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  • Kyle Grevengoed

A Multi-Fractal Walk Down Wall Street


Summary


A Multi-Fractal Walk Down Wall Street is an article that appeared in the February 1999 issue of the “Scientific American.” The title is in reference to a book entitled, “A Random Walk Down Wall Street” by Burton G. Malkeil. If you are unfamiliar with this book it can be summed with a quick little journey.


Imagine yourself riding the scrambler at the fair or amusement park. You are sitting in a quickly rotating chair AND that chair is rotating around another axis. When you get off you are most certainly a little dizzy (and if you are like me, feeling sick, if not actually sick, for the rest of the day). Now imagine that in the state of dizziness you throw a dart at a wall covered in every stock you could possibly buy. This book, summed up, says you have an equal chance to make money as someone who researched all those stocks and carefully selected one.


As you might imagine this is a hotly debated subject, and “A Multi-Fractal Walk” counters this theory, saying you can use a form of technical analysis to predict the performance of an investment.


First, if you do not know what a fractal is, it is reductionism, or breaking down the whole into individual parts. The smaller parts are then evaluated to determine what the whole is likely to do. If you ever watch CNBC you have seen them show the performance of an investment over a set time period. Sometimes this time period is a few hours, sometimes it is many years. Either way this is a fractal.


The multi in multi-fractal is in reference to forecasting. The analyst will take the fractal and “squish” it so that the final return is the same, but the gains/losses occur faster. The analyst will also expand the fractal, slowing down the speed of the gains/losses. This gives the analyst multiple versions of the same pattern believed to occur in the market, of which the analyst can use to make a projection.


The essay argues that Modern Portfolio Theory (using historical averages to project future investment growth does not account for extreme movements in the market, such as the 2008 crash, and therefore your projections are likely to be inaccurate.


The author concludes the essay with some applications of multi-fractal use, stating the best way to project future returns is to use the actual historical returns, rather than an average return. Essentially, he promoted running a Monte Carlo simulation.


My Takeaway


Samuel Clemons (AKA Mark Twain) said, “History does not repeat itself, but it does rhyme.”


The human brain naturally seeks patterns. We want order and structure in our lives and we often find patterns and create explanations with little to no real basis for such claims. There are essays, blog posts, and books that tackle this research topic. Even the author of this article starts with a quote on this subject, “The geometry that describes the shape of coastlines and the patterns of galaxies also elucidates how stock prices soar and plummet.” The bulk of this theory is based upon looking for patterns in the market which is a manmade thing, constantly changing as new investment theories and approaches are designed. "Fooled By Randomness" by Nassim Taleb is an excellent book that demonstrated why the market is not a collection of predictable patterns.


One item that this idea is correct is that Modern Portfolio Theory does not always do a good job of considering pro-longed and large ups and downs.


For example, lets pretend it is the beginning of 2018 and you are evaluating investing in the S&P 500. You decide to use the period of 1998 to 2017 to estimate a projected return. If you average the returns you will project an average return each year for 20 years of 8.83% leading you to estimate a final value of $54,356.55.


If you instead use the actual returns for each year you would project a final value of $40,301.56. This $14,054.99-dollar projection difference is close enough that a quick average is enough for general planning, but large enough that you should probably get more detailed in your projections.


This whole thing may sound complex, that is why a Accredited Financial Counselor and Investment Advisor are important. The professional can do the complex work and give you a simple process.

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