Quantitative Methods and Statistics
Core toolkit
Be fluent with descriptive statistics (mean, median, variance, skewness, kurtosis), probability distributions, and the difference between population parameters and sample estimates. Know the central limit theorem and why it justifies t-tests and normal approximations for sample means, and understand why standard error shrinks with 1/sqrt(n).
Inference and regression
Hypothesis testing: null versus alternative, one- and two-sided tests, Type I and Type II errors, power, p-values and confidence intervals. In OLS, interpret coefficients as partial effects, distinguish R-squared from adjusted R-squared, know the Gauss-Markov assumptions and the consequences of heteroskedasticity, autocorrelation, multicollinearity and omitted variables. Recognise nonstationarity, unit roots and spurious regression; know when to difference or to use cointegration.
Traps
- A p-value is not the probability that the null hypothesis is true.
- High R-squared does not imply causality or out-of-sample predictive power.
- Annualising a Sharpe ratio with sqrt(T) assumes i.i.d. returns; autocorrelation breaks it.
- Correlations are conditional and unstable; a low full-sample correlation can hide crisis co-movement.
- Regressing one trending series on another without a stationarity check produces spurious significance.
Worked example
A strategy has a daily Sharpe ratio of 0.08 over 252 trading days. Under i.i.d. returns the annualised Sharpe is 0.08 x sqrt(252) = 1.27. For significance, a coefficient with a t-statistic of 2.6 is significant at 5% two-sided in a large sample; t-statistics near 2 are the rough threshold, but the bar rises sharply when many hypotheses are tested.