ch7 利率的期限结构2015_货币银行学

1、ch7. 利率的结构利率的结构: 期限结构期限结构了解: 为什么一种资产的期限term或剩余到期日period to maturity影响这种资产的收益率。什么是期限溢价term premium为什么一种高流动性的资产仍被要求支付期限溢价？? 利率期限结构的理论:1. 纯预期利率（无偏预期理论） 2. 流动性溢价理论 3. 市场分割理论 Segmented of markets7.1 利率的期限结构利率的期限结构7.1.1 定义定义 期限结构：在具有相同的风险、流动性和税收待遇以及相同的真实利率的情况下，债券的收益率和其剩余到期日的关系称为期限结构。 金融资产的剩余到期日会影响其利率水平。有相

2、同风险、流动性和其他特点的债券，由于其剩余到期日不同，可能具有不同的利率水平。 利率的期限结构可以近似地用“收益率曲线 yield curve of securities”表示。收益率期限描述了持有期的收益和其剩余到期日之间的关系。7.1.2 收益率曲线和期限结构：收益率曲线和期限结构： 收益率曲线是一个或一组曲线，用来描述某种具有相某种具有相同风险和其他特征的证券的同风险和其他特征的证券的收益率和剩余到期日之间关系。 绘制收益率曲线: 将具有相同风险、流动性和其他特征而期限不同的债券收益率水平标在收益剩余到期日的坐标系中，将各个点连接起来，就得到这种证券的收益率曲线。收益率曲线的形状:向上倾

3、斜: 长期利率高于短期利率。水平形状:长期利率等于短期利率。向下倾斜: (反转收益率曲线）长期利率低于短期利率。承诺利率 vs. 持有期利率(“actual” nominal rates)关于收益率的实证事实:1. The YCs 大多数是向上倾斜的;2. 当短期利率水平较低时，YC更倾向于向上倾斜;3. 当短期利率水平较高时，YC更倾向于向下倾斜;4. 有不同到期日的债券的利率运动的方向相同；5. 短期利率的倾斜度较大; 7.2. 期限结构的无偏预期假说期限结构的无偏预期假说7.2.1 理论假设理论假设：1.投资者风险中性，追求投资利润的最大化。 2.债券的期限对投资者来说无差异。3.不同期

4、限的（同种）证券之间可以完全相互替代。4.没有交易成本。 5.投资者在其预期的基础上进行投资，他们对未来利率的预期是无偏的预期unbiased estimates6.由于在预期基础上进行套利，不同期限债券应带来相同的收益。7.一旦投资者发现在不同期限的债券中有套利的机会，他们将改变其资产组合，进行套利活动，最终使得假设6成立。7.2.2. 模型模型: 套利均衡套利均衡arbitrage of equilibrium & 结论：结论： 期限结构反应了对未来利率水平的预期。 其他因素不影响期限结构和收益率曲线的形状。 收益率曲线反映了投资者对未来利率趋势的预期。例子: 套利套利 &

5、 均衡均衡 ,2%4:average arithmetic1%)41)(1(:average geometric)1 (%)41)(1 (:mequilibriumarket 111211112111tntnntiIiIIAiA7.2.3 模型模型: 长期利率，短期利率，预期利率和远期利率长期利率，短期利率，预期利率和远期利率nntnnttnttttttnttntttttntIIiiIiiiii)1 ()1 ()1).(1)(1 ()1)(1).(1)(1 (1111111111111111)1).(1)(1(/111111ntnttttntiiiI)1).(1)(1)(1 ()1 (1112

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7、ttntt tiitin- tIttt7.2.4 纯预期理论的应用: shape of YCsExplain with process: expectation & arbitrage behavior )1).(1)(1)(1 ()1 (1112111tnttttttnntiiiiIniiiiItnttttttnt).(11121112)(1112ttttiiI)(2111112iiiIttttt2)(1112ttttiiI预期决定YC的形状7.2.5 implying of pure expectation theory: 政策应用1）期限结构是分析如下问题的重要工具:远期利率水平

8、远期利率水平 远期通胀预期远期通胀预期 )1)(1 ()1 (11122ttttiiI1)1()1(12211iIittttpritt111)1 ()1 (1122riIptt12112iIitttt+)(2112riIptt2）货币政策和期限结构应用: 中央银行影响短期利率；中央银行影响短期利率； 观察、利用预期影响长期利率观察、利用预期影响长期利率),(/),(),(),(&ttDRtiYfPMIwIfwkfTLKfY)1)(1 ()1 (11122ttttiiI7.2.6 预期理论的检验预期理论的检验)(21)()(21)(21)(21)(2121)(21)(21 ; )( si

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10、IbaiEiiIiiiEiiEiiiEiIiEiIiEiI由于：hold. becan n theory expectatio pure), 0()(21 ; 1 0; :)(21)()(2111111112111NiiiffiiiIiitttttttttt11111tttttiif0 Testing Result: Uncertainty and term premiums1. The longer the maturity of the security, the greater of the risk of fluctuation in value of principal to the

11、 investor. Lender prefer lend short, securities are not perfect substitutes.2. Premium must be offered to induce investors to purchase long-term securities.3. Forward rates would be biased estimates of future interest rates, exceeding them by the amount of term premium. rate. forward in the embodied

12、 premium term erm,Hicksian t :111nnttnttnttntLLiftntttttttLLLL1131211.07.3 liquidity preference theory: term premium theory)1).(1)(1)(1 ()1 (1111121211111tnttnttttttttttnntLiLiLiiI7.3.1 the assumption & model ntentetetttnlniiiii121.11)(21tttttttllliEiI)1)(1 ()1 (1212122ttttLiiI)(2/1121212ttttLii

13、I)(/1).(/1111111111ttnttnttttntLLniiinItttttLiiiI12112122/1 2/17.3.2 Application for the theory: shape of YCsDownward slope: decreasing of the difference of expected future rate over current rate is excess the term premium.012112tttLii6.3.2 Application for the theory: bill only strategyIf the short

14、nominal rate is not high, transaction cost is not high, it would be better for borrower to issue the short-term bond Assumptions: (Culbertson, 1957; Modigliani & Sutch, 1966)1.securities in different maturity ranges are considered to be imperfect substitutes. 2.Transaction cost should not be neg

15、lected3.Legal and behavioral restrictions cause lenders have preferred maturity ranges in which they operate. (preferred maturity habitats, preferred maturity areas)4.Borrowers demand of funds for certain maturity is related to their need of debt. 5.Both lender and borrower have their own maturity p

16、references and not deviate from these preferences unless there is an extreme attractive yields for other maturities.7.4. The Segmented Markets Approach7.4.1 assumptions & modelEvidence of assumption:(commercial banks have short-term liabilities, hence, for liquidity purposes, they hold large amo

17、unts of short-term assets. Insurance companies, have liabilities that extend into the distant future, they hold large amounts of long-term securities to be sure that the revenues that they need will be available when time arrives.)Conclusions: The segmented market behavior of lenders and borrowers b

18、asically determines the shape of the yield curve. Supply and demand analysis are applied to determinate prices of securities. An increase in the supply of securities in one maturity range will lead to a decline in prices (rise in yields )of those securities. With partial market segmentation, lenders

19、 and borrowers will leave their preferred maturity areas only if there are yield inducements on either side.7.4.2 Application for the theory: shape of YCsUpward slope: risk in long term, lender prefer short termdownward slope: savers are risk averse, short term high yield may not attract them to cha

20、nge the preferred maturity habitats unless the yield of short-term securities are too attractive. 7.4.3 implying for policy: 1. “bill only” or not “bill only”At the segment market, “bill only” policy may has problem of .2. “short term rate only” or not “short term rate only”If the market is segment,

21、 short term rate monetary policy target will .3. Can manipulate or can not manipulateWeather the Central Bank can manipulate the term structure the term structure at the segment market?4. Monetary policy, expected inflation & term structure) ,( :) ,( :1tiYfLMIYfIStn%5 .11%5 . 1%3)11106(:term-long%9%1%3)996(term)-(shortpolicy after %10%1%3)999(premiumrisk 3)(policy befor 333131213IIIiiiItttttttSummery of theories of term structure of interest ra