Math and Statistics
46 lessons in this track so far, in the order we suggest reading them.
Probability
IntermediateProbability for TradersProbability is the language of uncertainty in trading. Learn the core rules, independent vs dependent events, odds, and how probability shapes sizing and edge.IntermediateExpected ValueExpected value is the average result of a bet over many repetitions. Learn the formula, trading and prediction market examples, and why EV alone is not enough.IntermediateLaw of Large NumbersThe law of large numbers says averages converge to the true value as samples grow. Learn what it means for judging strategies and how many trades you need.IntermediateConditional ProbabilityConditional probability is the chance of an event given that another has happened. Learn the formula, trading examples, base rates and how to use filters properly.IntermediateBayes' TheoremBayes' theorem shows how to update a probability when new evidence arrives. Learn the formula, trading and prediction market examples, and base rate errors.IntermediateRandom VariablesA random variable assigns numbers to uncertain outcomes, like a trade's profit. Learn discrete and continuous variables, expectation and variance, with examples.
Statistics
IntermediateMean, Median and ModeThe mean, median and mode measure the centre of data in different ways. Learn when each is best for trading data, how outliers distort averages and geometric means.IntermediateVariance and Standard DeviationVariance and standard deviation measure how spread out values are. Learn the formulas, sample vs population, annualising volatility and their role in trading risk.IntermediatePercentiles, Quantiles and Z-ScoresA z score shows how many standard deviations a value is from its mean. Learn the formula, its uses in mean reversion and pairs trading, and the pitfalls.IntermediateCovariance and CorrelationCovariance and correlation measure how two assets move together. Learn the formulas, how to read them, why correlations change in crises and their portfolio role.IntermediateSampling and Standard ErrorStandard error measures how much an estimate like a win rate or average return varies between samples. Learn the formulas and what they mean for backtests.IntermediateCentral Limit TheoremThe central limit theorem says averages of many independent values tend toward a normal distribution. Learn what it means for trading statistics and when it fails.IntermediateConfidence IntervalsA confidence interval gives a range of plausible values for a statistic. Learn how to calculate them for returns and win rates and how to read them in backtests.IntermediateHypothesis Testing and P-ValuesHypothesis tests check whether results are likely due to chance. Learn null hypotheses, test statistics and p values, a strategy test and how p values mislead.IntermediateStatistical Power and Type I and II ErrorsType I errors are false positives; type II errors are missed real effects. Learn how they apply to strategy testing, the trade off between them and power.IntermediateBootstrap and Permutation TestsBootstrap and permutation tests use resampling to measure uncertainty and test significance without strict assumptions. Learn how they work, examples and pitfalls.IntermediateOutliers and Robust StatisticsOutliers can distort averages, correlations and backtests. Learn how to detect them, robust measures like the median and MAD, winsorising and when they matter.IntermediateStatistical Significance in TradingStatistical significance helps judge whether trading results reflect a real edge or luck. Learn the t statistic rule of thumb, sample size and multiple testing.IntermediateRegression AnalysisRegression models how one variable relates to others. Learn linear regression, beta, R squared, multiple regression for factors, hedge ratios and common pitfalls.IntermediateMaximum LikelihoodMaximum likelihood estimation finds the model parameters that make observed data most probable. Learn the idea, simple examples, its use in GARCH and its limits.IntermediateBayesian StatisticsBayesian statistics combines prior beliefs with data to estimate uncertain quantities. Learn priors and posteriors, shrinkage, credible intervals and trading uses.
Distributions
AdvancedProbability Distributions ExplainedProbability distributions describe the range and likelihood of outcomes. Learn the main ones used in trading, their shapes and when each applies.AdvancedNormal DistributionThe normal distribution is the bell curve behind many financial models. Learn its properties, the 68 95 99.7 rule, where traders use it and why markets break it.AdvancedLognormal DistributionA lognormal distribution describes values whose log is normal, like prices that cannot go negative. Learn log returns, volatility drag and its option uses.AdvancedStudent's t-DistributionThe Student's t distribution has fatter tails than the normal. Learn how it is used for small sample tests and to model fat tailed returns, with examples.AdvancedBinomial and Bernoulli DistributionsThe binomial distribution gives the probability of a number of wins in a set of trades. Learn the formula, trading examples and its link to option trees.AdvancedPoisson and Exponential DistributionsThe Poisson distribution models how many rare events occur in a period, like large moves or trade arrivals. Learn the formula, examples and its limits.AdvancedFat TailsFat tails mean extreme market moves happen far more often than the normal curve predicts. Learn the evidence, the causes, how to measure them and how to manage them.AdvancedSkewness and KurtosisSkewness measures whether returns lean to one side; kurtosis measures tail heaviness. Learn the formulas, what they reveal about strategies and how to use them.AdvancedEmpirical and Mixture DistributionsA mixture distribution blends several distributions, such as calm and volatile regimes. Learn how mixtures create fat tails, how they are fitted and their uses.
Time Series
AdvancedTime Series BasicsMarket data is a time series: values ordered in time. Learn the components of a time series, why order matters, returns vs prices and the core tools for analysis.AdvancedWhite Noise and Random WalksA random walk is a path built from random steps; white noise is pure randomness. Learn how they model prices, the random walk hypothesis and the evidence against it.AdvancedAutocorrelation and Partial AutocorrelationAutocorrelation measures how a series relates to its own past values. Learn the formula, the ACF, what positive and negative autocorrelation mean and why it matters.AdvancedStationarity, Differencing and Unit RootsA stationary series has stable statistical properties over time. Learn why prices are non stationary, how to test with ADF and KPSS and how to make data stationary.AdvancedCointegrationCointegration means two non stationary series share a long run relationship. Learn the Engle Granger and Johansen tests, hedge ratios and pairs trading uses.AdvancedGranger CausalityGranger causality tests whether past values of one series help predict another. Learn how the test works, market lead lag examples and its limits.AdvancedRolling and Expanding WindowsRolling windows use a fixed recent period; expanding windows use all data so far. Learn when to use each, window length trade offs and how to avoid look ahead bias.AdvancedStructural Breaks and Regime ChangesMarkets switch between regimes such as calm and turbulent, or trending and ranging. Learn how to detect regimes, the models used and how to adapt strategies.AdvancedARIMAARIMA models forecast a time series from its own past values and errors. Learn the AR, I and MA terms, how to choose orders and why returns are hard to predict.AdvancedGARCHGARCH models capture volatility clustering, where big moves follow big moves. Learn the GARCH(1,1) formula, persistence, forecasting and uses in risk and options.
Other Math
AdvancedCompounding and Geometric vs Arithmetic ReturnsCompounding means returns earn returns over time. Learn the formulas, why losses hurt more than gains help, volatility drag and how it shapes position sizing.AdvancedTime Value of MoneyA dollar today is worth more than a dollar tomorrow. Learn present and future value, discounting, annuities and NPV, the maths behind bonds, valuations and options.AdvancedLinear Algebra for TradersLinear algebra handles many assets at once using vectors and matrices. Learn portfolio variance with covariance matrices, PCA, regressions and the Python tools.AdvancedCalculus for TradersCalculus describes how quantities change. Learn derivatives, integrals and Taylor approximations, and how they underpin Greeks, duration and optimisation.AdvancedOptimizationOptimisation finds inputs that maximise or minimise an objective, from portfolio weights to strategy settings. Learn the methods and how to avoid overfitting.AdvancedEconometricsEconometrics applies statistics to economic and financial data. Learn its core tools, common problems like endogeneity and spurious results, and how traders use it.