 In this video, I will challenge your scientific knowledge, your beliefs and your understanding of financial markets as a whole. I will demonstrate a total invalidity of the efficient market hypothesis and state the beginning of a new era of quantitative finance research, namely financial chaos originating from evolutionary finance, nonlinear dynamics and econophysics. Please note that this will be the introduction to an upcoming subsequent video series, so do not fret if you cannot follow every insight. The video is structured as follows. First, the efficient market hypothesis or EMH in short will be recapitulated briefly. Second, I will propose the reasons for the total invalidity of the EMH. Third, I will give an overview of the subsequent video series, in which I will elaborate on the stated reasons in much more detail. Finally, I will grant concluding remarks for this video. All scientific references are given in the caption of this video, as always. The EMH originally stated by Fama, which builds upon the insights of Bachelier, requires to fulfill two major presuppositions. First, price changes reflect all available information, thus the price alterations or price movements are only determined by novel information becoming available. This implies the premised absence of autocorrelation within market returns, or to put it differently, the missing temporal interconnection of subsequent market price evolutions. Further, this indicates that whatever has happened yesterday does not yield any impact on today's price formation process, since no correlation between the timely developments of returns is assumed. To put it drastically, yesterday's crisis has no impact on today's prices. Second, the referring returns are following a Gaussian or normal distribution with a bell shape, indicating symmetric mean-centration with no fat tails, which means no higher probability of extreme events such as financial crisis as well as low outlier probability at the same time. Further, no differences between positive and negative return distribution is made. In conclusion, the EMH proposition is best modeled quantitatively via standardized stochastic processes such as a Wiener process or Brownian motion in continuous time, random walks in discrete time, or martingales. Due to major past critiques, the assumptions have been loosened into several weaker forms of the EMH. Said weakened assumptions are best fulfilled by the Markovian presuppositions. This means being quantitatively displayable via discrete Markov chains or continuous Markov processes. So, what does the EMH imply? Or what does it mean anyway? Under the assumption of the validity of the EMH, trend analysis or technical analysis, such as conducted by chartists or many day traders, are not capable of creating additional information, which can potentially be exploited to predict the future price evolutions of financial instruments such as stocks. To phrase it differently, it is neither possible to beat the market nor to generate outperformance displayable via positive alphas. Building upon the lack of positive alpha generation possibility, meaning the impossibility to outperform or beat the markets, active investment styles are inferior to passive index investments. This is reasoned by the impossibility to outperform the markets, which means generating alphas and the subsequent lack of market timing possibilities. Please note that I will neglect the discussion about active managers yielding worse performance after costs than passive index funds. This is not the point, since some, not all, managers before costs are indeed capable to generate better than market returns. Yet, this is not the discussion topic and unrelated with the EMH. In short, EMH validity means no market outperformance, no alphas, no beating the markets, inferiority of active investment styles and avoidance of trend and technical analysis, which then are basically useless. As you may have already suggested, the validity of the EMH seems somewhat spurious and neither does it seem realistic nor does it just feel intuitively right. But are there profound facts, academic insights or practical experiments which could sustain the bold claim of total EMH in validity? Yes, those exist since decades, even if some professors, researchers or even practitioners persistently neglect to accept this new reality. As of now, I will be the avocados diabolii and I will structurally dismantle those rigid, old and overhauled beliefs and present you the latest insights taken out of quantitative research incorporating scientific facts and implications taken out of a multitude of fields such as non-linear dynamics, quantitative finance, evolutionary finance, econophysics or behavioral finance. It is my declared goal to present you with the current state of the art and work against teachings which not in the least aim towards the current reality of financial markets, be it real trading or academic pursuits. As indicated above, the critiques of the EMH stem from several scientific domains – mayorly, behavioral finance, applied mathematics and empirical experiments. This displays our reality overall, ranging from the human behavior over mathematical theoretical insights to practical, empirical, real market experiments and insights. The total invalidity of the EMH renders itself visible in all levels of reality in terms of financial markets, from active traders to academic insights. My display of the invalidity of the EMH will be non-exhaustive, which means that there are many more insights to be taken into account besides the one I will elucidate for you in this video. The first aspect is represented by empirical observations or stylized facts observed on the markets. The second aspect is taken out of non-linear dynamics, chaos theory and fractals, displaying financial market structure in a whole new perspective. This is quite contrary to the perception in classical financial theory and its believers' viewpoints. Third, seen as a stylized fact, yet bearing prominence is the existence of momentum effects, which means winners will win and losers will lose, stating the timely interconnection of returns, scaling, trending as well as the possibility to beat the markets. Finally, I will talk about human behavior and insights taken out of behavioral finance and psychology. Since this video is just high level, a brief overview of stylized empirical facts is shown. These stylized facts are observed, empirical characteristics or financial market data and are all well-documented in current financial and quantitative literature. The most dominant ones are, for example, volatility dynamics, volatility clusters, non-linearity, asymmetry, scaling, trending, momentum, heterogeneity of investor expectations on different timescales as well as multi-fractality, among others, which may lead to massive financial crisis triggered by their interplay. Yes, the interconnection and cause and effect relations of those stylized facts, among others, are prone to be responsible for the building of bubbles, meltdowns and crashes on financial markets. If you are an EMH believer, these are all labeled as anomalies, which indicate being outliers. Outliers are to be neglected since these are spars and do not follow fixed rules and do not occur frequently. Nonetheless, there exist overwhelming empirical evidences in scientific literature claiming otherwise, namely, these outliers to be fully structured and naturally inherent in financial markets thus not to be disregarded as outliers. Sorry, EMH friends, fun fact on the side, according to the EMH, a financial crisis is such a scarce event that it levels even with the probability of a meteor hitting earth, since the returns are assumed Gaussian and outliers, therefore not very likely. Nonetheless, every millennial can count a number of financial meltdowns of the past two decades and compare the number of occurrences with the number of deadly meteors that have hit earth. I guess you see the indicated pattern. Since I can count way too many meltdowns and still no meteor inside. To get into the latest scientific insights taken out of non-linear dynamics and chaos theory, I will present you some excerpts taken out of my current VHD ceases, which will soon be completed and be published. What you can see here is a multi-fractal spectrum, displaying the fractal growth or scaling coefficients on a log-log plot. Note that black lines indicate the local maximum and minimum Hearst exponents. We will elaborate on Hearst exponents later in the video. To display the multi-fractal characteristics graphically, I implemented a multi-fractal detrendent fluctuation analysis or MFDFA in short in Python and applied it to the SMP500 cascadic wavelet-filtered, so denoised return series. What you see is the existence of multi-fractal building laws within SMP500 return time series, which has nothing at all to do with gaussianity and standardized stochastic processes indicated by the EMH. A multi-fractal spectrum has vast indications on the time series under analysis, which I will demonstrate on the next slide in more detail, so please just stick with me a little longer. Furthermore, it is possible to calculate complementary cumulative distribution functions or CCDFs in short and compare those with several theoretical distributional fits via coherence tests and via log-log plots. The straight line represents a theoretical power law distribution, while the CCDF displays the distributional empirical insights taken out of the SMP500 return series. Finally, the coherence test can be applied to verify the graphical insights, hence yield an insight into the least worst fit of distributions. Nevertheless, coherence tests are no goodness of fit, but just a comparison measure, so be aware when you implement them. What you see in the graph is that A. The SMP500 returns follow a power law and B. The power law exhibits fat tails. Referring back to the MFDFA spectrum, there exist two rationales for multi-fractality occurrences. One, the existence of fat-tailed probability distributions, as we can see in the graph, and two, nonlinear temporal correlations. Before bringing all insights together, I quickly will demonstrate the chaotic or strange or fractal attractor of the financial SMP500 system. This states chaotic evolutionary dynamics and has nothing to do with the Markovian stochastic processes implemented by the weak form of EMH assumption. Yet, what have multi-fractal spectrums, power law and chaotic attractors in common? How are they interrelated? In short, a dissipative or chaotic dynamical system will reveal its phase space over timely evolution to deflate onto its own strange attractor, which is characterized via a fractal set. Generally, a fractal set yields a non-integer, non-Euclidean dimension, namely, most commonly applied the Hausdorff-Besykovich dimension, and is further characterized via self-similarity, which means multi-scaling, in addition to irregularities, nondifferentiability and recursiveness. Henceforth, a multi-fractal or fractal system requires a local power law contributing to the mentioned scaling properties. Therefore, a power law is defined as a scalar relationship between two quantities and thus is characterized via scale invariance. A fractal system with one scaling exponent is labeled monothructal, yet multi-fractal systems require a singularity spectrum of exponents, which we saw in the MFDFA spectrum graphic, referring back to a dissipative dynamical system, which deflates onto its strange attractor, thus is represented by fractal sets. The fractal set of a strange attractor is rendered visible via its Poincaré section, which show intersections of set's strange attractor. To be more detailed, the intersections of strange attractors are fractal sets, which are described via multi-scaling and thus via power laws. This means the strange attractor of the S&P 500 returns you see here incorporates multi-fractality, scaling and chaotic dynamics in one graph, fully rejecting classical financial thinking and building upon the dynamical timely evolution of the system, which in our case is the elaboration on the underlying empirical data-generating process of the S&P 500 index. Note that I will provide you with another detailed video on the topic. To continue, we will relate the stated multi-fractal scaling with the practical world through the concept and practically conducted momentum effect or momentum trading in short. Thus first, the Hearst exponent needs to be explicated. In controversy with Mandelbrot's opinion of Hearst exponent's measuring long memory effect, it has been shown via experiments that the Hearst exponent measures the existence of fractal trends, thus is applicable to test the existence of trending and therefore of momentum in financial markets. Furthermore, in one of my papers, I applied rolling window Hearst exponents to check the latest and last straw of saving the EMH, namely time-varying market efficiency assumption. With those rolling windows, we can directly check the existence of momentum and subsequently the occurrence of momentum crashes as well as the validity of the EMH. So how does the Hearst exponent work? If the exponent is exactly 0.5, the underlying time series is a stochastic process, thus the EMH is valid. If the exponent is less than 0.5, the underlying time series indicates mean reversion, which means a smooth mean with high frequency components. Finally, if the exponent exceeds 0.5, it indicates persistent fractal trends leading to the momentum effect. Taken out of the paper of Bercorn et al. 2018, the Bloomberg World Index X-Gina is displayed. For each financial instrument component, the Hearst exponent minus 0.5 is displayed. Should all stocks ETC follow the EMH, the Hearst exponent should be very close or equal to 0.5. Hence, the differences should be minor or inexistent. This is indicated by the red bar I inserted for you. EMH is valid if Hearst exponent minus 0.5 lies on the red line. As you can see, almost all titles reveal large positive divergence from the EMH, indicating fractal trends, thus momentum, and no pure stochastic process. Stating the existence of persistent fractal trends, thus momentum, clearly indicates the possibility of outperformance beating the markets and generating positive alphas. If you are an EMH believer, you may think okay, theoretically potentially worth a thought yet practically irrelevant. Wrong. You want to see outperformance? Here you have outperformance. Taken out of Bercorn et al. 2019, state the outperformance of the market based upon a momentum trading strategy, which more than clearly shows that A, it is possible to beat the market, B, positive alphas can be generated and C, momentum is not only an outlier, yet an underlying building block of the empirical data generating process of financial returns. If the EMH should be valid, those returns should not exist at all, yet here they are. As implied before, I calculated rolling window Hearst exponents, thus building upon an existing research stream of iconophysical papers, a smaller window indicates longer time scales and vice versa. In the upper left, you see the return data of the S&P 500 returns and in orange the filtration via cascadic wavelet filter banks. In the upper right, you can see the long-term behavior of the S&P 500 underlying data generating process represented by the Hearst 100 window. The Hearst 100 is quite hard to work with, thus I will only focus on the mid- and short-term insights stated at the bottom. What is a momentum crash? A momentum crash is the aim to follow trends in the absence of trends to follow, which leads to massive drawdowns in this respective strategy. Please take a look at the Hearst 1000 in the bottom left. The rolling window Hearst exponents indicate that the strength of fractal trends and the underlying evolutionary nature of the S&P 500 itself is time-varying. Further, during crisis and meltdown periods such as 2001.com, 2008 big financial crisis and the Covid pandemic and so on, the building mechanics switch from strong momentum into mean reversion, which will blow up every trend following system and leading to momentum crashes. Why? Try to follow high-frequently shifting components instead of persistent trends with an automated trend following system. You will fail miserably. Finally, regarding the Hearst 2500 as well as other Hearst scales, the red lines indicate the validity of the EMH, only and only if the Hearst exponents level closely or equally to 0.5 and the red line, the EMH holds, which they never do. During non-crisis periods, major fractal and persistent trends generate the momentum effect, which can be followed. During meltdowns, the market alters its total behavior and displays mean reversion, which leads to momentum crashes. Unfortunately, those shifts occur mostly during recessions and meltdowns, leading to vast negative impacts and drawdowns in performance. Nonetheless, as introductory indicated, I am not yet sure whether the shift is due to the crisis or is causing the crisis. To conclude, EMH is fantasy and does not, in the least, reflect the reality of financial markets which can be directly seen in the graphs. Finally, similar to the stylized facts, I present you with a non-exhaustive overview of behavioral human biases taken out of behavioral finance and psychological research. The EMH believer, or classical finance researcher, believes in rational investors in order for their models to work. Unfortunately, and very surprisingly for many, sarcasm intended, humans are not rational and are prone to many cognitive biases such as overconfidence, cognitive dissonance, heterogeneity of expectations on different timescales among others. All those effects are given in a human-made, interacting system of humans such as financial markets. No rationality in sight, taken together all stylized facts, chaotic dynamics and human biases form the empirical building blocks of the data-generating process of market returns. All at once, at different timescales simultaneously. No efficiency, no rationality, just complexity. Since this video is overloaded with various scientific information which many of you are probably not familiar with in detail, this shall denote the start of a subsequent video series. I will present three subsequent videos, elucidating every major aspect in more detail. The first video will elaborate on stylized facts, a second on chaos and fractals, and a third video on momentum trading and behavioral biases. This will allow me to present you more underlying details and respect the fact that many of you surely aim for more in-depth explanations. To conclude and to summarize, stylized facts exist are not only ignorable outliers and are based upon a vast, well-documented scientific literature. Chaotic dynamics, multi-fractality and strange attractors exist in financial systems, rendering long-term predictions impossible due to exponentially growing error terms and are potentially the cause of meltdowns, crises, bubbles or crashes. Time-varying Hearst exponents allow for the direct determination of fractal trending, which means momentum effect, and the possibility to elucidate the EMH validity directly. Note that the Hearst exponents are all testable for significance, and for the presented series all of those exponents are significant. The existence of fractal trends and momentum allows the generation of positive alpha returns in combination with potential market neutral positioning. This allows for outperformance with, at the same time, lower risk than just buy-and-hold passive investment. Finally, rationality is not given in human investors. In combination, this only leads to one logical conclusion. The EMH, the Efficient Market Hypothesis, does not exist and is invalid in its totality. Thank you for watching. Please subscribe and let me know in the comments if you want to see more content like this.