+n-year HPY of one-year bonds)1/n 1 Based on the example of previous slide Yield of 2-year bonds=(1+two-year HPY of 1-year bonds)1/2 1=(1.188)1/2 1=0.08995 or 8.995%.3.Expected year n interest rate

42、,in,(or forward rate)It is obtained as follows:(1+yield of n-1 year bonds)n-1(1+in)=(1+yield of n-year bonds)n (1+in)=(1+yield of n-year bonds)n/(1+yield of n-1 year bonds)n-1 in=(1+yield of n-year bonds)n/(1+yield of n-1 year bonds)n-1 1 Based on previous example the expected year 2 interest rate(o

43、r forward rate)is (1+i2)=(1+yield of two years bonds)2/(1+yield of one year bonds)1=i2 =(1.08995)2/1.08-1 =1.0999-1=9.999 10%28Solve the following problemsAssume the Expectations Theory holds 1.a)Determine the One-year HPY(or yield,assumed annual)for 1-year bonds reinvested 3 periods such as the exp

44、ected interest rates are 5,6 and 7 percent,for years 1,2 and 3,respectively.b)Determine the yield for 3-year bonds.2.Determine the three-year HPY for 3-year bonds that have yields to maturity(or yields,assumed annual)of 5.9968%Assume that two-year maturity bonds offer yields(assumed annual)of 5.4988

45、%,and three-year bonds have yields of 5.9968%.Determine the expected one-year interest rate(forward rate)for the third year.What does this tell you about the monetary policy to purse by the Bank of Canada?29B)Market Segmentation TheoryThis theory holds that long-and short-term maturity bonds are tra

46、ded in essentially distinct or segment markets(bonds are not perfect substitutes)The trading of long-term borrowers and lenders determine rates on long-term bonds.Similarly,the trading of short-term borrowers and lenders determine rates on short-term bonds.Various equilibrium rates(according to matu

47、rity of bonds)Their explanation of upward sloping yield curve?A:?This view of the market is not supported by empirical facts.It does not explain the shape of the yield curve(for low and high short term interest rates)and why yields on bonds of different maturities tend to move together(See Figure 5,

48、p.117,Mishkin et al.)30 2005 Pearson Education Canada Inc.6-10Interest Rates on Different Maturity Bonds Move Together31C)Liquidity Premium Theory The theory that investors demand a risk premium on longterm bonds.The risk premium required to hold longer term bonds is called liquidity premium Investo

49、rs and firms are willing to hold these bonds.Why?A:Yield curve will be upward sloping even in the absence of any expectations of future increases in rates.If the liquidity preference theory is valid,the forward rate of interest is not a good estimate of market expectations of future interest rates.W

50、hy?A:32Pure Expectations Theory Yield CurveLiquidity Premium TheoryYield CurveInterest RateYears to MaturityRelationship between the Expectations Theory and the Liquidity Premium TheoryLiquidity Premium5101520 25 30033What theory explains better the TSIR?The Liquidity premium theory explains better