利率风险管理课件(PPT 55张)
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2019/2/21
15
Interest Rate Uncertainty & Forward Rates
Example：
Suppose that most investors have short-term horizons and 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-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 confirm that f2=8%. The yield to maturity on the 2-year zeros selling at $881.83 is 6.49%, and 2 2
13
2019/2/21
Interest Rate Uncertainty & Forward Rates Example(Certainty): Suppose that today’s rate is r1=5%, and that the expected 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?
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)
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
Chap2.利率风险管理
wanghaiyan@tongji.edu.cn
课程内容
1. 2. 3.
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Biblioteka Baidu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
2019/2/21 11
Forward Rates
( 1yn) ( 1yn1) ( 1r n)
n n 1
( 1yn) ( 1r n) n 1 ( 1yn1)
n
Total growth factor of an investment in an (n-1)-year zero
2019/2/21
14
Interest Rate Uncertainty & Forward Rates Example(Certainty): Now consider a short term investor who wishes to invest only for 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?
中央银行货币政策的影响
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 curve（收益率曲线）： 收益与到期期限的关系 flat, upward-sloping, downward-sloping, humped-shaped
-
2019/2/21
17
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 sensitivity 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）
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.
2019/2/21 10
Example
We compare two 3-year strategies. One is to buy a 3-year zero, with 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.
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。
Term Structure of interest Rate
Yield Curve under Certainty Consider 2-year bond strategies: 1. buying the 2-year zero offering a 2-year yield to maturity of 6%, and holding it until maturity
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。
- The sensitivity of a bond’s price to a change in its yield is inversely related to the yield to maturity at which the 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） 2019/2/21 19
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。
RSA<RSL, 金融机构面临再融资风险（利率上升的情况） RSA>RSL, 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）
Bond stripping / bond reconstitution
5
2019/2/21
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。
例1. 再定价缺口
1 资产 1. 1天 2. 1天-3个月 3. 3个月-6个月 4. 6个月-12个月 5. 1年-5年 6. 5年期以上 $20 30 70 90 40 10 $260 2 负债 $30 40 85 70 30 5 $260 3 缺口 $-10 -10 -15 +20 +10 +5 4 累计缺口 $ -10 -20 -35 -15 -5 0
18
-
2019/2/21
Interest Rate Sensitivity
- Interest rate risk is inversely related to the bond’s 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）
2019/2/21
16
( 1 y ) 1 . 0649 2 1 f 1 . 08 2 1 y 1 . 05 1
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 bond’s yield to maturity 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）
12
2019/2/21
Interest Rate Uncertainty & 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.
15
Interest Rate Uncertainty & Forward Rates
Example：
Suppose that most investors have short-term horizons and 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-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 confirm that f2=8%. The yield to maturity on the 2-year zeros selling at $881.83 is 6.49%, and 2 2
13
2019/2/21
Interest Rate Uncertainty & Forward Rates Example(Certainty): Suppose that today’s rate is r1=5%, and that the expected 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?
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)
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
Chap2.利率风险管理
wanghaiyan@tongji.edu.cn
课程内容
1. 2. 3.
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Biblioteka Baidu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
2019/2/21 11
Forward Rates
( 1yn) ( 1yn1) ( 1r n)
n n 1
( 1yn) ( 1r n) n 1 ( 1yn1)
n
Total growth factor of an investment in an (n-1)-year zero
2019/2/21
14
Interest Rate Uncertainty & Forward Rates Example(Certainty): Now consider a short term investor who wishes to invest only for 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?
中央银行货币政策的影响
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 curve（收益率曲线）： 收益与到期期限的关系 flat, upward-sloping, downward-sloping, humped-shaped
-
2019/2/21
17
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 sensitivity 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）
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.
2019/2/21 10
Example
We compare two 3-year strategies. One is to buy a 3-year zero, with 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.
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。
Term Structure of interest Rate
Yield Curve under Certainty Consider 2-year bond strategies: 1. buying the 2-year zero offering a 2-year yield to maturity of 6%, and holding it until maturity
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。
- The sensitivity of a bond’s price to a change in its yield is inversely related to the yield to maturity at which the 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） 2019/2/21 19
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。
RSA<RSL, 金融机构面临再融资风险（利率上升的情况） RSA>RSL, 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）
Bond stripping / bond reconstitution
5
2019/2/21
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。
例1. 再定价缺口
1 资产 1. 1天 2. 1天-3个月 3. 3个月-6个月 4. 6个月-12个月 5. 1年-5年 6. 5年期以上 $20 30 70 90 40 10 $260 2 负债 $30 40 85 70 30 5 $260 3 缺口 $-10 -10 -15 +20 +10 +5 4 累计缺口 $ -10 -20 -35 -15 -5 0
18
-
2019/2/21
Interest Rate Sensitivity
- Interest rate risk is inversely related to the bond’s 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）
2019/2/21
16
( 1 y ) 1 . 0649 2 1 f 1 . 08 2 1 y 1 . 05 1
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 bond’s yield to maturity 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）
12
2019/2/21
Interest Rate Uncertainty & 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.