Professional traders often speak of a “fast” market or a “slow” one, depending on how they judge the volatility at that moment. Black Swans are extremely unpredictable events that have massive impacts on human society. These include positive Black Swans, like the invention of the Internet and the discovery of antibiotics, as well as negative Black Swans, like the 2008 recession.

Book Summary: The Misbehavior of Markets by Benoit Mandelbrot and Richard L. Hudson

Financial markets can be represented by models that capture the system’s volatility across various scales, which are known as multifractal models.
The concept that financial markets exhibit complexities and behaviors similar to chaotic natural systems was initially introduced through Mandelbrot’s development of fractal finance.
It is not designed to meet your personal financial situation – we are not investment advisors nor do we give personalized investment advice.
As he did for the physical world in his classic The Fractal Geometry of Nature, Mandelbrot here uses fractal geometry to propose a new, more accurate way of describing market behavior.
Creating new mathematical tools is essential for uncovering the intrinsic inconsistencies found in real-world financial market data.
And now a practical point, which helps explain why this formula became so popular in the world of finance.

We discuss how multiplicative cascades and related multifractal ideas might be relevant to model the main statistical features of financial time series, in particular the intermit-tent, … A massive bestseller now in its 12th edition, Burton Malkiel’s A Random Walk Down Wall Street provides a comprehensive and entertaining introduction to the world of finance. Malkiel leverages his experience as an academic economist and former Wall Street portfolio manager to explain for the lay reader the intricacies of security analysis, asset valuation, and investment theory.

Financial theory, as experts like Markowitz have pointed out, is built on a foundation of assumptions that do not stand up to scrutiny. Employing the bell curve as a measure for stock-market risk is troublesome, as it presumes that such risk correlates with mild, autonomous, and gradually changing price fluctuations. The presumption that price movements are independent and conform to a typical distribution is especially significant, despite a wealth of evidence to the contrary. Abstract A market is said to be efficient with respect to an information set if the price ‘fully reflects’ that information set, ie if the price would be unaffected by revealing the information set to all market participants. The efficient market hypothesis (EMH) asserts that financial markets are efficient. On the one hand, the definitional ‘fully’is an exacting requirement, suggesting that no real market could ever be efficient, implying that the EMH is almost certainly false.

We study the multifractal nature of daily price and volatility returns of Latin-American stock markets employing the multifractal detrended fluctuation analysis. Comparing with the results obtained for a developed country (US) we conclude that the multifractality degree is higher for emerging markets. Moreover, we propose a stock market inefficiency ranking by considering the multifractality degree as a measure of inefficiency. Finally, we analyze the sources of multifractality quantifying the contributions of two factors, the long-range correlations of the time series and the broad fat-tail distributions. We find that the multifractal structure of Latin-American market indices can be mainly attributed to the latter.

Book SummaryThe Misbehavior of Markets, by Benoit B. Mandelbrot and Richard L. Hudson

The text argues that fractal models map pricing data more accurately than bell curve models, allowing for superior risk assessment and investment strategies. As the financial world recognizes the limitations of current methods, Mandelbrot’s fractal approach offers an alternative path toward market regulation and economic stability. The third chapter of The Misbehavior of Markets focuses on the unpredictable nature of markets. Mandelbrot and Hudson argue that markets are not always rational and can be influenced by a variety of factors, including emotions, rumors, and other external events. They provide examples of how market misbehavior can lead to crashes and other financial disasters. The fifth chapter of The Misbehavior of Markets explores the role of government in regulating financial markets.

Compiled from Buffett’s annual reports to Berkshire Hathaway shareholders, The Essays of Warren Buffett provides a glimpse into the mind of a man whose ideas contrast with those of the typical Wall Street mogul. His insights on investing are simple yet difficult to put into practice, while his thoughts on the culture of the wider business world shine a light on the values that shape modern finance. A new tool to measure, not how long, heavy, hot, or loud something is, but how convoluted and irregular it is. Large changes, of more than five standard deviations from the average, happened two thousand times more often than expected. Under Gaussian rules, you should have encountered such drama only once every seven thousand years; in fact, the data showed, it happened once every three or four years.

The paper explores the complexity and misinterpretations within financial market behavior, emphasizing the inadequacy of traditional models like the random-walk model. Through comparative analysis of price change charts, it highlights the erratic nature of actual market fluctuations versus theoretical projections. The author critiques existing models such as GARCH and advocates for multifractal models that better encapsulate market dynamics, illustrating with examples and referencing previous research that supports the use of these advanced analytical frameworks. The first chapter of The Misbehavior of Markets introduces the concept of fractal geometry and how it can be used to understand market behavior.

Financial markets exhibit complex patterns, suggesting flaws in mainstream economic models built on simplified assumptions.
This behavior of security returns contradicts the random walk hypothesis of efficient capital markets which assumes symmetric normality and finite variance.
Furthermore, because of our cognitive biases, we’re more vulnerable than ever to misunderstanding Black Swans and their impact.
They provide examples of how government regulation has failed in the past and suggest ways in which it could be improved.
We study the multifractal nature of daily price and volatility returns of Latin-American stock markets employing the multifractal detrended fluctuation analysis.
From 495 calculations for a thirty-stock portfolio with Markowitz and portfolio theory, you simplify to thirty-one with Sharpe and the Capital Asset Pricing Model, as it came to be called.

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We also classify financial markets of different countries by the level of their efficiency and reaffirm that financial markets of developed countries are more efficient than the developing ones. Based on Ukrainian financial market analysis we show the reasons of inefficiency of financial markets and provide some recommendations on their solution and thus improving the efficiency. Mandelbrot’s innovative use of geometric techniques, which involve fractals and multifractals, has significantly deepened our understanding of the complex characteristics of financial markets. Creating new mathematical tools is essential for uncovering the intrinsic inconsistencies found in real-world financial market data.

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Furthermore, because of our cognitive biases, we’re more vulnerable than ever to misunderstanding Black Swans and their impact. The theory’s supplementary fundamental premises, particularly the notion that the likelihood distribution of price fluctuations remains constant over time, have been repeatedly proven to be inaccurate. Price changes don’t typically follow the expected normal distribution with most being minute and few large; they are, in reality, far less predictable. Modern finance theory, praised for transforming investing into a scientific discipline, encounters substantial challenges because it is based on flawed assumptions and struggles to predict market movements with precision. Warren Buffett is the world’s most successful investor, but he also thinks of himself as a teacher in the field of investing and economics.

The Misbehavior of Markets

Seeing nature through the lens of probability theory is what mathematicians call the stochastic view. The word comes from the Greek stochastes, a diviner, which in turn comes from stokhos, a pointed stake used as a target by archers. We cannot follow the path of every molecule in a gas; but we can work out its average energy and probable behavior, and thereby design a very useful pipeline to transport natural gas across a the misbehavior of markets continent to fuel a city of millions. This study analyses the multifractal properties of the most prominent oil-related derivative which is ‘‘WTI’’ since the West Texas Intermediate grade of crude oil for delivery at Cushing, Oklahoma. To be able to test multifractality of the WTI prices, we used two different methodologies which are multifractal detrended fluctuation analysis (MF – DFA) and wavelet transform modulus maxima (WTMM).

very fascinating, but hard to apply

The concept that financial markets exhibit complexities and behaviors similar to chaotic natural systems was initially introduced through Mandelbrot’s development of fractal finance. Mandelbrot’s theory, which incorporates elements of fractal geometry, has shifted the perspective from a firm belief in entirely rational and orderly markets to a recognition of their unpredictable and volatile nature. This paper presents a basic theory of intelligent¯nance as a new paradigm of¯nancial investment. In stock markets, the theory exhibits itself in the form of an Intelligent Dynamic Portfolio Theory, which integrates predictive modeling of a bullbear market cycle, sector rotation, and portfolio optimization with a reactive trend following trading strategy.

Discontinuity, far from being an anomaly best ignored, is an essential ingredient of markets that helps set finance apart from the natural sciences. This sounds sort of weird, but the history of early financial and economic theory is closely tied in with physics. Black Swans compel people to explain why they happened—to show, after the fact, that they were indeed predictable. Taleb’s thesis, however, is that Black Swans, by their very nature, are always unpredictable.

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He also offers a wealth of practical investment principles that will be useful for novice and seasoned investors alike. And now a practical point, which helps explain why this formula became so popular in the world of finance. It takes all of Markowitz’s tedious portfolio calculations and reduces them to just a few. Work up a forecast for the market overall, and then estimate the β for each stock you want to consider. From 495 calculations for a thirty-stock portfolio with Markowitz and portfolio theory, you simplify to thirty-one with Sharpe and the Capital Asset Pricing Model, as it came to be called. The fact that one particle in physics does something doesn’t increase or decrease the likelihood that another particle will.