On the lognormal distribution of stock market data

Box WashingtonDC In general, when we gather data, we expect to see a particular pattern to the data, called a normal distribution.

A normal distribution is one where the data is evenly distributed around the mean in a very regular way, which when plotted as a histogram will result in a bell curve.

If you plot that a set of data with a normal distribution on a graph, you get something that looks like a bell, with the hump of the bell positioned at the mean. I generated 1 million random numbers between 1 and 10; divided them into groups of ten; and then took the sum of each group of The height of each point in the graph at each x coordinate is the number of times the sum was was that number. The number of times that 55 occurred wasThe closer a value is the the mean, the more often it occurs in the population; the farther it is from the mean, the less often in occurs.

For example, the salary example from the mean, median, and mode post is also using this. The reason that the median is so different from the mean is because the distribution is severely skewed away from a normal distribution.

Remember, in a proper normal distribution, the number of values included at the same distance either side of the mean should be equal. For example, the last round of tax cuts put through by the Bush administration was very strongly biased towards wealthy people. But during the last presidential election, in speech after speech, ad after ad, we heard about how much the average American taxpayer saved as a result of the tax cuts.

For a different example, the high school that I went to in New Jersey was considered one of the best schools in the state for math. But the vast majority of the math teachers there were just horrible — they had three or four really great teachers, and a dozen jackasses who should never have been allowed in front of a classroom.

But the top performing math students in the school did so well that we significantly raised the mean for the school, making it look as the the typical student in the school was good at math.

Basics: Normal Distributions – Good Math, Bad Math

Income is one of those data points that follows a power law distribution i. Using a normal distribution to describe stock market returns are also problematic, as the tails tend to follow gets dividend call option ex-dividend date power law therefore having theoretically infinite variance so the stock options as collateral never quite quick way to get money in dragonvale to normal ala the central limit theorem.

The crash was a standard deviation event, which should only occur with the probability of 7. In regard to the Bush tax cuts they were a boon to the middle class and the very wealthy saw little benefit except for the reduction in cap gains rates because they tend to all be in AMT.

Reminds me of a binomial I think distribution trading binary options insurance number generator that someone told me about years ago.

If you have a uniform distribution random number generator that yields numbers between 0. The result will be a fast, pretty good, simulation of a normal distribution with a mean of 1.

He pretty convincingly demonstrates that markets do not follow a normal distribution. That means that events that, if we used a normal distribution, we would think would never occur, instead happen with surprising frequency.

The Mathematics of Money Management: Risk Analysis Techniques for Traders - Ralph Vince - Google Livres

Certain stock market crashes fall into that category. How many year floods did we have in a given area last century?

Remembered wrong — I should know better the algorithm above gives a mean of 0. Yes, the Mandelbrot book is excellent, if perhaps marred by some overzealous iconoclasm. I am not sure how useful his multi-fractal models are in pricing derivatives or other applications where lognormal distributions are used.

Levy Stable Distributions are a good compromise as they can handle skewness and fat tails.

The other easy excel cell function is normsinv rand. Depending on the depth of historical data used to make the estimate, the October 19,U. Financial markets, particularly derivatives markets, violate any number of assumptions routinely made in estimating market on the lognormal distribution of stock market data, including assumptions about distributional stationarity, temporal price independence, continuous price movement, and liquidity the assumption that there will be a willing buyer at some price.

To be blunt, anyone who depends on the usual sorts of statistical estimates of risk in the markets e. One of those critical assumptions is lack of history each event is independent of the previous event. One can get away with that, how is futures trading taxed, in the hard-physical sciences, but it is easy to forget that the violation of that is endemic elsewhere.

As Mandelbrot mentions in his book, most phenomenon of importance in the world is governed by power laws, not Gaussian bell curves. The financial markets are a good example of this.

I just used them as an example of how making an invalid assumption of normal distribution can be misleading. It is interesting to know why different distributions occur. I think I just realized that lognormal distributions independent factors contribute multiplicatively are situated between normal distributions independent factors contribute additively and power-law distributions factors contribute in many ways, on all scales. I have encountered lognormal distributions as describing some side effect growth process, for example size distributions of slag or bubble inclusions in melts.

Suits, between the simple and the complex. My understanding is that Lognormals i. Now these criteria would apply to anything with a growth rate over time as the basic process is geometric Brownian motion.

As someone brought up a method for simulating a normal distribution, one of the faster methods used nowadays is called the Monty Python method. English is a living language. To customize this sidebar, go add some!

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Chu-Carroll on January 15, Look up first, then then open mouth. Ahcuah wrote That means that events that, if we used a normal distribution, we would think would never occur, instead happen with surprising frequency. Search This Blog Search for: RSS2 Atom Subscribe via a feed reader. ScienceBlogs is a registered trademark of ScienceBlogs LLC.

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