Lecture 4 2012 valuation and risk

固定收益课题 4 ：债券定价和风险 / Valuation and Risk 陈国辉博士／南洋理工大学商学院

债券定价模式 ,[object Object],[object Object],[object Object],[object Object],[object Object]

价格和收益率的关系 (Price-Yield Relationship) Price Yield ,[object Object],[object Object],[object Object]

到期收益率 ( Yield-to-Maturity,YTM) 的局限性 ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

总收益 Total Return ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Reinvestment Risk

总收益 Total Return ,[object Object],[object Object],[object Object],[object Object],[object Object],Price Risk

平均到期期限 Average Maturity ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

久期 Duration ,[object Object],[object Object],[object Object]

久期：债券价格对利率变动的敏感度 ,[object Object],[object Object]

国债的久期在付息期间（ w ＝从今天到下个付息日的部分时间）：在付息日（ w ＝ 1 ）：

久期 Duration ,[object Object],Bond Yr 1 Yr 2 Yr 3 Yr 4 Yr 5 Duration A 5 5 5 5 105 4.5 Yr B 20 20 20 20 120 3.8 Yr C 0 0 0 0 100 5.0 Yr

久期的特性（ 1 ） ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Zero coupon bond Discount bond Par bond Premium bond Perpetual bond Maturity Duration

久期的特性（ 2 ） ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Duration (in year) of a 12%, 12% yield 20 years bond

久期实用案例 1 ,[object Object],[object Object],[object Object]

久期实用案例 2 ,[object Object]

案例 : 19.5 year 12% coupon bond priced at 12% yield. A 10 bp change in yield. ,[object Object]

久期实用案例 3 ,[object Object],[object Object],[object Object],[object Object]

久期实用案例 4 ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

久期实用案例 5 ,[object Object],[object Object],[object Object]

久期实用案例 6 – 组合 ,[object Object],If yield curve shift up by 100 bp, what is the percentage value change of portfolio? Bond Market Value (mil $) Weight Mod Duration Weight x Mod Dur A 10 0.1 4 0.4 B 40 0.4 7 2.8 C 30 0.3 6 1.8 D 20 0.2 2 0.4 Total 100 1 5.4

凸性 Convexity ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

从 Dp/Dy 到 D 2 p/Dy 2 ,[object Object],[object Object]

测量凸性 Measure Convexity 有些人用以下定义：我们对凸性的定义 : ,[object Object],[object Object]

凸性的特性 ,[object Object],[object Object],[object Object],[object Object]

凸性的特性 Coupon bond ’s convexity is sum of a duration-matched zero’s convexity.

凸性的特性 ,[object Object],[object Object],[object Object]

近似凸性 Approximate Convexity

应用久期和凸性测量价格变化应用泰勒系列关系式 Taylor series expansion ： http://en.wikipedia.org/wiki/Taylor_series

Duration Approximation Duration and Convexity Approximation Yield Price

举例 ,[object Object],[object Object]

近似久期 Approximate Duration ,[object Object],[object Object],[object Object],[object Object],[object Object]

久期实用案例 7 －相对久期 Matching $Duration ,[object Object],[object Object],Bond Price Par Amount (PA) Market Value (MV) Modified Duration (MD) Dollar Duration ($D) X 80 10 mill 8 mill 5 8 mil x 5 / 100 = $400,000 (for 1% change in yield) Y 90 ? ? 4 $400,000 (imposed)

久期实用案例 7 －相对久期 Matching $Duration

债券免疫 Bond Immunization ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

资金不足和资金过分充足 Under-funding and Over-funding ,[object Object],[object Object],Year Pension Payment Present value (5% yield) 1 10,000 9,523.81 2 10,000 9,070.29 3 10,000 8,638.38 4 10,000 8,227.02 5 10,000 7,835.26 Total 50,000 43,294.77

[object Object],[object Object],[object Object],Modified Duration Value today If yield is 5% If yield is 6% Assets 4.33 $43,294.77 $43,294.77 $41,471.04 Liabilities 2.76 $43,294.77 $43,294.77 $42,123.64 Difference 0 0 -$652.6 (under-funded)

债券免疫理论 Bond Immunization Theorem ,[object Object],Where P 1 = Value after yield change （利率变化后的价值） P 0 = Value before yield change （利率变化前的价值） MD = Modified duration （修正久期） Δ y = change in yield （利率变化） C = Convexity （凸性）

债券免疫理论 Bond Immunization Theorem ,[object Object],[object Object]

债券免疫理论 Bond Immunization Theorem ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

债券免疫理论 Bond Immunization Theorem ,[object Object],[object Object],[object Object],[object Object]

债券免疫理论 Bond Immunization Theorem ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

债券免疫理论应用时的问题 Bond Immunization in Practice ,[object Object],[object Object],[object Object]

Max imize Yield （收益率最大化） ,[object Object],[object Object],[object Object]

债券免疫理论应用时的问题－重新组合 Bond Immunization in Practice － Rebalancing ,[object Object],[object Object],[object Object],[object Object],[object Object]

为负债免疫的最佳方法是什么？ What is the best way to immunize a liability? ,[object Object],[object Object]

Lecture 4 2012 valuation and risk

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