Stochastic modelling of financial time series with memory and multifractal scaling

Financial processes may possess long memory and their probability densities may display heavy tails. Many models have been developed to deal with this tail behaviour, which reflects the jumps in the sample paths. On the other hand, the presence of long memory, which contradicts the efficient market hypothesis, is still an issue for further debates. These difficulties present challenges with the problems of memory detection and modelling the co-presence of long memory and heavy tails. This PhD project aims to respond to these challenges. The first part aims to detect memory in a large number of financial time series on stock prices and exchange rates using their scaling properties. Since financial time series often exhibit stochastic trends, a common form of nonstationarity, strong trends in the data can lead to false detection of memory. We will take advantage of a technique known as multifractal detrended fluctuation analysis (MF-DFA) that can systematically eliminate trends of different orders. This method is based on the identification of scaling of the q-th-order moments and is a generalisation of the standard detrended fluctuation analysis (DFA) which uses only the second moment; that is, q = 2. We also consider the rescaled range R/S analysis and the periodogram method to detect memory in financial time series and compare their results with the MF-DFA. An interesting finding is that short memory is detected for stock prices of the American Stock Exchange (AMEX) and long memory is found present in the time series of two exchange rates, namely the French franc and the Deutsche mark. Electricity price series of the five states of Australia are also found to possess long memory. For these electricity price series, heavy tails are also pronounced in their probability densities. The second part of the thesis develops models to represent short-memory and longmemory financial processes as detected in Part I. These models take the form of continuous-time AR(∞) -type equations whose kernel is the Laplace transform of a finite Borel measure. By imposing appropriate conditions on this measure, short memory or long memory in the dynamics of the solution will result. A specific form of the models, which has a good MA(∞) -type representation, is presented for the short memory case. Parameter estimation of this type of models is performed via least squares, and the models are applied to the stock prices in the AMEX, which have been established in Part I to possess short memory. By selecting the kernel in the continuous-time AR(∞) -type equations to have the form of Riemann-Liouville fractional derivative, we obtain a fractional stochastic differential equation driven by Brownian motion. This type of equations is used to represent financial processes with long memory, whose dynamics is described by the fractional derivative in the equation. These models are estimated via quasi-likelihood, namely via a continuoustime version of the Gauss-Whittle method. The models are applied to the exchange rates and the electricity prices of Part I with the aim of confirming their possible long-range dependence established by MF-DFA. The third part of the thesis provides an application of the results established in Parts I and II to characterise and classify financial markets. We will pay attention to the New York Stock Exchange (NYSE), the American Stock Exchange (AMEX), the NASDAQ Stock Exchange (NASDAQ) and the Toronto Stock Exchange (TSX). The parameters from MF-DFA and those of the short-memory AR(∞) -type models will be employed in this classification. We propose the Fisher discriminant algorithm to find a classifier in the two and three-dimensional spaces of data sets and then provide cross-validation to verify discriminant accuracies. This classification is useful for understanding and predicting the behaviour of different processes within the same market. The fourth part of the thesis investigates the heavy-tailed behaviour of financial processes which may also possess long memory. We consider fractional stochastic differential equations driven by stable noise to model financial processes such as electricity prices. The long memory of electricity prices is represented by a fractional derivative, while the stable noise input models their non-Gaussianity via the tails of their probability density. A method using the empirical densities and MF-DFA will be provided to estimate all the parameters of the model and simulate sample paths of the equation. The method is then applied to analyse daily spot prices for five states of Australia. Comparison with the results obtained from the R/S analysis, periodogram method and MF-DFA are provided. The results from fractional SDEs agree with those from MF-DFA, which are based on multifractal scaling, while those from the periodograms, which are based on the second order, seem to underestimate the long memory dynamics of the process. This highlights the need and usefulness of fractal methods in modelling non-Gaussian financial processes with long memory.

A note on trader Sharpe Ratios

Traders in the financial world are assessed by the amount of money they make and, increasingly, by the amount of money they make per unit of risk taken, a measure known as the Sharpe Ratio. Little is known about the average Sharpe Ratio among traders, but the Efficient Market Hypothesis suggests that traders, like asset managers, should not outperform the broad market. Here we report the findings of a study conducted in the City of London which shows that a population of experienced traders attain Sharpe Ratios significantly higher than the broad market. To explain this anomaly we examine a surrogate marker of prenatal androgen exposure, the second-to-fourth finger length ratio (2D:4D), which has previously been identified as predicting a trader's long term profitability. We find that it predicts the amount of risk taken by traders but not their Sharpe Ratios. We do, however, find that the traders' Sharpe Ratios increase markedly with the number of years they have traded, a result suggesting that learning plays a role in increasing the returns of traders. Our findings present anomalous data for the Efficient Markets Hypothesis.

Principles of investments

"Emphasises asset allocation while presenting the practical applications of investment theory. The authors concentrate on the intuition and insights that will be useful to students throughout their careers as new ideas and challenges emerge from the financial marketplace. It provides a good foundation to understand the basic types of securities and financial markets as well as how trading in those markets is conducted. The Portfolio Management section is discussed towards the end of the course and supported by a web-based portfolio simulation with a hypothetical $100,000 brokerage account to buy and sell stocks and mutual funds. Students get a chance to use real data found in the Wall Street Survivor simulation in conjunction with the chapters on investments. This site is powered by StockTrak, the leading provider of investment simulation services to the academic community. Principles of Investments includes increased attention to changes in market structure and trading technology. The theory is supported by a wide range of exercises, worksheets and problems."--publisher website Contents: Investments: background and issues -- Asset classes and financial markets -- Securities markets -- Managed funds and investment management -- Risk and return: past and prologue -- Efficient diversification -- Capital asset pricing and arbitrage pricing theory -- The efficient market hypothesis -- Bond prices and yields -- Managing bond portfolios -- Equity valuation -- Macroeconomic and industry analysis -- Financial statement analysis -- Investors and the investment process -- Hedge funds -- Portfolio performance evaluation.

Portfolio selection using artificial intelligence

The application of artificial intelligence in finance is relatively new area of research. This project employed artificial neural networks (ANNs) that use both fundamental and technical inputs to predict future prices of widely held Australian stocks and use these predicted prices for stock portfolio selection over a long investment horizon. The research involved the creation and testing of a large number of possible network configurations and draws conclusions about ANN architectures and their overall suitability for the purpose of stock portfolio selection.

Essays on momentum investing strategies

The momentum investment strategy, which buys recent winner stocks and sells recent loser stocks, earns returns that are simply too good to be explained by traditional finance theories. This thesis extends our understanding of the sources of momentum profits. The research shows that part of the seemingly anomalous returns can be explained by the market's reaction to public news, is affected by how delisting returns are calculated, and is biased by ignoring the time-varying risk of the trading strategy.

Essays on volatility and liquidity in financial markets

The price formation of financial assets is a complex process. It extends beyond the standard economic paradigm of supply and demand to the understanding of the dynamic behavior of price variability, the price impact of information, and the implications of trading behavior of market participants on prices. In this thesis, I study aggregate market and individual assets volatility, liquidity dimensions, and causes of mispricing for US equities over a recent sample period. How volatility forecasts are modeled, what determines intradaily jumps and causes changes in intradaily volatility and what drives the premium of traded equity indexes? Are they induced, for example, by the information content of lagged volatility and return parameters or by macroeconomic news, changes in liquidity and volatility? Besides satisfying our intellectual curiosity, answers to these questions are of direct importance to investors developing trading strategies, policy makers evaluating macroeconomic policies and to arbitrageurs exploiting mispricing in exchange-traded funds. Results show that the leverage effect and lagged absolute returns improve forecasts of continuous components of daily realized volatility as well as jumps. Implied volatility does not subsume the information content of lagged returns in forecasting realized volatility and its components. The reported results are linked to the heterogeneous market hypothesis and demonstrate the validity of extending the hypothesis to returns. Depth shocks, signed order flow, the number of trades, and resiliency are the most important determinants of intradaily volatility. In contrast, spread shock and resiliency are predictive of signed intradaily jumps. There are fewer macroeconomic news announcement surprises that cause extreme price movements or jumps than those that elevate intradaily volatility. Finally, the premium of exchange-traded funds is significantly associated with momentum in net asset value and a number of liquidity parameters including the spread, traded volume, and illiquidity. The mispricing of industry exchange traded funds suggest that limits to arbitrage are driven by potential illiquidity.

Can book-to-market and size be risk factors that predict economic growth in Asia's emerging economies?

We investigate whether the two 2 zero cost portfolios, SMB and HML, have the ability to predict economic growth for markets investigated in this paper. Our findings show that there are only a limited number of cases when the coefficients are positive and significance is achieved in an even more limited number of cases. Our results are in stark contrast to Liew and Vassalou (2000) who find coefficients to be generally positive and of a similar magnitude. We go a step further and also employ the methodology of Lakonishok, Shleifer and Vishny (1994) and once again fail to support the risk-based hypothesis of Liew and Vassalou (2000). In sum, we argue that search for a robust economic explanation for firm size and book-to-market equity effects needs sustained effort as these two zero cost portfolios do not represent economically relevant risk.

Elliptic curves, group law, and efficient computation

This thesis is about the derivation of the addition law on an arbitrary elliptic curve and efficiently adding points on this elliptic curve using the derived addition law. The outcomes of this research guarantee practical speedups in higher level operations which depend on point additions. In particular, the contributions immediately find applications in cryptology. Mastered by the 19th century mathematicians, the study of the theory of elliptic curves has been active for decades. Elliptic curves over finite fields made their way into public key cryptography in late 1980’s with independent proposals by Miller [Mil86] and Koblitz [Kob87]. Elliptic Curve Cryptography (ECC), following Miller’s and Koblitz’s proposals, employs the group of rational points on an elliptic curve in building discrete logarithm based public key cryptosystems. Starting from late 1990’s, the emergence of the ECC market has boosted the research in computational aspects of elliptic curves. This thesis falls into this same area of research where the main aim is to speed up the additions of rational points on an arbitrary elliptic curve (over a field of large characteristic). The outcomes of this work can be used to speed up applications which are based on elliptic curves, including cryptographic applications in ECC. The aforementioned goals of this thesis are achieved in five main steps. As the first step, this thesis brings together several algebraic tools in order to derive the unique group law of an elliptic curve. This step also includes an investigation of recent computer algebra packages relating to their capabilities. Although the group law is unique, its evaluation can be performed using abundant (in fact infinitely many) formulae. As the second step, this thesis progresses the finding of the best formulae for efficient addition of points. In the third step, the group law is stated explicitly by handling all possible summands. The fourth step presents the algorithms to be used for efficient point additions. In the fifth and final step, optimized software implementations of the proposed algorithms are presented in order to show that theoretical speedups of step four can be practically obtained. In each of the five steps, this thesis focuses on five forms of elliptic curves over finite fields of large characteristic. A list of these forms and their defining equations are given as follows: (a) Short Weierstrass form, y2 = x3 + ax + b, (b) Extended Jacobi quartic form, y2 = dx4 + 2ax2 + 1, (c) Twisted Hessian form, ax3 + y3 + 1 = dxy, (d) Twisted Edwards form, ax2 + y2 = 1 + dx2y2, (e) Twisted Jacobi intersection form, bs2 + c2 = 1, as2 + d2 = 1, These forms are the most promising candidates for efficient computations and thus considered in this work. Nevertheless, the methods employed in this thesis are capable of handling arbitrary elliptic curves. From a high level point of view, the following outcomes are achieved in this thesis. - Related literature results are brought together and further revisited. For most of the cases several missed formulae, algorithms, and efficient point representations are discovered. - Analogies are made among all studied forms. For instance, it is shown that two sets of affine addition formulae are sufficient to cover all possible affine inputs as long as the output is also an affine point in any of these forms. In the literature, many special cases, especially interactions with points at infinity were omitted from discussion. This thesis handles all of the possibilities. - Several new point doubling/addition formulae and algorithms are introduced, which are more efficient than the existing alternatives in the literature. Most notably, the speed of extended Jacobi quartic, twisted Edwards, and Jacobi intersection forms are improved. New unified addition formulae are proposed for short Weierstrass form. New coordinate systems are studied for the first time. - An optimized implementation is developed using a combination of generic x86-64 assembly instructions and the plain C language. The practical advantages of the proposed algorithms are supported by computer experiments. - All formulae, presented in the body of this thesis, are checked for correctness using computer algebra scripts together with details on register allocations.

Public awareness of “green” and “energy efficient” residential property : an empirical survey based on data from New Zealand

Purpose – The purpose of this paper is to examine the buyer awareness and acceptance of environmental and energy efficiency measures in the New Zealand residential property markets. This study aims to provide a greater understanding of consumer behaviour in the residential property market in relation to green housing issues ---------- Design/methodology/approach – The paper is based on an extensive survey of Christchurch real estate offices and was designed to gather data on the factors that were considered important by buyers in the residential property market. The survey was designed to allow these factors to be analysed on a socio-economic basis and to compare buyer behaviour based on property values. ---------- Findings – The results show that regardless of income levels, buyers still consider that the most important factor in the house purchase decision is the location of the property and price. Although the awareness of green housing issues and energy efficiency in housing is growing in the residential property market, it is only a major consideration for young and older buyers in the high income brackets and is only of some importance for all other buyer sectors of the residential property market. Many of the voluntary measures introduced by Governments to improve the energy efficiency of residential housing are still not considered important by buyers, indicating that a more mandatory approach may have to be undertaken to improve energy efficiency in the established housing market, as these measures are not valued by the buyer. ---------- Originality/value – The paper confirms the variations in real estate buyer behaviour across the full range of residential property markets and the acceptance and awareness of green housing issues and measures. These results would be applicable to most established and transparent residential property markets.

James Street market, Brisbane : a subtropical retail case study

Climate change mitigation is driving demand for energy-efficient and environmentally conscious commercial buildings in Australia. In the Australian subtropics, high rainfall, warm weather and humidity present unique challenges and opportunities for the architects tasked with designing eco-sensitive projects. The case of the James Street Market in Brisbane’s Fortitude Valley shows that climate-responsive design is an effective approach for reducing the environmental impact of commercial developments. The James Street Market combines climate-responsiveness, environmentally sensitive design strategies and smart planning to create a more sustainable retail precinct. This paper details the design strategies featured in the James Street Market, the project that kicked off a renaissance in climate-responsive commercial building design in Brisbane.

An investigation of market segmentation theory and its impact on effective fundraising

This paper presents the findings of an indepth study into the effects and success of marketing segmentation, target marketing and fundraising. Organisations are constantly seeking new ways and more efficient means to raise funds so that they can fulfill their objectives. These organisations review and evaluate their resources to gain competitive advantage and increased fundraising success...

Market orientation in the nonprofit sector

As the nonprofit sector moves into a more competitive environment it is being required by the community to become more efficient and effective. One response is for nonprofit organisations to become market oriented, which is the familiar response in the for-profit sector. Two components of market orientation, that is market segmentation and customer oriented products, fit well within the peculiarities of a nonprofit organisation. This is usually accompanied by the desire to obtain a competitive advantage causes problems for various stakeholders within the organisation. This paper contends that three factors, management, scarcity of resources, and conflict between organisational objectives and market orientation, are major influences on the adoption of a market oriented culture for a nonprofit organisation.

Developing an efficient and reliable dry powder inhaler for pulmonary drug delivery : a review for multidisciplinary researchers

Pulmonary drug delivery is the focus of much research and development because of its great potential to produce maximum therapeutic benefit. Among the available options the dry powder inhaler (DPI) is the preferred device for the treatment of an increasingly diverse number of diseases. However, as drug delivery from a DPI involves a complicated set of physical processes and the integration of drug formulations, device design and patient usage, the engineering development of this medical technology is proving to be a great challenge. Currently there is large range of devices that are either available on the market or under development, however, none exhibit superior clinical efficacy. A major concern is the inter- and intra-patient variability of the drug dosage delivered to the deep lungs. The extent of variability depends on the drug formulation, the device design and the patient’s inhalation profile. This article reviews recent advances in DPI technology and presents the key factors which motivate and constrain the successful engineering of a universal, patient-independent DPI that is capable of efficient, reliable and repeatable drug delivery. A strong emphasis is placed on the physical processes of drug powder aerosolisation, deagglomeration, and dispersion and on the engineering of formulations and inhalers that can optimise these processes.

The creative instability hypothesis

This paper provides an analysis of why many ‘stars’ tend to fade away rather than enjoying ongoing branding advantages from their reputations. We propose a theory of market overshooting in creative industries that is based on Schumpeterian competition between producers to maintain the interest of boundedly rational fans. As creative producers compete by offering further artistic novelty, this escalation of product complexity eventually leads to overshooting. We propose this as a theory of endogenous cycles in the creative industries.

The impact of a congestion pricing exemption on the demand for new energy efficient vehicles in Stockholm

As governments seek to transition to more efficient vehicle fleets, one strategy has been to incentivize ‘green’ vehicle choice by exempting some of these vehicles from road user charges. As an example, to stimulate sales of Energy-Efficient Vehicles (EEVs) in Sweden, some of these automobiles were exempted from Stockholm’s congestion tax. In this paper the effect this policy had on the demand for new, privately-owned, exempt EEVs is assessed by first estimating a model of vehicle choice and then by applying this model to simulate vehicle alternative market shares under different policy scenarios. The database used to calibrate the model includes owner-specific demographics merged with vehicle registry data for all new private vehicles registered in Stockholm County during 2008. Characteristics of individuals with a higher propensity to purchase an exempt EEV were identified. The most significant factors included intra-cordon residency (positive), distance from home to the CBD (negative), and commuting across the cordon (positive). By calculating vehicle shares from the vehicle choice model and then comparing these estimates to a simulated scenario where the congestion tax exemption was inactive, the exemption was estimated to have substantially increased the share of newly purchased, private, exempt EEVs in Stockholm by 1.8% (+/- 0.3%; 95% C.I.) to a total share of 18.8%. This amounts to an estimated 10.7% increase in private, exempt EEV purchases during 2008 i.e. 519 privately owned, exempt EEVs.