Contents
  1. 1. Basic Feature
    1. 1.1. Issuer
    2. 1.2. Temr to maturity
    3. 1.3. Bond Market
    4. 1.4. Collateral
    5. 1.5. Credit Enhancements
      1. 1.5.1. Internal enhancements
      2. 1.5.2. External enhancements
      3. 1.5.3. Cash collateral account
    6. 1.6. Covenants
    7. 1.7. Tax
    8. 1.8. Cash flow structure
    9. 1.9. Bonds with embedded options 含权债券
      1. 1.9.1. Callable bond
      2. 1.9.2. Putable bond
      3. 1.9.3. Convertible bond
      4. 1.9.4. Warrants
      5. 1.9.5. contingent convertible bond
  2. 2. Classification of Fixed-income markets
  3. 3. Primary Market and secondary market
  4. 4. Classification of corporate bond
  5. 5. Short-term funding available to banks 银行的融资方式
  6. 6. Bond valuation
  7. 7. Relationship between price and time
  8. 8. 无套利定价
  9. 9. Accrued interest
  10. 10. Matrix Pricing
  11. 11. Yield measure
  12. 12. Floating-rate notes valuation
  13. 13. Yield curve
  14. 14. Yield spread
  15. 15. Asset-baced securities
  16. 16. Collateralized mortgage obligations (CMO)
  17. 17. CMBS
  18. 18. Non-mortgage asset-backed securities
  19. 19. Collateralized debt obligations
  20. 20. Coupon 再投资下的债券的 Annualized holding period return
  21. 21. Duration 久期
    1. 21.1. Macaulay duration
    2. 21.2. Modified duration
    3. 21.3. Effective duration
    4. 21.4. Money duration
    5. 21.5. PVBP (price value of a basis point)
    6. 21.6. 影响 duration 的因素
  22. 22. Convexity 凸性
  23. 23. Credit Analysis

占比 10%,24 题。
三大类计算:

  1. 求债券价格
  2. 反求收益率
  3. 衡量利率风险 (duration)

Basic Feature

Issuer

  1. Supranational organizations:

    1. IMF
    2. World Bank

      Repayment source:

      • previous loans
      • paid-in cash from members
  2. Sovereign governments
    主权国家发债用本币计价,债券质量更好,因为可以印钞,不受外币储备限制。
    Repayment source:

    * tax revenues
    * print money
    
  3. Non-sovereign governments 市政债,也叫 municipal bonds
    分成:

    1. GO / Tax-backed debt: 由税收支撑,没有风险,需要 voter approval
    2. Revenue bonds: 由融资项目产生的收入来支撑,更高风险,更高收益
    

    Repayment source:

    * taxing authority
    * csah flow of financed project
    * special taxes or fees
    
  4. Quasi-government entities 准政府机构,也叫 agency bonds. Explicitly or implicitly backed by government.

  5. Companies/Corporation 公司债
    Repayment source:

    * cash flow from operations
    

关于 securitized bonds 资产证券化债券
是由特殊机构 Special Purpose Entities (or SPV) 发行。好处是:

  1. bankruptcy remote 破产隔离
  2. lower the wall between ultimate investors and originating borrowers.
  3. reduce liquidity risk in financial system
  4. enable innovations

Repayment source:

* cash flows generated by one or more underlying financial assets

Temr to maturity

  1. money market securities: <= 1 year
  2. capital market securities: > 1 year
  3. perpetual bonds: make periodic int. payments, but no promise to repay the principal

Tenor 是指从现在到到期日的时间。

Payments currency

  • dual-currency bond: coupon 和 par value 的支付是两种不同的货币。
  • currency option bond: 指的是债券的 coupon 和 par value 的还款币种投资者可以进行选择。

Bond Market

必考,一定掌握,判断是哪种 bond market。
判断三方面:issuer, location, currency.

If location = currency -> national bond
If issuer = currency -> domestic bond
if issuer != currency -> foreign bond

If location != currency -> euro bond

如果在 national market 和 eurobond market 都发行的,称为 global bond.

Collateral

Secured bond: 有抵押品
Unsecured bond: 无抵押品,也叫 debentures 纯信用债

Credit Enhancements

考试让选出是哪种信用增级

Internal enhancements

  1. Overcollateralization 过度抵押
  2. Excess spread 超额息差
  3. divide a bond into tranches with different seniority of claims

External enhancements

  1. surety bonds: issued by insurance companies
  2. bank guarantee: issued by a bank
  3. letter or credit: promise to lend money

Cash collateral account

担保公司先取出钱存到 cash collateral account 中,之后双方都不能再动这笔钱。此时 counterparty risk 最小。

Covenants

  • Affirmative convenants: issuer must do / should do 发行人承诺
  • Negative convenants: issuer musnt’ do 限制发行人

Tax

债券征税分两部分:

  1. interest income: 按照正常收入税征税
  2. capital gain: 资本利得部分征税更低

结论:

  1. capital gains are taxed at a lower rate
  2. 只有地方政府债券是免税的,美国国债都不是免税的
  3. 零息债券是没有利息征税的,只有 capital gain 的税。

Original issue discount (OID) bonds:
Capital gain 的部分分摊到每一期,每一期的部分按照利息去征税。到期的时候,capital gain 的部分不需要再征税。

Cash flow structure

按照还款现金流不同来对债券进行分类。

  1. Principal repayments structures 本金偿还的结构

    1. plain vanilla/bullet bond: 非摊销型,到期最后才还本金,最后一笔还款也叫 balloon payment.
    2. amortizing bond 摊销型债券:本金摊销到每一期来偿还
      1. fully amortizing:最后一期的本金就是 0
      2. partially amortizing: 摊销部分本金,最后一期还有一笔 balloon payment
    3. Sinking fund provision 偿债基金:特殊的摊销债券,发债之前先拿出来一笔钱用于以后还债。要求 issuer 在一定的时间就 retire a portion of a bond.
      Advantage: reduce credit risk
      Disadvantage: investors face reinvestment risks.
  2. Coupon Payment structures 利息支付的结构

    1. floating-rate notes:
      coupon rate = reference rate +- quoted margin
      The coupon rate determined at the coupon reset date is the rate that issuer promises to pay at the next coupon date.

      Upper limit is called the cap.
      Lower limit is called the floor.

      If have both upper & lower limit, also called a collar.

    特殊的 floating-rate notes:
        1. variable-rate note: 连 quoted margin 也不是固定的
        2. inverse floaters
            coupon rate = quoted margin - reference rate
            与市场利率变动方向相反
2. Deferred coupon rate
    会有一个锁定期,这段时间内 coupon 不支付。

3. Pay-in-kind (PIK) bond
    可以借新债还旧债。

4. Index-linked notes:coupon 和指数挂钩
    1. Equity-linked notes: 债券期间不支付任何利息,到期时的支付和 equity index 挂钩。
    2. Treasury Inflation Protected Securities (TIPS):
        保护投资者的钱不贬值,不受通货膨胀影响。
        Principal 本金和通胀率挂钩,coupon rate 固定不变,但是因为本金在变化,每期拿到的 coupon 也是随着通胀而变化的。

Bonds with embedded options 含权债券

Callable bond

允许 issuer 按约定价提前赎回,对 issuer 有利,卖给 investor 更便宜,V_callable = V_pure - V_call.

当 interest rate 下降的时候,issuer 选择 call。
债券价格的上涨能力比较小。

Concepts:

  1. deferred call, 这段时间不能 call
  2. call price
  3. call premium: the amount the call price is above par
  4. first call date: the date when it’s first callable at par value
  • American style: can be called anytime after the first call date
  • European style: can be called only on the call date
  • Bermuda style: can be called on specified dates, often on coupon payment dates.

Make-whole call provision
利率下降提前赎回时,issuer 把投资者损失的钱补回来。

Putable bond

允许 investor 提前售回,对 investor 有利,卖给 investor 更贵, V_putable = V_pure + V_put.

当 interest rate 上升的时候,issuer 选择 put。
债券价格上证能力大。

Convertible bond

可转股票,赋予 investor 的一个权利。

  1. conversion price: 转成股票后每股多少钱
  2. conversion rate = par value / conversion price
  3. conversion value = current share price * conversion ratio,债券立马转成股票的话,价值是多少
  4. conversion parity:
    1. at parity: conversion value = convertible bond’s price
    2. aboe parity: conversion value > convertible bond’s price
    3. below parity: conversion value < convertible bond’s price

Warrants

类似 option,不算 embedded optoin,算 attached option,benefit investor。
允许 investor 在到期时以约定价格购买公司的股票,与 option 的区别是公司需要发行新的股票。

contingent convertible bond

不是赋予 bondholder 的权利,只是当特定事件发生时,债券自动转成股票。

Classification of Fixed-income markets

  1. By issuer:

    1. government and government-related
      1. supranational organizations
      2. sovereign governments
      3. non-sovereign governments
      4. quasi-government
    2. corporate sector
      1. financial company
      2. non-financial company
    3. securitized sector
  2. By credit quality

    1. investment grade:
      1. Baa3 or above by Moody’s
      2. BBB- or above by S&P and Fitch
    2. Non-investment grade:
      1. Below investment grade

Primary Market and secondary market

  1. Primary market

    1. Public offering 公募

      1. Underwritten offering 包销:一次性把公司债券买断,之后发行的盈亏与公司无关。发行商希望价格越低越好。
        • Grey Market: 正式发行前的试发行市场,先对金融机构进行询价
      2. Best efforts offering 代销:券商只代理销售,赚取 commision,盈亏由公司承担。发行商希望价格越高越好。

      3. Auction
        Commonly used by issuing government debts

      4. Shelf registration 上架注册式发行: 注册一次连续发行,不需要向监管机构再次注册。
    2. Private placement 私募: 将整个 issue 完整发行给 qualified investor 或者一小批投资者,通常是大机构。
  2. Secondary market

    1. Exchange market: 有监管,违约风险低
    2. OTC Dealer market: 场外市场
    3. Electronic Trading Network

Trade Settlement 交割

  1. corporate bonds: T+3
  2. Government bonds: T+1
  3. Money market securities: T+0

Classification of corporate bond

  1. Bank debt 银行贷款
    1. bilateral loan: involve only one bank
    2. syndicated loan: funded by several banks
  2. Commercial paper 商业票据
    特征:

    1. 短期 < 1yr
    2. 无抵押纯信用债,又叫 debenture
    3. low rate
    4. 一般 directly placed 定向发行
    5. very little secondary market trading of commercial paper 一般持有到期
    6. rollover risk 滚动发行,借新债还旧寨
    

    考点:

    ![](https://i.imgur.com/WQW3KYZ.png)
    美国利息报价形式: discount yield,discount 部分分母 face value。
    欧洲利息报价形式:add-on yield,HPR 的形式,获得的真实的收益率,除以的分母是 purchase value。
    

Short-term funding available to banks 银行的融资方式

  1. customer deposits
  2. certificate of deposits
  3. central bank funds market 商业银行拆借存款准备金
  4. interbank funds 银行间无抵押贷款

Repurchase Agreement 回购协议

  1. repo rate
  2. repo margin (haircut),the difference between the market value of the collateral security and the value of the bond,就是不承认的部分。margin 越少意味着承认的部分越多。

逆回购:回购方的对手方,进行的就是逆回购。

Bond valuation

未来现金流折现求和,默认 par value 是 1000,默认一年计息两次。
利用计算器,N 是付的期数,I/Y 是每期的折现率,PMT 是每期 coupon,FV 是到期 par value,得到的 PV 就是债券现价。

Value of a zero-coupon bond
即使没有利息,也要按照一年两次付息来考虑。例如给定 YTM = 8%, maturity = 8 yr, 利用计算器求的时候,PMT 输入 0,但是 I/Y 还是要输入 4,N 还是要输入 16。

Relationship between price and time


在到期日那天,债券价格都是等于 par value 的。

价格变化:

  1. 溢价债券,YTM < coupon rate, 价格下降
  2. 这家债券,YTM > coupon rate, 价格上升

无套利定价

当题目中的债券没有给 YTM 的时候,依然要求债券价格,可以利用一些零息债券的 spot rate 作为每一期现金流的 discount rate。

Accrued interest

债券在两次计息日之间被交易的话,在下一次计息的时候,卖方要按持有时间比例得到期间的利息。

$\text{accrued interest}=coupon\times{}\frac{T_1}{T_1+T_2}$

  1. clean price: the agreed upon price of the bond
  2. full price: the actual amount the buyer pays to the seller, which equals the clean price plus any accrued interest: full price = clean price + accrued interest.

Matrix Pricing

常用在 bonds that are currently not traded or infrequently traded.

先找到一个 benchmark,再吧要估值的债券在 benchmark 的基础上加一个 spread。只考虑一个风险(和时间有关的 maturity risk,其它都认为是一致的)。

只能对 YTM 和 时间做 linear interpolation。如果能获取一致的 coupon rate 最好,不能也没有关系。

Yield measure

  1. Effective yield 实际年化收益率。
    YTM 认为是一年的名义年化收益率。
    计算: $\text{effective yield}=(1+\frac{\text{YTM}}{m})^m-1$,m 是一年有几期。

    For annual bond, effective yield = YTM.
    For bonds with greater periodicity, effective yield is greater than YTM.

  2. current yield 当期收益率,需要掌握!
    只考虑 coupon 部分的收益率的收益。
    $\text{current yield}=\frac{\text{sum of coupon payment received over the year}}{\text{flat bond price}}$

  1. yield for money market instruments

    1. yield quoted on a discount basis
      $\text{DR}=\frac{\text{year}}{\text{days}}\times{}\frac{FV-PV}{FV}$
    2. yield quoted on an add-on basis
      $\text{AOR}=\frac{\text{year}}{\text{days}}\times{}\frac{FV-PV}{PV}$
      这里面的 year 如果取 365 的话,该式又称 Bond Equivalent Yield. 这个 BEY 和数量的 BEY 是不一样的。
  2. Yield to call (put) 要掌握:
    N = duration before call date
    PV = bond price
    PMT = coupon
    FV = exercise price
    CPT PV

  3. Option-adjusted yield
    剔除 option 之后的收益率,只用于含权债券:

    1. callable bond: ODY < YTM,因为 call 对发行者有利,投资者需要更高的名义收益率。
    2. puttable bond: ODY > YTM,因为 put 对投资者有利,投资者接受更低的名义收益率。

Floating-rate notes valuation

$P=\sum\frac{CF_i}{(1+r)^t}$
coupon rate = L + quoted margin
discount rate = L + discount margin 折现率也要跟着浮动。discount margin 也叫 required margin。

计算 discount margin 的时候,算出 I/Y,再减去 libor rate。

Yield curve

不考计算,要知道有哪些收益率曲线。

  1. spot curve: 用 spot rate 标出来的曲线
  2. yield curve for coupon bonds: 选用付息债券的 YTM.
  3. par bond yield curve: 债券价格等于 par value 时一些列 coupon rate 构成的收益率。
  4. forward yield curve: 用 forward rate 标出来的曲线

如何求 forward rate
根据 spot rate 来求 forward rate:
$(1+S_3)^3=(1+S_1)(1+1y2y)^2$

S_3 的意思是三年期即期的年化利率,所以还是要三次方。

Yield spread

两个不同 bond 的 YTM 的差值。
Benchmark spread 的选择:

  1. G-spread 用 government bond yield
  2. I-spread: 用 swap rate
  3. Z-spread: 也是国债,只不过采用 spot-rate

Asset-baced securities

三大机构买走的 MBS,也叫 agency MBS。
不满足三大机构要求的,叫做 non-agency MBS。

Rights of lender in a foreclosure:

  1. recourse loan 有求偿权
  2. nonrecourse loan 无求偿权,只能卖抵押房,不能再求偿

Prepayment risk

  1. Contraction risk,prepayment 过快,MBS 的 average life 变短了,市场利率下降时更容易发生。
  2. Extention risk,prepayment 过慢,MBS 的 average life 变长了,市场利率上升时更容易发生。

Prepayment risk measurement

  1. Single monthly mortality (SMM)
    $\text{SMM}=\frac{\text{Prepayment for month}}{\text{beginning mortgage balance for month}-\text{scheduled principal repayment for month}}$
  2. CPR: $(1-SMM)^12=1-CPR$
  3. PSA: 100PSA 对应一定的 CPR,100 PSA 是基准,速率越大表示提前偿还的速率越大。150 PSA 就是 100 PSA 的 1.5 倍。

Collateralized mortgage obligations (CMO)

  1. sequential tranches
    分为 ABC 三个 tranche。
    现金流来了以后,同时还三者的利息。
    但是还本金的部分先还 A,A 的本金还完了再还 B,再还 C。

    A 是 short tranch,contraction risk 最大,extension risk 最小。
    C 是 long tranch,contraction risk 最小,extension risk 最大。

  2. PAC and support structure
    每一期 PAC 结构中收到的现金流是计划好是稳定的,配有一个 support tranch。
    如果 prepayment 很多,pac 的计划现金流付完好,被 support tranch 吸收,support tranch 也是债券,它的 contraction risk 很大。
    如果 payment 很少,support 结构就不要了,全部给 pac 结构,此时 support tranch 有 extension risk。

    support 结构的 contraction risk 和 extension risk 都很高。

    PAC 只能在 initial collar 的范围内能拿稳定现金流。prepayment 速率过快如果打爆了 support 的话,PAC 就不能保持稳定。

CMBS

上面是个人住房抵押贷款的资产证券化。
还有一种是商业房产抵押贷款的资产证券化(CMBS)。
No recourse.

Non-mortgage asset-backed securities

非住房贷款,如买车抵押贷款等

Collateralized debt obligations

垃圾债转为支持发行的。

Coupon 再投资下的债券的 Annualized holding period return

如果债券没有持有到期,而是在中间卖出了,求 yield?

  1. 找出 t0 时刻的债券购买价格
  2. 找出 coupon 考虑再投资的情形下带来的总现金流。coupon 和 coupon 再投资的部分可以考虑用年金一起求出来。
  3. 求出 holding period return。

结论:

  1. 如果 coupon 再投资利率一直是 YTM 的话,最后的 HPR 就是 YTM。
  2. 如果 coupon 再投资利率大于 YTM 的话,最后的 HPR > YTM.
  3. 如果 coupon 再投资利率小于 YTM 的话,最后的 HPR < YTM.

由于利率改变导致的再投资收益的改变,叫做 reinvestment risk.
由于利率改变导致的债券价格的改变,叫做 market price risk.

称它们为广义的利率风险,理想情况下我们期望这两种风险能够互相抵消。

Duration 久期

Duration: a measure of a bond’s interest rate risk. Sensitivity of a bond’s full price to a change in its yield.

久期越高,债券的利率风险越高。

Macaulay duration

以折现现金流作为权重的,现金流回流的平均时间:
$\text{Macaulay duration}=\sum^n_{t=1}\frac{PVCF_t}{P_0}\times{}t$

特例:

  1. Duration of zero-coupon bond is equal to time-to-maturity.
  2. Macaulay duration of perpetuity or perpetual bond: $\frac{1+YTM}{YTM}$
  3. Portfolio duration 就是 weighted sum of all durations.

Modified duration

A linear estimate of the percentage change in a bond’s price that would result from a 1% change in its YTM.
$\text{Modified duration}=\frac{\text{Macaulay duration}}{1+\text{periodic market yield}}$

Effective duration

更适合含权债券。
A linear estimate of the percentage change in a bond’s price that would result from a 1% change in the benchmark yield curve.
$\text{Effective duration}=\frac{V{-}-V{+}}{2\times{}V_0\times{}\Delta{}\text{curve}}$

Money duration

Stated in currency units and is sometimes expressed per 100 of bond value.
$\text{Money duration}=\text{annual modified duration}\times{}\text{full price of bond}$

PVBP (price value of a basis point)

The money change in full price of a bond when its YTM changes by one basis point (0.01%).

$\text{PVBP}=\frac{PV{-}-PV{+}}{2}$
$\text{PVBP}=\text{money duration}\times{}\text{full price of a bond}$

影响 duration 的因素

  1. lower coupon means higher duration
  2. longer maturity means higher duration
  3. lower market yield means higher duration
  4. a put or call provision means lower duration

Convexity 凸性

必背,凸度的调整:
$\frac{\Delta{P}}{P}=-\text{annual modified duration}\times{}(\Delta{}YTM)+\frac{1}{2}\times{}\text{annual convexity}\times{}(\Delta{}YTM)^2$

Callable bond

Puttable bond

结论:puttable bond 的 convexity 最高,callable bond 的 convexity 最低。

Duration gap
duratoin gap = macaulay duration - investment horizon.

If duration gap = 0,两种风险抵消
If duration gap > 0, macaulay duration 较大,market price risk 占上风
If duration gap < 0, investment horizon 较大,再投资风险占上风

Credit Analysis

Expected loss
expected loss = default probability * loss severity given default.
loss severity given default = 1 - recovery rate.

违约求偿顺序

  1. 带 first 的 loan/mortgage 最先
  2. senior 大于 junior
  3. 有抵押 > 无抵押 > subordinated

评级顺序
AAA > AA > A
AA+ > AA > AA-
A+ > A > A-
没有 AAA+

Notching
同一家公司的不同债券有不同评级,最容易出现在信用质量差的公司中。

Structural subordination
子公司的债券评级更高。

Credit 分析的 4C 原则
给定描述,要知道是属于哪个 C。

  1. Capacity: 行业基本面分析,如波特五力,周期。以及公司基本面分析。
  2. Collateral: 从公司角度看全公司的资产的质量和价值。
  3. Covenants
  4. Character
Contents
  1. 1. Basic Feature
    1. 1.1. Issuer
    2. 1.2. Temr to maturity
    3. 1.3. Bond Market
    4. 1.4. Collateral
    5. 1.5. Credit Enhancements
      1. 1.5.1. Internal enhancements
      2. 1.5.2. External enhancements
      3. 1.5.3. Cash collateral account
    6. 1.6. Covenants
    7. 1.7. Tax
    8. 1.8. Cash flow structure
    9. 1.9. Bonds with embedded options 含权债券
      1. 1.9.1. Callable bond
      2. 1.9.2. Putable bond
      3. 1.9.3. Convertible bond
      4. 1.9.4. Warrants
      5. 1.9.5. contingent convertible bond
  2. 2. Classification of Fixed-income markets
  3. 3. Primary Market and secondary market
  4. 4. Classification of corporate bond
  5. 5. Short-term funding available to banks 银行的融资方式
  6. 6. Bond valuation
  7. 7. Relationship between price and time
  8. 8. 无套利定价
  9. 9. Accrued interest
  10. 10. Matrix Pricing
  11. 11. Yield measure
  12. 12. Floating-rate notes valuation
  13. 13. Yield curve
  14. 14. Yield spread
  15. 15. Asset-baced securities
  16. 16. Collateralized mortgage obligations (CMO)
  17. 17. CMBS
  18. 18. Non-mortgage asset-backed securities
  19. 19. Collateralized debt obligations
  20. 20. Coupon 再投资下的债券的 Annualized holding period return
  21. 21. Duration 久期
    1. 21.1. Macaulay duration
    2. 21.2. Modified duration
    3. 21.3. Effective duration
    4. 21.4. Money duration
    5. 21.5. PVBP (price value of a basis point)
    6. 21.6. 影响 duration 的因素
  22. 22. Convexity 凸性
  23. 23. Credit Analysis