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2013 | OriginalPaper | Chapter

5. Trading Multifractal Markets

Author : Yasmine Hayek Kobeissi

Published in: Multifractal Financial Markets

Publisher: Springer New York

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Abstract

Each market phase has its trading opportunities. A dynamic management approach for trading in multifractal financial markets is introduced in this chapter to allow us to profit from a market’s characteristics. An offensive approach is presented based on the notion of diversification at the strategy level between directional and volatility strategies; and of a macro-design approach. Tools such as cyclical and psychological analysis, fundamental convergent analysis, and the estimation of risks, allow us to evaluate the market biases in order to establish an accurate estimation of the prevailing state of the system and the risk toward which it is heading. Once markets’ characteristics are grasped, risk forecasting models can be enhanced. Models can be built on the basis of multifractal markets but are not limited to using only fractal tools such as, for example, the Hurst exponent. In fact, fractal thinking allows us to discern the most appropriate way of developing models. Be it technical analysis, behavioral finance, cycle analysis, power laws, thermodynamic, and econophysics, etc.…all of these are useful as long as we know how to implement them in our models while remaining aware of their limits. A strategic investment decision must not only be based on the best information available, but also on the possibility of error in the systems of calculation and the development of management strategies. The art of successful tail risk management lies in the ability to hedge against sudden market drifts or any specific micro market risk as well as against long periods of low volatility; and to “time” the volatility to profit from its clustering behavior without having to rely on seismic events to gain profits. That said; total hedging is not possible in absolute terms and if so it does not work at all time. It is important to think in terms of affordable risks before thinking of potential gains. The chapter includes a discussion of recent developments in the various techniques in forecasting risk highlighting their advantages, applications, and limitations.

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previous chapter Macrostates Indicators

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The standard portfolio management types are: conservative, balanced, growth-oriented/dynamic, and aggressive.

Appendix B Equities valuation: FCV.

The sensitivity of a position to the variation of a risk factor measures the power of the risk factor. Here, we list some capital asset pricing model (CAPM) derivatives whose relevance is very limited and should be cautiously used when assessing risk. The beta (β) is the sensitivity coefficient of a stock with respect to its reference index. In mathematical terms, β is the slope of the curve that results from the linear regression between price and market yield, for a given period of time: $ {\text{dV}}\,{ = }\,\alpha + \beta {\text{I}}\,{ + }\,\varepsilon ,\,\beta \, = \,{\text{dV/dI,}} $ where ε is the specific risk and β the systemic risk. As for bonds, duration measures the sensitivity of a bond’s market price to yield variations. Convexity, on the other hand, is a measure of the sensitivity of the duration of a bond to changes in yield. We have to assess as well the sensitivity of options in relation to various factors: Delta measures an option’s sensitivity to changes in the price of the underlying asset; Gamma measures the Delta’s sensitivity to changes in the price of the underlying asset; Vega measures an option’s sensitivity to changes in the volatility of the underlying asset; Theta measures an option’s sensitivity to time decay; and Rho measures an option’s sensitivity to changes in the risk-free interest rate.

Martin Neil Professor of Computer Science and Statistics and Norman Fenton Professor of Risk and Information management, School of Electronic Engineering and Computer Science, Queen Mary University of London. Their book "Risk Assessment and Decision Analysis with Bayesian Networks", 2012, Taylor and Francis Group is much more of a “how–to” guide using existing Bayesian technology.

The Financial Services Authority (FSA) introduced the reverse stress test on December 2008. An underlying aim of this test requirement is to ensure that a firm could survive long enough after risks have formed either to restructure a business, or to transfer a business.

See Harrington, Weiss and Bhaktavatsalam (2010) for more details.

See Jones (2009) for more details.

According to Smith (2009), to compute the probability of a specific event, a predictive distribution may be much more meaningful than a posterior or likelihood-based interval for some parameter. Bayesian methods are used as a device for taking account of model uncertainty in extreme risk calculations. Only a Bayesian approach adequately provides an operational solution to the problem of calculating predictive distributions rather than inference for unknown parameters in the presence of unknown parameters (Smith 1998).

In 2011, for instance, factors such as the aging population and the ever-changing opportunities and innovations in health care technology influence the identification of promising health care stocks.

The price of price of equity is a function of the actualized forecast revenues and the yields corresponding to the investor’s investment horizon

$$ {\text{V}}_{ 0} = \sum\nolimits_{i = 1} {\frac{{{\text{D}}_{\text{i}} }}{{(1 + {\text{t}})^{\text{i}} }} + \frac{{{\text{V}}_{\text{n}} }}{{(1 + {\text{t}})^{\text{n}} }}} $$

where V₀ is the value of the share on the starting date;

D_i is dividend to be received in year i, with i varying from 1 to n;

V_n is the expected value of the share in year n; and t is the rate of discount.

An investor decides to buy a stock based on whether the market price is less than or equal to V₀.

The adjusted price earnings ratio (aPER): The most common method for measuring the difference between the fundamental and market values is to calculate the fundamental PER and to compare it to the equity market PER. Another method involves comparing the equity market PER to its peer group. In using either of these methods, note that the ratios are influenced by:(1) the phase of the economic cycle: e.g. it is completely normal that the PER increases in a growth environment; (2) the quality of management, position of the company in its industry and its long-term potential; (3) interest rates; and (4)Speculation or rumors surrounding the company affect its price premium

The self-financing ratio: The PER for some sectors including the media, pharmaceutical and technology sectors cannot be assessed accurately because companies in these sectors invest heavily in research and development and have significant financial needs. As such, it is preferable to base our analysis on the self-financing ratio

Dividends: Companies who get most of their yields from dividends are more sensitive to a change in interest rates than others. In order to keep attracting investors, these companies, well-established and mature, offer high dividends in order to compete with certificates of deposit. This method, however, is criticized because it can be sometimes difficult to identify a specific sector of activity for a given company. The peer group is not always easy to establish and if improperly identified, can lead to false market conclusions. Also, difficulties can arise given the weakness of all statistical and historical approaches and the fact that ratios are static. Take for example the crash of 1990. In How Can You Tell a Bear Market Is Over by Birinyini Associates, several indicators including the PER ratio, dividend yields and short and long term treasury bonds, were analyzed in order to identify those which could have detected the floor for the S&P 500 crash in October 1990. The three-month treasury bonds signaled to purchase on 10 May 1991. The long-term treasury bonds, gave the same signal in March 1993. Neither the PER nor the dividend yields gave such signals regarding the end of the bear market in early 1990.

This is the equivalent of a Richter scale in geology for financial markets. The list of scaling laws is on page 11 of Dupuis & Olsen paper.

These are either local minima where the share price falls before starting to rise again (also known as an “uptrend”) or local maxima where the price peaks before falling (a “downtrend”).

We analyze the most traded 531 stocks in U.S. markets during the 2 year period of 2001–2002 at the 1 min time resolution.

Title: Trading Multifractal Markets
Author: Yasmine Hayek Kobeissi
Publisher: Springer New York
Book: Multifractal Financial Markets
Print ISBN: 978-1-4614-4489-3

Electronic ISBN: 978-1-4614-4490-9

Copyright Year: 2013
DOI: https://doi.org/10.1007/978-1-4614-4490-9_5