--- title: "Return distribution, skew and kurtosis | RupeeCase" description: "The Return distribution histogram with its mean and VaR markers, and the skew and excess kurtosis figures, as the app works them out from weekly returns." source_url: "https://www.rupeecase.com/learn/terminal/shape-of-weekly-returns" --- ## Watch: Return distribution In Advanced, the Risk tab draws every return as a histogram.Return distribution: what do skew and kurtosis say? 5 chapters, 1:04, with voice and music 1. [Chapter 1Where it is0:10](/instiv2/media/tut4/shape-of-weekly-returns-where-phone-dark-v4-va2.mp4) 2. [Chapter 2What it means0:32](/instiv2/media/tut4/shape-of-weekly-returns-meaning-phone-dark-v4-va2.mp4) 3. [Chapter 3Worked example0:06](/instiv2/media/tut4/shape-of-weekly-returns-example-phone-dark-v4-va2.mp4) 4. [Chapter 4How to read it0:06](/instiv2/media/tut4/shape-of-weekly-returns-reading-phone-dark-v4-va2.mp4) 5. [Chapter 5Watch out0:10](/instiv2/media/tut4/shape-of-weekly-returns-watch-phone-dark-v4-va2.mp4) Screens from the RupeeCase app on sample data. Strategy figures are model, back tested, as of the date on screen. Formula and example numbers are illustrative. Mark as watched 4In this screen ## Every button the video points at. A still from each chapter with its buttons and fields numbered. Pick a number to zoom in on it; hover the still for a close up; Esc shows the whole screen again. Sample data, no order is placed. **1**Where it is**2**What it means ### Chapter 1: Where it is 1 Show the whole screen 1 Show the whole screen 1. 1**Return distribution**In Advanced, the Risk tab draws every return as a histogram. Shown in the video, not on this still ### Chapter 2: What it means 1 Show the whole screen 1 Show the whole screen 1. 1**Bars 1 percent wide**Each bar counts the periods in a 1 percent band; markers show the mean and VaR. Shown in the video, not on this still 2. 2**Lopsided** Skew: below zero, the long tail is on the losing side. Shown in the video, not on this still 3. 3**Heavy tails** Excess kurtosis: above zero, more extreme periods than a normal curve. Shown in the video, not on this still ## Where it is ScreenRisk tab, Return distributionAdvanced The Risk tab, in Advanced: the Return distribution card, and Skew and Excess kurtosis in the Risk figures card. On a portfolio both read the model since you invested. Index in this video: [Allcap](/strategies/allcap) (strategy page). ## What it means The histogram sorts every weekly return of the period into bars one percent wide, from -15% to +15% by default, refitted to the range the returns fill. Markers show the mean week, VaR 95 and VaR 99. Skew measures lopsidedness: below zero the long tail is on the losing side, above zero on the winning side. Excess kurtosis compares the tails with a normal curve: above zero means more extreme weeks than a normal curve would give. The card needs at least 20 weekly returns. ## The formula Count the weeks in each 1 percent band. Skew and excess kurtosis describe the shape: which side the long tail is on, and how heavy the tails are. As computed in the RupeeCase app`Bars: weekly returns, 1% wide, -15% to +15% (refitted; the ends fold into the end bars) Markers: Mean, VaR 95, VaR 99 Skew = m3 / m2 ^ 1.5 (population moments of weekly returns) Excess kurtosis = m4 / m2 ^ 2 - 3 Needs 20 weekly returns` ## Worked example Example only * 52 weeks: most between -2% and +3% * Two weeks at -9% and -11%, none past +6% * The long tail is on the left: skew below zero ## How to read it * Most bars near the middle and a few far left: the falls came in rarer, larger steps. * Excess kurtosis above 0: more extreme weeks than a normal curve gives. * Read VaR 95 against the bars: about 1 week in 20 lost more. ## Watch out * The caption says Kurtosis; the value is excess kurtosis, as the tile says. * This recording reads month end history, so its bars are months. * A few years of weeks is a small sample for the tails. ## Transcript Tap Sound on for voice and music. These are the captions of the video, chapter by chapter. 1. 0:00**Where it is.** In Advanced, the Risk tab draws every return as a histogram. 2. 0:10**What it means.** Each bar counts the periods in a 1 percent band; markers show the mean and VaR. 3. 0:42**Worked example.** Worked example, example only: 52 weeks: most between -2% and +3%. Two weeks at -9% and -11%, none past +6%. The long tail is on the left: skew below zero. 4. 0:48**How to read it.** How to read it: Most bars near the middle and a few far left: the falls came in rarer, larger steps. Excess kurtosis above 0: more extreme weeks than a normal curve gives. Read VaR 95 against the bars: about 1 week in 20 lost more. 5. 0:54**Watch out.** Watch out: The caption says Kurtosis; the value is excess kurtosis, as the tile says. This recording reads month end history, so its bars are months. A few years of weeks is a small sample for the tails. ## Terms in this tutorial * [Return distribution](/learn/glossary#return-distribution)A bar chart of how many weeks fell into each band of return, from big losses on the left to big gains on the right. * [Skew](/learn/glossary#skew)A measure of whether the big surprises in returns tend to be gains or losses. * [Excess kurtosis](/learn/glossary#excess-kurtosis)A measure of how often returns were extreme compared with a normal bell curve. * [VaR](/learn/glossary#var)Value at risk: a weekly loss that was matched or exceeded only rarely in the history. ## Learn it in depth * [Module 5.1: Statistical Foundations for Quant Investing9 min read, free](/learn/path-5/module-5-1-statistical-foundations) * [Module 4.5: Risk Management for Systematic Portfolios9 min read, free](/learn/path-4/module-4-5-risk-management) TKeep watching ## Next tutorial. [0:59Next tutorial, Make it yours and AdvancedTreynor, Omega and weeks ahead: three more ways to read risk?Treynor, Omega at 6% and Weeks ahead of benchmark on the Risk tab: what each one measures and how the app works it out from weekly returns.Watch next](/learn/terminal/treynor-omega-weeks-ahead) ### Related tutorials * [1:21Make it yours and Advanced, AdvancedAdvanced risk figures: Sortino, Calmar, VaR, beta and more1:21 video, AdvancedWatched](/learn/terminal/advanced-risk-figures) * [1:22Read a strategy, AdvancedDrawdown shape: what do ulcer, pain and time under water add?1:22 video, AdvancedWatched](/learn/terminal/how-the-falls-looked) * [1:12Read a strategy, BasicThe Return figures card: what do year to date and best week say?1:12 video, BasicWatched](/learn/terminal/return-figures-card) [All 67 terminal tutorials](/learn/terminal/) Try it in Practice ## See it on your own screen. Practice mode runs the whole terminal without real orders, so you can open any strategy and find every screen from this tutorial for yourself. [Sign up for RupeeCase](https://invest.rupeecase.com/signup)[Glossary](/learn/glossary) Explore next ## Keep learning the terminal. * [TutorialCustomise: how do I set what each page shows?1:26 video, Basic](/learn/terminal/customise) * [TutorialNumbers: how do lakh, crore, Short and Full change a figure?1:00 video, Basic](/learn/terminal/numbers-lakh-crore) * [TutorialRank table: how does a dynamic allocation share out its money?1:11 video, Advanced](/learn/terminal/rank-table-dynamic-allocation) * [TutorialExit rank and strength filters: when does a sleeve sell?1:18 video, Advanced](/learn/terminal/exit-rank-and-strength-filters) Community ## Join my WhatsApp group. Scan the code, fillFill one short form, and join my WhatsApp group. Slides, sources, factsheets and the rebalance logs live there, and members join a daily Google Meet with me. 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