20110405交大CFA一级å&frac14

20110405交大CFA一级å&frac14

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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 2-211 100% Contribution Breeds Professionalism 100% Topic Weightings in CFA Level I Content Session NO. Weightings Study Session 1 Ethics & Professional Standards 15 Study Session 2-3 Quantitative Analysis 12 Study Session 4-6 Economics 10 Study Session 7-10 Financial Reporting and Analysis 20 Study Session 11 Corporate Finance 8 Study Session 12 Portfolio Management and Wealth Planning 5 Study Session 13-14 Equity Investment 10 Study Session 15-16 Fixed Income 12 Study Session 17 Derivatives 5 Study Session 18 Alternative Investments 3 3-211 100% 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 4-211 100% 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 5-211 100% 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. 6-211 100% Contribution Breeds Professionalism 100% R5: Time Value of Money LOS 5.b explain an interest rate as the sum of a real risk-free rate, expected inflation, and premiums that compensate investors for distinct types of risk; Decompose required rate of return: Real risk-free rate = nominal risk-free rate + expected inflation rate Required interest rate on a security = nominal risk-free rate + default risk premium + liquidity premium + maturity risk premium 考察方法: Real risk-free rate和nominal risk-free rate的关系 风险的种类 7-211 100% 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. 8-211 100% 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 9-211 100% Contribution Breeds Professionalism 100% Example A money manager has $1,000,000 to invest for one year. She has identified two alternative one-year 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. 10-211 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 →∞ 11-211 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 12-211 100% 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 13-211 100% 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: 14-211 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. Money-weighted return & Time-weighted return 15-211 100% 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 16-211 100% 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 17-211 100% Contribution Breeds Professionalism 100% Example Calabash Crab House is considering an investment in kitchen-upgrade 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 18-211 100% 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 19-211 100% 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 20-211 100% 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 365-day 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. 21-211 100% Contribution Breeds Professionalism 100% Example Jane Peebles purchased a T-bill 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% 22-211 100% Contribution Breeds Professionalism 100% Example The bond-equivalent yield for a semi-annual pay bond is most likely: A. Equal to the effective annual yield. B. More than the effective annual yield. C. Equal to double the semi-annual yield to maturity. Correct answer: C Solution The bond equivalent yield for a semi-annual pay bond is equal to double the semiannual yield to maturity. 23-211 100% Contribution Breeds Professionalism 100% R6: Discounted Cash Flow Applications LOS 6. d calculate, interpret, and distinguish between the money-weighted and time-weighted rates of return of a portfolio, and appraise the performance of portfolios based on these measures; Money-weighted and time-weighted Rate of Return time-weighted return掌握概念及公式: 概念:Time-weighted 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)]. money-weighted 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time-weighted return时,如果不是年度的 HPR不用开方 24-211 100% Contribution Breeds Professionalism 100% Example Would a client making additions or withdrawals of funds most likely affect their portfolio’s: Time-weighted return? Money-weighted return? A. No No B. No Yes C. Yes No Correct answer: B Solution The time-weighted return is not affected by cash withdrawals or addition to the portfolio, the money-weighted return measure would be affected by client additions or withdrawals, if a client adds funds at a favorable time the money-weighted return will be elevated. 25-211 100% 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 time-weighted rate of return is closest to: 8% B. 27% C. 32% A. Correct answer: C 26-211 100% 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 27-211 100% 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) 28-211 100% 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. 29-211 100% 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 30-211 100% Contribution Breeds Professionalism 100% Example An analyst gathered the price-earnings 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 31-211 100% 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. 32-211 100% 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. 33-211 100% 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 34-211 100% 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 35-211 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 36-211 100% 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 37-211 100% Contribution Breeds Professionalism 100% Example James Investments is calculating an unweighted (equally-weighted) 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 38-211 100% 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 three-fourths 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. 39-211 100% 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 = 40-211 ( 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 41-211 100% 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1-1/k2,对任意k>1。 This relationship applies regardless of the shape of the distribution 42-211 100% 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 43-211 100% 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 44-211 100% 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 45-211 100% Contribution Breeds Professionalism 100% Example The scale-free 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 46-211 100% 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 47-211 100% 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. 48-211 100% 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 well-diversified 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 49-211 100% 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 50-211 100% Contribution Breeds Professionalism 100% R7: Statistical Concepts and Market Return Leptokurtic Normal Distribution Fat tail 51-211 100% 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. 52-211 100% 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 53-211 100% 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 54-211 100% 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 55-211 100% Contribution Breeds Professionalism 100% R8: Probability Concepts Objective Probability Priori probability Basic concepts Subjective probability 56-211 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 two-thirds, 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%. 57-211 100% 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 high-yield bonds. The analyst is best characterized as obtaining a(n): A. A priori probability. B. Objective probability. C. Subjective probability. Correct answer: C 58-211 100% 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)/(1-P(E)) Odds against an event (1-P(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 59-211 100% 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(A|B) 60-211 100% 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(A|B)×P(B)= P(B|A)×P(A) If A and B are mutually exclusive events, then: P(AB)=P(A|B)=P(B|A)=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) 61-211 100% 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 62-211 100% 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(A|B)=P(A) or P(B|A)=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) 63-211 100% 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 Market-to-Book 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 64-211 100% 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) 65-211 100% 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 66-211 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 antique-looking 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. 67-211 100% 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% 68-211 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[(X-E(X))(Y-E(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? 69-211 100% 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 70-211 100% 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 71-211 100% 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 72-211 100% 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 73-211 100% Contribution Breeds Professionalism 100% R8: Probability Concepts LOS 8. n. calculate and interpret an updated probability using Bayes’ formula; P(AB)=P(A|B)×P(B) =P(B|A)×P(A) P(A | B) = P (B | A) * P ( A) P(B) P(R)=P(R|S1)×P(S1)+P(R|S2)×P(S2)+…+ P(R|Sn)×P(Sn) P (Si | R ) = 74-211 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 75-211 100% 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 76-211 100% 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 )! 77-211 100% 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 Safety-first ratio Monte Carlo simulation 78-211 100% 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) 79-211 100% 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) 80-211 100% 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). 81-211 100% Contribution Breeds Professionalism 100% R9: Common Probability Distributions LOS 9.d. calculate and interpret probabilities for a random variable, given its cumulative distribution function; 82-211 100% 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)=1-p 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(1-p) Binomial random variable (X) 83-211 Variance np np(1-p) 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 ) 84-211 100% 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 85-211 100% 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 86-211 100% 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. 87-211 100% 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) 88-211 100% 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 U-2.58σ U-1.96σ U-1σ u U+1σ U+1.96σ U-2.58σ 68% 95% 99% 89-211 100% 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 90-211 100% 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 = Z-table F(-z)=1-F(z) P(Z>z) = 1 –F(z) 91-211 100% 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 z-value for an observation of 200 is closest to: A. –2.00. B. –1.75. C. 1.75. Correct answer: A 92-211 100% Contribution Breeds Professionalism 100% R9: Common Probability Distributions LOS 9.m. define shortfall risk, calculate the safety-first ratio, and select an optimal portfolio using Roy’s safety-first criterion; Shortfall risk: RL= threshold level return, minimum return required Minimize (Rp< RL) Roy’s safety-first criterion [E (RP ) − RL ] / σ P Maximize S-F-Ratio Maximize SFR= 93-211 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 safety-first criterion, the most appropriate allocation is: A. Allocation A. B. Allocation B. C. Allocation C. Correct answer: B 94-211 100% 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 95-211 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 96-211 100% 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) 97-211 100% 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 “What-If”. Limitations: the past can not indicate the future and historical simulation cannot address the sort of “what if ” questions that Monte Carlo simulation can. 98-211 100% Contribution Breeds Professionalism 100% Quantitative Methods: R10 Quantitative Sampling and Estimation Simple random and stratified random sampling, time-series 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 t-distribution的特点 Criteria for selecting the appropriate test statistic,计算confidence interval Five kinds of biases 99-211 100% 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. 100-211 100% Contribution Breeds Professionalism 100% R10: Sampling and Estimation LOS 10.c. distinguish between time-series and cross-sectional data; Time-series data consist of observations taken over a period of time at specific and equally spaced time intervals. Cross-sectional data a sample of observations taken at a single point in time. Time-series data Cross-sectional data a collection of data recorded over a period of time a collection of data taken at a single point of time. 101-211 100% Contribution Breeds Professionalism 100% Example Greg Goldman, research analyst in the fixed-income area of an investment bank, needs to determine the average duration of a sample of twenty 15-year 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 time-series data. Correct answer: C 102-211 100% 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 103-211 100% 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 104-211 100% 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 105-211 100% 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 106-211 100% 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. 107-211 100% 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 108-211 100% 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] 109-211 100% 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 110-211 100% Contribution Breeds Professionalism 100% R10: Sampling and Estimation LOS 10.i. describe the properties of Student’s t-distribution and calculate and interpret its degrees of freedom; Student’s t-distribution: Degrees of freedom (df) n-1 Symmetrical Less peaked than a normal distribution (“fatter tails”) As the degrees of freedom gets larger, the shape of t-distribution approaches standard normal distribution N (0,1) ν =9 ν =2 -3 111-211 -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 t-distribution: Become more peaked? Tails becoming less fat? A. No No B. No Yes C. Yes Yes Correct answer: C 112-211 100% 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 113-211 100% 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, data-mining bias, sample selection bias, survivorship bias, look-ahead bias, and time-period bias. Data-mining 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 Look-ahead bias Occurs when a study tests a relationship using sample data that was not a available on the test date. Time-period 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. 114-211 100% 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 out-of-sample data. Excluded stocks for which he could not determine the CEO’s birthday. Used a sample cut-off 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 time-period bias. B. Data mining, time-period bias, and look-ahead bias. C. Time-period bias and survivorship bias. Correct answer: A 115-211 100% 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 two-tailed test Test statistics的选择和计算 Type I and type II errors Decision rule The Chi-square test and F-test Parameter tests and non-parameter tests的对比 116-211 100% 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 one-tailed and two-tailed 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 117-211 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 One-tailed and Two-tailed tests of Hypothesis Two‐tailed One‐tailed 118-211 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. One-tailed test and can reject his null hypothesis. B. Two-tailed test and can reject his null hypothesis. C. One-tailed test and cannot reject his null hypothesis. Correct answer: B 119-211 100% 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 120-211 100% 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 121-211 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 Z-statistic? A. 4.00. B. 4.12. C. 8.00. Correct answer: B 122-211 100% 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. 123-211 100% 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 124-211 100% 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 125-211 100% 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 p-value 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) One-tail or two-tailed 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 P-value Method (more useful): P↓, easier to reject H0 126-211 100% 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 ****** 127-211 100% Contribution Breeds Professionalism 100% Example An analyst conducts a two-tailed test to determine if earnings estimates are significantly different from reported earnings. The sample size was over 100. The computed Z-statistic 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 128-211 100% 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 129-211 + + 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; 130-211 100% 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 z-test z-test Unknown variance t-test t-test or z-test 131-211 100% 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 132-211 H0 Test-statistic μ=0 Z= μ=0 t= x − μ0 σ/ n x − μ0 Critical value N(0,1) t(n-1) s/ n μ1−μ2=0 t t(n1 +n2 -2) μ1−μ2=0 t t μd=0 t= d t(n-1) 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. T-test B. χ2-test C. F-test Correct answer: C 133-211 100% 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, z-test. 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. 134-211 100% 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 135-211 100% 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. 136-211 100% 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. 137-211 100% 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. 138-211 100% 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. 139-211 100% 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. 140-211 100% 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 141-211 100% 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. 142-211 100% 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. 143-211 100% 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 144-211 100% 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. 145-211 100% 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). 146-211 100% 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 147-211 100% 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. 148-211 100% 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. 149-211 100% 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. 150-211 100% Contribution Breeds Professionalism 100% R12: Technical Analysis LOS 12.d. identify and interpret common chart patterns; Common chart patterns. Reversal patterns For uptrend: Head-and shoulders pattern, Double top and triple top For downtrend: inverse head-and shoulders pattern, Double bottom, and triple bottom Continuation patterns Triangles Rectangles 151-211 100% Contribution Breeds Professionalism 100% R12: Technical Analysis Head-and-shoulders pattern is used to project a price target for ensuing downtrend. The size of the head-and-shoulders pattern: the difference in price between the head and the neckline. 152-211 100% 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 short-term price charts. 153-211 100% Contribution Breeds Professionalism 100% R12: Technical Analysis Common analysis indicators Price-based 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 Short-term trading index Margin debt Mutual fund cash position New equity issuance 154-211 100% 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. 4-year presidential cycles: related to election years in the USA Decennial patterns: 10-year cycles Kondratieff wave: 18-year cycles, 54-year 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) 155-211 100% 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 156-211 100% 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. 157-211 100% 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. 158-211 100% 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. 159-211 100% 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. 160-211 100% 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 2-3 Quantitative Analysis 12 Study Session 4-6 Economics 10 Study Session 7-10 Financial Reporting and Analysis 20 Study Session 11 Corporate Finance 8 Study Session 12 Portfolio Management 5 Study Session 13-14 Equity Investment 10 Study Session 15-16 Fixed Income 12 Study Session 17 Derivatives 5 Study Session 18 Alternative Investments 3 162-211 100% 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 163-211 100% Contribution Breeds Professionalism 100% Portfolio Management: R52 Portfolio Risk and Return: Part I 164-211 100% 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 Money-weighted rate of return: IRR Other return measures Gross return: total return before management and administration fees Pretax nominal return After-tax nominal return Real return Leveraged return: the gain or loss as a percentage of an investor’s cash investment. (real estate) 165-211 100% 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. 166-211 100% 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 =1 167-211 100% 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 168-211 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. Two-asset portfolio: σp2=w12σ12+w22σ22+2w1w2COV1,2 = w12σ12+w22σ22+2w1w2σ1σ2ρ1,2 169-211 100% 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 170-211 100% 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 (%) 171-211 100% Contribution Breeds Professionalism 100% R52: Portfolio Risk and Return: Part I LOS 52.g. describe and interpret the minimum-variance and efficient frontiers of risky assets and the global minimum-variance 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: well-diversified or fully-diversified 172-211 100% 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. Risk-averse 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 173-211 100% Contribution Breeds Professionalism 100% R52: Portfolio Risk and Return: Part I Two-fund separation theorem: Combining a risky portfolio with a risk-free asset All investors’ optimum portfolios will be made up of some combination of an optimal portfolio of risky assets and the risk-free asset. CAL The line representing these possible combinations of risk-free assets and the optimal risky asset portfolio. 174-211 100% 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) risk-return 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 175-211 100% Contribution Breeds Professionalism 100% Portfolio Management: R53 Portfolio Risk and Return: Part II 176-211 100% Contribution Breeds Professionalism 100% R53: Portfolio Risk and Return: Part II LOS 53.a. discuss the implications of combining a risk-free 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 177-211 100% 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 178-211 100% 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 179-211 100% 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 risk-free asset. 180-211 100% 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, firm-specific 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 181-211 100% 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 182-211 100% 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. 183-211 100% 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 ) 184-211 100% 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) 185-211 100% 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. 186-211 100% 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 187-211 100% 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 188-211 100% 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 189-211 100% Contribution Breeds Professionalism 100% R53: Portfolio Risk and Return: Part II Evaluate relative portfolio performance (risk-adjusted returns) Sharpe ratio= RP − Rf σP The Sharpe ratio for any portfolio along the CML is the same. 190-211 100% Contribution Breeds Professionalism 100% R53: Portfolio Risk and Return: Part II The M-squared (M2) measure produces the same portfolio rankings as the Sharpe ratio but is stated in percentage terms. M 2 = ( RP − R f ) 191-211 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= 192-211 RP − Rf βP αP = (RP − Rf ) − βP (RM − Rf ) 100% Contribution Breeds Professionalism 100% Portfolio Management: R51 Portfolio Management: An Overview 193-211 100% 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. 194-211 100% 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. 195-211 100% Contribution Breeds Professionalism 100% R51: Portfolio Management: An Overview Characteristics of different types of investors 196-211 100% 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; top-down analysis & bottom-up Feedback step: monitor and rebalance the portfolio; Measure portfolio performance. 197-211 100% 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 Open-End Fund vs. Close-End Fund 1. Open-End Fund TRADING – Ready to redeem shares at the closing value on any trading day; LIQUIDITY – Provided by the investment company managing it 2. Close-End Fund TRADING – Traded (after issuance) in the secondary market through organized exchanges (e.g., NYSE) LIQUIDITY – Determined in the open market 198-211 100% 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. 199-211 100% Contribution Breeds Professionalism 100% R51: Portfolio Management: An Overview Other forms of pooled investment 1. Exchange Traded Fund (ETF) & its Features Comparison with Open/Close-End Fund Trading Like Close-End Fund Legal Structure Like Open-End Fund “In-Kind” Creation and Redemption Process 200-211 100% Contribution Breeds Professionalism 100% R51: Portfolio Management: An Overview The differences between ETFs and Open-end funds ETFs can be sold short, purchased on margin, and traded at intraday prices; open-end 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; open-end funds offer the alternative of reinvesting dividends in additional fund shares. Shareholders in ETFs incur a capital gains tax liability. 201-211 100% 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. 202-211 100% Contribution Breeds Professionalism 100% R51: Portfolio Management: An Overview Hedge fund strategies Long/short funds Equity market-neutral funds An equity hedge fund with a bias: long bias & short bias Event-driven funds: i.e., M&A Fixed-income 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. 203-211 100% 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. 204-211 100% Contribution Breeds Professionalism 100% Portfolio Management: R54 Basic of Portfolio Planning and Construction 205-211 100% 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 206-211 100% 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 207-211 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, inflation-adjusted return, after-tax return Total return perspective: balance between capital gains and income Stated return desire vs. Required return Consistent with risk objective 208-211 100% 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 209-211 100% 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 210-211 100% 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 short-term opportunities. Depend on: The manager’s ability to identify shot-term opportunities in specific asset classes; The existence of such short-term 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. 211-211 100% Contribution Breeds Professionalism 100% ...
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