利率风险管理课件
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Chap 2. 利率风险管理
课程内容
1. 利率的期限结构 2. 利率敏感性 3. 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
1. Term Structure of interest Rate
2022/3/23
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.
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。
What will be the price of each purchase? What is the holding-period return?
2022/3/23
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.
2022/3/23
11
Forward Rates
(1 yn )n (1 yn1)n1 (1 rn )
(1
rn )
(1 yn )n (1 yn1)n1
Total growth factor of an investment in an (n-1)-year zero
2022/3/23
12
Interest Rate Uncertainty & Forward Rates
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.
2022/3/23
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.
Bond stripping / bond reconstitution
2022/3/23
5
1. 利率期限结构
三Leabharlann Baidu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。
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
2022/3/23
13
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?
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
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.
课程内容
1. 利率的期限结构 2. 利率敏感性 3. 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
1. Term Structure of interest Rate
2022/3/23
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.
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。
What will be the price of each purchase? What is the holding-period return?
2022/3/23
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.
2022/3/23
11
Forward Rates
(1 yn )n (1 yn1)n1 (1 rn )
(1
rn )
(1 yn )n (1 yn1)n1
Total growth factor of an investment in an (n-1)-year zero
2022/3/23
12
Interest Rate Uncertainty & Forward Rates
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.
2022/3/23
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.
Bond stripping / bond reconstitution
2022/3/23
5
1. 利率期限结构
三Leabharlann Baidu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。
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
2022/3/23
13
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?
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
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.