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MindMap Gallery CFA level one quantitative mind map Chinese and English version

CFA level one quantitative mind map Chinese and English version

A super detailed CFA level 1 mind map overview. This version is a directory of all knowledge points. More detailed parts containing knowledge content will be updated and released in the future.

Edited at 2022-12-04 07:29:31

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CFA level one quantitative mind map Chinese and English version

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Outline

Quantity

time value of money

interest rate

Three ways to understand interest rates

required rate of return

Required rate of return refers to the minimum rate of return required by investors when investing

Discount Rate

The discount rate is the interest rate used to discount future cash flows

Opportunity Cost

Opportunity cost refers to the benefits that investors give up after choosing an investment (opportunity cost is not the real cost)

The composition of interest rates

Interest rate = real risk-free interest rate, inflation premium, default risk premium, liquidity risk premium, term risk premium

Real Risk-Free Interest Rate

The real risk-free interest rate refers to the rate of return on risk-free assets in a single period without taking expected inflation into account.

Nominal interest rate ≈ real interest rate expected inflation rate

Inflation Premium

Inflation premium refers to the portion of the premium used to compensate for the expected rate of inflation

Default Risk Premium

The default risk premium compensates investors for the default risk borne by the borrower, which is the risk that the borrower will not be able to make cash flows as contracted when due.

The borrower here is a broad concept, not only referring to bonds, but also including the party that needs to pay cash flow in asset transactions such as stocks and derivatives.

Liquidity Premium

Liquidity risk premium refers to the risk that assets cannot be quickly realized at fair market value in the short term.

Liquidity risk does not refer to the risk of not being able to sell, but the risk of being forced to sell at a discount due to rapid liquidation in the short term.

Maturity Premium

Maturity refers to the time until the principal is due to be paid.

Interest rates for different interest calculation methods

Simple Interest and Compounding Interest

Simple interest: only interest is charged on the principal, and the interest paid in each interest calculation period = principal * period interest rate

Compound interest: After each interest calculation cycle, the interest from the previous period must be added to the principal before interest is calculated (interest compounding)

Quoted interest rate and effective annual interest rate

Quoted Interest Rate (Stated Annual Interest Rate/Quoted Interest Rate)

The annual interest rate provided by the financial institution when quoting interest (the number of times the annual interest rate is calculated each year must be stated) (the quoted interest rate is not the investor’s real interest rate income within one year)

According to the quoted interest rate and the number of interest calculations, the periodic interest rate can be calculated = quoted interest rate / number of interest calculations in one year.

Effective Annual Rate (EAR)

EAR refers to the total interest income earned per unit of currency in 1 year

EAR=(1 interest period interest rate)^m-1=(1 rs/m)^m-1

rs is the quoted interest rate; m is the number of interest calculations within one year.

If the number of interest calculations within a year tends to be infinite, the formula for continuous compounding can be obtained (during the exam, continuous compounding is the maximum effective annual interest rate. Wrong options can be quickly eliminated through continuous compounding)

EAR=e^rs-1

present value and future value

The relationship between present value and future value

FV=PV*(1 r)^n

PV=FV/(1 r)^n

n represents the number of interest accrual periods, r represents the interest rate during the interest accrual period

law

Given the interest rate level r, FV increases as the number of interest calculation periods n increases.

Given the number of periods n, FV rises as the interest rate level rises

In a given time period, the greater the interest rate level r, the smaller the present value PV

annuity

Broadly speaking, it refers to a series of cash flows that are paid in equal amounts and regularly.

Ordinary Annuity

An equal amount of annuity is paid at the end of each period

Annuity Due

Annuity paid at the beginning of each period

Perpetuity Annuity

The annuity is paid indefinitely, and the payment time is at the end of each period.

The present value and future value of irregular cash flow (unequal cash flow)

Refers to a series of cash flows with varying cash flows in each period. The basic principles of cash flow discounting can be used to calculate the pv and fv of cash flows.

Organizing, visualizing and describing data

Data Classification

Numerical data and categorical data (Numerical Date vs Categorical Date)

Cross-sectional data, time series data and panel data (Cross-sectional Data vs Time-series Data vs Panel data)

Structured Data vs Unstructured Data

Data organization and visualization

Organize data

Data Visualization

Description of data

Basic concepts of statistics

central tendency

Degree of dispersion

Skewness and Kurtosis

Correlation between two variables

Basics of Probability Theory

Basic concepts of probability theory

Terminology of Probability

relationship between events

The definition and determination method of probability

Probability calculation

Multiplication Rule and Addition Rule

Total probability formula and Bayesian formula

statistics of random variables

expect

Variance and standard deviation of random variables

Covariance and correlation coefficient

Questions about permutations and combinations

Combination

Permutation

Common probability distributions

basic concept

Discrete vs Continuous Random Variable

Distribution Function

discrete distribution

Discrete Uniform Distribution

Binomial Distribution

continuous distribution

Contonous Uniform Distribution

Normal Distribution

Lognormal Distribution

Student's t-Distribution

Chi-square Distribution and F-Distribution

Multivariate Distribution

simulation

Moton Carlo Simulation

Sampling and Estimation

sampling

Sampling related concepts

sampling bias

estimate

Point Estimate

Central Limit Theorem

Confidence Interval Estimate

Resampling

hypothetical test

Hypothesis testing steps

Basic ideas and steps of hypothesis testing

Concepts related to hypothesis testing

Hypothesis test for normal population

Test for Normal Population Mean

Test for Normal Population Variance

Significance test of correlation coefficient

Non-parametric test

The difference between parametric and non-parametric tests

Non-parametric test of correlation coefficient

Independence test based on contingency table

Univariate linear regression

Simple Linear Regression

Basic concepts of linear regression

Ordinary Liner Sqares (OLS)

Assumptions of linear regression

Test of regression coefficients

Prediction of dependent variable

Analysis of Variance (ANOVA)

Cofficient of Determination

ANOVA Table

Different functional forms of linear regression

theme

computer use