这里总结了下我认为比较重要的CFA二级相关概念。方便索引。

Quantitative Methods

Reading 9: Correlation & Regression

sample covariance

Cov(X,Y)=i=1n(XiX)(YiY)n1Cov(X,Y) = \frac{\sum_{i=1}^{n}{(X_i - \overline{X})(Y_i - \overline{Y})}}{n-1}

sample correlation

r=Cov(X,Y)SxSyr = \frac{Cov(X,Y)}{S_x*S_y} Sx=i=1n(XiX)2n1S_x = \frac{\sum_{i=1}^{n}{(X_i - \overline{X})^2}}{n-1}

test hypothesis on correlation

t-distribution, degree is n-2:

t=rn21r2t = \frac{r\sqrt{n-2}}{\sqrt{1-r^2}}

standard error of estimation of linear regression

SEE=i=1n(YiYi^)2n2SEE = \sqrt{\frac{\sum_{i=1}^{n}{(Y_i - \hat{Y_i})^2}}{n-2}}

Cofficient of Determination

  • TV = total variation ( Total Sum of Squares )
  • EV = explained variation
  • UV = unexplained variation
R2=EVTV=TVUVTVR^2 = \frac{EV}{TV} = \frac{TV - UV}{TV} TV=i=1n(YiY)2TV = \sum_{i=1}^{n}{(Y_i - \overline{Y})^2} UV=i=1n(YiYi^)2UV = \sum_{i=1}^{n}{(Y_i - \hat{Y_i})^2}

对于只有一个变量的线性回归来说,决定系数的平方根就是correlation。

注意,这里的EV,和ANOVA里面的Regression sum of squares不是一个东西。

test hypothesis on linear regression

t-distribution, degree is n-2:

t=b1^b1sb1^t = \frac{\hat{b_1} - b_1}{s_{\hat{b_1}}}

ANOVA

用来判断linear regression是否有用。

F-test, 有两个df

F=RSS/df1SSE/df2F = \frac{RSS / df_1}{SSE / df_2} RSS=i=1n(Yi^Y)2RSS = \sum_{i=1}^{n}{(\hat{Y_i} - \overline{Y})^2} SSE=i=1n(YiYi^)2SSE = \sum_{i=1}^{n}{(Y_i - \hat{Y_i})^2}

SSE:

sum of squared errors 又名 residual sum of squares

RSS

regression sum of squares

df1是变量个数,df2是总的df减去df1,总的df是n-1。

Prediction Intervals

sf2=s2[1+1n+(XX)2(n1)sx2]s_f^2 = s^2[1 + \frac{1}{n} + \frac{(X-\overline{X})^2}{(n-1)s_x^2}]

Reading 10: Multiple Regression & Issues

Assumptions

  1. The relationship between the dependent variable, Y, and the independent variables, X1X_1, X2X_2, …, XkX_k, is linear.
  2. The independent variables (X1X_1, X2X_2, …, XkX_k) are not random. Also, no exact linear relation exists between two or more of the independent variables.
  3. The expected value of the error term, conditioned on the independent variables, is 0: E(εX1,X2,,Xk)=0E(\varepsilon | X_1,X_2, \cdots,X_k) = 0
  4. The variance of the error term is the same for all observations: E(εi2)=σi2E(\varepsilon_i^2) = \sigma_i^2
  5. The error term is uncorrelated across observations: E(εiεj)=0,ijE(\varepsilon_i\varepsilon_j) = 0, i \neq j
  6. The error term is normally distributed.

test hypothesis on multiple linear regression

和single的一样,只不过df不一样。既然single的df是n-2,那么推理出来,假设independent数量是k,那么就是 n-k-1

Adjusted R2R^2

R2=1(n1n1k)(1R2)\overline{R}^2 = 1 - (\frac{n - 1}{n - 1 - k})(1 - R^2)

Violations of Regression Assumptions

  1. Heteroskedasticity
  2. Serial Correlation
  3. Multicollinearity

Heteroskedasticity

指的是Assumption 4被破坏了。会导致standard errors被低估,从而导致t-statistic变高。这样的话就更容易显著。那会造成其实本来没什么关系的变量,你会认为有关系。

  • Unconditional
  • Conditional

Unconditional:异方差性存在在error term里面,但是和变量是无关的。不是很要紧。
Conditional:异方差性存在在error term里面,但是和变量有关(correlated)的。要紧。

异方差性的检测

Breusch and Pagan Test

one-tailed test
test statistic: nR2nR^2
distribution: χ2\chi^2
df: k (number of independent variable)

异方差性的修正

既然是standard error被低估,那么就要提高standard error。方法不用去记。

Serial Correlation

regression errors are correlated across observations.

指的是Assumption 5被破坏了。

后果是整个linear Regression的结果不consistent。

Model Specification

Principles

  1. Should be grounded in cogent economic reasoning
  2. The functinal form chosedn for the variables in the regression should be appropriate given the nature of the variables
  3. Should be parsimonious
  4. Should be examined for violations before being accepcted
  5. Should be tested and be found useful out of sample

Reading 11: Time-Series Analysis

AR model

Detect serially correlated errors

kth order autocorrelation:

ρk=Cov(xt,xtk)σx2=E[(xtμ)(xtkμ)]σx2\rho_k = \frac{Cov(x_t, x_{t-k})}{\sigma_x^2} = \frac{E[(x_t - \mu)(x_{t-k} - \mu)]}{\sigma_x^2}

该值一定小于等于1

做题目:

  1. 计算Autocorrelation的Standard Error:
1T\frac{1}{\sqrt{T}}

Random Walk

  • first diff之前,b0=0,b1=1,mean reverting level无意义。
  • first diff之后,b0和b1都是0,所以mean reverting level是0

检测random walk

  • Unit root
  • Dickey-Fuller test

原来的AR(1) model等式两边减掉 xt1x_{t-1}

最后就检测g1是否等于0,g1<0代表没有unit root。

Moving-Average Model

很简单

Seasonality

加上Seanonal lag

ARMA model

AR model + MA model

不太好用吧,有些limitations

AR conditional heteroskedasticity models

要会ARCH(1)的test

Economics

Reading 13: Currency Exchange Rates

Forward

利率上要加一个(Actual/360)的因子。

Mark-to-Market Value of A forward contract

  1. create an offsetting forward position
  2. determine the appropriate all-in forward rate
  3. calculate the cash flow at the settlement day
  4. calculate the PV of this cash flow

四个Interest Rate Parity

covered

(1+id[Actual360])=Sf/d(1+if[Actual360])(1Ff/d)(1+i_d[\frac{Actual}{360}]) = S_{f/d}(1 + i_f[\frac{Actual}{360}])(\frac{1}{F_{f/d}})

uncovered

%ΔSf/de=ifid\% \Delta S_{f/d}^e = i_f - i_d

forward rate parity

远期的利率就是那天的spot rate

random walk

如果是random walk理论,那么就是现在的spot rate就是远期的spot rate

PPP

分为absolute和relative两种。

absolute的assumption:goods & services tradable
relative的assumption:transaction costs are constant

absolute的公式

Sf/d=Pf/PdS_{f/d} = P_f / P_d

relative的公式

%ΔSf/de=πfeπde\% \Delta S_{f/d}^e = {\pi}_f^e - {\pi}_d^e

当uncovered成立的时候,以及real interest rate parity, 可以推出费雪效应:

费雪效应的假设: currency risk一样。

通胀预期的差只会造成名义利率的差,不会对两国实际利率有改变。

四个Interest Rate Parity的各种限制

uncovered

risk neutral

forward rate parity

covered & uncovered holds

FX Carry Trade

要求uncovered不成立。(短期确实不成立)

缺点:the negative skew and fat tails indicate that tended to have more frequent and larger losses than normal distribution.

Impact of Balance of Payments Flows

用来试图解决上面的framework无法预测短期的问题。

通常来说,capital account比current account对exchange rate的影响更大。

current account imbalances

  1. the flow suplly/demand channel
  2. the portfolio balance channel
  3. the debt sustainability channel

Monetary & Fiscal Policies

Mundell-Fleming Model

这个模型表述了:

政策发布 -> 改变利率,经济活动 -> 改变capital flow以及交易 -> 改变汇率

只能解决short run

这个模型只关注Aggregate Demand

Assumption:有足够的缺口,可以在价格不上涨的情况下增加产出。

分为High Capital Mobility和Low Captial Mobility两种情况。

High Capital Mobility

  1. 扩张的货币政策 -> 利率降低 -> 资本出逃 -> 汇率贬值
  2. 扩张的财政政策 -> 利率提高 -> 资本进入 -> 汇率升值

Low Capital Mobility

当capital是low,那么effect主要通过trade来进行。

  1. 扩张的货币政策 :老样子
  2. 扩张的财政政策 -> 增加进口 -> 增加赤字 -> 汇率贬值

The Portfolio Balance Approach

02

Reading 14: Economic Growth & Investment Decision

用什么货币来算GDP

不要用market上的exchange rate,有两个缺点(看书),要用PPP。

Potential Growth

The maximum amount of output an economy can sustainably produce without inducing an increase in the inflation rate.

宏经的推理一向很奇怪:

P=PP = P P=GDP(EGDP)(PE)P = GDP(\frac{E}{GDP})(\frac{P}{E}) (1/T)%ΔP=(1/T)%ΔGDP+(1/T)%Δ(E/GDP)+(1/T)%Δ(P/E)(1/T)\% \Delta P = (1/T)\% \Delta GDP + (1/T)\% \Delta (E/GDP) + (1/T)\% \Delta (P/E)

在短期,三个因素都会有影响,但是长期来看,GDP的改变百分比才是最重要的。

其中,这个GDP是nominal GDP,由real GDP和infation组成。

Production Function

Cobb-Douglas production function

Y=AF(K,L)Y = AF(K,L) F(K,L)=KαL1αF(K,L) = K^{\alpha}L^{1-\alpha}

alpha is the share of GDP paid out to the suppliers of capital

这个函数展示了constant returns to scale

Growth Accounting

Approach 1: Solow’s

ΔY/Y=ΔA/A+αΔK/K+(1α)ΔL/L\Delta Y/Y = \Delta A/A + \alpha \Delta K/K + (1-\alpha) \Delta L/L

Approach 2: labor productivity growth accounting equation

Growth rate in potential GDP = Long-term growth rate of labor force + Long-term growth rate in labor prodctivity

比较简单,但是无法分析capital deepening和TFP的影响

Theories of Growth

三个model

  • Classical Model
  • Neoclassical model
  • endogenous

classical

马尔萨斯主义

马尔萨斯人口论是马尔萨斯于1798年所创立的关于人口增加与食物增加速度相对比的一种人口理论,其主要论点和结论为:生活资料按算术级数增加,而人口是按几何级数增长的,因此生活资料的增加赶不上人口的增长是自然的、永恒的规律,只有通过饥饿、繁重的劳动、限制结婚以及战争等手段来消灭社会“下层”,才能削弱这个规律的作用。

Neoclassical

索罗经济增长模型(Solow growth model),罗伯特·索罗(Robert Solow)所提出的发展经济学中著名的模型,又称作新古典经济增长模型、外生经济增长模型,是在新古典经济学框架内的经济增长模型。

assumed a closed economy,储蓄率等于投资,即所有储蓄都拿来投资了。

所以这个“外生”,是: 储蓄率、人口增长率、技术进步率

索罗经济增长模型百度百科

ΔK=Incomedepreciation=sYδK\Delta K = Income - depreciation = sY - \delta K Δk/k=sY/Kδn\Delta k/k = sY/K - \delta - n

注意,在steady state里面

Δk/k=Δy/y\Delta k/k = \Delta y/y

推理得:

Δk/k=Δy/y=ΔA/A1α\Delta k/k = \Delta y/y = \frac{\Delta A/A}{1-\alpha}

所以 Growth Rate of output per capita = Growth rate of capital per worker,只取决于growth rate of TFP 以及 elasticity of output with respect to capital(alpha)

加上growth rate of labor(n),即得到以下两个公式:

03

将这个结论套入上面的公式,去计算Y/K,可知Y/K是一个常数。

所以,在steady state里面,output-to-captial ratio是一个常数。

结论是:

capital deepening is occurring, but it has no effect on the growth rate of the economy or on the marginal product of captial once ht steady state is reached.

如果用来做题的话,用以下公式:

sy=[(θ1α)+δ+n]ksy = [(\frac{\theta}{1-\alpha}) + \delta + n]k

Endogenous

内生增长理论是产生于20世纪80年代中期的一个西方宏观经济理论分支,其核心思想是认为经济能够不依赖外力推动实现持续增长,内生的技术进步是保证经济持续增长的决定因素。强调不完全竞争和收益递增。

no diminishing marginal returns to capital for the economy as a whole

Convergence的几个类型

新古典理论,分两个类型

  1. absolute convergence
  2. conditional convergence

然后有新增了一个:

club convergence

only rich and middle-income countries that are members of the club are converging to the income level of the richest countries in the world.
(Institute 651)

Institute, CFA. 2018 CFA Program Level II Volume 1 Ethical and Professional Standards, Quantitative Methods, and Economics

Reading 15: Economics of Regulation

三种分类

  1. statues
  2. administrative law: 行政法
  3. judicial law: 裁判法

substantive law & procedural law

法理学在研究法律和法律现象的过程中,依据不同的标准,将法律分为不同的种类。根据法律规定内容的不同来进行划分,可以分为实体法和程序法。
实体法(Substantive Law) 是指规定具体权利义务内容或者法律保护的具体情况的法律,如民法、合同法、婚姻法、公司法等等。程序法是规定以保证权利和职权得以实现或行使,义务和责任得以履行的有关程序为主要内容的法律,如行政诉讼法、行政程序法、民事诉讼法、刑事诉讼法、立法程序法等等。

Regulatory Capture

规制俘虏理论(Regulatory Capture Theory)描述了一种政治腐败或政府行政失败的现象。它指政府制定出的某种公共政策损害公众利益,使少数人的利益团体受益。通常政府作出这一类决策是由于受到某一行业从业者的重大影响,而短时期作出违背公众利益的行政决定。它将造成社会中某些公司以”遵守政府规章制度“为名,持续开展损害公众利益的经营行为。

Regulatory Competition & Regulatory arbitrage

Financial Reporting & Analysis

Reading 16: Intercorporate Investments

研究的标的:

  • Financial Assets
  • Associates
  • Business Combinations
  • Joint Ventures
  • SPE & VIE

比较

Financial Assets Associates Business Combinations Joint Ventures
Influence Not significant Significant Controlling Shared control
percentage interest < 20% 20%~50% >50%
Current IFRS · Held to maturity
· Available for sale
· Fair value through P&L
· Loans & receivables
Equity method Consolidation Equity method or proportinate consolidation
IFRS9 · Fair value through P&L
· Fair value through OCI
· Amortized cost
Equity method Consolidation Equity method

Current IFRS

Financial Assets

  • 一开始以fair value作为初始值
  • 利息和分红直接进入income statement

接下去,fair value的变动根据种类的不同记账方式不同。

  1. Held-to-Maturity
    用Effective interest rate method,以amortized cost形式记账。(除非要impairment)

  2. Fair Value through Profit or Loss
    就像我自己买股票那样,每个账期记录fair value,差额的进到P&L

  3. Available for Sale

差额直接进OCI,也就是直接进权益。当这个股票被卖了之后,累积的差额再进入P&L。

TODO: IFRS和GAAP对于汇率汇兑的差额有不同的处理。

  1. Loans & receivables

在GAAP中不存在这一项。IFRS中要有某些特定的情况才能算这个类别。用amortized cost方法。

IFRS 9

分类方式

01

几种method

  • Equity Method:比较重大的影响但是不control的时候用
  • Acquisition method:control的时候用
  • proportionate consolidation: Joint Venture时候用

Equity Method

注意,主要和被投资方的book value作比对,超出的部分,先减去各种asset和liabilities的fair value超出的部分(按照投资百分比),然后多出来的算商誉。

然后,asset和liabilities这边,多出来的部分,要amortizaiton

这个概念里面,要掌握的有以下几点

  1. income的计算
  2. goodwill计算
  3. amortizaiton
  4. upstream,downstream sale

和Associate的内部交易

有两种方式: upstream,downstream

对于upstream ,downstream sale来说,没有卖给第三方的income就不能被算入equity income。

Business Combination

GAAP里面,分为三个类型:

  1. merger
  2. acquisition
  3. consolidation based

现在IFRS和GAAP不允许用uniting(pooling) of interests method了

现在都用Acquisition Method(替代了purchase method)

Acquisition Method

Partial & Full Goodwill

GAAP一定要用Full。

可以先计算full,然后按照占比打个折,就是Partial了。

Reading 17: employee Compensation

Post-Employment Benefit Plans

类型:

  1. DC plan: 只定义每笔付多少,以后的升值贬值都靠投资,所以员工承担风险。
  2. DB plan:定义未来给多少,公司承担投资风险

所有不属于DC的,都被归为DB。

Measuring a DB pension Plan’s Obligations

IFRS和GAAP对这个称呼不同,算法一样的。

  • IFRS:PV of DB obligation(PVDBO)
  • GAAP: projected benefit obligation(PBO)

记账

DC很简单,当做费用当期出掉即可。

DB有点复杂。

Funded status = Fair value of the plan assets - PV of the DBO

如果小于0,在balance sheet上的net pension liability要记一笔。
如果大于0,在balance sheet上的net pension asset要记一笔,但是有一个ceiling。

期间费用:

见图片:

04

corridor appraoch

记住简单的计算:

期初PBO是5,000,FV of asset是4,850,unrecogised acturail losses是610。 还有10年。 那么:

corridor是10%的期初PBO->500。610大于500了,所以要amortise差额(110)

Reading 18: Multinational Operations

买东西,记账记在transaction date上,不要记在payment date上。

然后相关的记账方式例子如下:

05

如果两个日期跨了财报日,那么在前一个财报日要先实现一下,直接进income

current rate method & temporal method

这两个方法就是在决定,哪些用current rate来转换,哪些用historical rate来转化

equity一般都是按照historical rate来变的。

  • current rate method:所有都用current rate来算
  • temporal method:monetary + 用fair value来估值的non-moentary用current 来算。

关于到底哪里用哪里,书上第139页有。

hyperinflationary

简单来说,

IFRS要调整一下然后用current rate
GAAP要用temporal method

effective tax rates

Reading 19: Evaluating Quality of Financial Reports

用来检测misreport的可能性的模型

Beneish Model

M-Score由各种参数组成,相当于一个回归模型,其中参数分别为:

  • DSR: Days sales receivable index = 本期的(receivable/sales)除以上一期的
  • GMI: gross margin index,注意,t和t-1和其他相反的
  • AQI: asset quality index
  • SGI: sales growth index
  • DEPI: decreciation index,里面的值是Depreciation rate。t和t-1和其他相反的
  • SGAI: sales,general & admin expenses index
  • Accruals: (income before extraoridinry items - cash from operations) / Total Assets
  • LEVI: leverage index

这个Score是一个标准正态分布的随机变量。越高代表操纵的可能性越高。

Eearning Quality

  1. Recrring Earning

Bankruptcy Prediction Models

  1. Altman Model(z-score)

Cashflow Quality

OCF

Balance sheet quality

Corporate Finance

Reading 21: Capital Budgeting

EEA

先算NPV,然后以NPV作为PV,FV为0,N和i设定好,用计算机算PMT。

Effects of Inflation

(1 + Nominal rate) = (1 + real rate)(1 + inflation rate)

Economic income

the profit realized from an investment.

这玩意儿存在的目的是?

计算方法:

  1. 算出beginning market vlaue,就是当前的期初时间点之后所有CF的贴现
  2. 算出ending market vlaue,就是当前的期末时间点之后所有CF的贴现
  3. 相减,这个值又叫economic depreciation
  4. 加上CF

Economic Profit

EP = NOPAT - $WACC * capital

其中,$WACC里面的capital要每年递减(折旧),capital就是assets

NOPAT是EBIT(1-taxrate)

以EP为现金流算出来的就是Market Value Added(MVA)

EP是Residual Income章节里面的商业版本,又叫EVA。

Residual Income

RIt=NItreBt1RI_t = NI_t - r_e B_{t-1}

B就是公司的所有者权益

Reading 22 Capital Structure

整个章节的逻辑在此:

选择一个Capital Structure很重要。但是在最严格的假设中,Capital Structure不影响公司价值。随着放宽各种假设,Capital Structure开始影响公司价值了。目的是maximize the value of compnay by minimizing the weighted average cost of capital

MM Proposition

Assumptions:

  1. 期望一致
  2. 完美的资本市场,没佣金,没税
  3. 可以以无风险利率借钱
  4. 没有agency cost
  5. operrating income和Capital Structure无关

结论: 所有资本结构的公司价值都一样,那所有基本结构的r都一样。

MM Proposition II

把等式的r_wacc与r_0相等即可。

MM Proposition With Tax

VL=Vu+tDV_L = V_u + tD re=r0+(r0rd)(1t)DEr_{e} = r_0 + (r_0 - r_d)(1 - t)\frac{D}{E}

另外还有两个公式:

Vu=EBT(1t)WACCV_u = \frac{EBT(1-t)}{WACC} VL=EBIT(1t)WACCV_L = \frac{EBIT(1-t)}{WACC}

上面两个公式,其实是一个公式,要注意的是,Vu对应的wacc一定是r0。

随着举债,V会变化。因为有税收的作用,随着举债,E不会减少相同的份额,而是稍微少减少一点。

Cost of Financial Distress

agency cost

asymmtric information

pecking order theory

优序融资理论

优序融资理论亦译“啄食顺序理论”。关于公司资本结构的理论。1984年,美国金融学家迈尔斯与智利学者迈勒夫提出。以信息不对称理论为基础,并考虑交易成本的存在。认为,公司为新项目融资时,将优先考虑使用内部的盈余,其次采用债券融资,最后才考虑股权融资。即遵循内部融资、外部债权融资、外部股权融资的顺序。在MM理论的信息对称与不存在破产成本的前提假设条件下,认为,当存在公司外部投资者与内部经理人之间的信息不对称时,由于投资者不了解公司的实际类型和经营前景,只能按照对公司价值的期望来支付公司价值,因此如果公司采用外部融资方式,会引起公司价值的下降,所以公司增发股票是一个坏消息。如果公司具有内部盈余,公司应当首先选择内部融资的方式。当公司必须依靠外部资金时,如果可以发行与非对称信息无关的债券,则公司的价值不会降低,因此债券融资比股权融资优先。

Optimal Capital Structure

Static Trade-Off Theory:静态权衡理论

VL=Vu+tDPV(costsoffinancialdistress)V_L = V_u + tD - PV(costs of financial distress)

Reading 23: Dividends & Share Repurchases: Analysis

以CFO的角度去看待是否要Dividend以及Share Repurchase

DRP

Dividend reinvestment plan

分为

  • open-market DRP
  • new-issue DRP ( 在英国又叫:scrip dividend scheme,英国事情真多 )

homemade dividend

投资者自己考卖出股票的办法去模拟分红。

Stock Dividends

股份分红之后,EPS会变,Price也会变。所以P/E不变。

DEVIDEND 和公司价值的关系

一直在辩论。

  1. MM: 在MM的Assumption下,分红对公司价值没有影响
  2. 一鸟在林理论,(即使在perfect capital markets下,有分红的风险也更少)
  3. Tax Argument:分红和卖出股票的tax不一样,哪个低喜欢哪个。
  4. Clientele Effect:追随者效应理论也译为顾客效应理论,该理论最先也是由米勒(Miller)和莫迪格利安尼(Modigliani)提出来的。从股东的边际所得税税率出发,认为每个投资者所处的税收等级不同:有的边际税率高,如富有的投资者;而有的边际税率低,如养老基金等。由此会引致他们对待股利的态度不一样,前者偏好低股利支付率或不支付股利的股票,后者喜欢高股利支付率的股票。据此,公司会相应调整其股利政策,使股利政策符合股东的愿望。达到均衡时,高股利支付率的股票将吸引一类追随者,由处于低边际税率等级的投资者持有;低股利支付率的股票将吸引另一类追随者,由处于高边际税率等级的投资者持有。这种股东聚集在满足各自偏好的股利政策的公司的现象,就叫做“追随者效应”。

计算在有税收的情况下,分红后价格降低多少

等式左边为分红前卖出,等式右边为分红后卖出:

Pw(PwPb)TCG=Px(PxPb)TCG+D(1TD)P_w - (P_w - P_b)T_{CG} = P_x - (P_x - P_b)T_{CG} + D(1-T_D)

Taxation Methods

  1. double taxation
  2. imputation: (税务)归属方式(避免双重税方式)
  3. split-rate: 双轨税率法,用于分红的earnigns和留存的earnings的税率不同。

imputation里面有franking credit,是一个补偿方式,用来补偿双重税。

Payout Policies

关注点都是Earings per share,是基于Earings per share来计算分红的。

  1. Stable Dividend Policy
  2. Constant Dividend Payout Ratio Policy
  3. Residual Dividend policy

Stable Dividend Policy

有一个Adjustment Factor

Residual Dividend policy

实际上不太用,因为会造成比较大的分红波动。

Share Repurchases

几个方法:

  1. open-market
  2. fixed price tender offer
  3. dutch auction
  4. direct negotiation

对财报的影响

1) EPS

总的来说,对EPS可以有上升、下降或者不变,具体要计算。

2) BookValue

3) 计算份分红和回购的区别

Devidend coverage ratio

就是payout ratio的倒数。

FCFE coverage ratio = FCFE / (Dividends + Share repurchases )

Reading 24: Corporate Performance, Governance, and Business Ethics

Philosophical Approaches to Ethics

Friedman doctrine

企业应该对自己的股东做利益最大化,不应该超出法律限度得照顾员工福利,导致利润降低。企业唯一的社会责任就是利润最大化。

Utilitarian

功利主义者,按照结果来决定该不该做。只看结果不看过程。

Kantian

康德主义。

按照康德的解释,他的道德哲学是以“至善”为目的的,即人在自由意志的基础上,出自义务或职责,自愿地执行道德法则。这样的行为之所以“至善”,就在于它是绝对的、无条件的,与任何爱好、愿望、需求、利益或结果无关,而纯粹是为了“至善”。

Rights Theories

Justce Theories

Reading 25: Corporate Governance

2个Objective

  1. eliminate or mitigate confilicts of interest
  2. ensure the assets of the compnay are used efficiently & productively in the best interests of its investors & other stakeholders

5个core attributes

  1. delineation of the rights of shareholders and other core stakeholders
  2. clearly defined manager & director governance responsibilities to stakeholders
  3. identifiable & measurable accountabilities for the performance of the responsibilities
  4. fairness & equitable treatment in all dealings between managers, directors, & shareholders
  5. complete transparency & accuracy in disclosures regarding operations, performance, risk, & financial postion.

董事Independence的反应因素

  1. former employment with the company, including founders, executives, or other employees
  2. business relationships, for example, prior or current service as outside counsel, auditors, or consultants, or business interests involving contractual commitments and obligations;
  3. personal relationships, whether familial, friendship, or other affiliations;
  4. interlocking directorships, a director of another company whose independence might be impaired by the relationship with the other board or company, particularly if the director serves on interlocking compensation committees
  5. ongoing banking or other creditor relationships

Reading 26: Mergers & Acquisitions

类型

  • statutory merger
  • subsidiary merger
  • consolidation

conglomerate merger

一个公司吸收了一个和自己业务无关的公司。

动机

  • Synergy
  • Growth
  • Increasing Market Power
  • Acquiring Unique Capabilities & Resources
  • Diversification
  • Bootstrapping
  • Manager’s Personal Incentives
  • Tax
  • Unlocking Hidden Value
  • Cross-Border motivations

bootstrapping earnings

光合并,即使没有SYnergy和Growth效应,也能增加EPS

Form of Acquisition

  • stock purchase
  • asset purchase

HHI

超过1800,行业就比较集中了。

对收购的防范措施

shark repellents:

鲨鱼排斥法(Shark Repellent)是指用来避免接管发生的更加正式的反并购策略,其目的是使得接管更难发生。

先是Pre-Offer的措施

1. Poison Pills

有两点,flip-in pill , flip-over pill。
还有一个“dead-hand” provision.

flip-in pill: 让common shareholder可以以一个discount购买本公司股票。收购者会遭受dilution。

flip-over pill: 让common shareholder可以以一个discount购买对方公司股票?

2. Poison Puts

让债券拥有者可以把手头的债券卖还给公司。

3. Incorporation in a State with Restrictive Takeover Laws (United States)

4. Staggered Board of Directors

期分级董事会

5. Restricted Voting Rights

股票拥有量超过一定程度的人,默认不能有投票权,除非现有董事会同意。

6. Supermajority Voting Provisions

重大事件需要的投票权更大

7. Fair Price Amendments

必须高于某个价格

8. Golden Parachutes

给高管的离职补偿

然后是Post-Offer的措施

1. “Just Say No” Defense

2. Litigation

3. Greenmail

绿票讹诈(Greenmail)又译讹诈赎金、绿色勒索,直译为绿讹诈函又称:溢价回购,由green(美元的俚称)和blackmail(讹诈函)两个词演绎而来,指的是单个或一组投资者大量购买目标公司的股票。其主要目的是迫使目标公司溢价回购上述股票(进行讹诈)。出于防止被收购的考虑,目标公司以较高的溢价实施回购(给付赎金),以促使上述股东将股票出售给公司,放弃进一步收购的打算。这种回购对象特定,不适用于其他股东。 

  在欧美等国家,绿票讹诈是指投机者购买公司大量股票,企图加价出售给公司收购者,或者是以更高的价格把股票卖回给公司以避免这部分股份落入公司收购者之手。

4. Share Repurchase

Leveraged buyout

5. Leveraged Recapitalization

杠杆资本重组是指股票公开交易的公司通过提高杠杆程度来筹集现金,而且杠杆程度的提高幅度往往是惊人的。所筹集的现金通常以巨额股利方式分配给股东。与杠杆收购不同的是,股东继续持有该公司的股票,并且公司股票继续保持公开交易。

6. “Crown Jewel” Defense

“皇冠之珠”(Crown Jewel):指的是目标公司将其最有价值、对收购人最具吸引力资产(即所谓“皇冠之珠”)出售给第三方,或者赋予第三方购买该资产的期权,使得收购人对目标公司失去兴趣,放弃收购。

7. Pac-Man® Defense

“帕克门”战略(Pac-man):“帕克门”本来是80年代初流行的一款电子游戏的名称,在该游戏中,任何没有消灭敌手的一方将遭到自我毁灭。作为反收购措施,帕克门战略是指目标公司针锋相对地向收购公司发起要约收购

8. White Knight Defense

9. White Squire Defense

白衣护卫是一种与白衣骑士很类似的反收购措施。这里,不是将公司的控股权出售给友好的公司,而是将公司的很大比例的股票转让给友好公司。

Target Company Valuation

三种常用的估值方法

  1. DCF
  2. comparable Company analysis
  3. comparable transaction analysis

DCF

一般用Free cash flow作为CF。

这里涉及到一个叫NOPLAT的东西,用来替代Equity那个章节里面的NI

net operation profit less adjusted taxes

步骤:

  1. 计算unlevered net inome: net income + net interest after tax
  2. NOPLAT = unlevered net inome + change in the deferred taxes

comparable Company

takeover premium

PRM=(DPSP)SPPRM = \frac{(DP - SP)}{SP}

comparable transaction

直接用aquisition price计算各种ratio的平均值。

三种方法的优缺点:

Advantages of Using Discounted Cash Flow Analysis

  • Expected changes in the target company’s cash flows (e.g., from operating synergies and cost structure changes) can be readily modeled.

  • An estimate of intrinsic value based on forecast fundamentals is provided by the model.

  • Changes in assumptions and estimates can be incorporated by customizing and modifying the model.

Disadvantages of Using Discounted Cash Flow Analysis

  • It is difficult to apply when free cash flows do not align with profitability within the first stage.

  • Estimating cash flows and earnings far into the future is not an exact science. There is a great deal of uncertainty in estimates for the following year, and even greater uncertainty in perpetuity.

  • Estimates of discount rates can change over time because of capital market developments or changes that specifically affect the companies in question. These changes can also significantly affect acquisition estimates.

  • Terminal value estimates often subject the acquisition value calculations to a disproportionate degree of estimate error. The estimate of terminal value can differ depending on the specific technique used. Additionally, the range of estimates can be affected dramatically by small changes in the assumed growth and WACC estimates.

Advantages of Using Comparable Company Analysis

  • This method provides a reasonable approximation of a target company’s value relative to similar companies in the market. This assumes that “like” assets should be valued on a similar basis in the market.

  • With this method, most of the required data are readily available.

  • The estimates of value are derived directly from the market. This is unlike the discounted cash flow method where the takeover value is determined based on many assumptions and estimates.

Disadvantages of Using Comparable Company Analysis

  • The method is sensitive to market mispricing.

  • Using this approach yields a market-estimated fair stock price for the target company. In order to estimate a fair takeover price, analysts must additionally estimate a fair takeover premium and use that information to adjust the estimated stock price.

  • The analysis may be inaccurate because it is difficult for the analyst to incorporate any specific plans for the target (e.g., changing capital structure or eliminating duplicate resources) in the analysis.

  • The data available for past premiums may not be timely or accurate for the particular target company under consideration.

Advantages of Comparable Transaction Approach

  • It is not necessary to separately estimate a takeover premium. The takeover premium is derived directly from the comparable transactions.

  • The takeover value estimates come directly from values that were recently established in the market. This is unlike the discounted cash flow method where the takeover value is determined based on many assumptions and estimates.

  • The use of prices established through other recent transactions reduces litigation risk for both companies’ board of directors and managers regarding the merger transaction’s pricing.

Disadvantages of Comparable Transaction Approach

  • Because the value estimates assume that the M&A market has properly determined the intrinsic value of the target companies, there is a risk that the real takeover values in past transactions were not accurate. If true, these inaccurate takeover values are imputed in the estimates based on them.

  • There may not be any, or an adequate number of, comparable transactions to use for calculating the takeover value. In these cases, analysts may try to use data from related industries. These derived values may not be accurate for the specific industry under study.

  • The analysis may be inaccurate because it is difficult for the analyst to incorporate any specific plans for the target (e.g., changing capital structure or eliminating duplicate resources) in the analysis.

Bid Evaluation

一般来说,交易要付溢价。

合并之后,收购者会有一个Synergy的价值(S)

VA=VA+VT+SCV_{A^*} = V_A + V_T + S - C

其中,A指的是Aquirer,T指的是target。C指的是Cash。

Corporate Restructuring

An equity carve-out involves the creation of a new legal entity and sales of equity in it to outsiders.

spin off: shareholders of the parent company receive a proportional number of shares in a new, separate entity

split off: some of the parent company’s shareholders are given shares in a newly created entity in exchange for their shares of the parent company

Equity

整个Equity讲了Equity的估值流程、Return的计算以及各种具体的估值方法。

Reading 27:Equity Valuation,Applications & Processes

diversiture
分拆

spin-off
衍生

流程:

  1. Understading the business
  2. Forecasting company performance
  3. Selecting model
  4. Calculation
  5. Conclusion

Reading 28: Return Concepts

有一个Aplha的概念

Expected alpha=Expected returnRequired returnExpected\ alpha = Expected\ return - Required\ return Realized alpha=Actual Holding Period return=Contemporaneous required returnRealized\ alpha = Actual\ Holding\ Period\ return = Contemporaneous\ required\ return

Expected Return Estimate from Intrinsic Value Estimates

E(Rτ)=rτ+V0P0P0E(R_\tau) = r_\tau + \frac{V_0-P_0}{P_0}

在以上公式中,investor要估计出,多久会回到intrinsic value

如果不到一年

rτ=(rτ+1)month/year1r_\tau = (r_\tau + 1) ^ {month/year} - 1

计算Equity的Required Rate of Return的几个模型

  1. CAPM
  2. Multifactor
  3. Build-up

对于Nonpulibc compnies的beta估计

  1. 选一个benchmark
  2. 估计benchmark的beta
  3. unlever那个beta
  4. 用目标公司的财务杠杆去lever新beta
βU=[11+(1t)(D/E)]βE\beta_U = [\frac{1}{1+(1-t)(D/E)}]\beta_E

Arbitrage Pricing Theory

套利定价理论APT(Arbitrage Pricing Theory) 是CAPM的拓广,由APT给出的定价模型与CAPM一样,都是均衡状态下的模型,不同的是APT的基础是因素模型。

r=RF+(Risk premium)1+...+(Risk premium)kr = R_F + (Risk\ premium)_1 + ... + (Risk\ premium)_k

Fama-French Model

三因子模型.

Fama和French 1992年对美国股票市场决定不同股票回报率差异的因素的研究发现,股票的市场的beta值不能解释不同股票回报率的差异,而上市公司的市值、账面市值比、市盈率可以解释股票回报率的差异。Fama and French 认为,上述超额收益是对CAPM中β未能反映的风险因素的补偿。”

ri=RF+βimktRMRF+βisizeSMB+βivalueHMLr_i = R_F + \beta_i^{mkt} RMRF + \beta_i^{size} SMB + \beta_i^{value} HML

其实就是CAPM多了两个因子

Pastor-Stambaugh Model

在FFModel的基础上,加了个LIQ

宏观经济多因子模型

supply side estimation.

Ibboston-Chen Model

re=(1+EINFL)(1+EGREPS)(1+EGPE)1.0+EINCr_e = (1+EINFL)(1+EGREPS)(1+EGPE) - 1.0 + EINC

注意,这里一般题目会要求求Equity risk premium。所以要减去一个Rf

Build-up Method

被各种持有private business的投资者使用。

ri=RF+Equity risk premium+One or more premia(discounts)r_i = R_F + Equity\ risk \ premium +- One\ or \ more\ premia(discounts)

Bond Yield Plus Risk Premium

对于有公开的债券的公司,可以用bond来获得required return

risk premium在跨国中的调整

Reading 29: Industry & Company Analysis

用于预测现金流

Balance Sheet and Cash Flow Statement Modeling

  • ROIC: 不受leverage影响,比ROE更好
  • ROCE: 不受Tax影响,比ROE更好

Reading 30: Discounted Dividend Valuation

为什么要用residual income

当公司不分红,或者Expected Free Cash Flow是negative的时候。

Gordon Growth Model

V0=D1rgV_0 = \frac{D_1}{r-g}

PVGO

Present value of growth opportunities

把公司的价值分解为no-growth value per share和PVGO,然后可以看出市场上大家对公司未来增长的预期。

V0=E1r+PVGOV_0 = \frac{E_1}{r} + PVGO

leading & trailing justified(fundamental) P/E

用预测的数字来获得的P/E

  • trailing P/E,又叫current P/E,是用今天的价格与过去12个月的EPS作比较。
  • leading P/E,又叫forward P/E,是用今天的价格与预测未来12个月的EPS作比较。
trailingP/E=P0E0trailing P/E = \frac{P_0}{E_0} leadingP/E=P0E1leading P/E = \frac{P_0}{E_1}

H-model

这是2 stage的一个优化,对2 stage中的2段增长率做更smooth的处理。

V0=D0(1+gL)+D0H(gSgL)rgLV_0 = \frac{D_0(1+g_L) + D_0H(g_S-g_L)}{r-g_L}

对于growth rate在财务上的解释

g = b * ROE

Reading 31: Free Cash Flow Valuation

Free cash flow to the firm 的定义:

the cash flow available to the company’s suppliers of investments after all operating expenses have been paid and necessary investments in working capital & fixed capital have been made

Free cash flow to the equity 的定义:

the cash flow available to the company’s holders of common equity after all operating expenses, interests, and principal payments have been paid and necessary investments in working capital & fixed capital have been made

如果公司的capital structure比较stable,那么用FCFE更简单。

但是,以下两种情况用FCFF:

  1. a levered company with negative FCFE
  2. a levered company with a changing capital structure

FCFF和FCFE的计算

记住他们原则上是什么概念。

首先,公司captial的来源大致有三个:

  1. common stock
  2. debt
  3. preferred stock

FCFF可以从好几个地方计算

  1. Net Income为起点
  2. CFO为起点

从Net Income开始

注意,要加回Interest expense,并且要乘以(1-tax rate)作为调整。

从CFO开始

不需要减掉working capital

计算FCFE

除了要把interest expense去掉,还要加上net borrowing。

计算估值

  • 用FCFF计算出来的是公司的value,用FCFE计算出来的是公司equity的value。
  • FCFF要用wacc来计算,FCFE要用r来计算。

预测FCFF和FCFE

  1. 简单的预测:一个constant growth
  2. 复杂的预测:以sales的百分比作为各种component的预测。其中Netborrowing = DR(FC - Depr) + DR * WC

算出来FCFE之后,就可以直接除以股数,以获得每股价值。

Reading 32: Market-Based Valuation: Price & Enterprise Value Multiples

Analyst Adjustments for Business-Cycle Influences

Molodovsky Effect:是指企业处于商业周期底部时,所呈现的每股盈余下降但市盈率较高的现象;但在商业周期顶部时,通常有每股盈余较高而市盈率较低的现象。

计算normalized EPS

有两种方法:

  1. 用历史平均EPS来代替
  2. 用average ROE来计算。乘以current book value per share

Earings Yield

P/E的倒数

NTM vs. TTM

Next twelve month vs. trailing twelve month

forward P/E和NTM P/E是不同的。NTM要根据月份来。

Justified 三金刚

P0E0=(1b)(1+g)rg\frac{P_0}{E_0} = \frac{(1-b)(1+g)}{r-g} P0B0=ROEgrg\frac{P_0}{B_0} = \frac{ROE-g}{r-g}

上面这个公式,可以通过Residual Income里面的公式导出来

P0S0=ProfitMarginP0E0\frac{P_0}{S_0} = ProfitMargin * \frac{P_0}{E_0}

PEG

P/E to growth,越低越好。

算法是P/E除以growth(但是growth要去掉百分比,比如10%,那就直接除以10)

通过P/E来计算terminal value

Vn=Benchmark value of trailing P/EEnV_n = Benchmark\ value\ of\ trailing\ P/E*E_n Vn=Benchmark value of forward P/EEn+1V_n = Benchmark\ value\ of\ forward\ P/E*E_{n+1}

P/S

price-to-sales ratio

EV

Market value of common equity (Number of shares outstanding × Price per share)

Plus: Market value of preferred stock (if any)

Plus: Market value of debt

Less: Cash and investments (specifically: cash, cash equivalents, and short-term investments)

Equals: Enterprise value

Momentum Indicators

  • earnings surprise
  • SUE:standardized unexpected earnigns
  • relative strength

SUE

SUEt=EPStE(EPSt)σ[EPStE(EPSt)]SUE_t = \frac{EPS_t - E(EPS_t)}{\sigma[EPS_t - E(EPS_t)]}

Reading 33: Residual Income Valuation

官方定义:

NI - Equity Charge

但是还有一个commercial版本的定义:

EVA = NOPAT - (C% * TC)

所以题目中要注意用的是NetInome还是NOPAT

TC,是total capital charge,和NI版本里面的Equity Charge不一样。

NOPAT的计算

EBIT里面,不要去除利息,直接扣除tax。(除息前为计算基础)

估值公式

V0=B0+t=1RIt(1+r)tV_0 = B_0 + \sum_{t=1}^{\infty}{\frac{RI_t}{(1+r)^t}} RIt=EtrBt1=(ROEr)Bt1RI_t = E_t - rB_{t-1} = (ROE - r)B_{t-1} Bt=Bt1+EtDtB_t = B_{t-1} + E_t - D_t

注意,上面的各种数值的单位,如果是B是per share,那么RI也要是per share

Tobin’s q

Market Value Added

这里的定义似乎和公司理财的定义不同。

MVA = Market Value of Captial - Total captial

Edwards-Bell-Ohlson model

Reading 34: Private Company Valuation

strategic buyer vs. financial buyer

strategic就是买了之后有synergy效应的。

估值的几种方法:

  1. income approach:有Free cash flow, CCM,excess earnings methods
  2. Market Apporach:GPCM(guideline public company method), GTM(guideline transactions method), PTM(prior transaction method)
  3. Asset-Based Approacho (cost approach)

Capitalized cash flow (CCM)

看起来好像就是FCFF的变种,但是多了一个capitalization rate。

excess earnings method

通常用来估值intangible assets或者很小的公司。

Intangible assets的估值:

earning 减掉 tangible asset的机会成本。

Fixed Income

Reading 35: The Term Structure & Interest Rate Dynamics

要知道P(1),F(1,2)的定义。

  • P(T)= T年期,一块钱的现值。
  • F(T*, T)= T年期,一块钱在T*时间点的现值

这章和CFA1级最大的差别就是,每一年的spot rate不一样了。

所以,债券的价格变为:

P=i=1nDi(1+r(i)i)+F1+r(n)nP = \sum_{i=1}^{n}{\frac{D_i}{(1+r(i)^i)}} + \frac{F}{1+r(n)^n}

比较重要的公式:

F(T,T)=P(T+T)P(T)F(T^*,T) = \frac{P(T^*+T)}{P(T^*)}

各种Curve

纵坐标是r,横坐标是期限

当spot curve上升的时候,forward的一定在spot上方。

par curve: 价格是par,付coupon的政府债券的curve。

从par curve转化到zero-coupon yield curve的过程叫bottstrapping

YTM & expected return

YTM并不等于expected return。

YTM有严格的要求,要求持有到期,所有coupon和principle全部付完,并且拿到的钱以YTM重新投资。

你可以用YTM来预测expected return,但是以下情况下,你的预测会很差:

  1. 利率变化很大
  2. yield curve is steeply sloped.
  3. 有高风险违约
  4. 债券有option

一个结论

当未来的即时spot rate和现在的forward一样,那forward contract price保持不变。

TODO:Page19-20没看懂。

Riding the yield curve/rolling down the yield curve

先记住结论吧:

当yield curve是向上的时候,你不相信未来的利率会保持向上。那么可以买比较长期的债券,在到期前抛售。

Swap rate curve

swap rate指的是一个swap中,fixed rate这部分。

par swap:一开始没有money exchange

par curve: government par yield curve。

有些国家没有大于一年的债券,所以没办法来建立yield curve。那就用swap curve来建立。另外,如果有些国家私有部门比政府部门多,那么也可以用swap curve来作为标准。

从spot yield curve来计算swap curve

t=1Ts(T)[1+r(t)t]+1[1+r(T)]T=1\sum_{t=1}^{T}{\frac{s(T)}{[1+r(t)^t]}} + \frac{1}{[1+r(T)]^T} = 1

用swap spread来给bond定价

没看懂

各种spread

  • Z-spread
  • I-spread
  • TED-spread
  • Libor-OIS spread

四种影响yield curve的理论

  1. Local Expectations Theory(纯粹预期理论):认为“只有”预期的未来短期利率,决定收益率曲线的形状;当预期未来短期利率上升时,会有上升的收益率曲线,反之,收益率曲线呈下降态势。
  2. Liquidity Preference Theory(流动性偏好理论):长期债券收益要高于短期债券收益,因为短期债券流动性高,易于变现。而长期债券流动性差,人们购买长期债券在某种程度上牺牲了流动性,因而要求得到补偿。
  3. Segmented Markets Theory(市场分隔理论):因为人们有不同的期限偏好,所以长期、中期、短期债券便有不同的供给和需求,从而形成不同的市场,它们之间不能互相替代。根据供求量的不同,它们的利率各不相同。
  4. Prefrred Habitat Theory:债券市场不是分割的。投资者会考察整个市场并选择溢价最高的债券品种进行投资。

3个关于利率的模型

  1. Cox-Ingersoll-Ross model
  2. Vasicek model
  3. Ho-Lee model

Cox-Ingersoll-Ross model vs Vasicek model

两者都是equilibrium term structure models(均衡利率期限结构模型),是用fundamental economic variables来建模的。

两个模型只差一个参数:

Cox-Ingersoll-Ross model:

dr=a(br)dt+σrdzdr = a(b-r)dt + \sigma \sqrt{r} dz

Vasicek model少一个根号r

Ho-Lee model

基于无套利机会假设的利率期限结构变动模型

  Ho-Lee模型认为现在的利率期限结构包含有现时人们对利率预测的足够信息,因此在没有套利机会的假设下,利率期限结构的变动只能反映出这些信息,因而其变化情况是可测的。Ho-Lee模型分成两个部分,一是利率期限结构变动的模型,另一部分是该模型在利率期权定价中的应用。

Yield Curve Factor Models

用来分析利率的risk的。

其中,由Litterman和Scheinkman建立的三因素模型是书中所讲的。三因素分别为:

level, steepness, curvature.

关于到期时间和yield curve波动性的关系。

通常来说,越短期的东西波动越大。

Key-Rate Durations

基本上可以认为,久期就是volatility

  • effective duration: measures the sensitivity of a bond’s price to a small parallel shift in a benchmark yield curve.
  • key rate duration: measures a bonds’ sensitivity to a small change in a benchmark yield curve at a specific maturity segment.

当bond时0 coupon的时候,effective duration就是bond的maturity。

Reading 36: The Arbitrage-Free Valuation Framework

从Arbitrage-Free的角度看债券

所有债券都可以看做是若干个zero-coupon的组合。这个行为被称为stripping

Binomial Interest Rate Tree

这个树用lognormal random walk来建立

i1,H=i1,Le2σi_{1,H} = i_{1,L}e^{2\sigma}

其中i_x的计算,要通过Calibrating的方法来做。先通过S1,S2算出F1,1。然后算出F1,1d,再通过软件进行具体数值的查找。

Binomial Interest Rate Tree的计算

两种方法:

  1. backward induction
  2. pathwise valuation

Reading 37: Valuation & Analysis:Bonds with Embedded Options

putable bond

putable bond没有American style

callable bond是发行者可以预先赎回。

Interest Rate Volatility的影响

任何的option,因为都是contigent的,所以肯定是Volatility越大价值越高。

对于有default risk的bond的估值调整

两种方法:

  1. 增加discount rate(industry-standard approach)
  2. 用期望值的方法,把default的概率估计出来

在第一种方法的情况下,一般用Z-Spread。Z-spread的意思是zero-Volatility spread

如果债券有option,那么用option-adjusted spread(OAS)

OAS很多实用用来作为一个bond价值标准的benchmark。

如果全局的OAS比相同风险结构的bond的OAS大,那么这个bond就被低估了。

OAS的值随着Volatility的变化

对于callable bond来说,是一个减函数

Duration

duration分为两类:

  1. yield duration
  2. curve duration

yield duration是用来衡量债券的full price对于债券的maturity的敏感度的。
curve duration是用来衡量债券的full price对于yield curve的敏感度的。

yield duration只能去衡量option-free bond。

effective duration就是option-adjusted duration

但是effective duration也能衡量straight bond

effective duration=PVPV+2(ΔCurve)PV0effective\ duration = \frac{PV_- - PV_+}{2(\Delta Curve)PV_0}

effective duration可以通过OAS计算得到。

One-sided duration

因为当有了option之后,其实bond的价值在某一个方向不会改变的,所以这个时候用one-sided duration比较好。

Effective Convexity

一个二阶的值

effective convexity=PV+PV+2PV0(ΔCurve)2PV0effective\ convexity = \frac{PV_- + PV_+ - 2PV_0}{(\Delta Curve)^2PV_0}

Convertible Bond

要记住几个metrics和ratio

  1. conversion value
  2. minimum value of a convertible bond
  3. market conversion price, market conversion premium per share, market conversion premium ratio
  4. downside risk
  5. upside potential

Conversion price

Conversion price = Issue Price / Conversion ratio

Conversion Value

Conversion value = Underlying share price * Conversion ratio

Downside risk

这个risk指标在理论上是有缺陷的。但是实际使用还是有人在用。

Premium over straigth value = Convertible bond price / Straight value - 1

Reading 38: Credit Analysis Models

4个对于credit risk的衡量方法

  1. probability of default
  2. loss given default & recovery rate
  3. expected loss
  4. PV(expected loss)

2个traditional credit model

  1. credit scoring
  2. credit ratings

credit score并不一定需要根据当前的宏观经济状况改变。并且,credit score的准确性并不重要,因为很多投资者比较关注credit score的改变。

credit rating要记住:

investmetn-grade是BBB-以上或者是Baa3以上

Structural Models

Holdling the company’s equity is economically equivalent to owning a European call option on the company’s asset.

Owning the company’s debt is economically equivalent to owning a riskless bond that pays K dorlls with certainty at time T, and simulaneously selling a European put option on the assets of the compnay with strike price K and matruity T

然后套入BSM

Structural Model有三个assumption,其中第二个assumption比较弱,不是很现实,就是假设市场利率是恒定的。

三个假设分别是:

  1. asset所在的市场没有摩擦
  2. 无风险利率不变
  3. 在time T时,asset的价格是遵循lognormal分布,且mean是uT, 方差是delta^2*T

总结一下:

  1. 债券的价值可以通过BSM模型得到
  2. BSM模型里面的N(d2)就是不会default的概率。
  3. 计算default概率的时候要把r替换成u
  4. loss given default = K - A_T
  5. expected loss
6. PV of expected loss

expected loss

loss given defaultprob(AT<K)=(KAT)N(e2)=KN(e2)AtN(e2)loss\ given\ default * prob(A_T<K) = (K - A_T) * N(-e_2) = KN(-e_2) - A_tN(-e_2) KN(e2)Ateu(Tt)N(e1)KN(-e_2) - A_te^{u(T-t)}N(-e_1)

注意题目中的time to maturity就是T-t

Reduced Form Models

简化模型

用来解决Structural Models里面一个假设的弱点:company’s asset trade

公式太复杂了,以后看。

2个模型的优缺点

Structural

优点:

  1. option analogy
  2. using only current market risk

缺点

  1. input依赖于假设
  2. credit risk是biased(因为要假设财务结构)
  3. 不考虑business cycle

Reduced Form

优点:

  1. 参数可被观察(不需要靠假设)
  2. 反映了business cycle
  3. 不需要假设财务结构

缺点

  1. Harzard rate是估计的,所以要对这个值好好地back test。

Credit Spread的期限结构

这章,要知道如何用Credit Spread来预测PV(expected loss),expected percentage loss per year.

Reading 39: CDS

Upfront premium

(credit spread - rate) * duration

Reading 40: Pricing & Valuation of Forward Commitments

术语:

at market:market value=0

价格公式

F0(T)=S0e(r+θγ)TF_0(T) = S_0e^{(r + \theta - \gamma)T}

注意这里theta和gamma的符号

Advance set等等

  • advance set, settled in arrears:预先设定,拖欠结算
  • advance set, advance settled: 预先设定,预先结算

公式

公式很简单,只要记住算的都是S的FV就可以了。记得算Value的时候,这个差额一般是终值的差额,要贴现回来。

其中有几个特殊点记一下:

FRA:

  1. 用add-on rate来标记
  2. 一般购买方这边都是付float
  3. 一张时间图(0,g,h,m)

Fixed Income:

  1. 有AI
  2. 有conversion factor(QF * CF = F)
  3. 最终求的都是QF

Interest Swap

计算Swap的rate:

present value factors的和作为被除数, 1-最后一期present value factor作为除数。

算Value的时候,要把除数乘回来。

Reading 41: Valuation of Contigent Claims

Binomial Option Valuation Model

hedge ratio

构建Binomial的核心步骤:

  1. write a call option
  2. buy h underlying
  3. borrow or lend

目的是让未来的现金流为0。

做出来一个公式,就是no-arbitrage approach。

这个公式相当于说,我们通过买若干个S,并且借钱,就相当于复制了一个c了。

c=hS+PV(hS+c)c = hS + PV(-hS^- + c^-)

然后用expectatoin来做

里面的关键是,为什么probability of one upmove的值是:

π=FV(1)dud\pi = \frac{FV(1)-d}{u-d}

Reading 42: Derivatives Strategies

covered call:

  1. long share
  2. sell call

protective put

  1. long share
  2. long put

Reading 43: Private Real Estate Investments

有个啥highest & best use的概念。

basic forms

  • Equity/Debt
  • Private/Public

三种Valuation方法

  1. income approach
  2. cost approach
  3. sales comparison approach

income approach

里面分为direct capitalization method和DCF method,还有个layer method,两个都用NOI的概念:

06

这里的逻辑是:

  1. 先算full capacity的收入
  2. 然后在预估一个打折
  3. 再去掉expense

direct capitalization method就是pertuity。

term rent & market rent

term rent就是已经签好的租金价格(血亏价格)

cost approach

based on adjusted replacement cost。

最终的价值 = land的价值 + build的replacement cost

这个replacement cost还要做一些depreciation

  1. physical deterioration
  2. functional obsolescence
  3. external obsolescence( Locational obsolescence)

三种办法三选一

  1. active market with lots of transactions: 选comparison
  2. week market: income

INDEXES

  1. Appraisal-Based Indexes
  2. Transaction-Based Indexes

其中,Appraisal-Based Indexes的return的计算方法是,收入的升值 - 资本费用 + 本身fair value的升值 / 期初的fair value。

Transaction-Based Indexes又分为:

  1. repeat sales index:同一间房子反复出售的价格波动
  2. hedonic index: 回归出来的(根据市场价格和房子参数进行回归)

PRIVATE MARKET REAL ESTATE DEBT

debt service coverage ratio (DSCR) = NOI/Debt service

Equitiy Dividend Rate

有了债务之后,CF / Equity的值。这个和记账一样的,要减去债务。

Leveraged & Unleveraged IRR

这就很简单啦,Leveraged是借债时候的IRR,Unleveraged是如果不借,那么IRR是多少。

Reading 46: Commodities & Commodity Derivative

contango

期货溢价

当spot price小于于futures prices时

backwardation

现货溢价。
当spot price大于futures prices时

the basis

The difference between spot and futures prices

roll return

The component of the return on a commodity futures contract attributable to rolling long futures positions forward through time. Also called roll yield.

Instead, roll return is an accounting calculation used to replicate a portion of the total return for a fully collateralized (i.e., with no leverage) commodity index. As defined, the roll return is effectively the accounting difference (in percentage terms) between the near-term commodity futures contract price and the farther-term commodity futures contract price

展期收益
商品指数基金一部分依赖于Backwadation市场下所能够获得的展期收益(roll return)。如果指数组成中的所有商品成为Contango市场,并且现货价格开始下跌,那么大量资金将很快陷入熊市市场,并成为价格下跌的压力

Reading 48: Multifactor Models

种类

  1. macroeconomic
  2. funamental
  3. statistical

active return的来源

  1. security selection
  2. factor tilts

macroeconomic factor model

里面的参数全部是surprises。

所谓surprises,指的是actual value - expected value。

然后输出的y其实也是surprise。就是return surprise。return surprise是actual return - expected return

return surprise = 各种因素

Carhart model

就是Fama-French Model多了个WML

Return Attribution

active return是portfolio的return和benchmark return的差额。

Active return=k=1K[(Portfolio sensitivity)k(Benchmark sensitivity)k](Factor return)k+Security selectionActive\ return = \sum_{k=1}^{K}{[(Portfolio\ sensitivity)_k - (Benchmark\ sensitivity)_k](Factor\ return)_k} + Security\ selection

Risk Attribution

可以被表示为active return的标准差:

TE=s(RpRB)TE = s(R_p - R_B)

Informatoin Ratio

信息比率衡量某一投资组合优于一个特定指数的的风险调整超额报酬

IR=RpRBTE=RpRBs(RpRB)IR = \frac{\overline{R_p}-\overline{R_B}}{TE} = \frac{\overline{R_p}-\overline{R_B}}{s(R_p - R_B)}

Active risk squared = Active factor risk + Active specific risk

要会把表转化为百分比形式。

Portfolio construction

Rules-based active management

对着一个index,只调整各种weight?大概是这样。

这一部分与其说是Portfolio construction,不如说是对已经构建完成的Portfolio进行selection

Strategic portfolio decisions

根据自己的情况(比如相比别人更能接受长期投资)而调整portfolio的决策。

Reading 49: Market Risk

VaR

典型句子:

The 5% VaR of a portfolio is 2.2 milllion over a one-day period

有几个要素:

  1. 最小损失
  2. period of time
  3. 1 - level of confidence

以上的话,可以由其他表述方式:

  1. 2.2 million is the minimum loss we would expect 5% of the time
  2. 5% of the time, losses would be at least 2.2 million
  3. we would expect a loss of no more than 2.2 million 95% of the time

估计VaR的方法

  1. the parametric(variance-covariance) method
  2. the historical simulation method
  3. Monte Carlo simulation method

估计VaR的步骤

  1. risk decompostion
  2. gathering histroy data(三种方法在这里稍有不同)
  3. make estimate(三种方法在这里显著不同)

parametric(variance-covariance) method

假设return distributions for the risk factor是normal distribution的

  1. 先根据portfolio中各个资产自己的Return和volatility来算出整个portfolio的Return和volatility。
  2. 根据日期调整,算出新的Return和volatility
  3. 根据normal distribution的图上面去找。

在这里再记一下百分比和standard devation的关系

  • 1% ~ 2.33
  • 5% ~ 1.65
  • 16% ~ 1
  1. 找到Return和volatility后,通过以下z来求出平群损失,再乘以资金大小
z=Rμσz = \frac{R-\mu}{\sigma}

historical simulation method

用 excel的=percentile(x,y)去算。

VaR的优势

  1. Simple Concept
  2. Easily communicate
  3. easy comparison
  4. facilitates capital allocation decisions
  5. performance evaluation
  6. reliability can be verified
  7. widely accepted by regulators

VaR的缺点

  1. subjectivity
  2. underestimating the freqency of extreme events
  3. not take into account liquidity
  4. sensitivity to correlation risk
  5. vulnerability to trending or volatility regimes
  6. misunderstanding the meaning of VaR
  7. oversimplification
  8. disregard of right-tail events

VaR的扩展

  • conditional VaR: The average loss conditional on exceeding the VaR cutoff。又被称为expected tail loss, expected shortfall
  • incremental VaR: 如果portfolio里面一个资产的postion变化了,VaR的变化
  • marginal VaR: 和incremental差不多。
  • ex ante tracking error( relative VaR )

Reading 50: Economics & Investment Markets

Inter-temporal rate of substitution

跨期替代率

Reading 51: Analysis of Active Portolio Management

可以通过IC,score, volatility来算出active weight。

几个概念

  • IC: Information Coefficient
  • TC: Transfer coefficient

做题目的时候,IC一般是给的。

μi=ICσiSi\mu_i = IC*\sigma_i*S_i

其中,S是score。算出来是forecasted active return。

BR

breadth

IR

SRP2=SRB2+IR2SR_P^2 = SR_B^2 + IR^2 IR=ICBRIR^* = IC*\sqrt{BR} IR=TCICBRIR = TC*IC*\sqrt{BR} E(RA)=ICBRσAE(R_A)^* = IC*\sqrt{BR}*\sigma_A E(RA)=IRσAE(R_A)^* = IR^* * \sigma_A