2021 CFA® Level 1 Quantitative Methods- Learn by Practice

Explore descriptive and inferential statistics, population versus sample concepts, and measurement scales, then master central tendency, dispersion, skewness, kurtosis, and market return measures.

Examine statistical concepts in market returns, including fat-tailed distributions, skewness and outliers, and the roles of geometric vs arithmetic means, ratio scales, and central tendency.

Understand normal distribution properties, including zero skewness, and compute sample mean and standard deviation using n-1 variance. Learn harmonic mean for fixed-dollar purchases and bound observations within ±1.7 std devs.

Analyze questions 31–35 from CFA level 1 quantitative methods, focusing on mean versus median with outliers, skewness and kurtosis in risk, and definitions of variance, standard deviation, and sample statistics.

Compute a weighted portfolio return from allocations, and contrast arithmetic versus geometric means for next-year estimates and historical averages. Explain positive excess kurtosis with no skewness and mean absolute deviation.

Explore concepts from reading seven market returns, including coefficient of variation, cumulative relative frequency, and the third quartile. Analyze skewness and kurtosis, noting mean, median, and mode relations.

Explore probability concepts, including mutually exclusive and exhaustive events, empirical, subjective, and apriori probabilities; apply unconditional and conditional probability, addition and multiplication rules, Bayes, covariance, and portfolio risk.

Master probability concepts from subjective and objective probabilities to empirical and conditional probability, with CFA level 1 examples on portfolio variance, covariance, and correlation.

Master probability concepts through questions 51–55, applying factorial (labeling) formulas for grouping, Bayes' formula for updated probabilities, and combination calculations to choose stocks from a pool.

Compute covariance from a correlation coefficient and stock standard deviations using a probability model. Derive mean returns and apply unconditional and total probability rules to evaluate covariances and correlations.

Explore probability distributions, including discrete and continuous types, binomial distributions and trees, normal distributions with F(X), z-scores, confidence intervals, and Monte Carlo versus historical simulations.

Delve into common probability distributions through binomial-like stock moves, shortfall risk and safety-first ratio, distribution choices for stock prices, and 90% confidence intervals for CFA selection.

Explain common probability distributions and CFA concepts, comparing continuously compounded and holding-period returns, distinguishing discrete versus continuous random variables, applying the safety-first ratio, and contrasting historical and Monte Carlo methods.

Explore normal and lognormal distributions, binomial probabilities, Monte Carlo versus historical simulation, the properties of the continuous uniform distribution, and the Roy safety first ratio for portfolio choice.

Explore key probability distributions through questions 81–85: normal and lognormal models, stock return z-scores, binomial defaults, and computing probabilities with confidence intervals.

Convert a continuously compounded 11% rate to its effective annual rate with the exponential formula, then apply cumulative probability, confidence intervals, and Roy’s safety-first measure to pick the best fund.

Compare the t distribution to the normal as degrees of freedom rise, noting symmetry and a less peaked shape, and recall unbiased, efficient, and consistent estimators for confidence intervals.

Analyze the central limit theorem effects on sample mean and variance, compute standard error, evaluate test applicability, and explore stratified sampling, cross-sectional data, and sampling bias.

practice with small-sample t-tests and confidence intervals for normally distributed data, using standard error (sd over sqrt(n)), degrees of freedom, and choosing t vs z based on population variance.

examine time series data by analyzing historical stock prices and identify survivorship bias in hedge funds while applying simple random and stratified sampling, and the 95% confidence interval lower bound.

In CFA level 1 quantitative methods, explore sampling estimation tradeoffs between sample size and cost, and note lookahead bias in year-end PE ratios and the role of alpha.

Analyze sampling and estimation concepts by examining time period bias, survivorship bias, and lookahead bias in 2008 real estate data, and explore data mining and spurious correlations.

Master hypothesis testing through a disciplined, step-by-step approach, covering null and alternative hypotheses, significance levels, and key tests (z, t, f, chi-square) along with type I/II errors and p-values.

practice questions on hypothesis testing using a z test with known population standard deviation, formulating null and alternative hypotheses, and comparing z to 5% and 1% critical values.

Learn when to use nonparametric tests for rank data, distinguish statistical from economic decisions, and apply the f-test for variances and z-test decision rules in hypothesis testing.

Learn to perform hypothesis tests with one- and two-tailed z- and t-tests, interpret p-values, critical values, and decision rules for rejecting or failing to reject the null.

Review type I and II errors, p-values, significance levels, and test power in hypothesis testing; apply to z and t tests and null–alternative setups for stock returns.

Explore hypothesis testing concepts through exam-style questions 141–145, covering Spearman correlation (nonparametric), F-test for variances, chi-square test, t-test for means, and alpha effects on type I/II errors and power.

Learn to distinguish null and alternative hypotheses, decide to reject or not, and apply correlation tests with n-2 degrees of freedom and the r statistic for economic decisions.