Equation Library
The mathematical foundations behind everything else on this site. This is my proof of work: rather than assume the standard formulas, I re-derive and re-implement them so I understand exactly what each one assumes and where it breaks.
Every entry follows the same template:
- the equation itself,
- what each symbol means,
- a plain-English explanation,
- why it matters in markets,
- a simple worked numerical example,
- a Python implementation,
- a manual / Excel calculation,
- a real financial-market example,
- and the common mistakes people make with it.
Entries are being written and published one at a time, to the standard on the home page. The map below is the plan.
Core statistics
Mean return · variance · standard deviation · covariance · correlation · skewness · kurtosis · Z-score · normal distribution · t-statistic · p-value · confidence interval.
Quant finance
Simple return · log return · cumulative return · volatility · annualised return · annualised volatility · Sharpe ratio · Sortino ratio · maximum drawdown · Value at Risk · Expected Shortfall · beta · alpha · CAPM · Kelly criterion · CAGR · profit factor · win rate · expectancy.
Time series
Autocorrelation · moving average · exponential moving average · AR model · MA model · ARIMA · GARCH · Hurst exponent · cointegration · stationarity · Augmented Dickey–Fuller test.
Machine-learning mathematics
Cost function · gradient descent · mean squared error · cross-entropy loss · sigmoid · softmax · entropy · information gain · Gini impurity · regularisation · L1 and L2 penalties · backpropagation.