## Everything You Need from Quantitative Methods for CFA Level 1

**Why Quantitative Methods Matters so Much for Passing the CFA L1**

Quantitative methods is unique to the Level one exam.

It introduces key aspects of time value of money, probability, the normal distribution, and hypothesis testing. The frameworks introduced in this section carry through as we compare different investments and evaluate their risk and return tradeoffs throughout the rest of the CFA curriculum.

In other words, the mathematical concepts introduced here are cornerstones of finance. Compound interest/time value of money and discounted cash flows show up both as stand-alone problems and as crucial parts of other problems throughout the curriculum. Mastering the basics will be key. Probability will also be directly tested but becomes even more important conceptually when thinking about risk and return.

Quant is also a long and often time-consuming set of readings.

As a result many Candidates hit the quantitative section and get bogged down as they start to struggle with certain concepts or get lost with the minutiae of the section. This is a terrible mistake, especially if it is one of the first sections you read. Don’t be one of those Candidates (for more tips on how to get started studying see this post). Keep your momentum going even if you sacrifice complete understanding of everything the first time around. As you start seeing the concepts embedded in other parts of the curriculum you can revisit the section or relevant practice problems.

What follows is our list of what we view as the most testable components from these 8 readings. We've strived to make this comprehensive while still deliberately skipping material we think is "in the weeds" and a waste of your time (so staying true to the GoStudy mantra). If you know everything here you ** should** get over 70% on this section--all while not getting too bogged down in myraid details that often slow candidates down in this section.

### Time Value of Money

- What is time value? The relationship (equation) between present value and future value
- Solving TVM using your financial calculator
- The 3 interpretations of an interest rate
- The components of the interest rate (risk free, inflation, default risk, and other risk premiums)
- Calculating the effective annual rate and dealing with non-annual compounding periods
- Annuity calculations for ordinary annuities, annuity due, and perpetuities
- Generally being able to use a timeline to bring different CFs to one point in time (*cash flow additivity principle*)

### Discounted Cash Flows (DCF)

*For more on DCF see our post covering the five main testable concepts in greater depth.*

- The Net Present Value (NPV) equation and calculating it on your financial calculator
- A conceptual understanding of IRR and the ability to solve for IRR on your calculator
- The pros/cons of IRR vs. NPV and an ability to compare/contrast the two
- NPV/IRR decision rules, why they might yield different results for non-exclusive projects
- Calculating the Time Weighted Rate of Return (TWRR)
- Comparing/contrasting when TWRR and MWRR (money weighted rate of return) would yield different values and which would have a higher/lower value given timing of cash flows and investment performance
- Holding Period Return, Bank Discount Yield, Effective Annual Yield, Money Market Yield and the relationship between them

### Key Statistical Concepts

- Basic difference between populations and samples
- The Measurement Scales (NOIR)
- Histograms and reading an Absolute, Relative, and Cumulative Frequency table
- Measures of central tendency - Calculate mean, median, mode, geometric mean & know their relative values with left/right skew
- Measures of dispersion - calculate range, variance, standard deviation semivariance, and the coefficient of variation
- Calculate a weighted average and compound return
- Understand the normal distribution, its key properties, and the observations within X # of standard deviations
- Be able to calculate and interpret confidence intervals
- Be able to talk about positive and negative skew as well as kurtosis and what that means for risk and returns
- Calculate and interpret the Sharpe ratio and Roys Safety First Criteria

### Probability & Probability Concepts

- Probability of an event happening and an event not happening
- Understanding conditional and unconditional probability
- Calculate the joint probability of two events _both_ happening (multiplication rule of probability)
- Calculate the probability of *at least* one event happening (addition rule of probability)
- Expected value calculation
- Calculate an expected value using a Tree Diagram
- Covariance and correlation, the properties of correlation, and how it affects risk
- Variance of a 2 asset portfolio
- Bayes formula
- Factorial, Combination, and Permutation calculation / when is each appropriate
- Reinforcement of anything and everything to do with the normal distribution including building a confidence interval
- Calculating the Z-score and using a Z-table
- Articulating limitations of standard deviation as a risk measure and the use of Roys Safety First criteria, shortfall risk
- Defining Monte Carlo Simulation, Historical Simulation
- The different sampling methods (especially stratified random sampling), understanding the statistical properties of a good estimator, and the idea of sampling error/calculation of standard error
- Basic understanding of time series vs. Cross-sectional data,
- The central limit theorem
- The Z-test vs. the T-test and properties of the T-test
- The types of data biases - data mining, selection bias, survivorship, look ahead bias, time period bias

### Hypothesis testing -The 7 steps of constructing a hypothesis test

- Defining / distinguishing between a null and alternative hypothesis
- Understanding the rejection area for H-null, picking the right test statistic, and reading a t/z table for either a 1-sided or 2-sided test using a critical value in order to use a decision rule
- The tradeoff between the level of significance and Type I/Type II errors
- Distinguishing between a Type I/Type II error
- Basic understanding of the p-value, chi-squared test, and F-test

### Technical Analysis - Key assumptions of technical analysis

See our mini-series on technical analysis for a complete run down

- How technical analysis differs from fundamental analysis
- Line charts, Bar charts, Candlesticks, and Point/Figure Charts
- Support & Resistance, Trendlines and Breakouts, and the idea of polarity
- Reversal patterns - Head & shoulders, Double/Triple top & calculating price target from the move
- Continuation patterns - Triangles, Rectangles, Flags/Pennants
- Price-based indicators - moving averages, bollinger bands,
- Momentum oscillators - ROC, RSI, MACD, Stochastic
- Sentiment indicators - Put/Call ratio, VIX, Margin Debt, Short interest ratio, Flow of Funds Indicator, New Equity Issuances
- Elliot Wave Theory

**Additional Resources**