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1、1第五章 风险和期限如何影响利率第一节第一节 利率的风险结构利率的风险结构 第二节第二节 利率的期限结构利率的期限结构2Chapter Preview 本章主要研究风险对利率的影响和期限结构对利率的影响。利率的风险结构 Risk Structure of Interest Rates利率的期限结构 Term Structure of Interest Rates3Risk Structure of Long Bonds in the U.S.4Two important features of interest-rate behavior for bondsFigure 1 shows the
2、 features as following:在任何一年内，不同种类的债券利率各不相同；利率之间的利差(spread)随着时间的推移而变动。5Factors Affecting Risk Structure of Interest RatesDefault Risk(违约风险)Liquidity(流动性)Income Taxes Factor(所得税因素)6一、Default Risk(违约风险)影响债券利率的一个特征是其违约风险(risk of default)。当债券发行者不能或不愿按事先约定支付利息或面值时，就出现违约风险。美国联邦政府的债券通常是没有违约风险的(美国政府可以通过增加税收
3、来履行还款义务)。这种债券被称为无风险债券(default-free bonds).7Risk Premium(风险溢价)具有违约风险的债券和无违约风险的债券之间的利差称为风险溢价(risk premium)，它表明人们持有高风险债券所必须获得的利息。具有违约风险的债券通常具有正的风险溢价，而且违约风险越大风险溢价越大。8Increase in Default Risk on Corporate Bonds 9公司债违约风险增长的分析Corporate Bond Market1.Risk of corporate bonds,Dc,Dc shifts left2.Pc,ic Treasury
4、Bond Market3.Relative risk of Treasury bonds,DT,DT shifts right4.PT,iT Outcome5.Risk premium,ic-iT,rises10债券的评级Bond RatingsBaa(Moody)or BBB(S&P)或以上级别的称为投资级投资级别证券别证券；以下级别的称为称为垃圾债券垃圾债券Junk bonds。11二、Liquidity(流动性)影响债券利率的另一个因素是流动性 liquidity;债券的流动性越强越受欢迎。在众多长期债券中，美国的国债流动性最强。因为其交易范围广泛，容易被出售，而且交易成本低。12Liq
5、uidity Premium(流动性溢价)公司债券的流动性比国债要差。Because fewer bonds for any one corporation are traded and it may be hard to find buyers quickly.公司债券与国债之间的利差(that is,the risk premiums)不仅反映了公司债券的违约风险，还反映了其流动性风险。所以风险溢价有时也被称为流动性溢价。13Decrease in Liquidity of Corporate BondsRisk premium reflects not only corporate bo
6、nds default risk but also lower liquidity14公司债流动性降低的反应公司债流动性降低的反应Corporate Bond Market1.Liquidity of corporate bonds,Dc,Dc shifts left2.Pc,ic Treasury Bond Market3.Relatively more liquid Treasury bonds,DT,DT shifts right4.PT,iT Outcome 5.Risk premium,ic-iT,rises15三、Income Taxes Factor(所得税因素)美国的市政府债券
7、(municipal bonds)的利息支付不用缴纳联邦所得税(federal income taxes)。这对于市政债券的需求来说，与提高预期收益具有相同的影响效果。16市政府债券的税收优势市政府债券的税收优势17市政府债券的税收优势分析市政府债券的税收优势分析Municipal Bond Market1.Tax exemption raises relative Re on municipal bonds,Dm,Dm shifts right2.Pm,im Treasury Bond Market3.Relative Re on Treasury bonds,DT,DT shifts le
8、ft4.PT,iT Outcome5.im iT18第二节第二节 利率的期限结构利率的期限结构具有相同风险、流动性和税收因素的债券也可能因为到期期限的差异而具有不同的利率水平。19不同到期期限的债券的利率变动不同到期期限的债券的利率变动 20收益率曲线收益率曲线Yield CurvesDynamic yield curve that can show the curve at any time in historyhttp:/ 利率的期限结构利率的期限结构 具有不同到期期限的债券的利率会同时变动。当短期利率较低时，收益率曲线更有可能陡峭向上倾斜；当短期利率较高时，收益率曲线更有可能向下倾斜。收
9、益率曲线通常是向上倾斜。23期限结构理论期限结构理论Pure Expectations Theory 纯预期理论纯预期理论Pure Expectations Theory explains 1 and 2,but not 3Market Segmentation Theory 市场细分理论市场细分理论Market Segmentation Theory explains 3,but not 1 and 2Liquidity Premium Theory 流动性溢价理论流动性溢价理论Solution:Combine features of both Pure Expectations Theor
10、y and Market Segmentation Theory to get Liquidity Premium Theory and explain all facts24一、一、纯预期理论纯预期理论Key Assumption关键假设关键假设:Bonds of different maturities are perfect substitutes(完全替代品)。Implication隐含假设隐含假设:Re on bonds of different maturities are equal.25纯预期理论纯预期理论投资策略投资策略考虑两种投资策略：1.Buy$1 of one-year
11、 bond and when matures buy another one-year bond2.Buy$1 of two-year bond and hold it26Expected return from strategy 2Since(i2t)2 is extremely small,expected return is approximately 2(i2t).27Expected return from strategy 1Since it(iet+1)is also extremely small,expected return is approximately it+iet+
12、1.28纯预期理论纯预期理论投资策略投资策略From implication above expected returns of two strategies are equal;ThereforeSolving for i2t(1)29n周期债券的利率周期债券的利率Equation 2 states:n周期债券的利率等于在这个周期内出现的短期债券利率的平均值(2)30Numerical exampleOne-year interest rate over the next five years is expected to be 5%,6%,7%,8%,and 9%Interest rate
13、 on two-year bond:(5%+6%)/2=5.5%Interest rate for five-year bond:(5%+6%+7%+8%+9%)/5=7%Interest rate for one-to five-year bonds:5%,5.5%,6%,6.5%and 7%31纯预期理论对期限结构的解释纯预期理论对期限结构的解释当预计未来的短期利率上升时，未来短期利率的平均值比当前的短期利率高，所以收益率曲线向上倾斜。当预计未来的短期利率不变时，未来短期利率的平均值与当前的短期利率相同，所以收益率曲线是平坦的。当预计未来的短期利率下降时，收益率曲线向下倾斜。32纯预期理论
14、与第纯预期理论与第1个事实个事实短期利率的提高将会提高人们对未来短期利率的预期。If it today,iet+1,iet+2 etc.average of future rates int Therefore:it int (i.e.,short and long rates move together)33纯预期理论与第纯预期理论与第2个事实个事实短期利率较低，人们会认为未来短期利率将会提高，所以长期利率会高于当前的短期利率。yield curve will have steep upward slope.短期利率较高，人们会认为未来短期利率将会降低，所以长期利率会低于当前短期利率。yie
15、ld curve will have downward slope.34纯预期理论与第纯预期理论与第3个事实个事实收益率曲线向上倾斜，意味着预期未来的短期利率会上升。而短期利率既有可能上升也有可能下降，按照纯预期理论的解释收益率曲线最常见的形式应该是水平的。Doesnt explain fact 3that yield curve usually has upward slope.35二、二、市场分割理论市场分割理论Key Assumption:Bonds of different maturities are not substitutes(替代品)at allImplication:市场是
16、完全独立的，不同到期期限的债券利率由该债券自身的供求状况决定。36市场分割理论对期限结构的解释市场分割理论对期限结构的解释Explains fact 3that yield curve is usually upward slopingPeople typically prefer short holding periods and thus have higher demand for short-term bonds,which have higher prices and lower interest rates than long bonds37市场分割理论对期限结构的解释市场分割理论
17、对期限结构的解释Does not explain fact 1 or fact 2 because its assumes long-term and short-term rates are determined independently38三、流动性溢价理论三、流动性溢价理论This theory modifies Pure Expectations and it also has features of Market Segmentation Theory.39三、流动性溢价理论三、流动性溢价理论Key Assumption:Bonds of different maturities
18、are substitutes,but are not perfect substitutesImplication:一种债券的预期回报率影响不同期限的另一种债券的预期回报率，但是投资者对于不同到期期限的债券有所偏好。40Liquidity Premium Theory Main PointInvestors prefer short rather than long bonds must be paid positive liquidity premium,lnt,to hold long term bonds41Liquidity Premium Theory Yield Curve42L
19、iquidity Premium Theory-EquationResults in following modification of Pure Expectations Theory(3)43流动性溢价理论对期限结构的解释流动性溢价理论对期限结构的解释Comparing with those for the pure expectations theory,liquidity premium theory produces yield curves more steeply upward slopedExplains fact 3that usual upward sloped yield
20、 curve by liquidity premium for long-term bonds44Yield Curves and the Markets Expectations of Future Short-Term Interest Rates45四、用期限结构对利率进行预测四、用期限结构对利率进行预测Pure Expectations Theory:Invest in 1-period bonds or in two-period bond Solve for forward rate,(4)46Numerical example(P80)i1t=5%,i2t=5.5%即期利率Spo
21、t Rates and 远期利率Forward Rates(P80)47四、用期限结构对利率进行预测四、用期限结构对利率进行预测Compare 3-year bond versus 3 one-year bondsUsing iet+1 derived in(4),solve for iet+248Forecasting Interest Rates with the Term StructureGeneralize to:(5)49Forecasting Interest Rates with the Term StructureLiquidity Premium Theory:int-lnt=same as pure expectations theory;replace int by int-lnt in(5)to get adjusted forward-rate forecastUsing this equation in forecasting,firstly we need to estimate the value of the liquidity premium.(6)