Category Archives: Financial

Inequality, Lorenz-Curves and Gini-Index

In a previous post we looked at inequality of profits and the useful abstraction of the Whale-Curve to analyze Customer Profitability. Here I want to focus on inequality and its measurement and visualization in a broader sense.

A fundamental graphical representation of the form of a distribution is given by the Lorenz-Curve. It plots the cumulative contribution to a quantity over a contributing population. It is often used in economics to depict the inequality of wealth or income distribution in a population.

Lorenz Curve (Source: Wikipedia)

The Lorenz-Curve shows the y% contribution of the bottom x% of the population. The x-axis has the population sorted by increasing contributions; (i.e. the poorest on the left and the richest on the right). Hence the Lorenz-Curve is always at or below the diagonal line, which represents perfect equality. (By contrast, the x-axis of the Whale-Curve sorts by decreasing profit contributions.)

The Gini-Index is defined as G =  A / (A + B) , G = 2A  or G = 1 – 2B

Since each axis is normalized to 100%, A + B = 1/2 and all of the above are equivalent. Perfect equality means G = 0. Maximum inequality G = 1 is achieved if one member of the population contributes everything and everybody else contributes nothing.

An interesting interactive graph demonstrating Lorenz-Curves and corresponding Gini-Index values can be found here at the Wolfram Demonstration project.

The GINI Index is often used to indicate the income or wealth inequality of countries. The corresponding values of the GINI index are typically between 0.25 and 0.35 for modern, developed countries and higher in developing countries such as 0.45 – 0.55 in Latin America and up to 0.70 in some African countries with extreme income inequality.

GINI index of world countries in 2009 (Source: Wikipedia)

Graphically, many different shapes of the Lorenz-Curve can lead to the same areas A and B, and hence many different distributions of inequality can lead to the same GINI index. How can one determine the GINI index? If one has all the data, one can numerically determine the value from all the differences for each member of the population. An example of that is shown here to determine the inequality of market share for 10 trucking companies.
Another approach is to model the actual distribution using a formal statistical distribution with known properties such as Pareto, Log-Normal or Weibull. With a given formal distribution one can often calculate the GINI index analytically. See for example the paper by Michel Lubrano on “The Econometrics of Inequality and Poverty“. In another example, Eric Kemp-Benedict shows in this paper on “Income Distribution and Poverty” how well various statistical distributions match the actually measured data. It is commonly held that at the high end of the income the Pareto distribution is a good model (with its inherent Power law characteristic), while overall the Log-Normal is the best approximation.

After studying several of these papers I started to ask myself: If x% of the population contribute y% to the total, what’s the corresponding GINI index? For example, for the famous “80-20 rule” with 20% of the population contributing 80% of the result, what’s the GINI index for the 80-20 rule?

To answer this question I created a simple model of inequality based on a Pareto distribution. Its shape parameter controls the curvature of the distribution, which in turn determines the GINI index. The latter is visualized as color-coded bands using a 2D contour plot in the following graphic:

GINI index contour plot based on Pareto distribution model

The sample data point “A” corresponds to the 80-20 rule, which leads to a GINI index of about 0.75 (strongly unequal distribution). Data point “B” is an example of an extremely unequal distribution, namely US political donations (data from 2010 according to a statistic from the Center of Responsive Politics recently cited by CNNMoney):

“…a relatively small number of Americans do wield an outsized influence when it comes to political donations. Only 0.04% of Americans give in excess of $200 to candidates, parties or political action committees — and those donations account for 64.8% of all contributions”

0.04% contribute 64.8% of the total! Here is another way of describing this: If you had 2500 donors, the top donor gives twice as much as the other 2499 combined. This extreme amount of inequality corresponds to a GINI index of 0.89 (needless to say that this does not seem like a very democratic process…)

As for US income I created a separate graphic with data points from the high end of the income spectrum (where the underlying Pareto distribution model is a good fit): The top 1% (who earn 18% of all income), top 0.1% (8%), and top 0.01% (3.5%).

GINI Index Contour Plot with high end US Income distribution data points

These 3 data points are taken from Timothy Noah’s “The United States of Inequality“, a 10-part article series on Slate, which in turn is based on data and research from 2008 by Emmanuel Saez and visualizations by Catherine Mulbrandon of This shows the 2008 US income inequality has a GINI Index of approximately 0.46, which is unusually high for a developed country. Income inequality has grown in the US since around 1970, and the above article series analyzes potential factors contributing to that – but that’s a topic for another post. In the spirit of visualizing data to create insight, I’ll just leave you with this link to the corresponding 10-part visual guide to inequality:

Postscript: In April 2012 I came across a nice interactive visualization on the DataBlick website created by Anya A’Hearn using Tableau. It shows the trends of US income inequality over the last 90 years with 7 different categories (Top x% shares) and makes a good showcase for the illustrative power of interactive graphics.


Posted by on September 2, 2011 in Financial, Industrial, Scientific, Socioeconomic


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Customer Profitability

Inequality is often at the root of structure and contrasts. Exposing inequality can often lead to insight. For example, take the well-known Pareto principle, which states that roughly 80% of the effects come from 20% of the causes (hence also referred to as the 80-20 rule).

From the above Wikipedia page on the Pareto principle, chapter on business:

The distribution shows up in several different aspects relevant to entrepreneurs and business managers. For example:
80% of your profits come from 20% of your customers
80% of your complaints come from 20% of your customers
80% of your profits come from 20% of the time you spend
80% of your sales come from 20% of your products
80% of your sales are made by 20% of your sales staff
Therefore, many businesses have an easy access to dramatic improvements in profitability by focusing on the most effective areas and eliminating, ignoring, automating, delegating or re-training the rest, as appropriate.

Visualization can be a powerful instrument for such analysis. For customer profitability, a graphical representation of this inequality is often used as a starting point for analysis. A commonly used visualization is the so-called Whale-Curve. I created a short, 4 min video recording of a dynamic Whale-Curve Demonstration:

In case you’re curious, the above demonstration uses an underlying model I created in Mathematica. You can dynamically interact with it yourself using the free CDF (Computable Document Format) Player:

I have provided it as a contribution to the Wolfram Demonstration project, so you can download it, and even look at the source code if you are a Mathematica user.

If you are interested in applying customer profitability analysis to your business, you may want to consider the company RapidBusinessModeling, which has an elaborate analysis approach starting with such Whale-Curves.

The underlying notion of Inequality is a fundamental concept. We will look at it in other contexts in a later post.


Posted by on August 18, 2011 in Financial, Industrial, Scientific


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StockTouch – interactive stock monitoring tool

Financial markets have always been an area of rapid innovation, with the evolution of graphical stock information being no exception. It looks like the famous stock-ticker could be replaced with the stock-toucher. A new iPad application by Visible Market Inc. provides an excellent example of the use of highly aggregated color graphics and touch-interaction. Here is the main UI showing 9 sectors and the 100 largest stocks (by market capitalization) in each sector:

Market Overview by Sector, 100 largest market cap companies per sector, color-coded heat-map of volume changes.

You can zoom in (expand- or tap-gesture), zoom out (pinch-gesture) to navigate between levels (market, sector, company) or use the auto-complete search-box for a list of company names matching the search string.

The 10*10 items can be organized either alphabetically or by market cap. Display is of Price or Volume changes between current values compared to a variable time-period (time-frame slider with values {1D, 1W, 1M, 3M, 6M, 1Y, 5Y}) at the company level and averages at the sector level.

From their website:

“Our vision for StockTouch is that it represents the first of a new genre of apps that look at the financial markets in new, powerful and useful ways. It is our belief that the act of touching and diving into data will change the way users engage with this data, and consequently translate it into information and knowledge.”

Price changes of 100 largest market cap companies by sector, Green-Red color-coded heat-map. Note market trends for three timeframes: Last month (green = advance), last week (mixed), last day (red = retreat).

The use of colors is particularly useful for Price changes: There is a heat map from light green (strong positive change) via darker tones (gray = neutral, no change) to light reds (strong negative change). This shows at a glance how the entire sector or market is doing. In the above example the last month saw a broad advance (majority of companies across all sectors in green); the last week more of a mixed bag, and the last day a broad retreat across the entire market (almost all red). Think about how much information is aggregated into this dashboard! 900 companies, grouped by sector, sorted by market cap, color-coded for price/volume change. No wonder they post a quote on their website:

“StockTouch tells you more in five seconds than you would learn reading financial news all day.”


Posted by on July 11, 2011 in Financial


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Branded Data Visualizations: LUMAscapes

In this article on the Spotfire Blog Amanda Brandon recently posed the question: Can Data Visualizations Change the Business Decision Game? The article recounts the creation of data visualizations by Terrence Kawaja to show the complex online advertising space with over 1200 companies involved in a $10b annual business. The graphics show the flow of information and involved service providers from advertiser to consumer. It is said that the original chart published in 2009 became a “go-to tool for advertising executives”.

Advertising Technology Landscape by Terrence Kawaja (2009)

Kawaja of investment firm LUMA Partners refined this approach and created six such landscapes called LUMAscapes for display, video, search, mobile, commerce, and social online advertising.

Search online advertising technology landscape (Source: Lumascapes from

The Spotfire Blog conlcudes with four takeaways for business analysts from the approach to use such visualizations:

Data visualizations are the ultimate content marketing. The simplification of complex data in a visually appealing format can take your information and brand viral. Giving away data on the major players and how they work together to drive an industry set the stage for authority and respect. …

Data visualizations can become an industry standard. Simply look at how Kawaja was able to help ad executives navigate the digital ad space.

Data visualizations can become a game-changer. Kawaja is branding these tools and using the graphics as a tool in generating business for his investment firm.

Data visualizations can be central to business decision-making. According to the WSJ, these new visualizations could enhance discussions at the Digital Media Summit, a meeting of top execs from the investment and Internet advertising space.

A picture can be worth more than a thousand words…

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Posted by on June 23, 2011 in Financial, Industrial


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Composite Graphs

Today’s edition of the Wall Street Journal features an article on the nation-wide decline of housing values across the US. There is a good example of a composite graph illustrating a lot of data at once:

From the chart legend:

“Charts show percentage change since 2000 in S&P/Case-Shiller national quarterly home-price index and in monthly indexes for U.S. metropolitan areas through March 2011.”

Think about the amount of data aggregated in these charts! The S&P Case-Shiller home price index is calculated monthly using a three-month moving average and published with a two month lag on the Standard & Poors website. Each of the 8 metropolitan indices shown on the right is composed of thousands of individual data points on changes in property values in the respective area. (Specifically, those data points are measured using the repeat sales technology, which uses sales pairs of two successive transactions for one property to calculate home-price changes.) Every month that data is aggregated to one new data point, some 120+ of which compose the graph over more than 10 years. That’s already more than 100.000 data points aggregated in each of the 8 charts on the right. Looking at the National average on the left – which is an aggregate of all the 20 metropolitan areas in the index – you are literally looking at an aggregate of millions of data points!

An interesting exercise is to google for images on the S&P Case-Shiller index. Here is a collection of the first of some 300.000+ results:

Image search results on indices are an excellent source of examples on how to aggregate numerical data graphically.

Addendum: Alex Kerin from Data Driven Consulting published this interactive chart of the Case-Shiller index using Tableau Public. It clearly shows how an interactive chart goes beyond static images in bringing data to live and telling the underlying story.


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Posted by on June 1, 2011 in Financial, Socioeconomic


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Evolution of Visual Presentations in Meetings

A few weeks ago I participated in a lunch-&-learn meeting sponsored by an investment firm. The focus was on a well-establish fund targeting high net-worth individuals and the underlying investment approach / philosophy. As sophisticated and successful as their investment strategy was, I was somewhat disappointed by the presentation. If ever there was a “death-by-PowerPoint”, this was it. Slides upon slides with numbers upon numbers… Yet as painful as it was to sit through, it struck me how the ability to use information during meetings has evolved to create insight.

Step 1: Printed Document – Color, Convenience

We used to work at meetings or conferences primarily with printed documents – books, brochures, white-papers – occasionally armed with a pocket calculator to check some facts or do some quick calculations. For the most part, we accepted the printed document as the most convenient, if static representation of the meeting subject. Here, everyone in the audience received some nice color handouts with the main information about the fund. There were some good charts in there, primarily the cumulative returns of the fund with its three different portfolios based on risk tolerance.

Step 2: Static Webpage – Access, Anytime

Then we got used to replacing static information on paper with web-sites online. As long as you are connected, you can bring it up in your browser. While not necessarily very good for reading, its consumption during meetings for quick lookup certainly adds flexibility. I was the only person in the audience with a computing device so I could go online and browse the fund’s website and double-check some background, facts and figures.

The fact that I used my new iPad 2 and its convenient form factor and touch-screen ease-of-use caused some ohhs and ahhs in my immediate vicinity, with several of the finance professionals mumbling that it’s time for them to get their own iPad. I agree, but I digress.

Using a computer also allows to create content during the meeting (for example draft meeting minutes or brainstorming topics) and present it to the audience. This works well during a workshop-type meeting with relatively few participants, and/or during a web-meeting with remote participants.

Step 3: Dynamic Content – Interactivity, Insight

The purpose of this meeting was to convey information, to build trust and to convince attendees of the value in investing with this particular company. For all these intents I posit that the attendee is best served with dynamic, more interactive media. You need to be able to browse, search, calculate, compare. When you can start asking your own questions and get specific answers, customized to your scenario, then you are most likely to remember the information and to get new insight.

Most meetings leverage printed documents. Some bring static online content into the mix. Few are starting to leverage interactive content during meetings. Like with eBooks, technology brings new capabilities to this space, for example the new Computable Document Format (CDF), which we will look at in another post.

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Posted by on May 31, 2011 in Financial


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