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Unformatted text preview: 金程教育2011年6月CFA一级强化班
金程教育
Quantitative Methods
讲师：何旋
日期：2011年4月
地点： ■ 上海 □北京 □深圳
上海金程国际金融专修学院 何旋
职称：金程教育高级培训师、金程教育资深研究员、通过FRM、通过CFA二级考试、CFA三级
候选人
工作经验：2009年至今，担任金程教育CFA（注册金融分析师）高级培训师，主要负责《经
济学》、《固定收益》、《衍生产品》和《组合管理》的课程讲解；2007年至今，在金程教
育金融研究院内担任研究员，主要负责包括CFA项目研发以及的相关内训课程的课程体系开
发，主要项目经验包括：摩根史丹利项目（组长）：组织小组内成员定期讨论；搜集金融基
础知识方面的英文资料，撰写英文课件，确保项目质量；中国银行项目：负责企业财务报表
粉饰及合并报表、关联交易模块的研究与课件撰写；中国工商银行CFA培训项目：CFA一级二
级辅导员；金程教育CFA三级课程体系的整体开发及相关课件、资料制作；金融热点专题研
究，包括：次级债、IPO、一行三会等，形成研究报告，并开发相关课程（形成大纲，研究
编写课件及各类辅助材料）；基于内训客户的培训课程体系开发：南京银行、兴业基金、瑞
穗实业银行等。
授课：讲授CFA® Level I 20次，CFA® Level II 15次等。授课范围广泛：经济学、固定收
益投资、衍生品投资、投资组合、资产配置、个人理财、数量分析等。
专业能力：金融理论知识扎实，在金融教学中有自己独到的方法。多年对CFA考试体系的研
究使她全面掌握考试重点，尤其擅长经济学课程的讲授，能将复杂的理论具体化。，在授课
过程中能够从考生角度出发，提供自己在备考过程中的经验和方法，帮助考生更好的准备考
试。
客户：摩根史丹利、工商银行、中国银行、瑞穗实业银行、南京银行、兴业基金等。
联系方法：hexuanf@gmail.com
2211 100% Contribution Breeds Professionalism
100% Topic Weightings in CFA Level I
Content Session NO. Weightings Study Session 1 Ethics & Professional Standards 15 Study Session 23 Quantitative Analysis 12 Study Session 46 Economics 10 Study Session 710 Financial Reporting and Analysis 20 Study Session 11 Corporate Finance 8 Study Session 12 Portfolio Management and Wealth Planning 5 Study Session 1314 Equity Investment 10 Study Session 1516 Fixed Income 12 Study Session 17 Derivatives 5 Study Session 18 Alternative Investments 3 3211 100% Contribution Breeds Professionalism
100% Quantitative Methods
Time Value Calculation
R5 The Time Value of Money
R6 Discounted Cash Flow Applications Probability & Statistics
R7 Statistical Concepts and Market Returns
R8 Probability Concepts
R9 Common Probability Distributions Inferential statistics
R10 Sampling and Estimation
R11 Hypothesis Testing
4211 100% Contribution Breeds Professionalism
100% Quantitative Methods: R5
Quantitative
Time Value of Money
1. Required interest rate on a security的组成 2. EAR 3. Annuities的计算：FV, PV, required payment 5211 100% Contribution Breeds Professionalism
100% R5: Time Value of Money
LOS 5.a interpret interest rates as required rate of return, discount rate, or
opportunity cost; Required rate of return is
affected by the supply and demand of funds in the market;
the return that investors and savers require to get them to willingly
lend their funds;
usually for particular investment.
Discount rate is
the interest rate we use to discount payments to be made in the future.
usually used interchangeably with the interest rate.
Opportunity cost is
also understood as a form of interest rate. It is the value that investors
forgo by choosing a particular course of action.
6211 100% Contribution Breeds Professionalism
100% R5: Time Value of Money
LOS 5.b explain an interest rate as the sum of a real riskfree rate, expected
inflation, and premiums that compensate investors for distinct types of risk; Decompose required rate of return:
Real riskfree rate = nominal riskfree rate + expected inflation rate
Required interest rate on a security
= nominal riskfree rate + default risk premium + liquidity premium +
maturity risk premium
考察方法：
Real riskfree rate和nominal riskfree rate的关系
风险的种类 7211 100% Contribution Breeds Professionalism
100% Example
Example
Two corporation bonds have different nominal risk free rate,
because of which component?
A. Liquidity B. Maturity C. Default risk Correct answer: B
Solution
Risk free rate dose not include default risk. Different corporation
bonds have corresponding government bonds with different nominal
risk free rate because of their different maturity. 8211 100% Contribution Breeds Professionalism
100% R5: Time Value of Money
LOS 5. c calculate and interpret the effective annual rate, given the stated
annual interest rate and the frequency of compounding;
EAR calculation: m m EAR=(1+periodic rate) − 1 ⎛ r⎞
1+ EAR = ⎜1+ ⎟ = em
⎝ m⎠ 那么如果是semi, m=2; 如果是quarterly, m=4
如果是连续复利，公式则变为EAR = e annual int * yr
考察方法：
计算——算EAR，或者是算计息次数
定性（EAR和计息次数有关）
The EAR for a stated rate compounded annually is not the same as the
EAR compounded semiannually, or quarterly.
The greater the compounding frequency,
the greater the EAR will be in comparison to the stated rate
the greater the difference between EAR and the stated rate
9211 100% Contribution Breeds Professionalism
100% Example
A money manager has $1,000,000 to invest for one year. She has
identified two alternative oneyear certificates of deposit (CD)
shown below:
Compounding frequency
Quarterly
Continuously CD1
CD2 Annual interest rate
4.00%
4.95% Which CD has the highest effective annual rate (EAR) and how
much interest will it earn?
Highest EAR
A. CD1 $41,902 B. CD1 $40,604 C.
10211 Interest earned CD2 $50,700 100% Contribution Breeds Professionalism
100% R5: Time Value of Money (LOS 5.d)
LOS 5.d solve time value of money problems when compounding periods
are other than annual; If interests are compounded annually, given the quoted interest rate r, the
FV formula is:
FV=PV(1+r)N
If interests are compounded m times per year,
FV=PV（1+ r/m）mn
Where: m is the compounding frequency;
r is the nominal/quoted annual interest rate.
When we calculate the future value of continuously compounding, the
formula is:
FV=PV lim (1+
m →∞ 11211 r nm
) =PVe n r
m
100% Contribution Breeds Professionalism
100% R5: Time Value of Money
LOS 5. e calculate and interpret the future value (FV) and present value (PV)
of a single sum of money, an ordinary annuity, an annuity due, a perpetuity
(PV only), and a series of unequal cash flows; What’s annuities?
 is a stream of equal cash flows that occurs at equal intervals over a given
period
内容：
N = number of periods
I/Y = interest rate per period
PMT = amount of each periodic payment
FV= 0
Compute (CPT) present value (PV)
考察方法：计算——N, I/Y, PMT, FV, PV中任意给定四个，求另外一
个
12211 100% Contribution Breeds Professionalism
100% R5: Time Value of Money
R5:
An example of ordinary annuities（后付年金）:
Example 1:What’s the FV of an ordinary annuity that pays 150 per
year at the end of each of the next15 years, given the discount rate is
6%
Solutions: enter relevant data for calculate.
N=15, I/Y=6, PMT=150, PV=0, CPT→FV=3491.4
Notice: if we were given that FV= 3491.4, N=15, I/Y=6, PMT=150,
we also could calculate PV.
0 1 2 3 +150 +150 +150 ……
…… 13 14 15 +150 +150 +150 FV=3491.4 PV=0
13211 100% Contribution Breeds Professionalism
100% R5: Time Value of Money
About an annuity due（先付年金）
Definition: an annuity where the annuity payments occur at the
beginning of each compounding period.
Calculation:
Measure 1: put the calculator in the BGN mode and input relevant data.
Measure 2: treat as an ordinary annuity and simply multiple the
resulting PV by (1+I/Y) About perpetuity
Definition: A perpetuity is a financial instruments that pays a fixed
amount of money at set intervals over an infinite period of time.
Calculation: 14211 PV= PMT
PMT
PMT
PMT
+
+
+...=
1+I/Y (1+I/Y)2 (1+I/Y)3
I/Y 100% Contribution Breeds Professionalism
100% Quantitative Methods: R6
Quantitative
Discounted Cash Flow Applications
1. NPV & IRR 2. 计算，HPY，EAY，，以及它们相互之间的转化 3. Moneyweighted return & Timeweighted return 15211 100% Contribution Breeds Professionalism
100% R6: Discounted Cash Flow Applications
LOS 6. a calculate and interpret the net present value (NPV) and the internal
rate of return (IRR) of an investment;
LOS 6. b contrast the NPV rule to the IRR rule, and identify problems
associated with the IRR rule;
NPV = CF 0 + NPV = 0 = CF0 + CF 1
( 1 + r )1 + CF1
(1 + IRR )1 + CF 2
(1 + r ) 2 + ... + CF2
(1 + IRR )2 + ... + CF N
(1 + r ) N CFN
(1 + IRR )N N = ∑ t =0 N = CF t
(1 + r ) t ∑ (1 + IRR )
CFt t =0 IRR（Internal Rate of Return） When NPV= 0, the discount rate.
Multiple solutions Problem of the IRR calculation (# sign changes)
Basic assumption: Reinvestment rate = IRR
16211 100% Contribution Breeds Professionalism
100% t R6: Discounted Cash Flow Applications
Project Decision Rule
Single project Case
NPV method: Accept it if NPV>0
IRR method: Accept it if IRR>r (required rate of return) Two Projects Case
Independent Projects
Similar to Single projects case Mutually Exclusive Projects
NPV method: Choose the one with higher NPV
IRR method: Choose the one with higher IRR
NPV and IRR methods may conflict with each other
17211 100% Contribution Breeds Professionalism
100% Example
Calabash Crab House is considering an investment in kitchenupgrade projects
with the following cash flows:
Project A Project B Initial Year $10,000 $9,000 Year 1 2,000 200 Year 2 5,000 2,000 Year 3 8,000 11,000 Year 4 8,000 15,000 Assuming Calabash has a 12.5 percent cost of capital, which of the following
investment decisions has the least justification? Accept:
A. Project B because the net present value (NPV) is higher than that of Project
A.
B. Project A because the IRR is higher than the cost of capital.
C. Project A because the internal rate of return (IRR) is higher than that of
Project B.
Correct answer: C
18211 100% Contribution Breeds Professionalism
100% R6: Discounted Cash Flow Applications
LOS 6. c define, calculate, and interpret a holding period return (total
return); Define: the holding period return is simply the percentage change in the
value of an investment over the period it is hold.
Calculate: P − P0 + CF1
HPR = 1
P0 19211 100% Contribution Breeds Professionalism
100% R6: Discounted Cash Flow Applications
LOS 6.e calculate and interpret the bank discount yield, holding period yield,
effective annual yield, and money market yield for a U.S. Treasury bill;
LOS 6.f convert among holding period yields, money market yields, effective
annual yields, and bond equivalent yields. rBD = ( F − P0 ) 360
×
F
t EAY = (1 + HPY)365/ t − 1 rMM HPY = P1 − P0 + CF1
P0 t
)
360
HPY =
t
1 rBD ( )
360
rBD ( 360 ⋅ rBD
rBD
360
= HPY ×
=
=
t
360 − t ⋅ rBD 1 − t ⋅ rBD / 360 t
t
t
rc *
FV
B E Y 2* 365
365
365
=e
= 1 + H P Y = (1 +
)
= (1 + E A R )
PV
2 20211 100% Contribution Breeds Professionalism
100% R6: Discounted Cash Flow Applications
The HPY is the actual return an investor will receive if the money
market instrument is held until maturity.
The EAY is the annualized HPY on the basis of a 365day year and
incorporates the effects of compounding.
The rMM is the annualized yield that is based on price and a 360day year and dose not account for the effects of compounding – it
assumes simple interest. 21211 100% Contribution Breeds Professionalism
100% Example
Jane Peebles purchased a Tbill that matures in 200 days for
$97,500. The face value of the bill is $100,000. What is the
money market yield on the bill?
A. 4.500%. B. 4.615%. C. 4.756%. Correct answer: B
Solution
First find the bank discount rate and then the money market yield on
the bill.
(2,500/100,000) × (360/200) = 4.5%.
(360 × 0.045)/(360 – (200× 0.045)) = 16.2/(360 – 9) = 4.615%
22211 100% Contribution Breeds Professionalism
100% Example
The bondequivalent yield for a semiannual pay bond is most
likely:
A. Equal to the effective annual yield. B. More than the effective annual yield. C. Equal to double the semiannual yield to maturity. Correct answer: C
Solution
The bond equivalent yield for a semiannual pay bond is equal to
double the semiannual yield to maturity. 23211 100% Contribution Breeds Professionalism
100% R6: Discounted Cash Flow Applications
LOS 6. d calculate, interpret, and distinguish between the moneyweighted
and timeweighted rates of return of a portfolio, and appraise the
performance of portfolios based on these measures; Moneyweighted and timeweighted Rate of Return
timeweighted return掌握概念及公式：
概念：Timeweighted rate of return measures compound growth.
步骤及公式：Firstly, compute the HPR; then, compute (1+HPR) for
each subperiod to obtain a total return for the entire measurement period
[eg. (1+HPR1) * (1+HPR2)…(1+HPRn)].
moneyweighted return掌握概念及公式：
概念：the IRR based on the cash flows related to the investment
步骤及公式：Firstly, determine the timing of each cash flow; then,
using the calculation to compute IRR, or using geometric mean.
考察方法：计算；注意计算timeweighted return时，如果不是年度的
HPR不用开方
24211 100% Contribution Breeds Professionalism
100% Example
Would a client making additions or withdrawals of funds most likely
affect their portfolio’s:
Timeweighted return? Moneyweighted return? A. No No B. No Yes C. Yes No Correct answer: B
Solution
The timeweighted return is not affected by cash withdrawals or
addition to the portfolio, the moneyweighted return measure would
be affected by client additions or withdrawals, if a client adds funds at
a favorable time the moneyweighted return will be elevated.
25211 100% Contribution Breeds Professionalism
100% Example
An analyst gathered the following information ($ millions) about
the performance of a portfolio:
Quarter Value at Beginning of Cash inflow (outflow) Value at Quarter End
Quarter (Prior to
At Beginning of Quarter
inflow or outflow) 1 2.0 0.2 2.4 2 2.4 0.4 2.6 3 2.6 (0.2) 3.2 4 3.2 1.0 4.1 The portfolio annual timeweighted rate of return is closest to:
8%
B. 27%
C. 32%
A. Correct answer: C
26211 100% Contribution Breeds Professionalism
100% Quantitative Methods: R7
Quantitative
Statistical concepts
1. Types of measurement scales 2. Measures of central tendency 3. Quantile 4. MAD和Var计算以及比较 5. Chebyshev’s inequality 6. CV & Sharp ratio 7. Skewness & Kurtosis 27211 100% Contribution Breeds Professionalism
100% R7: Statistical Concepts and Market Return
LOS 7. a differentiate between descriptive statistics and inferential
statistics, between a population and a sample, and among the types of
measurement scales; Descriptive statistics
Summarize the important characteristics of large data sets. Inferential statistics
Make forecasts, estimates, or judgments about a large set of
data on the basis of the statistical characteristics of a smaller set
(a sample) 28211 100% Contribution Breeds Professionalism
100% R7: Statistical Concepts and Market Return
Types of measurement scales:
Nominal scales
distinguishing two different things, no order, only has mode
example: assigning the number 1 to a municipal bond fund, the number 2
to a corporate bond fund.
Ordinal scales (>, <)
making things in order, but the difference are not meaningful
example: the ranking of 1,000 small cap growth stocks by performance
may be done by assigning the number 1 to the 100 best performing stocks
Interval scales (>, <, +, )
subtract is meaningful
example: Temperature
Ratio scales (>, <, +, , *, /)
with original point
example: money, if you have zero dollars, you have no purchasing power,
but if you have $4.00, you have twice as much purchasing power as a
person with $2.00. 29211 100% Contribution Breeds Professionalism
100% Example
1. Which scale represents the most refined measurement?
Ratio scale
B. Ordinal scale
C. Interval scale
A. Correct answer: A
2. An analyst creates a nominal scale to categorize the investment
style of a sample of managers. The most appropriate measure of
central tendency for the analyst to use is the:
Mean
B. Mode.
C. Median.
A. Correct answer: B
30211 100% Contribution Breeds Professionalism
100% Example
An analyst gathered the priceearnings ratios (P/E) for the firms in
the S&P 500 and then ranked the firms from highest to lowest P/E.
She then assigned the number 1 to the group with the lowest P/E
ratios, the number 2 to the group with the second lowest P/E ratios,
and so on. The measurement scale used by the analyst is best
described as:
A. Ratio. B. Ordinal. C. Interval. Correct answer: B 31211 100% Contribution Breeds Professionalism
100% R7: Statistical Concepts and Market Return
LOS 7.b define a parameter, a sample statistic, and a frequency distribution; A measure used to describe a characteristic of a population is referred to
as a parameter.
In the same manner that a parameter may be used to describe a
characteristic of a population, a sample statistic is used to measure a
characteristic of a sample.
A frequency distribution is a tabular presentation of statistical data that
aids the analysis of large data sets. 32211 100% Contribution Breeds Professionalism
100% R7: Statistical Concepts and Market Return
LOS 7. c calculate and interpret relative frequencies and cumulative relative
frequencies, given a frequency distribution; Relative frequency
The relative frequency is calculated by dividing the absolute
frequency of each turn interval by the total number of observations. Frequency Distribution
A frequency distribution is a tabular presentation of statistical data
that aids the analysis of large data sets. Cumulative frequency/Cumulative Relative Frequency
Could be calculated by summing the absolute or relative
frequencies starting at the lowest interval and progressing through
the highest.
33211 100% Contribution Breeds Professionalism
100% R7: Statistical Concepts and Market Return
Frequency distribution
Interval
Relative
($ 1,000) Absolute
Frequency Relative Cumulative Cumulative Frequency Absolute Frequency Frequency 10  5 3 0.97% 3 0.97% 5 – 0 35 11.29% 38 12.26% 0–5 176 56.77% 214 69.03% 5 – 10 74 23.87% 288 92.90% 10  15 22 7.10% 310 100% Total 310 34211 100% 100% Contribution Breeds Professionalism
100% R7: Statistical Concepts and Market Return
LOS 7. d describe the properties of a data set presented as a histogram or a
frequency polygon; ■histogram Histogram and Polygon polygon 8
7
6
5
4
3
2
1
0 35211 40％～50％ 30％～40％ 20％～30％ 10％～20％ 0～10％ －10％～0 －20％～－10％ －30％～－20％ Histogram is graphical presentation of the absolute frequency distribution
To construct a frequency polygon, the midpoint of each interval is plotted on the horizontal axis, and the absolute frequency for that interval is plotted on the vertical axis. 100% Contribution Breeds Professionalism
100% R7: Statistical Concepts and Market Return
LOS 7. e define, calculate, and interpret measures of central tendency, including the
population mean, sample mean, arithmetic mean, weighted average or mean
(including a portfolio return viewed as a weighted mean), geometric mean, harmonic
mean, median, and mode;
N The arithmetic mean： X= ∑X i i =1 n
n The weighted mean： XW = ∑ wi Xi = (w1 X1 + w2 X 2 + L+ wn X n )
i =1 N ∏ G
The geometric mean： = N X1X2 X3...XN = ( Xi )1/ N i =1 XH = The harmonic mean： n
n ∑(1/ X )
i i =1 harmonic mean<= geometric mean<=arithmetic mean
36211 100% Contribution Breeds Professionalism
100% Example
Which is the most accurate?
Harmonic mean Arithmetic mean Geometric mean A. 13 15 18 B. 15 15 18 C. 13 18 15 Correct answer: C 37211 100% Contribution Breeds Professionalism
100% Example
James Investments is calculating an unweighted (equallyweighted)
index on a four stock portfolio. Use the following information to
calculate the value of the index using the geometric and arithmetic mean.
Stock Number of Shares Initial Cost Current Cost A 100 5.00 5.00 B 1,000 10.00 12.50 C 500 7.50 10.00 D 1500 5.00 8.00 Price using geometric Price using arithmetic
1.277
B. 1.462
C. 1.277 1.295
1.295
1.379 A. Correct answer: A
38211 100% Contribution Breeds Professionalism
100% R7: Statistical Concepts and Market Return
LOS 7. f describe, calculate, and interpret quartiles, quintiles, deciles, and
percentiles; Quantiles
Quartile /Quintile/Deciles/Percentile
The third quartile: 75%, or threefourths of the observations fall below
that value. Calculation Ly = (n+1)y/100, Ly is the position.
Example: Observers：8 10 12 13 15 17 17 18 19 23 24
N=11，Ly=(11+1)*75%=9,i.e. the 9th number is 75%
The third quartiles = 19 Quantitles and measures of central tendency are known collectively
as measures of location.
39211 100% Contribution Breeds Professionalism
100% R7: Statistical Concepts and Market Return
LOS 7. g define, calculate, and interpret 1) a range and a mean absolute
deviation and 2) the variance and standard deviation of a population and of
a sample;
Range = maximum value – minimum value
N MAD = ∑X i −X i =1 n
N For population: σ 2 = ( X i − μ )2
∑
i =1 N n For sample: s2 =
40211 ( Xi − X )2
∑
i =1 n −1
100% Contribution Breeds Professionalism
100% Example
The least accurate statement about measures of dispersion for a
distribution is that the:
A. Range provides no information about the shape of the data
distribution. B. Mean absolute deviation will always be smaller than the standard
deviation. C. Arithmetic average of the deviations around the mean will always be
equal to one. Correct answer: C 41211 100% Contribution Breeds Professionalism
100% R7: Statistical Concepts and Market Return
LOS 7.h calculate and interpret the proportion of observations falling within
a specified number of standard deviations of the mean using Chebyshev’s
inequality; For any set of observations (samples or population), the proportion of
the values that lie within k standard deviations of the mean is at least 1
– 1/k2, where k is any constant greater than 1.
对任何一组观测值，个体落在均值周围k个标准差之内的概率不小
于11/k2，对任意k>1。
This relationship applies regardless of the shape of the distribution 42211 100% Contribution Breeds Professionalism
100% Example
Assume a sample of beer prices is negatively skewed.
Approximately what percentage of the distribution lies within plus
or minus 2.40 standard deviations of the mean?
A. 82.6% B. 58.3% C. 17.36% Correct answer: A 43211 100% Contribution Breeds Professionalism
100% R7: Statistical Concepts and Market Return
LOS 7. i define, calculate, and interpret the coefficient of variation and the
Sharpe ratio; Coefficient of variation measures the amount of dispersion in a
distribution relative to the distribution’s mean. (relative dispersion) sx
CV= ×100%
X
The sharp ratio measures excess return per unit of risk. R P Rf
Sharp ratio=
σP 44211 100% Contribution Breeds Professionalism
100% Example
An analyst gathered the following information about a portfolio's
performance over the past ten years:
Mean annual return 12.8% Mean excess return 7.4% Standard deviation of annual returns
Portfolio beta 15.7%
1.2 The coefficient of variation and Sharpe measure, respectively, for the
portfolio are closest to:
Coefficient of variation Sharpe measure A 0.82 0.39 B 0.82 0.47 C 1.23 0.47 Correct answer: C
45211 100% Contribution Breeds Professionalism
100% Example
The scalefree measure of relative dispersion that is useful in
making direct comparisons among different asset classes is the:
A. Range. B. Variation. C. Coefficient of variation. Correct answer: C 46211 100% Contribution Breeds Professionalism
100% R7: Statistical Concepts and Market Return
LOS 7. j define and interpret skewness, explain the meaning of a positively
or negatively skewed return distribution, and describe the relative locations
of the mean, median, and mode for a nonsymmetrical distribution; Mean=Median=Mode Mode<Median<Mean Symmetrical Positive (right) skew Mean<Median<Mode
Negative (left) skew Positive skewed：Mode<median<mean, having a right fat tail
Negative skewed：Mode>media>mean, having a left fat tail
考察方法：
根据描述的特点判断是Positively skewed还是Negative skewed
根据已知的偏度，选择都有哪些特点
47211 100% Contribution Breeds Professionalism
100% Example
The distribution of a security’s return over time has a mode of 9.5
percent, a median of 10.0 percent, and a mean of 10.5 percent.
The distribution can best be described as:
A. positively skewed, with a long tail on the left side B. negatively skewed, with a long tail on the left side C. positively skewed, with a long tail on the right side Correct answer: C
Solution
Because mean > median >mode, the distribution is positive skewed,
a long tail on the right side. 48211 100% Contribution Breeds Professionalism
100% Example
As analyst gathered the following information about the return
distribution of four investment. Based only on the information above, a
welldiversified investor would most likely prefer Portfolio:
Portfolio Skewness Sharp Ratio 1 Positive 0.6 2 Positive 0.8 3 Negative 0.6 A. 1 B. 2 C. 3 Correct answer: B 49211 100% Contribution Breeds Professionalism
100% R7: Statistical Concepts and Market Return
LOS 7. k define and interpret measures of sample skewness and kurtosis; Leptokurtic vs. platykurtic
It deals with whether or not a distribution is more or less “peaked”
than a normal distribution
Excess kurtosis = sample kurtosis – 3
leptokurtic Normal distribution platykurtic
Sample kurtosis >3 =3 <3 Excess kurtosis >0 =0 <0 考察方法：
根据描述的特点判断是leptokurtic还是platykurtic
根据已知的峰度，选择都有哪些特点
可能在考试中会和skew合并考核综合知识
50211 100% Contribution Breeds Professionalism
100% R7: Statistical Concepts and Market Return
Leptokurtic Normal
Distribution Fat tail 51211 100% Contribution Breeds Professionalism
100% R7: Statistical Concepts and Market Return
LOS 7. l discuss the use of arithmetic mean or geometric mean when
determining investment returns. The use of arithmetic mean and geometric mean when determining
investment returns
The arithmetic mean is the statistically best estimator of the next
year’s returns given only the three years of return outcomes.
Since past annual returns are compounded each period, the geometric
mean of past annual returns is the appropriate measure of past
performance. 52211 100% Contribution Breeds Professionalism
100% Quantitative Methods: R8
Quantitative
Probability concepts
Two defining properties of probability
Empirical, subjective, and priori probabilities
Odds for or against
计算joint probability & the probability that at least one of two events
will occur
Dependent and independent events
Covariance & correlation
Expected value, variance, and standard deviation of a random
variable and of returns on a portfolio
Bayes’ formula 53211 100% Contribution Breeds Professionalism
100% R8: Probability Concepts
LOS 8. a define a random variable, an outcome, an event, mutually
exclusive events, and exhaustive events; Basic Concepts
Random variable is uncertain quantity/number.
Outcome is an observed value of a random variable.
Event
Mutually exclusive events—can not both happen at the same time.
Exhaustive events—include all possible outcomes.
LOS 8. b explain the two defining properties of probability and distinguish
among empirical, subjective, and a priori probabilities; Two Defining Properties of Probability
0≤ P(E) ≤ 1
P(E1)+ P(E2)+……+ P(En)=1
54211 100% Contribution Breeds Professionalism
100% Example
Which of the following statements about the defining properties of
probability is TRUE?
A. The probability of any event is between 0 and 1, exclusive. B. If the device that generates an event is not fair, the events can be
mutually exclusive and exhaustive. C. The sum of the probabilities of events E1 though Ex equals one if
the events are mutually exclusive or exhaustive. Correct answer: B 55211 100% Contribution Breeds Professionalism
100% R8: Probability Concepts Objective
Probability Priori probability Basic
concepts
Subjective
probability 56211 分析过去
得到将来 Empirical
probability 分析过去
得到过去的推理 Based on intuition or
subjective estimates 100% Contribution Breeds Professionalism
100% R8: Probability Concepts
Empirical probability 经验概率
eg. Historically, the Dow Jones Industrial Average has closed higher
than the previous close two out of every three trading days. Therefore,
the probability of the Dow going up tomorrow is twothirds, or 66.7%.
Priori probability 先验概率
eg. Yesterday, 24 of the 30 DJIA stocks increased in value. Thus, if 1
of 30 stocks is selected at random, there is an 80%(24/30) probability
that its value increased yesterday
Subjective probability 主观概率
will close higher tomorrow is 90%. 57211 100% Contribution Breeds Professionalism
100% Example
An analyst adjusts the historical probability of default for highyield bonds to reflect her perceptions of changes in the quality of
highyield bonds. The analyst is best characterized as obtaining
a(n):
A. A priori probability. B. Objective probability. C. Subjective probability. Correct answer: C 58211 100% Contribution Breeds Professionalism
100% R8: Probability Concepts
LOS 8. c state the probability of an event in terms of odds for or against the
event;
Odds for an event
P(E)/(1P(E))
Odds against an event
(1P(E))/P(E)
Example:
Last year, the average salary increase for Poultry Research Assistants was 2.5
percent. Of the 10,000 Poultry Research Assistants, 2,000 received raises in
excess of this amount. The odds that a Poultry Research Assistant received a
salary increase in excess of 2.5 percent are:
A. 1 to 4.
B. 2 to 10.
C. 20%.
Correct answer: A
59211 100% Contribution Breeds Professionalism
100% R8: Probability Concepts
LOS 8.d distinguish between unconditional and conditional probabilities; Unconditional Probability (marginal probability): P(A)
Conditional probability : P(AB) 60211 100% Contribution Breeds Professionalism
100% R8: Probability Concepts
LOS. 8. e define and explain the multiplication, addition, and total probability
rules;
LOS 8. f calculate and interpret 1) the joint probability of two events, 2) the
probability that at least one of two events will occur, given the probability of
each and the joint probability of the two events, and 3) a joint probability of
any number of independent events;
Joint probability : P(AB)
Multiplication rule:
• P(AB)=P(AB)×P(B)= P(BA)×P(A)
If A and B are mutually exclusive events, then:
P(AB)=P(AB)=P(BA)=0
Probability that at least one of two events will occur:
Addition rule:
• P(A or B)=P(A)+P(B)P(AB)
If A and B are mutually exclusive events, then:
P(A or B)=P(A)+P(B)
61211 100% Contribution Breeds Professionalism
100% Example
The probability that two or more events will happen concurrently
is best characterized as:
A. Joint probability. B. Multiple probabilities. C. Concurrent probability. Correct answer: A 62211 100% Contribution Breeds Professionalism
100% R8: Probability Concepts
LOS 8. g distinguish between dependent and independent events; The occurrence of A has no influence of on the occurrence of
B
P(AB)=P(A) or P(BA)=P(B)
P(AB)=P(A)×P(B)
P(A or B)=P(A)+P(B)P(AB) Independence and Mutually Exclusive are quite different
If exclusive, must not independence;
Cause exclusive means if A occur, B can not occur, A influents B.
P(AB)=P(A)×P(B) 63211 100% Contribution Breeds Professionalism
100% Example
A fundamental analyst studying 100 potential companies for inclusion
in her stock portfolio uses the following three screening criteria:
Screening Criterion Number of Companies meeting screen MarkettoBook Ratio >4 20 Current Ratio >2 40 Return on Equity >10% 25 Assuming that the screening criteria are independent, the probability
that a given company will meet all three screening criteria is closest to:
A. 2.0%.
B. 8.5%.
C. 20.0%
Correct answer: A
64211 100% Contribution Breeds Professionalism
100% Example
P (A) =0.5, P (B) =0.5, odd for concurrent A and B is 3/5, the
relationship between A and B?
A. dependent B. Independent C. Mutually exclusive Correct answer: A
Solution
P(AB)=(3/5)/(1+3/5), P(A/B)=P(AB)/P(B)=3/4, P(A/B)不等于P(A) 65211 100% Contribution Breeds Professionalism
100% R8: Probability Concepts
LOS 8.h calculate and interpret, using the total probability rule, an
unconditional probability; For unconditional probability of event A,
P ( A ) = P ( A S 1 ) P ( S 1 ) + P ( A S 2 ) P ( S 2 ) + ... + P ( A S N ) P ( S N ) {S1 , S 2 ,...S N } where the set of events
exhaustive. is mutually exclusive and LOS 8.i explain the use of conditional expectation in investment applications; Expected value: E ( X ) = ∑ P( X )X
i i E(X) = ∑ x i * P ( xi ) = x1 * P ( x1 ) + x2 * P ( x2 ) + L + xn * P ( xn )
σ= σ
66211 2 N σ = ∑ Pi ( X i − EX ) 2
2 i =1 100% Contribution Breeds Professionalism
100% Example
Aubrey Goscheim recently accepted a position of Vice President of Planning in
the bedroom furniture division of Attic&Cellar Inc., a company that
manufactures new antiquelooking furniture. Her compensation package
stipulates that she will receive a bonus of 5 percent of division earnings if
division earnings exceed $1.0 million. The table below shows the probability
that divisional earnings will comprise a stated percentage of Division sales,
which are projected at $10 million.
Probability
0.10
0.10
0.15
0.10
0.25
0.30
Sum = 1.00 Table 1: Probability Distribution for Cellar, Inc.
Div. Earnings/ Sales (%)
Div. Earnings ($mill)
10%
1.0
20%
2.0
15%
1.5
12%
1.2
10%
1.0
8%
0.8 The expected value of Goscheim’s bonus is approximately: $27,250.
67211 100% Contribution Breeds Professionalism
100% R8: Probability Concepts
LOS 8.j diagram an investment problem using a tree diagram; Prob. Of good
economy=60% 30%
70% Expected
EPS=$1.51 60%
Prob. Of poor
economy=40% 68211 40% EPS=$1.8,prob=18%
EPS=$1.7,prob=42%
EPS=$1.3,prob=24% EPS=$1.0,prob=16% 100% Contribution Breeds Professionalism
100% R8: Probability Concepts
LOS 8.k calculate and interpret covariance and correlation;
Covariance:
Covariance measures how one random variable moves with another
random variable
The covariance of RA with itself is equal to the variance of RA
Covariance ranges from negative infinity to positive infinity
COV(X,Y) = E[(XE(X))(YE(Y))]
COV(X,X) = E[(X  E(X))(X  E(X))] = σ 2 (X) Correlation: ρ XY = COV(X,Y)
Var(X)Var(Y) Correlation measures the linear relationship between two random
variables
Correlation has no units, ranges from –1 to +1, standardization of
covariance
Understand the difference between correlation and independence
If ρ=0, this indicates?
69211 100% Contribution Breeds Professionalism
100% Example
The covariance of returns for two stocks:
A. must have a value between 1.0 and +1.0 B. must have a value equal to the weighted average of the standard
deviations of the returns of the two stocks C. will be positive if the actual returns on both stocks are consistently
below their expected returns at the same time Correct answer: C 70211 100% Contribution Breeds Professionalism
100% Example
The joint probability of returns, for securities A and B, are as follows:
Joint Probability Function of Security A and Security B Returns
(Entries are joint probabilities)
Return on security B=30% Return on security B=20%
Return on security A=25% 0.60 0 Return on security A=20% 0 0.40 The covariance of the returns between securities A and B is closest to:
A. 3(%)2. B. 12 (%)2. C. 24 (%)2. Correct answer: B
71211 100% Contribution Breeds Professionalism
100% R8: Probability Concepts
LOS 8. l calculate and interpret the expected value, variance, and standard
deviation of a random variable and of returns on a portfolio;
LOS 8. m. calculate and interpret covariance given a joint probability
function;
n E (rp ) = ∑ wi E ( Ri )
i =1 σ 2 n p n = ∑∑ wi w j cov(Ri , R j )
i =1 j =1 72211 100% Contribution Breeds Professionalism
100% Example
An individual wants to invest $100,000 and is considering the following
stocks:
stock Expected Return Standard Deviation of Returns A 12% 15% B 16% 24% The expected correlation of returns for the two stocks is +0.5. If the
investor invests $40,000 in Stock A and $60,000 in Stock B, the
expected standard deviation of returns on the portfolio will be:
A. equal to 20.4%
B. less than 20.4%
C. greater than 20.4% because the correlation coefficient is greater than
zero
Correct answer: B 73211 100% Contribution Breeds Professionalism
100% R8: Probability Concepts
LOS 8. n. calculate and interpret an updated probability using Bayes’ formula;
P(AB)=P(AB)×P(B) =P(BA)×P(A) P(A  B) = P (B  A)
* P ( A)
P(B) P(R)=P(RS1)×P(S1)+P(RS2)×P(S2)+…+ P(RSn)×P(Sn) P (Si  R ) = 74211 P (R  Si )P (Si )
P(R) 100% Contribution Breeds Professionalism
100% Example
Example
Abbey Conti, CFA, is an options trader interested in increasing her return on put
options. She develops a model that uses the magnitude of the Price Earnings (P/E)
ratio to forecast whether a stock’s price will increase or decrease in the next
period. She is tracking a group of 30 middle market firms. After using her model
and researching historical data, Conti determines the following: Given experience a price decrease in the next period, there are 60% of
firms with a P/E ratio of greater than 30
Given experience a price increase in the next period, there are 30% of
firms with a P/E ratio of greater than 30.
The probability that a firm in the sample will experience a price
decrease in the next period is 0.40.
Conti randomly selects a stock from the sample. Given that the stock has a P/E of
greater than 30, the probability that the stock price will decline next period is
approximately:
A. 0.57
B. 0.43
C. 0.18 Correct answer: A
75211 100% Contribution Breeds Professionalism
100% Example
An analyst has developed a ratio to identify companies expected to
experience declining earnings per share (EPS). Research shows that 70
percent of firms experiencing a decline in EPS have a negative ratio,
while only 20 percent of firms not experiencing a decline in EPS have a
negative ratio. The analyst expects that 10 percent of all publicly traded
companies will experience a decline in EPS next year. The analyst
randomly selects a company and its ratio is negative. Based on Bayes’
theorem, the posterior probability that the company will experience a
decline in EPS next year is closest to:
A. 14%
B. 28%
C. 30%
Correct answer: B 76211 100% Contribution Breeds Professionalism
100% R8: Probability Concepts
LOS 8. o. identify the most appropriate method to solve a particular
counting problem, and solve counting problems using the factorial,
combination, and permutation notations. Multiplication rule: n1×n2×……×nk
Factorial: n！ n!
Labeling: n !×n !×… × n !
1
2K
k
Combination: ⎛n⎞
n!
Cr = ⎜ ⎟ =
n
⎜ r ⎟ ( n − r )!× r !
⎝⎠ Permutation: n!
n Pr =
( n − r )! 77211 100% Contribution Breeds Professionalism
100% Quantitative Methods: R9
Quantitative
Common Probability Distributions
Properties of discrete distribution and continuous distribution
Uniform random variable and a binomial random variable
The key properties of the normal distribution
Standardize a random variable
Confidence interval for a normally distributed random variable
Lognormal distribution
Safetyfirst ratio
Monte Carlo simulation 78211 100% Contribution Breeds Professionalism
100% R9: Common Probability Distributions
LOS 9.a. explain a probability distribution and distinguish between discrete
and continuous random variables;
LOS 9.b. describe the set of possible outcomes of a specified discrete
random variable; Probability Distribution
Describe the probabilities of all the possible outcomes for a random
variable.
Discrete and continuous random variables
Discrete random variables: the number of possible outcomes can be
counted, and for each possible outcome, there is a measurable and
positive probability.
Continuous variables: the number of possible outcomes is infinite,
even if lower and upper bounds exist.
P (x)=0 even though x can occur.
P (x1<X<x2)
79211 100% Contribution Breeds Professionalism
100% R9: Common Probability Distributions
LOS 9.c. interpret a probability function, a probability density function, and a
cumulative distribution function; Probability function: p(x)=P(X=x)
For discrete random variables
0 ≤ p(x) ≤ 1
Σp(x)=1
Probability density function (p.d.f) : f(x)
For continuous random variable commonly
Cumulative probability function (c.p.f) : F(x)
F(x)=P(X<=x) 80211 100% Contribution Breeds Professionalism
100% Example
Which of the following statements about probability distributions is
FALSE?
A. For a probability distribution for the number of days the air pollution
is above a specified level, p(x) = 0 when x cannot occur, or p(x) > 0
when it can.
B. For a probability distribution for the specific level of air pollution on
a given day, p(x) = 0 even if x can occur.
C. A cumulative distribution function gives the probability that a
random variable takes a value equal to or greater than a given
number.
Correct answer: C
Solution
A cumulative distribution function gives the probability that a
random variable takes a value equal to or less than a given number:
P(X ≤ x), or F(X).
81211 100% Contribution Breeds Professionalism
100% R9: Common Probability Distributions
LOS 9.d. calculate and interpret probabilities for a random variable, given its
cumulative distribution function; 82211 100% Contribution Breeds Professionalism
100% R9: Common Probability Distributions
LOS 9.e. define a discrete uniform random variable and a binomial random
variable;
LOS 9.f. calculate and interpret probabilities given the discrete uniform and
the binomial distribution functions; Binomial distribution
Bernoulli random variable
P(Y=1)=p P(Y=0)=1p
Binomial random variable，the probability of x successes in n trails ⎛n⎞ x
p ( x ) = P ( X = x ) = ⎜ ⎟ p (1 − p ) n − x
⎜⎟
⎝ x⎠
Expectations and variances
Expectation
Bernoulli random variable (Y) p p(1p) Binomial random variable (X)
83211 Variance np np(1p) 100% Contribution Breeds Professionalism
100% R9: Common Probability Distributions
R9:
LOS 9.i. describe the continuous uniform distribution and calculate and
interpret probabilities, given a continuous uniform probability distribution; Continuous Uniform Distribution
is defined over a range that spans between some lower limit, a, and
upper limit, b, which serve as the parameters of the distribution.
Properties of Continuous uniform distribution
For all a ≤x1< x2 ≤b
P (X<a or X>b) = 0 P ( x 1 ≤ X ≤ x 2 ) = ( x 2 − x 1) /( b − a ) 84211 100% Contribution Breeds Professionalism
100% Example
1. Which of the following statements about probability distributions is TRUE?
A. A continuous uniform distribution has a lower limit but no upper limit.
B. A cumulative distribution function defines the probability that a random
variable is greater than a given value.
C. A binomial distribution counts the number of successes that occur in a
fixed number of independent trials that have mutually exclusive (i.e.
yes or no) outcomes.
Correct answer: C
2. A random variable with a finite number of equally likely outcomes is best
described by a:
A. Binomial distribution.
B. Bernoulli distribution.
C. Discrete uniform distribution.
Correct answer: C
85211 100% Contribution Breeds Professionalism
100% Example
3. 4. An analyst has recently determined that only 60 percent of all U.S. pension
funds have holdings in hedge funds. In evaluating this probability, a random
sample of 50 U.S. pension funds is taken. The number of U.S. pension funds in
the sample of 50 that have hedge funds in their portfolio would most accurately
be described as:
A. A binomial random variable.
B. A Bernoulli random variable.
C. A continuous random variable.
Correct answer: B
An energy analyst forecasts that the price per barrel of crude oil five years from
now will range between USD$75 and USD$105. Assuming a continuous
uniform distribution, the probability that the price will be less than USD$80
five years from now is closest to:
A. 5.6%.
B. 16.7%.
C. 44.4%.
Correct answer: B
86211 100% Contribution Breeds Professionalism
100% R9: Common Probability Distributions
LOS 9.h. define, calculate, and interpret tracking error; Tracking error is the difference between the total return on a
portfolio and the total return on the benchmark against which its
performance is measured. 87211 100% Contribution Breeds Professionalism
100% R9: Common Probability Distributions
LOS 9.j. explain the key properties of the normal distribution, distinguish
between a univariate and a multivariate distribution, and explain the role of
correlation in the multivariate normal distribution; The shape of the density function
f(x) x
Properties:
X~N(µ , σ²)
Symmetrical distribution: skewness=0; kurtosis=3
A linear combination of normally distributed random variables is also
normally distributed.
The tails get thin and go to zero but extend infinitely, asympotic (渐近）
88211 100% Contribution Breeds Professionalism
100% R9: Common Probability Distributions
LOS 9.k. determine the probability that a normally distributed random
variable lies inside a given interval;
The confidence intervals 68% confidence interval is [ μ − σ , μ + σ ]
90% confidence interval is [ μ − 1.65σ , μ + 1.65σ ]
95% confidence interval is [ μ − 1.96σ , μ + 1.96σ ]
99% confidence interval is [ μ − 2.58σ , μ + 2.58σ ]
Probability U2.58σ U1.96σ U1σ u U+1σ U+1.96σ U2.58σ 68%
95%
99% 89211 100% Contribution Breeds Professionalism
100% Example
An analyst determined that approximately 99 percent of the
observations of daily sales for a company were within the interval
from $230,000 to $480,000 and that daily sales for the company
were normally distributed. The mean daily sales and standard
deviation of daily sales, respectively, for the company were
closest to:
Mean daily sales Standard deviation of daily sales
A. $351,450 $48,450 B. $351,450 $83,333 C. $355,000 $48,450 Correct answer: C 90211 100% Contribution Breeds Professionalism
100% R9: Common Probability Distributions
LOS 9.l. define the standard normal distribution, explain how to standardize
a random variable, and calculate and interpret probabilities using the
standard normal distribution; Standard normal distribution
N(0,1) or Z
Standardization: if X~N(µ , σ²), then Z =
Ztable
F(z)=1F(z)
P(Z>z) = 1 –F(z) 91211 100% Contribution Breeds Professionalism
100% X −μ σ ~ N(0,1) Example
Based on a normal distribution with a mean of 500 and a standard
deviation of 150, the zvalue for an observation of 200 is closest
to:
A. –2.00. B. –1.75. C. 1.75. Correct answer: A 92211 100% Contribution Breeds Professionalism
100% R9: Common Probability Distributions
LOS 9.m. define shortfall risk, calculate the safetyfirst ratio, and select an
optimal portfolio using Roy’s safetyfirst criterion; Shortfall risk: RL= threshold level return, minimum return required
Minimize (Rp< RL)
Roy’s safetyfirst criterion [E (RP ) − RL ] / σ P
Maximize SFRatio
Maximize SFR= 93211 E(R P )R L
<=> Minimize P (Rp< RL)
σP 100% Contribution Breeds Professionalism
100% Example
A portfolio manager gathered the following information about four possible
asset allocations:
Allocation Expected annual return Standard deviation of return A 10% 6% B 25% 14% C 18% 17% The manager's client has stated that her minimum acceptable return is 8%.
Based on Roy's safetyfirst criterion, the most appropriate allocation is:
A. Allocation A. B. Allocation B. C. Allocation C. Correct answer: B
94211 100% Contribution Breeds Professionalism
100% R9: Common Probability Distributions
LOS 9.n. explain the relationship between normal and lognormal
distributions and why the lognormal distribution is used to model asset
prices; Definition: If lnX is normal, then X is lognormal, which is used to
describe the price of asset
Right skewed
Bounded from below by zero 0 95211 2 4 6 8 100% Contribution Breeds Professionalism
100% 10 Example
1. Compared to a normal distribution, a lognormal distribution is least likely
to be:
A. Skewed to the left.
B. Skewed to the right.
C. Useful in describing the distribution of stock prices.
Correct answer: A
2. An analyst stated that lognormal distribution are suitable for describing
asset returns and that normal distributions are suitable for describing
distributions of asset prices. Is the analyst’s statement correct with respect
to:
Lognormal distribution
Normal distribution
A. No
No
B. No
Yes
C. Yes
No
Correct answer: A
96211 100% Contribution Breeds Professionalism
100% R9: Common Probability Distributions
R9:
LOS 9.o. distinguish between discretely and continuously compounded rates
of return, and calculate and interpret a continuously compounded rate of
return, given a specific holding period return; Rm
Discrete: EAY = (1 + ) − 1
m Rm
Continuous: EAR = lim(1 + ) −1 = eR −1
m→∞
m
S1
=1+HPR=e R CC (持有一年)
S0 1+HPRT = eRCC ×T (持有T年)
97211 100% Contribution Breeds Professionalism
100% R9: Common Probability Distributions
R9:
LOS 9.p. explain Monte Carlo simulation and historical simulation, and describe their
major applications and limitations. Monte Carlo simulation vs Historical simulation
Monte Carlo simulation uses randomly generated values for risk factors,
based on their assumed distributions, to produce a distribution of possible
security values, to analyze the complex instrument;
Limitations:
It is fairly complex and will assume a parameter distribution.
It is not an analytic method but a statistical one, and cannot
provide the insights that analytic methods can.
Historical simulation uses randomly selected past changes in these risk
factors to generate a distribution of possible security values, can’t answer
the “WhatIf”.
Limitations: the past can not indicate the future and historical
simulation cannot address the sort of “what if ” questions that Monte
Carlo simulation can.
98211 100% Contribution Breeds Professionalism
100% Quantitative Methods: R10
Quantitative
Sampling and Estimation
Simple random and stratified random sampling, timeseries and crosssectional data
Central limit theorem
Standard error of the sample mean的意义并计算
The desirable properties of an estimator
Student’s tdistribution的特点
Criteria for selecting the appropriate test statistic，计算confidence
interval
Five kinds of biases 99211 100% Contribution Breeds Professionalism
100% R10: Sampling and Estimation
LOS 10.a. define simple random sampling, sampling error, and a sampling
distribution, and interpret sampling error;
LOS 10.b. distinguish between simple random and stratified random
sampling; Sampling and estimation
Simple random sampling
Stratified random sampling: to separate the population into smaller
groups based on one or more distinguishing characteristics. Stratum
and cells=M*N
Sampling error: sampling error of the mean= sample mean population
mean
The sample statistic itself is a random variable and has a probability
distribution. 100211 100% Contribution Breeds Professionalism
100% R10: Sampling and Estimation
LOS 10.c. distinguish between timeseries and crosssectional data; Timeseries data
consist of observations taken over a period of time at specific
and equally spaced time intervals.
Crosssectional data
a sample of observations taken at a single point in time.
Timeseries data Crosssectional data a collection of data recorded over a
period of time a collection of data taken at a single
point of time. 101211 100% Contribution Breeds Professionalism
100% Example
Greg Goldman, research analyst in the fixedincome area of an investment bank,
needs to determine the average duration of a sample of twenty 15year fixedcoupon investment grade bonds. Goldman first categorizes the bonds by risk
class and then randomly selects bonds from each class. After combining the
bonds selected (bond ratings and other information taken as of March 31st of
the current year), he calculates a sample mean duration of 10.5 years.
Assuming that the actual population mean is 9.7 years, which of the following
statements about Goldman’s sampling process and sample is FALSE?
A. Goldman used stratified random sampling. B. The sampling error of the means equals 0.8 years. C. Goldman is using timeseries data. Correct answer: C 102211 100% Contribution Breeds Professionalism
100% R10: Sampling and Estimation
LOS 10.d. interpret the central limit theorem and describe its importance; Central Limit Theory
For simple random samples of size n from a population with a mean
µ and a variance σ² but without known distribution, the sampling
distribution of the sample mean approaches N(µ , σ²/n) if the
sample size is sufficiently large (n ≥30). 条件: 1. n ≥ 30 2.总体均值方差已知 结论: 1.服从正态分布 2. μ population = μsample s 2 = σ 2 n 103211 100% Contribution Breeds Professionalism
100% Example
According to the central limit theorem, a sampling distribution of
the sample mean will be approximately normal only if the:
A. sample size n is large B. underlying distribution is normally distributed C. variance or population mean of the underlying distribution is known Correct answer：A 104211 100% Contribution Breeds Professionalism
100% R10: Sampling and Estimation
LOS 10.e. calculate and interpret the standard error of the sample mean; Standard error of the sample mean
Known population variance σx =σ / n Unknown population variance sx = s / n 105211 100% Contribution Breeds Professionalism
100% Example
An analyst gathered the following information:
Sample mean 12% Sample size 50 Sample variance 30(%)2 The standard error of the sample mean is closest to:
A. 0.47%. B. 0.64%. C. 0.77%. Correct answer: C 106211 100% Contribution Breeds Professionalism
100% R10: Sampling and Estimation
LOS 10.g. identify and describe the desirable properties of an estimator
(unbiased, efficient, consistent); The desirable properties of an estimator：
Unbiasedness: expected value of the estimator is equal to the parameter
that are trying to estimate
Efficiency: for all unbiased estimators, if the sampling dispersion is
smaller than any other unbiased estimators, then this unbiased estimator
is called efficient.
Consistency: the accuracy of the parameter estimate increases as the
sample size increases. (the standard deviation of the parameter
estimate decreases as the sample size increases)
As the sample size increases, the standard error of the sample mean
falls.
107211 100% Contribution Breeds Professionalism
100% Example
Shawn Choate is thinking about his graduate thesis. Still in the preliminary
stage, he wants to choose a variable of study that has the most desirable
statistical properties. The statistic he is presently considering has the following
characteristics:
The expected value of the sample mean is equal to the population mean.
The variance of the sampling distribution is smaller than that for other
estimators of the parameter.
As the sample size increases, the standard error of the sample mean rises
and the sampling distribution is centered more closely on the mean.
Select the best choice. Choate’s estimator is:
A. Unbiased, efficient, and consistent. B. Efficient and consistent. C. Unbiased and efficient. Correct answer: C
108211 100% Contribution Breeds Professionalism
100% R10: Sampling and Estimation
LOS 10.f. distinguish between a point estimate and a confidence interval
estimate of a population parameter; Point estimate: the statistic, computed from sample information, which
is used to estimate the population parameter
Confidence interval estimate: a range of values constructed from
sample data so the parameter occurs within that range at a specified
probability. α—the level of significance
LOS 10.h. explain the construction of confidence intervals; Interval Estimation（also see Chapter: Hypothesis Testing ）
Level of significance （alpha）
Degree of Confidence （1－alpha）
Confidence Interval = [ Point Estimate +/ (reliability factor) *
Standard error]
109211 100% Contribution Breeds Professionalism
100% Example
The width of a confidence interval most likely will be smaller if the
sample variance and number of observations, respectively, are:
Sample variance Number of observations A. Smaller Smaller B. Smaller Larger C. Larger Smaller Correct answer: B 110211 100% Contribution Breeds Professionalism
100% R10: Sampling and Estimation
LOS 10.i. describe the properties of Student’s tdistribution and calculate
and interpret its degrees of freedom; Student’s tdistribution: Degrees of freedom (df) n1
Symmetrical
Less peaked than a normal distribution (“fatter tails”)
As the degrees of freedom gets larger, the shape of tdistribution
approaches standard normal distribution N (0,1) ν =9 ν =2
3
111211 2 1 0 1 2 3 100% Contribution Breeds Professionalism
100% Example
An analyst stated that as degrees of freedom increase, a tdistribution will become more peaked and the tails of the tdistribution will become less fat. Is the analyst’s statement correct
with respect to the tdistribution:
Become more peaked? Tails becoming less fat? A. No No B. No Yes C. Yes Yes Correct answer: C 112211 100% Contribution Breeds Professionalism
100% R10: Sampling and Estimation
LOS 10. j. calculate and interpret a confidence interval for a population
mean, given a normal distribution with 1) a known population variance, 2)
an unknown population variance, or 3) an unknown variance and a large
sample size;
σ
s
x ± zα 2 n x ± tα When sampling form a: 2 n Test Statistic small
sample (n<30)
Normal distribution with known variance
z Statistic
Normal distribution with unknown variance
t Statistic
Nonnormal distribution with known variance
not available
Nonnormal distribution with unknown variance not available
113211 100% Contribution Breeds Professionalism
100% large
sample (n>=30)
z Statistic
t Statistic/z
z Statistic
t Statistic/z R10: Sampling and Estimation
LOS 10.k. discuss the issues regarding selection of the appropriate sample size,
datamining bias, sample selection bias, survivorship bias, lookahead bias, and
timeperiod bias. Datamining bias
Refers to results where the statistical significance of the pattern is
overestimated because the results were found through data mining.
Sample selection bias
Some data is systematically excluded from the analysis, usually because of the
lack of availability.
Survivorship bias
Usually derives from sample selection for only the existing portfolio are
included
Lookahead bias
Occurs when a study tests a relationship using sample data that was not a
available on the test date.
Timeperiod bias
Time period over which the data is gathered is either too short or too long. If
the time period is too short, research results may reflect phenomena specific to
that time period, or perhaps even data mining.
114211 100% Contribution Breeds Professionalism
100% Example
Sunil Hameed is a reporter with the weekly periodical The Fun Finance Times.
Today, he is scheduled to interview a researcher who claims to have developed
a successful technical trading strategy based on trading on the CEO’s birthday
(sample was taken from the Fortune 500). After the interview, Hameed
summarizes his notes (partial transcript as follows). The researcher:
Was defensive about the lack of economic theory consistent with his results.
Used the same database of data for all his tests and has not tested the
trading rule on outofsample data.
Excluded stocks for which he could not determine the CEO’s birthday.
Used a sample cutoff date of the month before the latest market correction.
Select the choice that best completes the following: Hameed concludes that the
research is flawed because the data and process are biased by:
A. Data mining, sample selection bias, and timeperiod bias.
B. Data mining, timeperiod bias, and lookahead bias.
C. Timeperiod bias and survivorship bias.
Correct answer: A
115211 100% Contribution Breeds Professionalism
100% Quantitative Methods: R11
Hypothesis testing
The steps of hypothesis testing
假设的分类：The null hypothesis and alternative hypothesis, onetailed and twotailed test
Test statistics的选择和计算
Type I and type II errors
Decision rule
The Chisquare test and Ftest
Parameter tests and nonparameter tests的对比 116211 100% Contribution Breeds Professionalism
100% R11: Hypothesis Testing
R11:
LOS 11.a. define a hypothesis, describe the steps of hypothesis testing,
interpret and discuss the choice of the null hypothesis and alternative
hypothesis, and distinguish between onetailed and twotailed tests of
hypotheses; Step 1 Step 2 Step 3 State null and
alternative
hypotheses Identify the test
statistic Select a level of
significance Step 5 Step 4 Do not reject Reject 117211 Take a sample,
arrive at
decision Formulate a
decision rule 100% Contribution Breeds Professionalism
100% R11: Hypothesis Testing
Define Hypothesis
Statistical assessment of a statement or idea regarding a population
parameter.
Null hypothesis and Alternative hypothesis (we want to assess) H 0 : μ = μ0 H a : μ ≠ μ0 The fact we suspect and want to reject
Statistical assessment
For population not sample
Onetailed and Twotailed tests of Hypothesis
Two‐tailed One‐tailed 118211 H 0 : μ = μ0 H a : μ ≠ μ0 H 0 : μ ≤ μ0 H a : μ > μ0 or , H 0 : μ ≥ μ 0 H a : μ < μ0 100% Contribution Breeds Professionalism
100% Example
An analyst conducted a significance test to determine if the relationship
between two variables was real or the result of chance, His null hypothesis
is that the population correlation coefficient is equal to zero and his
alternative hypothesis is that the population correlation coefficient is
different from zero. He developed the following information:
Value of the test statistic 2.8092 Critical value at the 0.05 significance level 1.96 Critical value at the 0.01 significance level 2.58 The analyst conducted a:
A. Onetailed test and can reject his null hypothesis. B. Twotailed test and can reject his null hypothesis. C. Onetailed test and cannot reject his null hypothesis. Correct answer: B
119211 100% Contribution Breeds Professionalism
100% Example
In the hypothesis testing, assess whether if mean excess the
benchmark, how to set the null hypothesis?
A. μ p μ0 B. μ ≤ μ 0
C. μ f μ0 Correct answer: B 120211 100% Contribution Breeds Professionalism
100% R11: Hypothesis Testing
LOS 11.b. define and interpret a test statistic, a Type I and a Type II error,
and a significance level, and explain how significance levels are used in
hypothesis testing; Test statistic
Test Statistic = Sample statistics − Hypothesized value
stanard error of the sample statistic Test Statistic follows Normal, T, Chi Square or F distributions
Test Statistic has formula. Calculate it with the sample data.
This is the general formula but only for Z and T distribution.
Examples： X − μ0
Test Statistic =
σ/ n
121211 Test Statistic = 100% Contribution Breeds Professionalism
100% X − μ0
s/ n Example
Given the following hypothesis:
The null hypothesis is H0: = 5
The alternative is H1: does not equal 5
The mean of a sample of 17 is 7
The population standard deviation is 2.0 What is the calculated Zstatistic?
A. 4.00. B. 4.12. C. 8.00. Correct answer: B 122211 100% Contribution Breeds Professionalism
100% R11: Hypothesis Testing
Decision True condition H 0 is true
Do not reject Correct Decision Incorrect Decision
Type Ⅱ error Incorrect Decision
Significance levelα
=P (Type I error) Correct Decision
Power of test =
1 P (Type Ⅱ error) H0
Reject H0 H 0 is false With other conditions unchanged, either error probability arises at the cost
of the other error probability decreasing.
How to reduce both errors? Increase the Sample Size.
123211 100% Contribution Breeds Professionalism
100% Example
1. Kyra Mosby, M.D., has a patient who is complaining of severe abdominal pain.
Based on an examination and the results from laboratory tests, Mosby states the
following diagnosis hypothesis: Ho: Appendicitis, HA: Not Appendicitis. Dr.
Mosby removes the patient’s appendix and the patient still complains of pain.
Subsequent tests show that the gall bladder was causing the problem. By taking
out the patient’s appendix, Dr. Mosby:
A. Made a Type I error.
B. Is correct.
C. Made a Type II error.
Correct answer: C
2. If the sample size increases, the probability of get the Type Ⅰand Type Ⅱ error
will
TypeⅡ
Type Ⅰ
A. increase
increase
B. not change
not change
C. decrease
decrease
Correct answer: C
124211 100% Contribution Breeds Professionalism
100% Example
3. All else equal, is specifying a larger significance level in a hypothesis
test likely to increase the probability of a:
Type I error? Type II error? A. No No B. No Yes C. Yes No Correct answer: C
4. What is the definition of the power test? Power test is the probability to:
A. Reject the true null hypothesis while it is true B. Reject the false null hypothesis while it is indeed false C. Can not reject the true hypothesis Correct answer: B
125211 100% Contribution Breeds Professionalism
100% R11: Hypothesis Testing
LOS 11.c. define and interpret a decision rule and the power of a test, and
explain the relation between confidence intervals and hypothesis tests;
LOS 11.e. explain and interpret the pvalue as it relates to hypothesis testing;
Critical value (关键值，实际就是分位数） The distribution of test statistic (z, t, x2, F)
Significance level (α)
Onetail or twotailed test
Decision rule Significance Level? Critical Value Method Two tailed or one tailed test?
Reject region? Critical Value under the condition
Compare the Test Statistic and Critical Value Pvalue Method (more useful): P↓, easier to reject H0
126211 100% Contribution Breeds Professionalism
100% R11: Hypothesis Testing
2.5% 2.5% 95% 1.96 Reject H0 1.96 Fail to
Reject H0 5% 95% 1.65 Reject H0 Fail to
Reject H0 Reject H0 Reject H0 if test statistic>critical value
Fail to reject H0 if test statistic<critical value
Statement cannot say “accept the null hypothesis”, only can say “cannot reject”
***** is significantly different from ******
*****is not significantly different from ******
127211 100% Contribution Breeds Professionalism
100% Example
An analyst conducts a twotailed test to determine if earnings
estimates are significantly different from reported earnings. The
sample size was over 100. The computed Zstatistic is 1.25. Using
a 5 percent confidence level, which of the following statements is
TRUE?
A. Both the null and the alternative are significant. B. You cannot determine what to do with the information given. C. Fail to reject the null hypothesis and conclude that the earnings
estimates are not significantly different from reported earnings. Correct answer: C 128211 100% Contribution Breeds Professionalism
100% R11: Hypothesis Testing
R11:
Confidence Interval = [ Point Estimate +/ (reliability factor) * Standard error]
Width of CI
Confidence level
Significance level  Sample size  Degree of freedom  Sample/population
standard deviation 129211 + + 100% Contribution Breeds Professionalism
100% R11: Hypothesis Testing
LOS 11.f. identify the appropriate test statistic and interpret the results for
a hypothesis test concerning the population mean of both large and small
samples when the population is normally or approximately distributed
and the variance is 1) known or 2) unknown;
LOS 11.g. identify the appropriate test statistic and interpret the results
for a hypothesis test concerning the equality of the population means of
two at least approximately normally distributed populations, based on
independent random samples with 1) equal or 2) unequal assumed
variances;
LOS 11.h. identify the appropriate test statistic and interpret the results
for a hypothesis test concerning the mean difference of two normally
distributed populations (paired comparisons test);
LOS 11.i. identify the appropriate test statistic and interpret the results for
a hypothesis test concerning 1) the variance of a normally distributed
population, and 2) the equality of the variances of two normally
distributed populations based on two independent random samples; 130211 100% Contribution Breeds Professionalism
100% R11: Hypothesis Testing
Test Population Mean 1. One normal population with known variance Z distribution 2. One normal population with unknown variance
Normal population,
n<30 n>30 Known variance ztest ztest Unknown variance ttest ttest or ztest 131211 100% Contribution Breeds Professionalism
100% Summary of Hypothesis Testing
Test type Assumptions Mean Normally distributed population,
hypothesis known population variance
testing Normally distributed population,
unknown population variance Independent populations,
unknown population variances
assumed equal
Independent populations,
unknown population variances
not assumed equal
Samples not independent,
paired comparisons test
Variance Normally distributed population hypothesis
testing Two independent normally
distributed populations
132211 H0 Teststatistic μ=0 Z= μ=0 t= x − μ0 σ/ n
x − μ0 Critical value
N(0,1)
t(n1) s/ n μ1−μ2=0 t t(n1 +n2 －2) μ1−μ2=0 t t μd=0 t= d t(n1) σ²=σ0²
σ1²=σ2² χ=
2 (n − 1) s 2 F= 100% Contribution Breeds Professionalism
100% sd σ 02
2
s1 s2
2 χ 2 (n − 1)
F (n1 − 1, n2 − 1) Example
Which type of test is used to test if the square deviations of the
two normal distribution population are equal?
A. Ttest B. χ2test C. Ftest Correct answer: C 133211 100% Contribution Breeds Professionalism
100% R11: Hypothesis Testing
LOS 11.j. distinguish between parametric and nonparametric tests and
describe the situations in which the use of nonparametric tests may be
appropriate. Parametric tests
rely on assumptions regarding the distribution of the population
specific to population parameters.
For example, ztest. Nonparametric tests
Nonparametric tests are used:
When there is concern about quantities other than the parameters of a
distribution.
When the assumptions of parametric tests can’t be supported.
When the data are not suitable for parametric tests.
134211 100% Contribution Breeds Professionalism
100% Quantitative Methods: R12
Quantitative
Technical Analysis
the principles of technical analysis, its applications, and its underlying
assumptions
Types of charts
the uses of trend
Common chart patterns
Common analysis indicators
the use of cycles 135211 100% Contribution Breeds Professionalism
100% R12: Technical Analysis
LOS 12.a. explain the principles of technical analysis, its applications, and
its underlying assumptions; Principles:
Prices are determined by the interaction of supply and demand.
Only participants who actually trade affect prices, and betterinformed participants tend to trade in greater volume.
Price and volume reflect the collective behavior of buyers and sellers. Assumptions:
Market prices reflect both rational and irrational investor behavior.
Investor behavior is reflected in trends and patterns that trend to repeat
and can be identified and used for forecasting prices.
Efficient markets hypothesis dose not hold. 136211 100% Contribution Breeds Professionalism
100% Example
1. Technical analysis relies most importantly on:
A. price and volume data. B. accurate financial statements. C. fundamental analysis to confirm conclusions. 2. Which of the following is not an assumption of technical
analysis?
A. Security markets are efficient. B. The security under analysis is freely traded. C. Market trends and patterns tend to repeat themselves. 137211 100% Contribution Breeds Professionalism
100% R12: Technical Analysis
The differences among technicians, fundamentalists and Efficient market
followers.
Fundamental analysis of a firm attempts to determine the intrinsic value of
an asset by using the financial statements and other information.
Technical analysis uses only the firm’s share price and trading volume data,
and it is not concerned with identifying buyers’ and sellers’ reasons for
trading, but only with the trades that have occurred.
Fundamentalists believe that prices react quickly to changing stock values,
while technicians believe that the reaction is slow. Technicians look for
changes in supply and demand, while fundamentalists look for changes in
value. 138211 100% Contribution Breeds Professionalism
100% R12: Technical Analysis
Advantages of technical analysis:
Actual price and volume data are observable.
Technical analysis itself is objective (although require subjective
judgment), while much of the data used in fundamental analysis is
subject to assumptions or restatements.
It can be applied to the prices of assets that do not produce future
cash flows, such as commodities.
It can also be useful when financial statement fraud occurs. Disadvantage:
The usefulness is limited in markets where price and volume data
might not truly reflect supply and demand, such as in illiquid markets
and in markets that are subject to outside manipulation. 139211 100% Contribution Breeds Professionalism
100% Example
Why is technical analysis especially useful in the analysis of
commodities and currencies?
A. Valuation models cannot be used to determine fundamental intrinsic
value for these securities. B. Government regulators are more likely to intervene in these markets. C. These types of securities display clearer trends than equities and
bonds do. 140211 100% Contribution Breeds Professionalism
100% R12: Technical Analysis
LOS 12.b. discuss the construction and interpretation of different types of
technical analysis charts; Charts of price and volume are used to analyze asset prices and
overall market movement.
Horizontal axis: usually time interval (daily, weekly, monthly)
Vertical axis: Price Types of charts:
Line charts
Bar charts
Candlestick charts
Point and figure charts 141211 100% Contribution Breeds Professionalism
100% R12: Technical Analysis Line Charts are the simplest technical analysis charts. They show closing prices for
each periods as a continuous line. 142211 100% Contribution Breeds Professionalism
100% R12: Technical Analysis Bar charts add the high and low prices for each trading period and often include the
opening price as well. 143211 100% Contribution Breeds Professionalism
100% R12: Technical Analysis Candlestick charts use the same data as bar charts but display a box bounded by the
opening and closing prices.
•Box is clear: closing price>opening price;
•Box is filled: closing price<opening price
144211 100% Contribution Breeds Professionalism
100% Example
A candlestick chart is similar to a bar chart except that the
candlestick chart:
A. represents upward movements in price with X's. B. also graphically shows the range of the period's highs and lows. C. has a body that is light or dark depending on whether the security
closed higher or lower than its open. 145211 100% Contribution Breeds Professionalism
100% R12: Technical Analysis Point and figure charts are helpful in identifying changes in the direction of price
movements.
•Starting form opening price;
•X: increase of one box size, O: indicate a decrease.
•Analyst will begin the next column when the price changes in the opposite
direction by at least the reversal size (3 times the box size).
146211 100% Contribution Breeds Professionalism
100% R12: Technical Analysis
Relative strength analysis: an analyst calculate the ratios of an
asset's closing prices to benchmark values, such as stock index or
comparable asset, and draws a line chart of the ratios.
Positive relative strength: an increasing trend indicates that the asset
is outperforming the benchmark
Negative relative strength: an decreasing trend indicates that the asset
is underperforming the benchmark 147211 100% Contribution Breeds Professionalism
100% R12: Technical Analysis
LOS 12.c. demonstrate the uses of trend, support, and resistance lines,
and change in polarity; Trend: is the most basic concept in technical analysis.
Uptrend: prices are consistently reaching higher highs and retracting
to higher lows. (Demand>Supply)
Downtrend: prices are consistently reaching higher lows and
retracting to lower highs. (Demand<Supply)
Trend line: can help to identify whether a trend is continuing or revering.
Uptrend line: connects the increasing lows in prices;
Downtrend line: connects the decreasing highs in prices;
When prices crosses the trend line by what the analyst considers a
significant amount, a breakout form a downtrend or a breakdown form
an uptrend is said to occur.
148211 100% Contribution Breeds Professionalism
100% Example
A downtrend line is constructed by drawing a line connecting:
A. the lows of the price chart. B. the highs of the price chart. C. the highest high to the lowest low of the price chart. 149211 100% Contribution Breeds Professionalism
100% R12: Technical Analysis
Support level: buying is expected to emerge that prevents further
price decreases.
Resistance level: selling is expected to emerge that prevents
further price increases.
Change in polarity: breached resistance levels become support
levels and that breached support levels become resistance levels. 150211 100% Contribution Breeds Professionalism
100% R12: Technical Analysis
LOS 12.d. identify and interpret common chart patterns; Common chart patterns.
Reversal patterns
For uptrend: Headand shoulders pattern, Double top and triple top
For downtrend: inverse headand shoulders pattern, Double bottom, and
triple bottom Continuation patterns
Triangles
Rectangles 151211 100% Contribution Breeds Professionalism
100% R12: Technical Analysis Headandshoulders pattern is used to project a price target for ensuing downtrend.
The size of the headandshoulders pattern: the difference in price between the
head and the neckline.
152211 100% Contribution Breeds Professionalism
100% R12: Technical Analysis Triangles: form when prices reach lower highs and higher lows over a period of time.
Rectangles: form when trading temporarily forms a range between a support level and
a resistance level.
Flags and pennants: refer to rectangles and triangles that appear on shortterm price
charts.
153211 100% Contribution Breeds Professionalism
100% R12: Technical Analysis
Common analysis indicators
Pricebased
Moving average lines
Bollinger bands Momentum oscillators LOS 12.e. discuss common
technical analysis indicators: pricebased, momentum oscillators,
sentiment, and flow of funds; Rate of change oscillator
Relative Strength Index
Moving average convergence/divergence
Stochastic oscillator Sentiment
Put/call ratio
Volatility Index
Margin debt
Short interest ratio Flow of funds
Shortterm trading index
Margin debt
Mutual fund cash position
New equity issuance
154211 100% Contribution Breeds Professionalism
100% R12: Technical Analysis
LOS 12.f. explain the use of cycles by technical analysts; Cycle theory: is the study of processes that occur in cycles.
4year presidential cycles: related to election years in the USA
Decennial patterns: 10year cycles
Kondratieff wave: 18year cycles, 54year cycles
LOS 12.g. discuss the key tenets of Elliott Wave Theory and the importance
of Fibonacci numbers; Elliott wave theory: is based on the belief that financial market
prices can be described by an interconnected sets of cycles.
Waves: refer to chart patterns associated with Elliott wave theory.
Fibonacci ratios: the sizes of these waves are thought to correspond
with Fibonacci ratios (0,1,1,2,3,5,8,13,21, and so on)
155211 100% Contribution Breeds Professionalism
100% R12: Technical Analysis Prevailing up trend: upward moves in prices consist of 5 waves and downward
moves occur in 3 waves
Prevailing down trend: downward moves in prices consist of 5 waves and
upward moves occur in 3 waves
156211 100% Contribution Breeds Professionalism
100% R12: Technical Analysis
LOS 12.h. describe intermarket analysis as it relates to technical analysis
and asset allocation. Intermarket analysis: refers to analysis of the interrelationships
among the market values of major asset classes, such as stocks,
bonds, commodities and currencies.
The approach is also useful for comparing the relative performance
of equity market sectors or industries and of various international
market. 157211 100% Contribution Breeds Professionalism
100% Example
Exhibit 1 depicts GreatWall Information Industry Co., Ltd., ordinary shares,
traded on the Shenzhen Stock Exchange, for late 2008 through late 2009 in
renminbi (RMB). Based on Exhibit 1, the uptrend was most likely broken at a level nearest to:
A. 7 RMB.
B. 8.5 RMB.
C. 10 RMB.
158211 100% Contribution Breeds Professionalism
100% Example
Exhibit 2 depicts Barclays ordinary shares, traded on the London Stock
Exchange, for 2009 in British pence. Based on Exhibit 2, Barclays appears to show resistance at a level
nearest to:
A. 50p.
B. 275p.
C. 390p.
159211 100% Contribution Breeds Professionalism
100% Example
Exhibit 3 depicts Archer Daniels Midland Company common shares,
traded on the New York Stock Exchange, for 1996 to 2001 in U.S.
dollars. Exhibit 3 illustrates most clearly which type of pattern?
A. Triangle.
B. Triple top.
C. Head and shoulders.
160211 100% Contribution Breeds Professionalism
100% 金程教育2011年6月CFA一级强化班
金程教育
Portfolio Management
讲师：何旋
日期：2011年4月
地点： ■ 上海 □北京 □深圳
上海金程国际金融专修学院 Topic Weightings in CFA Level I
Content Session NO. Weightings Study Session 1 Ethics & Professional Standards 15 Study Session 23 Quantitative Analysis 12 Study Session 46 Economics 10 Study Session 710 Financial Reporting and Analysis 20 Study Session 11 Corporate Finance 8 Study Session 12 Portfolio Management 5 Study Session 1314 Equity Investment 10 Study Session 1516 Fixed Income 12 Study Session 17 Derivatives 5 Study Session 18 Alternative Investments 3 162211 100% Contribution Breeds Professionalism
100% Framework of Portfolio Management
SS 12 — Portfolio Management
R51 Portfolio Management: An Overview
R52 Portfolio Risk and Return: Part I
R53 Portfolio Risk and Return: Part II
R54 Basic of Portfolio Planning and Construction 163211 100% Contribution Breeds Professionalism
100% Portfolio Management: R52 Portfolio Risk and Return: Part I 164211 100% Contribution Breeds Professionalism
100% R52: Portfolio Risk and Return: Part I
LOS 52.a. calculate and interpret major return measures and describe their
applicability; HPR
Average return
Arithmetic mean return: unbiased estimator of the true mean
Geometric mean return: compound annual rate
Moneyweighted rate of return: IRR
Other return measures
Gross return: total return before management and administration fees
Pretax nominal return
Aftertax nominal return
Real return
Leveraged return: the gain or loss as a percentage of an investor’s cash
investment. (real estate) 165211 100% Contribution Breeds Professionalism
100% R52: Portfolio Risk and Return: Part I
LOS 52.b. describe the characteristics of the major asset classes that
investors would consider in forming portfolios according to mean–variance
portfolio theory; Asset classes with the greatest average returns also have the highest
standard deviations of returns.
Liquidity should be considered when invest, especially in emerging
markets and for securities that trade infrequently. 166211 100% Contribution Breeds Professionalism
100% R52: Portfolio Risk and Return: Part I
LOS 52.c. calculate and interpret the mean, variance, and covariance (or
correlation) of asset returns based on historical data; An individual investment:
Expected Return n E( R) = ∑ Pi Ri = P R1 + P2 R2 +L+ Pn Rn
1
i =1 Variance of Return n Var = σ = ∑ [ Ri − E ( R)]2 Pi
2 i =1 Standard Deviation of Return SD = σ = n [Ri − E(R)]2 Pi
∑
i =1 167211 100% Contribution Breeds Professionalism
100% R52: Portfolio Risk and Return: Part I
Covariance
n Using expectation data Cov1, 2 = ∑ Pi [ Ri ,1 − E ( R1 )][Ri , 2 − E ( R2 )]
i =1 Using historical data Correlation 168211 ρ 1, 2 = Cov 1, 2 σ 1σ 2 1n
Cov1,2 =
∑[Rt,1 − R1][Rt,2 − R2 ]
n −1 t =1 Cov 1, 2 = ρ 1, 2σ 1σ 2 100% Contribution Breeds Professionalism
100% R52: Portfolio Risk and Return: Part I
LOS 52.e. calculate and interpret portfolio standard deviation; The portfolio standard deviation formula σP = σ =
2
P n n n ∑ w σ + ∑∑ w w Cov
i =1 2
i 2
i i j i, j i =1 j =1 The risk of a portfolio of risky assets depends on the asset weights
and the standard deviations of the assets returns, and crucially on the
correlation (covariance) of the asset returns.
The lower the correlation between the returns of the stocks in the
portfolio, all else equal, the greater the diversification benefits.
Twoasset portfolio:
σp2=w12σ12+w22σ22+2w1w2COV1,2 = w12σ12+w22σ22+2w1w2σ1σ2ρ1,2
169211 100% Contribution Breeds Professionalism
100% R52: Portfolio Risk and Return: Part I
LOS 52.f. describe the effect on a portfolio’s risk of investing in assets that
are less than perfectly correlated; Risk and return for different values of correlation 170211 100% Contribution Breeds Professionalism
100% R52: Portfolio Risk and Return: Part I
期望收益率(%)
20 15 有效前沿
(有效集) GMV 10 可行集 ·
·
5
方差前沿 5 10 15 20 25
标准差 (%) 171211 100% Contribution Breeds Professionalism
100% R52: Portfolio Risk and Return: Part I
LOS 52.g. describe and interpret the minimumvariance and efficient
frontiers of risky assets and the global minimumvariance portfolio; Minimum variance frontier
Portfolios that have minimum variance for each given level of
expected return
Global minimum variance portfolio Efficient frontier
All risky assets are contained
Efficient portfolio: welldiversified or fullydiversified 172211 100% Contribution Breeds Professionalism
100% R51: Portfolio Risk and Return: Part I
LOS 51.h. discuss the selection of an optimal portfolio, given an investor’s
utility (or risk aversion) and the capital allocation line. Risk aversion
Refers to the fact that individuals prefer less risk to more risk.
Riskaverse investors:
Prefer lower to higher risk for a given level of expected returns
Will only accept a riskier investment if they are compensated in the
form of greater expected return
E(R) Higher
Utility Lower Risk
173211 100% Contribution Breeds Professionalism
100% R52: Portfolio Risk and Return: Part I
Twofund separation theorem:
Combining a risky portfolio with a riskfree asset
All investors’ optimum portfolios will be made up of some
combination of an optimal portfolio of risky assets and the riskfree
asset. CAL
The line representing these possible combinations of riskfree assets
and the optimal risky asset portfolio. 174211 100% Contribution Breeds Professionalism
100% R52: Portfolio Risk and Return: Part I
The optimal portfolio for an investor
At the point of where an investor’s (highest) riskreturn indifference
curve is tangent to the efficient frontier.
Y
E(R) X I2 CAL
I1 I2 I1 Risk (σp) Optimal portfolio The highest indifference curve that is tangent to the efficient frontier
Different investors may have different optimal portfolios
175211 100% Contribution Breeds Professionalism
100% Portfolio Management: R53 Portfolio Risk and Return: Part II 176211 100% Contribution Breeds Professionalism
100% R53: Portfolio Risk and Return: Part II
LOS 53.a. discuss the implications of combining a riskfree asset with a
portfolio of risky assets; E ( RP ) = W A E ( R A ) + W B E ( RB )
2
2
σ P = W A2σ A + W B2σ B + 2W AW B ρ ABσ Aσ B
2
σ P = W A2σ A = W Aσ A 177211 100% Contribution Breeds Professionalism
100% R53: Portfolio Risk and Return: Part II
LOS 53.b. explain and interpret the capital allocation line (CAL) and the
capital market line (CML); Risky Portfolios and Their Associated Capital Allocation Lines for
Different investors If each investor has different expectations about the expected returns of, standard
deviations of, or correlations between risky asset returns, each investor will have
a different optimal risky asset portfolio and a different CAL
178211 100% Contribution Breeds Professionalism
100% R53: Portfolio Risk and Return: Part II
Capital market line
When investors share identical expectations about the mean returns,
variance of returns, and correlations of risky assets, the CAL for all
investors is the same and is known as the capital market line (CML):
E ( RP ) = RF + E ( RM ) − R F σM σP The market portfolio
Explanation of the CML Difference between the CML and the CAL 179211 100% Contribution Breeds Professionalism
100% R53: Portfolio Risk and Return: Part II
The Market Portfolio:
Is the tangent point where the CML touches the Markowitz efficient
frontier.
Consists of every risky assets
The weights on each asset are equal to the percentage of the market
value of the asset to the market value of the entire market portfolio. Investment using CML follow a passive investment strategy (i.e.,
invest in an index of risky assets that serves as a proxy for the
market portfolio and allocate a portion of their investable assets to
a riskfree asset. 180211 100% Contribution Breeds Professionalism
100% R53: Portfolio Risk and Return: Part II
LOS 53.c. explain systematic and nonsystematic risk, and why an investor
should not expect to receive additional return for bearing nonsystematic risk; Unsystematic risk (or unique, diversifiable, firmspecific risk):
The risk that disappears in the portfolio construction process
Systematic risk (or market risk):
The risk that is left cannot be diversified away.
Total risk = systematic risk + unsystematic risk 181211 100% Contribution Breeds Professionalism
100% R53: Portfolio Risk and Return: Part II
Risk vs. Number of portfolio Assets σ Total risk Unsystematic risk
Market Risk
Systematic risk Number of securities in the portfolio
182211 100% Contribution Breeds Professionalism
100% R53: Portfolio Risk and Return: Part II
Systematic Risk is Relevant in Portfolios
One important conclusion of capital market theory:
Equilibrium security returns depend on a stock’s or a portfolio’s
systematic risk, not its total risk as measured by standard deviation.
One of the assumptions of the model :
Diversification is free, because investors will not be compensated
for bearing risk that can be eliminated at no cost. 183211 100% Contribution Breeds Professionalism
100% R53: Portfolio Risk and Return: Part II
LOS 53.d. explain return generating models (including the market model) and
their uses; Return generating models: multifactor models
Macroeconomic factors: GDP growth, inflation, or consumer
confidence
Fundamental factors: earnings, earnings growth, firm size, and
research expenditures
Statistical factors
E ( Ri ) − RF = β i ,1 × E ( Factor1) + β i ,2 × E ( Factor 2) + ... + β i , k × E ( Factork ) Market model
A single factor model
The only factor is the expected excess return on the market portfolio
(market index)
E ( Ri ) − R f = β i ( E ( RM ) − R f )
184211 100% Contribution Breeds Professionalism
100% R53: Portfolio Risk and Return: Part II
LOS 53.e. calculate and interpret beta; Beta: the sensitivity of an asset’s return to the return on the market index
in the market model.
Covi , mkt
σi
βi =
=(
) × ρi , mkt
2
σ mkt
σ mkt
Asset characteristic line (regression of asset excess returns against market
asset returns) 185211 100% Contribution Breeds Professionalism
100% R53: Portfolio Risk and Return: Part II
LOS 53.f. explain the capital asset pricing model (CAPM), including the
required assumptions, and the security market line (SML);
LOS 53.g. calculate and interpret the expected return of an asset using the
CAPM; The Equation of SML
E (R i )= R F R + β i [E (R m kt )R F R ] Beta
A standardized measure of systematic risk. 186211 100% Contribution Breeds Professionalism
100% R53: Portfolio Risk and Return: Part II
Capital Asset Pricing Model E(Ri ) Security market line (SML) E(Rmkt ) Market portfolio RFR
2
Covmkt ,mkt = σ mkt 187211 100% Contribution Breeds Professionalism
100% Systematic risk R53: Portfolio Risk and Return: Part II
Differences between the SML and the CML
SML CML Measure of risk Uses systematic risk (nondiversifiable risk) Uses standard deviation
(total risk) Application Tool used to determine the
appropriate expected
(benchmark) returns for
securities Tool used to determine the
appropriate asset allocation
(percentages allocated to the riskfree asset and to the market
portfolio) for the investor Definition Graph of the capital asset
pricing model Graph of the efficient frontier Slope Market risk premium Market portfolio Sharpe ratio 188211 100% Contribution Breeds Professionalism
100% R53: Portfolio Risk and Return: Part II
LOS 53.h. illustrate applications of the CAPM and the SML. How to judge if a stock is properly valued
E(R) undervalued, buy SML . . Overvalued, Sell Beta, Systematic Risk 189211 100% Contribution Breeds Professionalism
100% R53: Portfolio Risk and Return: Part II
Evaluate relative portfolio performance (riskadjusted returns)
Sharpe ratio= RP − Rf σP The Sharpe ratio for any portfolio along the CML is the same.
190211 100% Contribution Breeds Professionalism
100% R53: Portfolio Risk and Return: Part II
The Msquared (M2) measure produces the same portfolio rankings
as the Sharpe ratio but is stated in percentage terms.
M 2 = ( RP − R f ) 191211 σM
− ( RM − R f )
σP 100% Contribution Breeds Professionalism
100% R53: Portfolio Risk and Return: Part II
Treynor measure & Jensen’s alpha (systematic risk)
Treynor measure= 192211 RP − Rf βP αP = (RP − Rf ) − βP (RM − Rf ) 100% Contribution Breeds Professionalism
100% Portfolio Management: R51 Portfolio Management: An Overview 193211 100% Contribution Breeds Professionalism
100% R51: Portfolio Management: An Overview
LOS 51.a. explain the importance of the portfolio perspective; Portfolio perspective
Definition: evaluate individual investments by their contribution to
the risk and return of an investor’s portfolio.
Diversification allows an investor to reduce portfolio risk without
necessarily reducing the portfolio’s expected return.
During periods of financial crisis, correlations tend to increase, which
reduces the benefits of diversification. 194211 100% Contribution Breeds Professionalism
100% R51: Portfolio Management: An Overview
LOS 51.b. discuss the types of investment management clients and the
distinctive characteristics and needs of each;
The types of investment management clients
Individual investors
DC pension plan: the individual makes the investment decisions and takes on
the investment risk.
DB pension plan: be funded by company contributions and have an
obligation to provide specific benefits to retirees.
Endowment: a fund that is dedicated to providing financial support on an
ongoing basis for a specific purpose.
Foundation: a fund established for charitable purposes to support specific
types of activities or to fund research related to a particular disease.
Bank
Insurance company
Investment companies
Mutual funds
Sovereign wealth funds: pools of assets owned by a government.
195211 100% Contribution Breeds Professionalism
100% R51: Portfolio Management: An Overview
Characteristics of different types of investors 196211 100% Contribution Breeds Professionalism
100% R51: Portfolio Management: An Overview
Los 51.c. describe the steps in the portfolio management process; Planning step:
Analysis of the investor’s risk tolerance, return objectives, time
horizon, tax exposure, liquidity needs, income needs, unique
circumstances;
IPS: details the investor’s investment objectives and constraints;
specify an objective benchmark; updated at least every few years and
anytime the investor’s objectives or constraints change significantly.
Execution step: asset allocation; topdown analysis & bottomup
Feedback step:
monitor and rebalance the portfolio;
Measure portfolio performance. 197211 100% Contribution Breeds Professionalism
100% R51: Portfolio Management: An Overview
LOS 51.d. describe, compare, and contrast mutual funds and other forms of
pooled investments. Mutual funds
OpenEnd Fund vs. CloseEnd Fund
1. OpenEnd Fund
TRADING – Ready to redeem shares at the closing value on any
trading day;
LIQUIDITY – Provided by the investment company managing it 2. CloseEnd Fund
TRADING – Traded (after issuance) in the secondary market through
organized exchanges (e.g., NYSE)
LIQUIDITY – Determined in the open market 198211 100% Contribution Breeds Professionalism
100% R51: Portfolio Management: An Overview
Types of mutual funds
Money market funds: interest income & low risk
Bond mutual funds
Stock mutual funds
Index funds
Actively managed funds: higher annual management fees; higher
turnover of portfolio securities; greater tax liabilities. 199211 100% Contribution Breeds Professionalism
100% R51: Portfolio Management: An Overview
Other forms of pooled investment
1. Exchange Traded Fund (ETF) & its Features
Comparison with Open/CloseEnd Fund
Trading Like CloseEnd Fund Legal Structure Like OpenEnd Fund “InKind” Creation and Redemption Process 200211 100% Contribution Breeds Professionalism
100% R51: Portfolio Management: An Overview
The differences between ETFs and Openend funds
ETFs can be sold short, purchased on margin, and traded at intraday
prices; openend funds are typically sold and redeemed only daily,
based on the share NAV calculated with closing asset prices;
Investors in ETFs must pay brokerage commissions;
Investors in ETFs receive any dividend income on portfolio stocks in
cash; openend funds offer the alternative of reinvesting dividends in
additional fund shares.
Shareholders in ETFs incur a capital gains tax liability. 201211 100% Contribution Breeds Professionalism
100% R51: Portfolio Management: An Overview
Other forms of pooled investment
2. Separately managed account: a portfolio that is owned by a
single investor and managed according to that investor’s needs and
preferences.
3. Hedge funds:
Not regulated to the extent that mutual funds are
Be limited in the number of investors who can invest in the fund and
are often sold only to qualified investors who have a minimum
amount of overall portfolio wealth. 202211 100% Contribution Breeds Professionalism
100% R51: Portfolio Management: An Overview
Hedge fund strategies
Long/short funds
Equity marketneutral funds
An equity hedge fund with a bias: long bias & short bias
Eventdriven funds: i.e., M&A
Fixedincome arbitrage funds: profit from minor mispricing &
minimizing the effects of interest rate changes
Convertible bond arbitrage funds: profit from a relative mispricing
between convertible bonds and the equity shares
Global macro funds: speculate on changes in international interest
rates and currency exchange rates. 203211 100% Contribution Breeds Professionalism
100% R51: Portfolio Management: An Overview
Other forms of pooled investment
4. Buyout funds (private equity funds): buy entire public
companies and take them private.
5. Venture capital funds
Both buyout funds and venture capital funds are very involved in the
management of their portfolio companies and often have expertise in
the industries on which they focus. 204211 100% Contribution Breeds Professionalism
100% Portfolio Management: R54 Basic of Portfolio Planning and Construction 205211 100% Contribution Breeds Professionalism
100% R54: Basic of Portfolio Planning and Construction
LOS 54.a. explain the reasons for a written investment policy statement (IPS);
LOS 54.b. list and explain the major components of an IPS; The need for a policy statement
Understand and articulate realistic investor goals, needs and risk tolerance
Ensure that goals are realistic
Provide an objective measure of portfolio performance
Major components of IPS
Description of client
Statement of the purpose
Statement of duties and responsibilities
Procedures to update IPS and to respond to various possible situations
Investment objectives
Investment constraints
Investment guidelines
Evaluation of performance
Appendices: information on asset allocation
206211 100% Contribution Breeds Professionalism
100% R54: Basic of Portfolio Planning and Construction
LOS 54.c. discuss risk and return objectives, including their preparation;
LOS 54.d. distinguish between the willingness and the ability (capacity) to
take risk in analyzing an investor’s financial risk tolerance; Investment objectives: risk and return
Risk objective
The risk objective limits how high the investor can set the return
objective
Risk measurement: absolute (std dev.), relative (tracking risk),
downside risk (VAR)
Risk tolerance: willingness and ability
Situation Risk tolerance willingness > ability ability (education) willingness < ability
207211 return objective = willingness willingness (reevaluation) return objective = ability ability (education) 100% Contribution Breeds Professionalism
100% R54: Basic of Portfolio Planning and Construction
Return objectives
Return measurement: total return, inflationadjusted return, aftertax
return
Total return perspective: balance between capital gains and income
Stated return desire vs. Required return
Consistent with risk objective 208211 100% Contribution Breeds Professionalism
100% R54: Basic of Portfolio Planning and Construction
LOS 54.e. describe the investment constraints of liquidity, time horizon, tax
concerns, legal and regulatory factors, and unique circumstances and their
implications for the choice of portfolio assets; Investment constraints
Liquidity—for cash spending needs (anticipated or unexpected)
Time horizon—the time between making an investment and needing
the funds
Tax concerns—the tax treatments of various accounts, and the
investor’s marginal tax bracket
Legal and regulatory factors—restrictions on investments in
retirement, personal, and trust accounts
Unique needs and preferences—constraints because of investor
preferences or other factors not already considered 209211 100% Contribution Breeds Professionalism
100% R54: Basic of Portfolio Planning and Construction
LOS 54.f. explain the definition and
specification of asset classes in
relation to asset allocation;
LOS 54.g. discuss the principles of
portfolio construction and the role of
asset allocation in relation to the IPS. Strategic asset allocation:
combine the IPS and capital
market expectations to
formulate weightings on
acceptable asset classes
Specify the percentage
allocations to the included
asset classes
Correlations within the class &
correlations between asset
classes
210211 100% Contribution Breeds Professionalism
100% R54: Basic of Portfolio Planning and Construction
Active portfolio management
Tactical asset allocation: a manager who varies from strategic
asset allocation weights in order to take advantage of perceived
shortterm opportunities. Depend on:
The manager’s ability to identify shotterm opportunities in specific
asset classes;
The existence of such shortterm opportunities. Security selection: deviation from index weights on individual
securities within an asset class. Depend on:
The manager’s skill
The opportunities with in a particular asset class. 211211 100% Contribution Breeds Professionalism
100% ...
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 Spring '11
 LiYang

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