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MindMap Gallery CFA Level 1 Quantitative Mind Map

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

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CFA Level 1 Quantitative Mind Map

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Outline

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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

I/Y

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

Univariate distributions(multivariate distribution)

Application

Shortfall risk

Safety first ratio

Lognormal Distribution

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