Return Distribution#
The distribution of asset returns, central to financial risk modelling.
Important
✨ AI-generated content. This page was written with the assistance of an AI language model and is provided as a learning aid. Despite careful review, it may still contain mistakes, omissions, or out-of-date information. Whether you are new to the topic, a team lead, or a senior practitioner, treat it as a starting point rather than an authoritative reference: read it critically and independently verify anything you act on (code, commands, figures, and factual claims) against official documentation and primary sources before relying on it.
What it is#
A return distribution is the probability distribution of an asset’s (or portfolio’s) returns over a period — the range of possible returns and how likely each is. From a price series \((S_0, \dots, S_n)\), the simple return is
(or, equivalently for many purposes, the log return).
Why it matters#
Every downside-risk measure is read off this distribution — for instance, Value-at-Risk is a tail quantile of it. Model the return distribution and you can price risk.
The reality: fat tails#
Empirical returns are not normal — they have heavy tails and skewness, so extreme moves happen far more often than a Gaussian predicts. Assuming normality understates tail risk; heavy-tailed (Student-t) or location-scale models fit better.
Theme: Risk & Probabilistic Forecasting · All terminology
Hint
Mind map — connected ideas
Value-at-Risk (VaR) · Risk Forecast · Probability Distribution · Normal Distribution · Quantile Level · Probabilistic Forecasts
Hint
More in Risk & Probabilistic Forecasting
Continuous Probabilistic Forecasts · Continuous Ranked Probability Score (CRPS) · Deterministic forecasts · Full Distribution · Pinball Loss (a.k.a. Quantile Loss) · Point Forecasts · Predicting Percentiles · Prediction Intervals (PI) · Probabilistic Forecasts · Probabilistic Scoring · Probability Forecasts · Quantile Forecasts · Quantile Level · Quantile Regression
See also
Source article Adapted (context, re-expressed) in our own words from: Return Distribution (insightful-data-lab.com).