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二级市场有交易所交易，OTC交易(dealer market)

央行货币工具：
1.discount rate
2.open market operations(最常用)
3.band reserve requirements
4.persuading banks to tighten or loosen their credit policies

Pure expectation theory, yield curve 只反映未来的短期利率的期望。
短期利率预期上升->upward sloping curve
预期下降->downward sloping curve
预期上升然后下降->humped yield curve
保持不变->flat yield curve

Liquidity preference theory， yield curve是upward sloping，反映时限越长，premium要求越高
Market segmentation theory，借贷双方对期限有各自偏好，yield curve的形状跟每一个期限段内的需求供给相关

Yield spread
名义Yield spread是2个bond的market yield的差，由credit quality, call features, tax treatment, maturity 影响
absolute yield spread绝对差
relative yield spread相对差
yield ratio

Bond valuation process
1.估计现金流
2.设定discount rate，基于现金流的风险
3.计算现金流的现值
4.timing of principal repayments is not known with certainty
5.coupon payments are not known with certainty
6.the bond is convertiable or exchangeable into another security

Bond price 可以表示成par value的百分比，或者yield。
YTM是半年付的未来现金流折现到目前价格的单一折现率。半年息X2=年息，也叫bond equivalent yield

zero coupon bond price = face value/(1+YTM/2) ^2N, 反过来可以算YTM

spot rate & no arbitrage value, 可用于套利

bond 收入的3种来源，coupon payments，本金回收资本利得，reinvestment income

bond selling at par， coupon rate= current yield=yield to maturity
at premium，coupon rate>current yield > yield to maturity
at discount, coupong rate < current yield < yield to maturity
算YTC用call price作为FV和合适的terminal period

bootstripping spot rate，知道头几年的spot rate算后一年的

forward rate

Option-Adjusted Spread OAS
Zero-Volatility Spread Z-spread
Z-spread – OAS = option cost in %

Duration & Convexity

衡量interest rate risk的两种方法：
1. full valuation/scenario analysis approach
1)start with a current market yield and price
2)estimate changes in yields
3)revalue bonds
4)compare new value to current value

2.duration/convexity approach, ?较简单
算effective duration= (V_-V+)/(2×V0×Δy)， ed用于有option的bond，modified duration用于option free的bond， 两个都是用于利率变化很小的情况下。变化较大还需引入convexity effect
% change in price = duration effect+convexity effect= [duration×Δy + convexity ×?Δy^2]×100
price value of a basis point(PVBP)=duration × 0.0001× value

derivative investment

衍生品是衍生自其他资产的价值或资产回]
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J 发布

四月 18th, 2008 at 9:41 下午

发表在 Secret Sauce - L1

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Notes 习题笔记 Fix income derevative and alternative investments

一个评论

Concept Checkers P20

  1. indenture是公司和债主之间的contract，包括covenants
  2. 半年pay的bond利率8.5%是名义利率，semiannual coupon payment=本金X coupon rate/2
  3. put option，conversion option和exchange option可以给straight bond增加价值，对bondholder有好处；call option，accelerated sinking fund provision，prepayment option都是减少价值，对issuer有好处。
  4. first payment deferred，是deferred coupon bond
  5. 浮动利率=LIBOR+Floating
  6. cap对issuer有利，floor对bondholder有利。
  7. coupon date 之间买bond=clean price+accrued interest
  8. call provision对issuer有利，可以在利率下降的时候call回bond发行低利率的新bond
  9. 有call provision的bond，在期限内，最高价就是call price
  10. 发行当年就能call的bond没有call protection。没有发行时的价格，没法判断会不会call
  11. 因为market rate<coupon rate,溢价交易，所以sinking fund provision对bondholder无利，因为sinking fund总是在par value的，对issuer有利
  12. margin loan必须付利息，利率比用repurchase agreements 的funding costs
  13. issuer想提前召回bond可以用，call option，repayment option和sinking fund。conversion option是bondholder提前转换成common stock
  14. mortgage是抵押贷款，可以early retirement，是amortizing security，但并不是highly predictable cash flows

Concept Checkers P40

  1. 新价格=(1+duration X change in yield ) X original price
  2. 价格波动会降低call option的价格，导致callable bond价格下降。pull option涨价，pullable bond涨价。option-free bond不变
  3. zero coupon bond 不会有reinvestment risk，double A的再选有很小的default risk，interest risk是最大的风险。没对inflation rate修正的bond都有inflation risk
  4. duration=%change in price/change in yield
  5. option减小duration/interest rate risk.低coupon rate的straight bond，利率风险最大，duration也大。
  6. floating rate的bond在reset date之后duration/interest rate risk最大。
  7. 同1
  8. call option value=option-free bond value-callable bond value
  9. 同上putable bond
  10. event risk是发生了事情导致firm不能pay debt，地震有可能，收购有可能，rate regulation的变化有可能。Fed改变money supply不会影响。
  11. zero coupon bond最有利率风险
  12. 利率高，到期时间短的bond利率风险最低
  13. treasury bond半年付息，所有有reinvestment风险，也有汇率风险。aaa bond也有credit 风险。有call protection的bond也有波动性风险，因为波动还是会影响call option的价值。
  14. 6个月的Tbill比10年期zero coupon的reinvestment风险大。
  15. 2年期的zero coupon bond有inflation风险，利率风险，currency风险(汇率)。

Concept Checkers P63

  1. 97-17= 97+17/32, 再 X  par value
  2. 年inflation rate是3%，那半年后调整par value就是+1.5%
  3. TIPS的分红是inflation调整后再 × coupon rate
  4. t-note principal strip跟t-bill有同样现金流，所以价格应该相等。不过由于市场的流动性区别，可能会有点不差别
  5. t-bill是zero coupon bond，不能用于组合strip。strip是由t-bond和t-note组成的zero coupon bond
  6. revenue bond 风险最大，yields也最大。
  7. prerefunded bonds是escrow pool of treasury securities产生的现金流。insured bonds有第三方担保。不存在，absolute priority bonds 和credit enhanced obligations
  8. shelf registration用于medium-term notes,允许库存发行上架，然后慢慢卖。Corporate MBS，double-barreled municipal bond都是一次性卖完。
  9. 作为special purpose vehicle销售asset可以保护不被general claims
  10. on the run issues是最新issued securities
  11. 私下交易，会要求higher yield来补偿less liquid
  12. bankers acceptances 是短期，中间不付息。跟 negotiable CDs一样，credit都很好，二级市场都比较有限。
  13. CDO, collateralized debt obligation是backed by an underlying pool of debt比如emerging market debt
    CMO，backed by a pool of mortgages
    ABS，backed by financial assets
    EMD不存在
  14. 一级市场不存在market making

Concept Checkers P80

  1. pure expectations theory，说inverted or downward-sloping yield curve 说明short-term rates are expected to decline in the future
  2. 理性投资者认为长期投资风险比短期投资风险大，而不是每人对长期投资态度不一样。投资者更喜欢短期投资，长期投资利率要高，有风险溢价。
  3. 特定的机构和投资者倾向于特定期限的fixed-income market，供给需求决定yield curve的形状
  4. 央行调整了利率的最常用方法是open market operations
  5. yield ratio=1+yield spread
  6. absolute yield spread = yield on X year corporate issue – yield on-the-run X year treasury issue
  7. relative yield spread= (corporate yield – treasury yield)/treasury yield
  8. 收缩经济说明lower corporate earning增加default的可能性，扩大corporate issues和treasury issues的spread
  9. yield ratio = higher yield bond/ lower yield bond
  10. marginal tax rate = 1- tax-exempt rate/taxable rate
  11. 经济扩张期，credit spread减小，因为企业收入增加，less likely to default
  12. less liquidity 要求higher spead，用于compensate
  13. spread缩小，不影响treasury的价格
  14. 有税和免税的债券换算。

Concept Checkers P89

  1. 央行不应该让markets drive policy。央行货币政策直接跟市场沟通，应该与长期政策目标一致，让市场理解。
  2. predictable 的政策用公布政策后的short-term rates来反映。
  3. 市场利率反映现在价格和未来的预期，所以市场要平滑吸收货币政策。
  4. 有效的平滑的实施政策，要credible，predictable和transparent。是不是要infrequently change要根据市场情况。

Concept Checkers P101

  1. 算coupon payment
  2. 所有的10%coupon rate的现金流，用15%折现。
  3. 同上，看清楚是半年付息
  4. 同上
  5. 同上
  6. required rate下降，价格上升。
  7. YTM=stated coupoin rate， 价格=par value
  8. 按新的yield to maturiry算价格，再除以现价看premium
  9. 根据不同期的YTM算现值，决定套利方向。
  10. 按20年算PV，再按17年算PV，相减算出3年后增加的value
  11. 算zero coupon bond的现值

Concept Checkers P127

  1. 溢价，YTM<coupon rate
  2. 试算YTM
  3. 试算YTC,用call的期限
  4. 试算YTP，用put的期限
  5. zero coupon bond的YTM=[(1000/现值)^1/期数-1] X 2
  6. 半年息实际年利率跟名义年利率的转换
  7. 知道月息，换成半年期，再换成年息
  8. 溢价购买的bond，premium会逐渐减少(capital loss),计算YTM已考虑
  9. 知道第四年的sopt rate，第三年的spot rate算第一年的forward rate。
    (1+y4)^4=(1+y3)^3 X (1+f13)
  10. put option cost <0, OAS>Z-spread
  11. spot rate，算S1=第一年利率，S2=根号(r1Xr2)-1,S3，S4。用4个S折现，加起来就是PV
  12. zero coupon 只管S3，折现。
  13. 假如yield curve 是flat，nominal spread=z-spread；假如option free，Z-spread=OAS; coupon rate没关系
  14. treasury spot yield curve会让t-bond在arbitrage-free price上，on-the-run treasury bond.所以Z-spread是0

Comprehensive problems
1.算coupon interest；算principal的gain/loss,算利息在投资。
2.实际利率和名义利率的换算。
3.反过来
4.算spot rate ，同11。算YTM；nominal spread=YTMbond- YTMtreasury,算z-spread

也可以用3个z-spread带入算最接近的。
5.6.7.略过

Concept Checkers P153

  1. negative convexity，required yield 减少，价格增加的速度减缓，到call price附近，level off
  2. 算现在的pv和YTM增加后的pv，interest rate exposure= (后PV-前PV)/前PV
  3. 算V_,V+, duration = (V_ – V+)/2V0*Δy
  4. callable 的V_=call price
  5. yield减少，price增加，
  6. convexity effect = convexity X (Δy)^2
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