Statistics for Finance
Returns are random variables. Risk is a standard deviation. Edge is a coefficient you have to prove is real. This is the statistical spine every quant course hangs from.
The statistics that underpins quantitative finance — probability and random variables, the distributions returns actually follow (normal, lognormal, fat-tailed), expectation, variance and higher moments, covariance, correlation and regression, the Central Limit Theorem and estimation, and hypothesis testing with its finance-specific traps. Worked numbers and interactive charts throughout.
Every number in quantitative finance is a statistic in disguise. A return is a draw from a random variable. “Risk” is a standard deviation. A trading edge is a regression coefficient you have to prove isn’t noise. Skip the statistics and the rest of the quant ladder — Value at Risk, portfolio theory, Bayesian finance, factor models — is built on sand.
This topic assembles that foundation properly. It assumes you’ve met returns, Sharpe ratios and volatility (from Investment Metrics) but no formal probability or statistics. You’ll learn:
- Probability and random variables — events, conditional probability, independence, and how a PDF/CDF describes a quantity you can’t predict.
- Distributions in finance — the normal, the lognormal that prices follow, and the fat tails that wreck models built on the bell curve.
- Expectation, variance and moments — mean, variance, and the skew and kurtosis that say how lopsided and how tail-heavy returns are.
- Covariance, correlation and regression — how two assets move together, and how to fit a line that estimates beta and explains R².
- The Central Limit Theorem and estimation — why averages go normal, what a standard error is, and how to put a confidence interval on an estimate.
- Hypothesis testing — null vs alternative, p-values, the two ways to be wrong, and why “I backtested 1,000 strategies” quietly breaks all of it.
Master these six and the expert quant courses stop being a wall of Greek letters — they become applications of tools you already own.
In this topic
- 1 Probability & Random Variables The grammar of uncertainty: sample spaces, events and the three axioms; conditional probability and independence for co-moving stocks; discrete vs continuous random variables; PMFs, PDFs and CDFs; and expectation as the probability-weighted average. 10 min
- 2 The Distributions Finance Runs On The handful of probability distributions every quant leans on: the normal bell curve and its 68–95–99.7 rule, the z-score, the lognormal model for prices, fat tails and the Student-t, equity skew, and why pretending returns are normal quietly underprices crashes. 11 min
- 3 Expectation, Variance & the Moments The four numbers that summarize any return distribution: expectation (the average), variance and volatility (the spread), skewness (the lopsidedness), and kurtosis (the fat tails). Worked from raw return series, with the n−1 correction and the √252 annualizer. 11 min
- 4 Covariance, Correlation & Regression How two assets move together — covariance and its standardized cousin correlation — and how a least-squares line turns that relationship into beta, alpha, and R², with the correlation-is-not-causation traps that ruin careers. 12 min
- 5 Sampling, the CLT & Estimation From a sample to the truth: how a statistic estimates a parameter, why the sample mean is itself a random variable, the Central Limit Theorem that makes averages normal, the standard error σ/√n, and confidence intervals — what they do and don't mean. 11 min
- 6 Hypothesis Testing & Significance How quants decide whether an edge is real: null vs alternative hypotheses, the t-test and the test statistic, the p-value (and its rampant misreading), Type I/II errors and power, plus finance's deadliest trap — data snooping — and why statistical significance is not economic relevance. 12 min
- 7 Final Exam: Statistics for Finance The graded final exam for Statistics for Finance: probability and random variables, distributions, expectation and moments, covariance, correlation and regression, sampling and the Central Limit Theorem, and hypothesis testing. 15 min
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