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1、Chap 2. 利率风险管理,王海艳 博士 副教授 ,课程内容,利率的期限结构 利率敏感性 利率风险的传统度量方法,影响利率的因素,中央银行的货币政策 中央银行货币政策的目标: 钉住某一利率/钉住银行准备金 金融市场全球一体化加速了利率的变动和各国利率波动之间的传递,中央银行货币政策的影响,2019/8/24,5,1. Term Structure of interest Rate,The structure of interest rates for discounting cash flows of different maturities. （不同证券的市场收益率或利率） Yield c
2、urve（收益率曲线）： 收益与到期期限的关系 flat, upward-sloping, downward-sloping, humped-shaped Bond stripping / bond reconstitution,1. 利率期限结构,三个主要理论： 无偏预期理论 流动性溢价理论 市场分割理论,1. 利率期限结构,无偏预期理论 某一特定时间下的收益曲线反映了当时市场对未来短期利率的预期。 长期利率是现行的短期利率与预期的短期利率的几何平均值。 缺陷：远期利率并非能对未来利率进行最佳预测（未来利率以及货币政策的不确定性，导致持有长期证券是有风险的）。,1. 利率期限结构,流动性溢价
3、理论 考虑了未来的不确定性； 长期利率等于现行利率与预期短期利率加上流动性溢价的几何平均数。流动性溢价随着期限增加而上涨。,1. 利率期限结构,市场分割理论 投资者有着各自特有的期限偏好，因此不同到期期限的证券之间不是完全的替代品，投资者意愿的持有期是由其拥有的资产和负债的性质决定的。 比较：银行，寿险公司 利率是由某个期限等级或某个分割市场内的供求条件决定的。,2019/8/24,10,Term Structure of interest Rate,Yield Curve under Certainty Consider 2-year bond strategies: 1. buying t
4、he 2-year zero offering a 2-year yield to maturity of 6%, and holding it until maturity 2. Invest the same price in a 1-year zero-coupon bond with a yield to maturity of 5%. Then reinvest in another 1-year bond.,2019/8/24,11,Example,We compare two 3-year strategies. One is to buy a 3-year zero, with
5、 a yield to maturity of 7%, and hold it until maturity. The other is to buy a 2-year zero yielding 6%, and roll the proceeds into a 1-year bond in year 3, at the short rate r3.,2019/8/24,12,Forward Rates,Total growth factor of an investment in an (n-1)-year zero,2019/8/24,13,Interest Rate Uncertaint
6、y & Forward Rates,In a certain world： Two consecutive 1-year investments in zeros would need to offer the same total return as an equal-sized investment in a 2-year zero.,2019/8/24,14,Interest Rate Uncertainty & Forward Rates,Example(Certainty): Suppose that todays rate is r1=5%, and that the expect
7、ed short rate for the following year is E(r2)=6%. If investors cared only about the expected value of the interest rate, what would be the price of a 2-year zero?,2019/8/24,15,Interest Rate Uncertainty & Forward Rates,Example(Certainty): Now consider a short term investor who wishes to invest only f
8、or 1 year. She can purchase the 1-year zero first, then purchase the 2-year zero with 1 year to maturity. What will be the price of each purchase? What is the holding-period return?,2019/8/24,16,Interest Rate Uncertainty & Forward Rates,Example： Suppose that most investors have short-term horizons a
9、nd therefore are willing to hold the 2-year bond only if its price falls to $881.83. At this price, the expected holding-period return on the 2-year bond is 7% . The risk premium of the 2-year bond, therefore, is 2%; it offers an expected rate of return of 7% versus the 5% risk-free return on the 1-
10、year bond. At this risk premium, investors are willing to bear the price risk associated with interest rate uncertainty. When bond prices reflect a risk premium, however, the forward rate, f2, no longer equals the expected short rate, E(r2). Although we have assumed that E(r2)=6%, it is easy to conf
11、irm that f2=8%. The yield to maturity on the 2-year zeros selling at $881.83 is 6.49%, and,2019/8/24,17,2. Interest rate sensitivity,Bond prices and yields are inversely related: as yields increase, bond prices fall; as yields fall, bond prices rise;(债券价格与收益成反比） An increase in a bonds yield to matur
12、ity results in a smaller price change than a decrease in yield of equal magnitude. （债券的到期收益率升高会导致其价格变化幅度小于等规模的收益下降）,2019/8/24,18,Interest Rate Sensitivity,Prices of long-term bonds tend to be more sensitive to interest rate changes than prices of short-term bonds. （长期债券价格对利率变化的敏感性比短期债券更高） The sensit
13、ivity of bond prices to changes in yields increases at a decreasing rate as maturity increases. In other words, interest rate risk is less than proportional to bond maturity.（当到期时间增加时，债券价格对收益率变化的敏感性以下降的比率增加，即：利率风险与债券到期时间不对称）,2019/8/24,19,Interest Rate Sensitivity,- Interest rate risk is inversely re
14、lated to the bonds coupon rate. Prices of low-coupon bonds are more sensitive to changes in interest rates than prices of high-coupon bonds （利率风险与债券息票率成反比。低息票债券的价格比高息票债券的价格对利率变化更敏感） - The sensitivity of a bonds price to a change in its yield is inversely related to the yield to maturity at which the
15、 bond currently is selling（债券价格对其收益率变化的敏感性与当前出售债券的到期收益率成反比）,3 . 利率风险的传统度量方法,再定价(或融资缺口)模型 期限模型 有效期限模型,衡量金融机构的资产负债缺口风险,再定价模型,又称融资缺口模型，是用帐面价值现金流量的分析方法分析再定价缺口（repricing gap），即分析在一定时期内，金融机构从其资产上所赚取的利息收入对其负债所承担的利息支出之间的再定价缺口。 银行通过计算资产负债表上每项利率敏感性资产（RSA）和利率敏感性负债（RSL），来报告每一组期限内的再定价缺口。,利率敏感度（rate sensitivity),
16、指大约按照当期的市场利率对某段时间内（或某组期限内）的资产或负债进行重新定价。 期限的不同分类（美联储）： 1天 ； 1天-3个月； 3个月-6个月； 6个月-12个月 1年-5年 ； 5年以上,例1. 再定价缺口,RSARSL, 金融机构面临再投资风险(利率下降的情况）,累计缺口（CGAP）,1年期累计缺口 （CGAP） CGAP = （RSA RSL） NII i=(CGAP)* R NII：净利息收入的变化 缺口比率： CGAP/A 1）符号：直接的利率风险情况 2）缺口比率反映风险的大小,RSA与RSL的利率变化相同时，CGAP对利率变化和净利息收入（NII）变化之间关系的影响,一般来说，当CGAP为正时，NII的变化与利率变化正相关；当CGAP为负时，即使RSA与RSL的利率上涨幅度相同，也会带来NII的下降。 在预期利率会上升的情况下，金融机构倾向于保持正的CGAP； 在预期利率会下调的情况下，金融机构往往倾向于保持负的CGAP，以获取利益。 CGAP效应,R
