Drift Bursts in Pure Jumps: Detection and Application to Bitcoin

The drift burst hypothesis

The Drift Burst Hypothesis postulates the existence of short-lived locally explosive trends in the price paths of financial assets. The recent US equity and treasury flash crashes can be viewed as two high profile manifestations of such dynamics, but we argue that drift bursts of varying magnitude are an expected and regular occurrence in financial markets that can arise through established mechanisms such as feedback trading. At a theoretical level, we show how to build drift bursts into the continuous-time Ito semi-martingale model in such a way that the fundamental arbitrage-free property is preserved. We then develop a non-parametric test statistic that allows for the identification of drift bursts from noisy high-frequency data. We apply this methodology to a comprehensive set of tick data and show that drift bursts form an integral part of the price dynamics across equities, fixed income, currencies and commodities. We find that the majority of identified drift bursts are accompanied by strong price reversals and these can therefore be regarded as “flash crashes” that span brief periods of severe market disruption without any material longer term price impacts.

The Feynman path integral is known to be a powerful tool in different domains of physics and various mathematical approaches to its construction were developed (see e.g. extensive reviews of the recent literature in [ABB], [SS], [K4], [K5]). However, most of them work only for very restrictive class of potentials. Moreover, they are often defined not as genuine integrals, but as some generalized functionals specified by some limiting procedure. In [K2], [K3] the author proposed a representation of the solutions to the Schrodinger equation in terms of the well defined infinite dimensional Feynman integral defined as a genuine integral over a bona fide σ-additive measure on an appropriate space of trajectories (usually the Cameron- Martin space). Thi s const ruct ion covers very general equations. In [K5] it is extend ed to the Schrodinger equations with magnetic fields with even singular vector potentials defined as Radon measures. The construction uses the idea of the regularization by means of the introduction of continuous quantum observations or complex times and extends the approach of Maslov-Chebotarev (see [MCh]) which was based on the pure jump processes that appear naturally in th e momentum representation of the Schrodinger equation, whose potential can be presented as a Fourier transform of a finite complex measure (Ito’s complex measure condition).Key wordsFeynman path integralpure jump processesWiener processFock spaceSchrödinger equationparabolic equationsAMS(MOS) subject classificationsAMS subject classification 2000: 35K0581Q0581QlO81S40

In the first of two papers, we present a factor-decomposition based framework that facilitates non-parametric risk analysis for complex hedge fund portfolios in the absence of portfolio level transparency. Our approach has been designed specifically for use within the hedge funds-offunds environment, but is equally relevant to those who seek to construct risk managed portfolios of hedge funds under less than perfect underlying portfolio transparency. Using dynamic multivariate regression analysis coupled with a top-down qualitative understanding of hedge fund return drivers, we are able to perform a robust factor decomposition to attribute risk within any hedge fund portfolio with an identifiable strategy. Furthermore, through use of Bayesian-adjusted correlated Monte Carlo simulation techniques, these factors can be employed to generate implied risk profiles at either the constituent fund or aggregate funds-of-funds level. As well as being pertinent to risk forecasting and monitoring, such methods also have application to style analysis, profit attribution, portfolio stress testing and diversification studies. In this first paper we present the technical foundations of such a framework. The follow-up paper (Part II) will present detailed application of the concepts discussed in Part I to a broad base of hedge fund strategies and funds-of-funds.

This paper illustrates how qualitative analysis can be incorporated into quantitative risk measurement in order to construct an expected distribution of hedge fund returns that explicitly allows for market, residual and tail risk. We show how the combination of statistical criteria with out-of-sample model evaluation techniques, coupled with a qualitative understanding of the particular hedge fund strategy can lead to more robust risk factor models that capture the out-of-sample rather than the historical variation in hedge fund returns. Using Monte Carlo simulation techniques, that allow the most appropriate data generating process for each risk factor, we proceed to build a market risk based expected distribution of returns which is then adjusted for the presence of residual and tail risk. The residual risk distribution of expected returns is entirely based on the out-of-sample errors of the risk factor model and by using the out-of-sample explanatory power of the model as the weighting parameter we allow the model to ‘self correct’ when the actual returns deviate significantly from the model conditional expected returns. The tail risk distribution of returns and the correlation of these tails are solely based on qualitative analysis. We propose a methodology for the quantification of the potential impact of factors such as leverage, liquidity and concentration on the size and probability of excess losses due to tail risks. The proposed framework allows investors to explicitly measure, monitor and manage the modelable and non-modelable risks in a hedge fund portfolio.

We present a general framework for the estimation of corporate default based on a firm’s capital structure, when its assets are assumed to follow a pure jump Lévy processes; this setup provides a natural extension to usual default metrics defined in diffusion (log-normal) models, and allows to capture extreme market events such as sudden drops in asset prices, which are closely linked to default occurrence. Within this framework, we introduce several pure jump processes featuring negative jumps only and derive practical closed formulas for equity prices, which enable us to use a moment-based algorithm to calibrate the parameters from real market data and to estimate the associated default metrics. A notable feature of these models is the redistribution of credit risk towards shorter maturity: this constitutes an interesting improvement to diffusion models, which are known to underestimate short-term default probabilities. We also provide extensions to a model featuring both positive and negative jumps and discuss qualitative and quantitative features of the results. For readers convenience, practical tools for model implementation and GitHub links are also included.

Dynamics and risk factors in hedge funds returns: Implications for portfolio construction and performance evaluation

Driven by vast historical growth and the recent crises, the hedge fund industry has undergone several changes. This thesis presents studies on the analysis of hedge fund returns within changing market states by applying different constant, asymmetric and time-varying factor loading models. Considered models include the CAPM, Fama-French 3-factor model, Carhart 4-factor model, Fama-French 5-Factor model, Agarwal-Naik 8-factor model and the Fung-Hsieh 7- and 8-factor models. In addition, and unlike previous research, 94 hedge fund strategy styles have been analysed individually to test whether the model performances differ among approaches. The first full-sample analysis exhibits generally low explanatory power whereby the more sophisticated models perform superiorly. Equity strategies, especially long-only funds, exhibit high adjusted R-Squared among all models, while fixed income, fundamental and technical hedge funds result in low significance. The CUSUM control chart based crisis/non-crisis dummy cannot substantially improve the explanatory power of the models. Hedge fund alpha and factor significance varies considerably among strategies and the power of the models remains similarly poor. Asymmetric up/down models exhibit slightly improved explanatory power while the significance of alpha diminishes. Replacing the conditional up/down variable by the crisis/non-crisis setting resulted in inferior results. Empirical analysis with asymmetric higher-moment models approves the asymmetries in hedge fund returns partially. Moreover, a time-varying approach substantially improves the explanatory power of all models while hedge fund alpha further diminishes. All dynamic models exhibit significant exposures on macro state variables for a high proportion of funds. To summarise, it has been shown how simple models can be fitted to increase the explanatory power. As a result, the adjusted R-Squared were improved by 73%. On a strategy level, equity funds are explained the best while fixed income, fundamental and technical hedge funds are the most difficult to analyse.

Can We Really 'Clone' Hedge Fund Returns? Further Evidence M.Kooli & S. Sharma Hedge Fund Replication: Does Model Combination Help? J. Teiletche Factor-Based Hedge Fund Replication with Risk Constraints R.D.F.Harris & M. Mazibas Takeover Probabilities and the Opportunities for Hedge Funds and Hedge Fund Replication to Produce Abnormal Gains A.Ravi , P.Mayall & J. Simpson Benchmarking of Replicated Hedge Funds M.D.Wiethuechter & L. Nemeth Insight - Distributional Hedge Fund Replication via State Contingent Stochastic Dominance C.H. Glaffig Non-Parametric Hedge Funds and Replication Indices Performance Analysis: A Robust Directional Application L. Germain , N. Nalpas & A. Vanhems Hedge Fund Cloning through State Space Models R. Savona Hedge Fund Return Replication via Learning Models R. McFall Lamm, Jr Linear Model for Passive Hedge Fund Replication G. Barone-Adesi & S. Siragusa Can Hedge Fund-like Returns be Replicated in a Regulated Environment? I. Markov & N. Tuchschmid A Factor-based Application to Hedge Fund Replication M. Rossi & S.L. Rodriguez

UCITS funds are mutual funds that are regulated by pan-European guidelines and can easily be distributed throughout Europe. We study the empirical performance of a survivorship bias-free sample of alternative UCITS funds. Most importantly, as alternative UCITS funds are often marketed as regulated hedge funds, we compare them with offshore hedge funds. Our results show that alternative UCITS offer similar raw returns but lower standard deviations during the full sample period. However, single-index models show that alternative UCITS funds provide only marginal exposure to variation in hedge fund returns. Multifactor models indicate that the most important risk factors for both alternative UCITS funds and matched hedge funds strategies are related to stock market risks. However, alternative UCITS funds exhibit a significantly lower exposure to these factors than hedge funds. Furthermore, they load on different risk factors, suggesting that alternative UCITS and hedge funds follow different strategies. We test more formally whether alternative mutual funds and hedge funds constitute different asset classes. In particular, we assess the degree of the value added for an investor in terms of enhanced diversification benefits by implementing a spanning test and find that both groups are different asset classes with time-varying diversification properties.

The hedge fund industry is starting to recognize that a main part of its returns corresponds to risk premia rather than market inefficiencies, i.e., from beta instead of alpha. This has some implication for the industry and investors, among which is the endeavor to construct investable benchmarks for hedge funds on the basis of an analysis of the underlying systematic risk factors and a subsequent replication of the corresponding risk premia with generic trading systems. The question touches further rationale on the sense and nonsense of the currently available investable versions of hedge fund indices. If possible, investable benchmarks based on risk factor analysis and replication offers a valid, theoretically more sound, and cheaper alternative to the currently offered hedge fund index products, especially as the latter reveal themselves more and more as questionable from a theoretical as well as practical standpoint. This article reflects on this most recent discussion within the global hedge fund industry about the beta versus alpha controversy, investable hedge fund indices, and finally, capacity issues. It illustrates how the current research activities in the quant groups of the large investment banks and financial academic centers might turn the hedge fund industry upside down in coming years. This article offers a follow up discussion on the broader treatment on the subject in the author's book 'Through the Alpha Smoke Screens: A Guide to Hedge Fund Return Sources'.

Based on the belief that hedge funds are able to generate positive risk-adjusted returns (alpha) and diversification benefits in a portfolio context, many investors have included hedge funds in their asset allocation in order to optimize the risk-return trade-off of their investments. We provide evidence that more optimistic prior beliefs about expected risk-adjusted returns (alpha) lead to higher allocations into hedge funds. It appears, however, that history may not be the best guide for future fund performance and that the diversification benefits have declined over time. One reason for the lower risk-adjusted returns is a capacity effect in that previously exceptional hedge fund returns caused higher inflows to these funds and consequently a competition for alpha among investors. In our empirical analysis we provide additional evidence of other explanations for decreasing hedge fund benefits such as an increase in correlations with other asset classes and changes in the style composition of hedge funds.

Using a nonparametric statistical methodology this thesis analyses nonlinear risk exposures in portfolios and individual hedge funds. At the portfolio level an out-of-sample evidence of nonlinearities is documented in most of the styles; however, nonlinear features are found to be more pronounced in arbitrage related hedge fund styles, rather than in directional styles. A nonparametric approach based on a Generalized Additive Model (GAM) captures nonlinearities better than the widely accepted seven-factor Fung and Hsieh (2004b) model and outperforms linear multi-factor models in out-of-sample tests. At the fund level, one-fifth of funds exhibit significant nonlinearities detected using GAMs. In addition, individual funds with nonlinear risk exposures have on average lower raw and risk-adjusted returns and higher left tail risk than funds with only linear risk exposures. Thus, nonlinearities do not signal skill among fund managers. Finally, linear and nonparametric models are employed to replicate broad hedge fund benchmarks as well as investable hedge fund indices. It is found that the nonparametric model better tracks hedge fund benchmarks than the linear model, confirming the importance of nonlinearities.

Hedge fund activism refers to the phenomenon where hedge fund investors acquire a strict minority block of shares in a target firm and then attempt to pressure management for changes in corporate policies and governance with the aim to improve firm performance. This study provides an updated empirical analysis as well as a comprehensive survey of the academic finance research on hedge fund activism. Beginning in the early 1990s, shareholder engagement by activist hedge funds has evolved to become both an investment strategy and a remedy for poor corporate governance. Hedge funds represent a group of highly incentivized, value-driven investors who are relatively free from regulatory and structural barriers that have constrained the monitoring by other external investors. While traditional institutional investors have taken actions ex-post to preserve value or contain observed damage (such as taking the “Wall Street Walk”), hedge fund activists target underperforming firms in order to unlock value and profit from the improvement. Activist hedge funds also differ from corporate raiders that operated in the 1980s, as they tend to accumulate minority equity stakes and do not seek direct control. As a result, activists must win support from fellow shareholders via persuasion and influence, representing a hybrid internal-external role in a middle-ground form of corporate governance. Research on hedge fund activism centers on how it impacts the target company, its shareholders, other stakeholders, and the capital market as a whole. Opponents of hedge fund activism argue that activists focus narrowly on short-term financial performance, and such “short-termism” may be detrimental to the long-run value of target companies. The empirical evidence, however, supports the conclusion that interventions by activist hedge funds lead to improvements in target firms, on average, in terms of both short-term metrics, such as stock value appreciation, and long-term performance, including productivity, innovation, and governance. Overall, the evidence from the full body of the literature generally supports the view that hedge fund activism constitutes an important venue of corporate governance that is both influence-based and market-driven, placing activist hedge funds in a unique position to reduce the agency costs associated with the separation of ownership and control.

In this study, we first conduct multinomial logistic regression analysis to see how hedge fund attributes affect hedge fund managers’ decision of whether to offer a hurdle rate and/or high-watermark. Hedge funds taking more risky position and collecting high performance fee are more likely to offer hurdle rate and/or high-watermark. Second, we conduct cross-sectional regression analysis to see how hedge fund attributes affect hedge fund performance. Our results indicate that hurdle rate and high-watermark are restrictions for hedge fund managers on collecting fee and that hurdle rate and high-watermark cannot be considered to be incentives. We also find that hedge funds collecting high performance fee and having large amount of funds are more likely to outperform those collecting low performance fee and having small amount of funds. While conducting cross-sectional regression analysis, we use three different measures of hedge fund performance: alpha, palpha and Sharpe ratio. Alpha and palpha are obtained from the optimal model by investment strategy controlling for hedge fund risk associated with risk factors different by its investment strategy. In addition, we control for survivorship and instant history biases. So, our results from alpha and palpha are more credible than those of Soydemir et al. (2012) which employs only Sharpe ratio.