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Fixed Income > V-Risk and Returns-2 > Flashcards

V-Risk and Returns-2 Flashcards

1
Q

计算债券 total return

  1. 三个组成部分
  2. 计算逻辑
A
  1. coupon and principle payment
  2. coupon reinvestment
  3. capital gain loss: 不持有至到期
  4. 根据YTM计算购入价格
  5. 根据出售时间（持有至到期）计算出售价格
  6. 计算coupon reinvestmen @YTM的终值
  7. （2+3）/1并年化，即total return
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2
Q

比较total return和YTM

  1. 持有到期，@YTM再投资，YTM不变
  2. 持有到期，@YTM再投资，YTM变化
  3. 提前出售，@YTM再投资，YTM不变
  4. 短期出售，刚购入后YTM变化
  5. 长期出售，刚构入后YTM变化
  6. interest risk包括
A
  1. total return = YTM
  2. total return 随YTM同向变化
  3. total return=YTM
  4. price risk影响更大，total return & YTM反向变化
  5. reinvestment risk影响更大，total return % YTM同向变化
  6. coupon reinvestment risk + price risk
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3
Q

【Duration】

  1. 含义
  2. 假设
  3. 区分yield/curve duration
A
  1. 弹性概念：sensitivity of bond full price to change in YTM
  2. 假设只有YTM变化，时间不变化，即考虑YTM变化之一瞬间

因此对于full price之变化，只在于flat price之变化，而accrued interest未变

  1. yield: 考虑bond own YTM
    curve: bond price change相对于整个市场 benchmark yield curve
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4
Q
  1. Macaulay Duration计算
  2. Modified Duration与MacDur转换
  3. ModDur与full price转换
A
  1. 以各现金流现值作为权重

CF1/PX1+CF2/PX2+CF3/PX3…..

  1. ModDur=MacDur/ (1+r) 注意期间利率
  2. %PVfull price = -AnnModDur X Δyield
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5
Q

【Approximate ModDur】

  1. 公式
  2. 意义
  3. 特点
  4. ApproxMacDur与ApproxModDur
A
  1. 见图
  2. 不使用数学计算，而是图中切线斜率原理，用计算器也可得出非常精确的估计
  3. 计算出本身即为annulized值
  4. ApproxMacDur=ApproxModDur`(1+r)
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6
Q

【Effective Duration】

  1. 公式
  2. 适合衡量何种债券？为何？
  3. 传统久期算法不适用于2
A
  1. 见图
  2. 含权债券，因含权债券does not have a well-defined internal rate of return，只能用benchmark衡量

传统久期算法YTM是针对债券本身的

  1. 含权，MBS (prepayment实质也是call option)
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7
Q
  1. EffDur 与传统久期的区别 3- option free bond
  2. EffDur 与ApproxDur的区别
A
  1. 即使不含权，计算结果也不相同
  2. 只有在yield curve complete flat的情况下两者会相同
  3. yield curve越平，time to maturity越短，price closer to par的情况下，两者差异会更小
  4. Appro可以通过选取更小的yield change来增加精确度

Eff这种做法无效

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8
Q

【Key Rate Duration】

用途

A

之前的久期计算，假设yield curve平移

在yield curve shaping 变化/变陡变平的情况下，

用Key Rate Duration计算

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9
Q

【Duration Property】

  1. MacDur随time to maturity变化的图形
  2. MacDur of zero coupon bond
  3. MacDur/ ModDur of perpetual bond
A
  1. 如图。考虑accrued interest
  2. 即等于maturity N
  3. MacDur = (1+r)/r = 1+1/r, = ModDur+1

ModDur=1/r

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10
Q

【Duration Property】

关于此图的5个结论

A
  1. 零息债券麦考利久期等于term
  2. 永续债券麦考利久期恒定(1+r)/r
  3. 普通债券，平价和溢价发行：随maturity变长，久期也升高，逼近(1+r)/r
  4. 普通债券折价发行：久期先增加（超过永续债），再减少
  5. 纵截面看：coupon effect，低coupon久期长
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11
Q

MacDur

与

coupon rate/ YTM的关系

A

YTM同coupon rate：

都遵循coupon effect, coupon/YTM和久期反向变动

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12
Q

Callable Bond

Price&Yield Chart

  1. 图形
  2. 价格特征2
  3. 久期理解方式2
A
  1. 见图
  2. 价格始终低于不含权
  3. YTM低于一定程度，issuer call，价格不再上升
  4. 字面理解：call则说明收回时间变短，久期变短
  5. 定义理解：call则价格不再变动，久期变小
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13
Q

Putable Bond

Price&Yield Chart

  1. 图形
  2. 价格特征2
  3. 久期理解方式2
A
  1. 如图
  2. 价格始终高于不含权
  3. YTM高到一定限度，put，价格不再下降
  4. 时间维度：put则提前收回，久期变短
  5. 定义维度：put则价格不再下降（变动），久期变小
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14
Q

【Portfolio Duration】

  1. 两种计算方式
  2. 第二种方式limitation
A
  1. 综合所有现金流，按现值加权，IRR也按估计计算

比较复杂，现实中不实用

  1. 以各债券的久期作为加权

limitation：assume only parallel shift in the yield curve

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15
Q

【Money Duration】

  1. Money Duration 公式
  2. 已知利率变化，求price change
  3. PVBP: 缩写
  4. PVBP两种求法
A
  1. Money Duration= AnnModDurXPVfull (100)
  2. 利用%ΔPV=annModDur * Δyield, 求价格变化的百分比，乘以current full price，得出price change
  3. price value of a basis point

4-1. PVBP={(PV-)-(PV+)}/2

4-2. 同2

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16
Q

【Convexity】

  1. ApproxCon 公式
  2. Convexity to Price change% 公式
  3. 以上公式注意
  4. Convexity of zero coupon bond
  5. Convexity年化时注意
A
  1. 见图
  2. %Δprice = (-AnnModDur*Δyield)+(0.5*AnnCon*Δyield2)

3注意符号：利率上升价格下降时

  1. = [N-(t/T)]*[N+1-()t/T]/ (1+r)2
  2. 年化:除以periodicity的平方。如半年债券，则除以4
17
Q

【Convexity】

  1. money convexity=
  2. 从money convexity求price change公式
A
  1. = ApproxCon*market value (or per 100 par)
  2. Δprice=(-MonDur*Δyield)+(0.5*MonCon*Δyield2)
18
Q

【Convexity】

  1. factors to greater convexity 2
  2. 结论2
A
  1. 同duration：longer time to maturity, lower coupon rate, lower YTM
  2. 特殊： dispersion of cash flow: 两个久期相同债券，greater dispersion of CF, bigger convexity
  3. 凸性大的债券，利率下降价格上升幅度大，利率上升价格下降幅度小，总是outperform
  4. 同样，这类债券价格也高。no free lunch
19
Q

【Yield Volatility】

measure interest rate risk

两个维度

A
  1. per basis point change: 实质就是久期和凸度。YTM每改变1bp
  2. number of bs change: 实质就是yield volatility
20
Q
  1. 比较investment horizon, MacDur

于interest risk之关系3

  1. Duration Gap
A
  1. 持有期长于MacDur，reinvestment主导，risk to lower interest rate

持有期等于MacDur，两者抵消，没有interest rate risk

持有期短于MacDur, price change主导，risk to higher interest rate

  1. Duration Gap=MacDur-Investment horizon

负数：长期

0：等于

正数：短期

21
Q

对于Callable bond/ putable bond

MacDur

ModDur

EffDur

哪个值最低？

A

EffDur,

because it takes the effect of the call option into account

22
Q

Calculate Capital gain/loss

  1. what brings cap gain/loss?
  2. compare basis
  3. calculate
A
  1. after purchase, YTM changes leads to price change.

(6%-7%)

  1. carrying value/ current value at the price trajectory at current time (this trajectory is preset with 6% at purchase)
  2. carrying value = purchase price + amortized discount/ - amortized premium

Fixed Income (6 decks)

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