EMH and FMH: Origin, Evolution and Tendency

This research paper delves into the application of chaos theory in finance, specifically focusing on the Fractal Market Hypothesis (FMH), within the evolving landscape of finance. It delves into the interconnectedness between seemingly unrelated events, referred as the butterfly effect, and how such interplays have significant repercussions on financial markets. Additionally, the research encompasses a case study of the 2008 financial crisis and the emergence of cryptocurrencies and their contemporary relevance within the framework of chaos theory and fractals. The study also includes the usage of fractal indicator along with a comparative analysis of the Efficient Market Hypothesis (EMH) and Fractal Market Hypothesis (FMH), shedding light on their respective strengths and limitations.

This chapter is a tutorial on portfolio risk management. It describes how to identify the primary sources of risk in complex portfolios—the “hot spots”—and how to identify the trades that will reduce those risks—the “hedges.” While this topic, identifying and reducing risk, would seem to be at the heart of risk management, many of the ideas presented here are not well-understood. Unfortunately, too much of the recent focus in risk management has been directed elsewhere—for example, toward under-standing and incorporating the risks of derivative securities. While derivtives can create complex and highly nonlinear payoffs, they are often not the primary source of risk in a portfolio. Also, while risk managers have focused much attention recently on developing firm wide systems to aggregate information from many traders or portfolio managers, they have generally not yet concentrated on how to use that information to obtain a comprehensive understanding of enterprise risk. More generally, while risk managers have also recently developed a greater appreciation of the statistical nature of risk and the need to use statistical measures such as value-at-risk (VaR)1 to quantify, monitor, and set limits on risk-taking activities, the tools required to understand and incorporate these statistical measures in portfolio risk management have lagged behind.2 This most important area of risk management—the development of portfolio analytics based on the statistical understanding of risk—has not received as much attention as it deserves. We hope this chapter helps to address this concern by describing a number of portfolio analysis tools that we have developed at Goldman Sachs in recent years to better understand, manage, and monitor the risks in our clients’ investment portfolios as well as our own trading positions. We focus on the concepts of risk management and how they apply in realistic trading and portfolio management contexts rather than on details of implementation.

Measuring the Degree of Financial Market Efficiency: An Essay

This paper provides a review of the Fractal Market Hypothesis (FMH) focusing on financial times series analysis. In order to put the FMH into a broader perspective, the Random Walk and Efficient Market Hypotheses are considered together with the basic principles of fractal geometry. After exploring the historical developments associated with different financial hypotheses, an overview of the basic mathematical modelling is provided. The principal goal of this paper is to consider the intrinsic scaling properties that are characteristic for each hypothesis. In regard to the FMH, it is explained why a financial time series can be taken to be characterised by a 1/t1−1/γ scaling law, where γ>0 is the Lévy index, which is able to quantify the likelihood of extreme changes in price differences occurring (or otherwise). In this context, the paper explores how the Lévy index, coupled with other metrics, such as the Lyapunov Exponent and the Volatility, can be combined to provide long-term forecasts. Using these forecasts as a quantification for risk assessment, short-term price predictions are considered using a machine learning approach to evolve a nonlinear formula that simulates price values. A short case study is presented which reports on the use of this approach to forecast Bitcoin exchange rate values.

A multi-agent deep reinforcement learning framework for algorithmic trading in financial markets

У статті розглянуто основні положення теорій динаміки ринків, зокрема, гіпотези ефективного ринку, гіпотези когерентного ринку, гіпотези фрактального ринку та гіпотези синергетичного ринку. Проаналізовано інструменти фрактального ринку для прийняття на їхній основі обґрунтованих інвестиційних рішень. Наведено та обґрунтовано інструменти технічного аналізу, заснованого на грі за трендом для прогнозування динаміки ринку, відповідно до гіпотези фрактального ринку, зокрема, хвильову модель Елліотта та застосування нейро-нечітких моделей.

Článek shrnuje teoretický koncept "Hypotéza Efektivního Trhu" a představuje nový koncept "Fraktální Hypotéza Akciového Trhu". Podle této hypotézy výnosy z akcií na trhu vykonávají zkreslenou náhodnou procházku, tzv. Hurstův persistentní proces, který je charakterizován svou dlouhou pamětí. Při ověření tohoto konceptu na českých indexech PX 50 byla provedena (R/S) analýza a byl vypočten Hurstův exponent. Ukazuje se, že výnosy z akciového indexu PX 50 vykonávají persistentní Hurstův proces s hodnotou Hurstova exponentu rovnající se 0,662. Tato hodnota je zcela odlišná od hodnoty pro náhodnou procházku a odpovídá výsledkům dosaženým v dřívějších pracích.

An empirical investigation on how portfolio risk management influences project portfolio success

The Indian commodity market is characterized by high volatility. When considering the agro-based commodity market, the prices may sometimes vary on a daily basis and regional basis. For the purpose of our research, we have restricted our region of study to the Indian national capital New Delhi. This paper aims to find out whether commodity markets follow a pattern with respect to prices, and if they do, then whether this could be determined by using basic fractal theory and determination of Hurst exponent. We have followed a suitable algorithm to find the Hurst exponent using statistical methods, specifically linear regression and time series analysis, wherein time is the independent variable and price of the commodity considered is dependent. The reason why time series analysis is chosen is because of the tendency of a time series to regress strongly to its mean. A statistical measure chosen to classify time series is the Hurst exponent. Initially, we have focused on onion prices for the years 2013 to 2017. The data set has been derived from the official website of the Consumer Affairs Department of the Government of India. The daily retail prices for Delhi for the month of June were observed and analyzed. We eventually aim to investigate if the market for onions has a long-term memory and will it be suitable to extend this conclusion to all other agro-based commodities. Our study has been motivated by the Fractal Market Hypothesis (FMH) that analyses the daily randomness of the market. We seek to find out whether the commodity market follows such a pattern provided that external factors remain constant. By external factors, we mean the variations that occur in the market with time, which include the demand, inflation, global price change, changes in the economy, etc. Keeping this in mind, we have attempted a time series analysis, using the monofractal analysis, at the end of which we would be estimating the Hurst exponent. The determination of Hurst exponent will help us to classify the time series as persistent or anti-persistent, i.e., how strong is the tendency of the time series to revert to its long-term mean value. Further, the multifractal analysis has been used to detect small as well as large fluctuations within the time series taken into consideration. This result would thus lead us to understand if prices in the commodity market could be remotely predicted, and what is the strength of the time series to return to its long-term mean value. Hence, this fractal analysis can be used to determine the characteristics of the prices in an agro-based economy.

Market inefficiency is a latent concept, and it is difficult to be measured by means of a single indicator. In this paper, following both the adaptive market hypothesis (AMH) and the fractal market hypothesis (FMH), we develop a new time‐varying measure of stock market inefficiency. The proposed measure, called composite efficiency index (CEI), is estimated as the synthesis of the most common efficiency measures such as the returns’ autocorrelation, liquidity, volatility, and a new measure based on the Hurst exponent, called the Hurst efficiency index (HEI). To empirically validate the indicator, we compare different European stock markets in terms of efficiency over time.

Green is the buzz word in the today's scientific arena. Saving energy, time, cost etc with increase in speed and ease of computation is the common goal for almost all computational scientists. As size of heterogeneous and unstructured data in the stock market continue to grow, a new technological framework for data base is always required. Forecasting methodologies for stock market requires a unique data set in which fractional values of prices has been either neglected or very less importance. Irrespective of the market hypothesis i.e. efficient market hypothesis (EMH), Fractal market hypothesis (FMH), Heterogeneous market hypothesis (HMH), Arbitrage pricing Theory (APT), Capital Asset Pricing Model (CAPM), etc used in the stock market, values required for forecasting and its respective tools is in the form of integers. This paper deals with integer value data set for the stock market and shows that how green it is without compromising the efficient forecasting methodologies.

This paper presents trend prediction results based on backtesting of the European Union Emissions Trading Scheme futures market. This is based on the Intercontinental Exchange from 2005 to 2019. An alternative trend prediction strategy is taken that is predicated on an application of the Fractal Market Hypothesis (FMH) in order to develop an indicator that is predictive of short term future behaviour. To achieve this, we consider that a change in the polarity of the Lyapunov-to-Volatility Ratio precedes an associated change in the trend of the European Union Allowances (EUAs) price signal. The application of the FMH in this case is demonstrated to provide a useful tool in order to assess the likelihood of the market becoming bear or bull dominant, thereby helping to inform carbon trading investment decisions. Under specific conditions, Evolutionary Computing methods are utilised in order to optimise specific trading execution points within a trend and improve the potential profitability of trading returns. Although the approach may well be of value for general energy commodity futures trading (and indeed the wider financial and commodity derivative markets), this paper presents the application of an investment indicator for EUA carbon futures risk modelling and investment trend analysis only.

The assessment and prediction of the impact of risks on the financial performance of portfolios is a very challenging task, and many portfolios in Qatar and worldwide are still suffering from cost overruns. This aspect is undeveloped in the body of literature on portfolio risk management, and very few studies have addressed this need. Therefore, organisations and portfolio managers are still looking for tools and techniques which enable them to incorporate the financial impacts of risks during the estimation of the cost and contract price of their portfolios. In this paper, a risk management-based methodology for the prediction of the cost and the financial performance of portfolios is presented and tested on real case studies based at Qatar Gas. The methodology is based on calculating the combined effect of multiple risks on the different work packages composing part the portfolio project, while considering the probabilistic occurrence of each risk. The methodology was tested on four projects in Qatar Gas and proved to be able to predict the effect of the identified risks on financial performance related to each portfolio. It also helped to prioritize the risks and identify the risks that most affected the financial performance of the portfolio and, thus, provide valuable information for particular stages of response planning. One of the limitations of the proposed methodology is that it calculates the impact of risks on the financial performance of a portfolio at a specific date, where risk impacts have a defined probabilistic distribution. However, the dynamic nature of risk attributes could be reflected by changing the values of those attributes in the risk management model of the portfolio every time the risk register is updated.

Understanding the dynamics of realized volatility is critical to effective investment management and portfolio risk management. Volatility measures can reach levels well above the median and are trending and mean reverting. Tradable volatility exposure is now available with VIX futures and exchange-traded products benchmarked to VIX futures indices. These tools are useful for modifying portfolio risk based on expected S&P 500 Index volatility rather than shifting fixed-income allocations.

A general, copula-based framework for measuring the dependence among financial time series is presented. Particular emphasis is placed on multivariate conditional Spearman's rho (MCS), a new measure of multivariate conditional dependence that describes the association between large or extreme negative returns—so-called tail dependence. We demonstrate that MCS has a number of advantages over conventional measures of tail dependence, both in theory and in practical applications. In the analysis of univariate financial series, data are filtered to remove temporal dependence as a matter of routine. We show that standard filtering procedures may strongly influence the conclusions drawn concerning tail dependence. We give empirical applications to two large data sets of high-frequency asset returns. Our results have immediate implications for portfolio risk management, derivative pricing and portfolio selection. In this context we address portfolio tail diversification and tail hedging. Amongst other aspects, it is shown that the proposed modeling framework improves the estimation of portfolio risk measures such as the value at risk.