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Fixed Income > III-Valuation-4 > Flashcards

III-Valuation-4 Flashcards

1
Q

【market discount rate valuation】

  1. deficiency/ excess per period
  2. total deficiency/ excess两种算法
A
  1. deficiency: 实际利率8%， 票面利率10%, deficiency per period即-2

2.

  1. 以实际利率算出债券价格，与par的差额即是
  2. deficiency/ excess per period每期按实际利率折现，现值即是
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2
Q

【Yield to Maturity YTM】

  1. 用途
  2. 三个假设
A
  1. 已知债券价格，算出YTM即是IRR
  2. investor holds to maturity

do not default

assume reinvest coupon at same yield

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3
Q

Bond Price vs 实际利率

关系四重

+

图形

A
  1. 价格与实际利率反向相关。实际利率下降，债券价格上升
  2. convex effect: 价格波动率大于实际利率波动率/ 利率下降时价格上升波动，大于利率上升时价格下降波动
  3. coupon effect: 低coupon债券价格受利率变化影响更大
  4. maturity effect: 长期债券价格受利率波动影响更大

有时会有例外：低coupon债券时，短期债券反而波动更大。但零息债券和溢价债券不属于例外，永远服从maturity effect

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4
Q

一道例题—与时间和利率的变化有关

  1. 时间因素导致的价格变化是？
  2. 利率因素导致的价格变化是？
A
  1. 保持YTM不变10%， N=6, PMT=8, 求价格，即是6年期10%YTM的价格
  2. 保持时间不变7y， I/Y=9%, PMT=8, 求价格，即是仍在7年前，市场利率由10变为9时，债券价格
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5
Q

【Spot Rate Valuation】

  1. 计算方法
  2. 计算出的价格叫做
A
  1. for each CF, 用不同的零息债券利率进行折现，算出PV
  2. 最准确算出债券价格。no arbitrage value
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6
Q
  1. full price 定义+特点
  2. flat price (clean price)定义+特点+存在意义
  3. Accrued Interest计算
  4. 以上三者关系
A
  1. full price: 真实的PV of DCF到今日（交易时间点）。因含有accrued interest, 故价格是增加的
  2. full price-accrued interest，随时间逐渐向par靠近“子弹头图形”

存在意义：用于标价。使得价格只受interest影响不受累计利息的影响

  1. AI=t/T*PMT
  2. full price=flat price+accrued interest
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7
Q

【full price】

  1. 价格变化图形
  2. 计算方法
A
  1. 标记上一期付息日，计算到maturity共多少期
  2. DCF折现至上一付息日，PV
  3. PV*(1+r)t/T

其中r为每期利率

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8
Q

【Yield Measures - Matrix Pricing】

  1. 用途
  2. underwrite new bonds中用途
  3. 做法
A
  1. for bonds with no market price available, 计算YTM
  2. estimate the yield spread over benchmark
  3. 例如想知道一个4年债券YTM，可以找来相似的3年债券、5年，分别有各自的YTM。在中间取linear interpolation
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9
Q

【Yield Measures - EAY】

  1. 比较两不同periodicity债券的EAY公式
  2. 解释APR
  3. 如何将YTM3.582%半年付息债券（A）与YTM3.556%月付息债券（B）相比较？
  4. 一个结论
A
  1. 见图。实质是是两债券EAR相同，就可以计算出另一债券的APR
  2. Annual Percentage Rate: 一个stated interest rate概念
  3. A/2，平方复利年化为EAY，等于B的EAY，开(1/12)次方乘以12，就是B的APR
  4. 相同EAR，付息次数越多，APR越低
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10
Q

【Yield Measures】

  1. street convention yield
  2. true yield
  3. 关于前两者的结论
  4. government equivalent yield
A
  1. 现实中付息日遇到周末将推迟至下周一发放。street convention忽略这一点，默认按付息日发放，简化计算
  2. true yield严格按现实情况计算yield
  3. true yield永远小于等于street convention，因为晚发放带来回报率变低
  4. gov将corp bond yield转化为按照实际情况计算的yield，由此计算spread over gov bond
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11
Q

【Yield Measures】

  1. current yield
  2. simple yield
  3. yield to call
  4. yield to worst
  5. current yield 同YTM, coupon rate关系
A
  1. 年内coupon payment/ flat price
  2. （all coupon payments +/- 折价/溢价部分）/flat price
  3. 同YTM计算方法，N=call date, FV=call price
  4. 有不同的yield to first/second/third call, 其中收益率最低者
  5. 见图
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12
Q

【Yield Measures】-FRN

  1. Quoted margin
  2. required margin定义+又叫
  3. 以上两者关系
A
  1. FRN债券票面规定的margin
  2. discount margin. 投资者需要的required rate of return
  3. 同固定利率债券，required>quoted,债券折价
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13
Q

【Yield Measures】-FRN

一道例题

求discount margin in bps

A
  1. 题目已经简单化：以第一次Libor作为整个持有期的benchmark
  2. coupon rate=1.8%, 半年0.9%, N=4, 求I/Y
  3. I/Y*2 得YTM
  4. YTM-1% 即是所求
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14
Q

【Money Market Yield】

discount rates

  1. 已知discount rate求现价P，公式
  2. 另一个underling 公式
  3. 一个结论
A
  1. PV=(1- days/year * DR)
  2. DR= (FV-PV)/FV * (year/days)
  3. DR以FV做分母，低估了实际收益率
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15
Q

【Money Market Yield】-AOR

  1. 已知add-on rate求现价，公式
  2. 另一个underlying 公式
  3. define: bond equivalent yield
A
  1. PV* (1+ AOR* days/year) = FV
  2. AOR= (FV-PV)/PV * (years/day)
  3. BEY = 以365天计的AOR
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16
Q

【Yield Curves】解释

  1. spot curve
  2. coupon bond curve
  3. par bond curve
  4. forward yield curve
A
  1. 连接不同maturity的零息债券YTM
  2. 对附息债券，YTM
  3. 存在这样一个coupon rate（PMT），使债券经spot rate valuation的价格等于par

该coupon rate相连接。实质是不同spot rate加权平均

  1. 对forward yield连接
17
Q

Implied Forward Rate计算

3年零息YTM3.65%

4年零息YTM4.18%

  1. 求3y1y
  2. 若半年付息，求3y1y
A

注意画时间轴帮助理解

  1. (1+3.65%)3*(1+3y1y)=(1+4.18%)4
  2. (1+3.65/2)6*(1+3y1y/2)2=(1+4.18/2)8
18
Q

【Yield Spread】

  1. benchmark/spread变化因素分别是
  2. spread分类及benchmark
A
  1. benchmark: macroeconomics, inflation, economic growth, exchange
    spread: focus on the bond itself and issuer: credit rating, liquidity, tax

2.

Government G-spread: gob bond yield

interpolated I-spread: swap rate (Libor)

Zero coupon Z-spread: spot rate

G/I 统称N-spread

19
Q

【Yield Spread】

  1. 公式区分N/Z-spread
  2. Z-spread与

Option-adjusted spread (OAS)比较

  1. N-spread and Z-spread difference will be larger when
A
  1. N-spread: 以constant YTM

Z-spread: 以各不相同的spot rate

2.

callable bond: Z>OAS

putable bond: Z

  1. yield curve is steep

Fixed Income (6 decks)

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