The statistical rigor behind everything you already sensed
Intermediate · Math track · levels 1–7
Level 1: Probability: the language of uncertainty
Formalizes with statistical rigor what the market theory course explained intuitively: what a probability is, how it is updated with new information, how uncertainty is turned into a number you can compute, and why the human brain reasons badly about chance in the markets.
- 1. What a probability is: no certainties
- 2. Conditional probability: why context changes everything
- 3. Random variables: how to turn 'maybe' into a number
- 4. Expected value: the rigorous foundation of expectancy
- 5. Variance and standard deviation: the exact arithmetic of volatility
- 6. Independence and dependence between events
- 7. The gambler's fallacy and other reasoning errors
Level 2: Distributions and why markets are not "normal"
Formalizes the concept of a probability distribution applied to financial returns: the Gaussian bell curve, its real limits (fat tails, skewness), the log-normal model of prices, VaR as a percentile of losses, the central limit theorem, and why black swans are more frequent than classical theory predicts.
- 1. What a probability distribution is and what it is for
- 2. The normal distribution: the Gaussian bell curve
- 3. Fat tails and skewness
- 4. The log-normal distribution: why prices are not modeled as a normal
- 5. Percentiles, quantiles and Value at Risk
- 6. The central limit theorem: why averaging tends toward the normal (and why that is not enough)
- 7. Black swans: when the improbable dominates the outcome
Level 3: Descriptive and inferential statistics applied to markets
Tools for summarizing financial data without fooling yourself, and for understanding why every backtest is an uncertain estimate and never a revealed truth about the future.
- 1. Mean, median and mode: why the mean can mislead you with financial data
- 2. Sample vs population: why a backtest is always a sample, never the complete truth
- 3. Confidence intervals: quantifying how much we do not know
- 4. Standard error: more data is not more certainty
- 5. Outliers: noise to ignore, or the real signal
- 6. Selection biases beyond survivorship bias
- 7. From descriptive to inferential statistics: the jump that serious backtesting demands
Level 4: Correlation, regression and the myth of causality
We formalize correlation with Pearson's coefficient and its traps, take apart the confusion between correlation and causation using real financial cases, and build up linear regression (simple and multiple) all the way to the CAPM and the problem of statistical overfitting.
- 1. Pearson correlation, beyond the number
- 2. Correlation does not imply causation
- 3. Simple linear regression: finding the best line
- 4. The R² coefficient: how much your model really explains
- 5. Multiple regression: when a single factor is not enough
- 6. The CAPM: beta as the slope of a regression
- 7. Overfitting in regression: why more variables do not always help
Level 5: Time series: why the past does not repeat itself the same way
The formal statistical basis for working with financial data ordered in time: stationarity, autocorrelation, the random walk, cointegration, volatility clustering, and why every metric computed on the past has an expiry date.
- 1. Financial data is different: order matters
- 2. Stationarity: not the price, almost the return
- 3. Autocorrelation: does today resemble yesterday?
- 4. The random walk: tomorrow does not follow today
- 5. Cointegration: the formal basis behind pairs trading
- 6. Volatility clustering: why calm and storm arrive in runs
- 7. Rolling windows: every metric has an expiry date
Level 6: Hypothesis testing and its traps in backtesting
Formalizes, through hypothesis testing, p-values, type I and type II errors, and the traps of multiple comparisons and data snooping, the statistical rigor needed to judge honestly whether a trading strategy has a real edge before risking capital.
- 1. The null hypothesis: doubting your own strategy
- 2. The p-value without formulas: what it is and, above all, what it is NOT
- 3. Statistical significance vs. practical significance
- 4. Type I and type II errors: false positives and false negatives when evaluating a strategy
- 5. The multiple comparisons problem: why testing 100 variants almost guarantees winners by chance
- 6. Data snooping and p-hacking: overfitting with a proper statistical name
- 7. An honest test before you risk a single euro
Level 7: Linear algebra and portfolio optimization
The closing level of the course: how a portfolio of several assets becomes a vector and a matrix, how Markowitz computes the optimal combination of risk and return, why that optimization demands a computer and why in practice it fails more than it promises, and how the Academy's three tracks connect once you finish.