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CFA Level 1 Quantitative Mind Map
An article about CFA level one quantitative mind map, including the time value of money, sampling and estimation, hypothesis testing, etc.
Edited at 2023-11-24 14:21:22- bacteria
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CFA Level 1 Quantitative Mind Map
- bacteria
This is a mind map about bacteria, and its main contents include: overview, morphology, types, structure, reproduction, distribution, application, and expansion. The summary is comprehensive and meticulous, suitable as review materials.
- Plant asexual reproduction
This is a mind map about plant asexual reproduction, and its main contents include: concept, spore reproduction, vegetative reproduction, tissue culture, and buds. The summary is comprehensive and meticulous, suitable as review materials.
- Reproductive development of animals
This is a mind map about the reproductive development of animals, and its main contents include: insects, frogs, birds, sexual reproduction, and asexual reproduction. The summary is comprehensive and meticulous, suitable as review materials.
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- Outline
Study Session 1-7 Quantitative Methods
R1 The Time Value of Money
1.Rate
Type
Required rate of return
R=RnRP
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
Adjust the decimal point to four places
Chain calculation/algebraic calculation
Function keys
Single variable numbers first then keys
Double variable number-key-number
Four of the five elements of Annuity are missing one
BGN and END settings
AMORT
Pn and Pn 1, from the beginning of the nth period to the end of the nth period
BAL's closing liability balance of period n
PRN’s principal repayment in the nth period
INT interest repaid in period n
R2 Organizing, Visualizing, and Describing Data
1.Types of Data
Structure Data
Numerical data
Continuous data
Discrete data
Categorical data
Nominal data
Application
Ordinary 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)
Excessive 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
two events
Mutually exclusive
Independent
two rules
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
Calculation of combinations of two or more types
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
Permutations
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 get farther from the mean, the probability density get smaller and smaller but are always positive.
The confidence intervals
The relationship between K and confidence interval (probability)
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 statistics
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
Rate next year's returns
The Weighted Mean
Apply Portfolio Weights
The Geometric Mean
Calculate using the average rate of return for each period
The idea of compound interest, evaluating past performance
The Harmonic Mean
Application to calculate average cost price
A>=G>=H
Absolute Dispersion
Range
MAD
Variance
population variance
sample variance
Standard deviation
population standard deviation
sample standard deviation
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 relationship
Skewness calculation power=3
Return
Kurtosis
Type
Mesokurtic
Leptokurtic
Platykurtic
Kurtosis calculation power=4
Excessive kurtosis
Sample kurtosis – 3
Leptokurtic——Fat tail
Calculator use
Calculate mean and variance