Bond duration and maturity are two key concepts in fixed-income investments, but they measure different things:
1. Bond Maturity
• Definition: The time remaining until the bond’s principal (face value) is repaid to the bondholder.
• Units: Measured in years.
• Key Role: Indicates when the bondholder will receive the final payment.
• Fixed Value: It does not change after the bond is issued (unless the bond is callable or convertible).
• Purpose: Used for understanding the time horizon of the investment.
2. Bond Duration
• Definition: A measure of a bond’s sensitivity to changes in interest rates. It is the weighted average time it takes to receive all cash flows (interest and principal).
• Units: Measured in years but reflects price sensitivity.
• Key Role: Indicates the percentage change in a bond’s price for a 1% change in interest rates.
• Example: If a bond has a duration of 5 years, its price will decrease by approximately 5% if interest rates rise by 1%.
• Dynamic Value: Changes over time as the bond approaches maturity and as market conditions evolve.
• Purpose: Helps assess interest rate risk and manage portfolios.
Comparison
AspectDurationMaturity
Measures Interest rate sensitivity Time until final payment
Focus Weighted cash flow timing Final repayment date
Changes Over Time Yes (affected by cash flows) No (fixed at issuance)
Relevance Risk management, pricing Investment time horizon
In short, maturity is a simple calendar date concept, while duration is a more complex measure tied to the bond’s cash flows and interest rate risk.
本来TLT应该归大千，但经常有人在这里提到，而我又不去大千，就在这里说几句。
TLT's duration 大概是 16年多点，这个没什么问题。但当我们在国债收益率曲线上找 maturity 时经常有人（包括糊涂大佬）说要看16年多点的 maturity，那就不对了。
TLT 的官名是 iShares 20+ Year Treasury Bond ETF，所以它持有的国债都是20年以上的。MorningStar 里可以看到所有的 holdings，20年以上一直到30年一共25个债券，Effective Maturity（也就是 market value weighted maturity）是 25.70年。国债收益率曲线上要对照25年的点，不是16年多的点。
MorningStar: TLT --- iShares 20+ Year Treasury Bond ETF
MorningStar 的数据好像有点老，也许是基金自己过去报的。Bloomberg 的数据，duration 短一点，average maturity 长一点。但 duration 16年左右、average maturity 25年左右总是差不多的。至于Effective Duration 与 Modified Duration 之间的差别，普通投资人就不要纠结了。
Bloomberg:
GV --- US Treasury On-the-run
SOFR OIS --- SOFR Interest Rate Swap
Bond duration and maturity are two key concepts in fixed-income investments, but they measure different things:
1. Bond Maturity
• Definition: The time remaining until the bond’s principal (face value) is repaid to the bondholder.
• Units: Measured in years.
• Key Role: Indicates when the bondholder will receive the final payment.
• Fixed Value: It does not change after the bond is issued (unless the bond is callable or convertible).
• Purpose: Used for understanding the time horizon of the investment.
2. Bond Duration
• Definition: A measure of a bond’s sensitivity to changes in interest rates. It is the weighted average time it takes to receive all cash flows (interest and principal).
• Units: Measured in years but reflects price sensitivity.
• Key Role: Indicates the percentage change in a bond’s price for a 1% change in interest rates.
• Example: If a bond has a duration of 5 years, its price will decrease by approximately 5% if interest rates rise by 1%.
• Dynamic Value: Changes over time as the bond approaches maturity and as market conditions evolve.
• Purpose: Helps assess interest rate risk and manage portfolios.
Comparison
Aspect Duration Maturity
Measures Interest rate sensitivity Time until final payment
Focus Weighted cash flow timing Final repayment date
Changes Over Time Yes (affected by cash flows) No (fixed at issuance)
Relevance Risk management, pricing Investment time horizon
In short, maturity is a simple calendar date concept, while duration is a more complex measure tied to the bond’s cash flows and interest rate risk.
modified duration：
也就是说利率每波动1%，价格波动17%而不是25%
TLT的duration是17年，这个数字本身就已经告诉我们，yield增加1%，TLT的价格大概下降17%。
所以还需要用17年算什么呢？
买了TLT也就是买了一堆20年以上的债券。假如16年债券收益率变动但20年以上的收益率没怎么动（等价于20年以上的价钱没怎么动），TLT 价钱也不怎么动。
25年只是个近似，更精确的要计算所谓key rate duration，把利率（或收益率）曲线上单个年份的收益率摄动一下，保持其他年份的不变，看看 portfolio 价钱会动多少。
利率（或收益率）曲线第一大 principal component 是大家一起上下，第二是所谓 steppening or flatterning，第三是 curvature 变动。因为第一大动作是利率一起上下，所以大家觉得16年收益率与20年以上收益率好像是一回事。其实还是有区别。
Effective Duration (HB_OAS_EFF_DURTN) 是 par curve parallel shift。具体的涉及 yield curve building，我几句话不可能讲明白。
Modified Duration (YAS_MOD_DUR) 是把 portfolio 里面所有债券cash flow 都算出来，然后按照 price and yield 公式算出 yield，然后 shift the yield number，计算 price sensitivity to yield。Bloomberg 计算这个 modified duration 比起 generative AI 只是一点点算力。这个计算不涉及 yield curve building，就是 price and yield 公式倒来倒去迭代计算（解析或数值牛顿法算一阶导数迭代）。
从前Bloomberg yield curve building 很差的，但现在好许多。从前 yield curve building 是 sell-side and hedge fund 的技术，2008年金融危机后都扩散开来了，大家都会了。