心智圖資源庫 CFA一級數量心智圖
一篇關於CFA一級數量心智圖,包含貨幣的時間價值、抽樣與估計、假設檢定等。
編輯於2023-11-24 14:21:22Microbiologia medica, Infezioni batteriche e immunità riassume e organizza i punti di conoscenza per aiutare gli studenti a comprendere e ricordare. Studia in modo più efficiente!
La teoria cinetica dei gas rivela la natura microscopica dei fenomeni termici macroscopici e le leggi dei gas trovando la relazione tra quantità macroscopiche e quantità microscopiche. Dal punto di vista del movimento molecolare, vengono utilizzati metodi statistici per studiare le proprietà macroscopiche e modificare i modelli di movimento termico delle molecole di gas.
Este é um mapa mental sobre uma breve história do tempo. "Uma Breve História do Tempo" é um trabalho científico popular com influência de longo alcance. Ele não apenas introduz os conceitos básicos da cosmologia e da relatividade, mas também discute os buracos negros e a expansão. Do universo. questões científicas de ponta, como inflação e teoria das cordas.
Microbiologia medica, Infezioni batteriche e immunità riassume e organizza i punti di conoscenza per aiutare gli studenti a comprendere e ricordare. Studia in modo più efficiente!
La teoria cinetica dei gas rivela la natura microscopica dei fenomeni termici macroscopici e le leggi dei gas trovando la relazione tra quantità macroscopiche e quantità microscopiche. Dal punto di vista del movimento molecolare, vengono utilizzati metodi statistici per studiare le proprietà macroscopiche e modificare i modelli di movimento termico delle molecole di gas.
Este é um mapa mental sobre uma breve história do tempo. "Uma Breve História do Tempo" é um trabalho científico popular com influência de longo alcance. Ele não apenas introduz os conceitos básicos da cosmologia e da relatividade, mas também discute os buracos negros e a expansão. Do universo. questões científicas de ponta, como inflação e teoria das cordas.
Study Session 1-7 Quantitative Methods
R1 The Time Value of Money
1.Rate
Type
Required rate of return
R=Rn RP
default risk premium
liquidity risk premium
maturity risk premium
Discount rate
Opportunity cost
Nominal risk-free rate
Rr=Rn-i^e
2.EAR
HPR=(FV-PV)/PV
EAR=(1 R/m)^m-1
EAR=e^r-1
FV=PV*(1 EAR)
FVn=PV*(1 EAR)^n=PV*(1 r/m)^(m*n)
Logarithm operation
a^b=c logac=b
3.Annuity
Elements
N
I/Y
PV
FV
PMT
Type
Annuity due
Ordinary Annuity
Perpetuity
PV=PMT1/R
Application
Uneven cash flows
Calculator usage
小數點調整成四位
鍊式計算/代數計算
功能鍵
單變數先數字後按鍵
雙變量數字-按鍵-數字
Annuity五元素四缺一
BGN和END設置
AMORT
Pn和Pn 1,第n期期初到第n期期末
BAL第n期期末負債餘額
PRN第n期償還的本金
INT第n期償還的利息
R2 Organizing, Visualizing, and Describing Data
1. Types of Data
Structure Data
Numerical data
Continuous data
Discrete data
Categorical data
Nominal data
Application
Ordinal data
Unstructured data (alternative source)
Variable
Observation
One-dimensional array
Time-series data
Application
Cross-sectional data
Two-dimensional rectangular array (data table)
Panel data
2. Data Visualization
Number data
Frequency distribution
Absolute Frequency
Relative Frequency
Cumulative Absolute Frequency
Cumulative Relative Frequency
Histogram
Polygon
Scatter Plot
Categorical Data
Contingency Table
Confusion matrix
Chi-square test of independence
Bar Chart
Pareto Chart
Grouped bar chart(clustered bar chart)
Stacked bar chart
Tree-Map
Application
Heat Map
Application
Line chart
Bubble line chart
Unstructured data
Word Cloud
3. Measures of Central Tendency
Mode
Median
Mean
The Arithmetic Mean
The Weighted Mean
The Geometric Mean
The Harmonic Mean
Selection of Different Means
A>=G>=H
4.Quantiles
Quartile /Quintile/Decile/Percentile
Ly = (n 1)y/100
Box and whisker plot
5. Dispersion
Absolute Dispersion
Range
MAD
Variance
For population
For sample
Semivariance
Target Semivariance
Calculator usage
Standard deviation
For population
For sample
Relative dispersion
Coefficient of variation
Sharpe ratio
6. Skewness & kurtosis
Skewness
Tpye
Symmetrical
Positive (right) skew
Negative (left) skew
Mode/Median/Mean
Skewness calculation(power=3)
Return
Kurtosis
Type
Mesokurtic
Leptokurtic
Platykurtic
Kurtosis calculation(power=4)
Excess kurtosis
Sample kurtosis – 3
Leptokurtic——Fat tail
7. Covariance &Correlation
Covariance
Correlation Coefficient
Limitations to Correlation Analysis
R3 Probability Concepts
1.Basic Concepts,odds for/against
Form
Objective Probability and Subjective probability
odds for/against
P(A)
P(A|B)
2.Calculation Rules for Probabilities
兩個事件
Mutually exclusive
Independent
兩個法則
Multiplication rule
Addition rule
Total probability formula
3.Expected value and variance
Expected value
Variance
4.Expected return and variance of portfolios
Expected return of portfolios
Variance of portfolios of portfolios
兩類以上組合的計算
With Correlation
Covariance &Correlation
Covariance
Correlation
5. Bayes' Formula
Application
6. Factorial & combination & permutation
Multiplication rule
Factorial
Labeling (or Multinomial)
Application
Combination
Permutation
Calculator usage
Factorial階乘
排列組合
R4 Common Probability Distributions
1. Properties of discrete distribution and continuous distribution
Discrete random variables
Continuous random variables
Probability density function (p.d.f): f(x)
Cumulative probability function (c.p.f): F(x)
2. Discrete distribution
Discrete uniform distribution
Binomial distribution
Expectation&variance
Probability Calculation
Application
3. Continuous distribution
Continuous Uniform Distribution
Normal Distribution
Properties
X~N(μ , σ²)
Symmetrical distribution: skewness=0; kurtosis=3; excess kurtosis=0
A linear combination of random variables these are in normally distribution is also normally distributed.
As the values of x gets farther from the mean, the probability density get smaller and smaller but are always positive.
The confidence intervals
K和信賴區間(機率)的關係
Standard normal distribution
Application
Application
Univariate distributions(multivariate distribution)
Application
Shortfall risk
Safety first ratio
Lognormal Distribution
Application
Application
Several Other Distributions
The Chi-Square (X^2)Distribution
Student's T-distribution
Application of T-distribution
Application
The F-Distribution
4. Monte Carlo simulation
Application
R5 Sampling and Estimation
1. Sampling methods
Probability Methods
Simple Random Sampling
Stratified Random Sampling
Systematic Sampling
Cluster Sampling
Non-Probability Methods
Convenience Sampling
Judgment Sampling
Application
Sampling error
2.Central Limit Theory
Standard error
3.Properties of Estimators
Unbiasedness
Efficiency
Consistency
Application
4. Point & confidence interval estimate
Point estimate
Confidence interval estimate
Application
Determining Statistics for Confidence Intervals
Application
5. Resampling
Bootstrapping
Jackknife
6. Biases
Data snooping bias/Data-mining bias
Sample selection bias
Survivorship bias
Self-selection bias
Implicit selection bias
Backfill bias
Look-ahead bias
Application
Time-period bias
R6 Hypothesis Testing
1. Critical value method
Test of mean
Step 1: State the hypothesis
Null hypothesis
Application
Alternative hypothesis
Step 2: Test statistic
Step 3: Significance Level
Critical value
Step 4: Decision rule
Reject region
Step 5: Draw a conclusion
Application1
Application2
Application3
Significance test of correlation
Application
Application2
Test of independence
Application
Other Hypothesis Tests
Mean hypothesis testing
Application
Variance hypothesis testing
Application1
Application2
Application3
2. P-value method
Application
3. Type I and type II errors
Application
4. Parameter tests and non-parameter tests
Parametric tests
Nonparametric tests
R7 Introduction to Linear Regression
1. Basics of simple linear regression
Linear regression
The dependent variable, Y
The independent variable, X
Dummy variable (indicator variable)
Application
Slope coefficient,b1
Intercept term, b0
The error term, εi
Assumptions of the Linear Regression
2. Estimate
Point estimate
Ordinary least squares (OLS)
Application
Confidence interval estimate
3. Hypothesis testing
Test of regression coefficients
By Critical value method
Application
Application2
By P-value method
Measure of model fitness
F-test
Analysis of variance (ANOVA) table
Multiple R
Application
4. Estimate of Y
Application
5. Forms of Simple Linear Regression
Application
Statistical Concepts and Market Returns(old version)
Measurement Scales
Types of measurement scales
Nominal scales
Ordinal scales (>, <)
Interval scales (>, <, , -)
Ratio scales (>, <, , -, *, /)
Population and Sample
Frequency distribution
Interval
Absolute Frequency
Relative Frequency
Cumulative Absolute Frequency
Cumulative Relative Frequency
Histogram
Polygon
Measures of Central Tendency
Mean
Mode
Median
The Arithmetic Mean
評價next year's returns
The Weighted Mean
應用Portfolio的權重
The Geometric Mean
應用各期的報酬率的平均值計算
複利思想,評價past performance
The Harmonic Mean
應用計算平均成本價格
A>=G>=H
Absolute Dispersion
Range
MAD
Variance
總體變異數
樣本變異數
Standard deviation
整體標準差
樣本標準差
Chebyshev's Inequality, CV and SR
Chebyshev's Inequality
Coefficient of variation
Sharpe ratio
Skewness &Kurtosis
Skewness
Tpye
Symmetrical
Positive (right) skew
Negative (left) skew
Mode/Median/Mean關係
Skewness計算power=3
Return
Kurtosis
Type
Mesokurtic
Leptokurtic
Platykurtic
Kurtosis計算power=4
Excess kurtosis
Sample kurtosis – 3
Leptokurtic——Fat tail
計算器使用
計算平均值和方差