On the tracking and replication of hedge fund optimal investment portfolio strategies in global capital markets in presence of nonlinearities, applying Bayesian filters: 1. Stratanovich – Kalman – Bucy filters for Gaussian linear investment returns distribution and 2. Particle filters for non-Gaussian non-linear investment returns distribution

Ledenyov, Dimitri O. and Ledenyov, Viktor O. (2013): On the tracking and replication of hedge fund optimal investment portfolio strategies in global capital markets in presence of nonlinearities, applying Bayesian filters: 1. Stratanovich – Kalman – Bucy filters for Gaussian linear investment returns distribution and 2. Particle filters for non-Gaussian non-linear investment returns distribution.

Abstract

The hedge fund represents a unique investment opportunity for the institutional and private investors in the diffusion-type financial systems. The main objective of this condensed article is to research the hedge fund’s optimal investment portfolio strategies selection in the global capital markets with the nonlinearities. We provide a definition for the hedge fund, describe the hedge fund’s organization structures and characteristics, discuss the hedge fund’s optimal investment portfolio strategies and review the appropriate hedge fund’s risk assessment models for investing in the global capital markets in time of high volatilities. We analyze the advanced techniques for the hedge fund’s optimal investment portfolio strategies replication, based on both the Stratonovich – Kalman - Bucy filtering algorithm and the particle filtering algorithm. We developed the software program with the embedded Stratonovich – Kalman - Bucy filtering algorithm and the particle filtering algorithm, aiming to track and replicate the hedge funds optimal investment portfolio strategies in the practical cases of the non-Gaussian non-linear chaotic distributions.

• Item Type: MPRA Paper
• Language: English
• Keywords: hedge fund, investment portfolio, investment strategy, global tactical asset allocation investment strategy, investment decision making, return on investments, value at risk, arbitrage pricing theory, Sharpe ratio, separation theorem, Sortino ratio, Sterling ratio, Calmar ratio, Gini coefficient, value at risk (VaR), Ledenyov investment portfolio theorem, stability of investment portfolio, Kolmogorov chaos theory, Sharkovsky chaos theory, Lyapunov stability criteria, bifurcation diagram, nonlinearities, stochastic volatility, stochastic probability, Markov chain, Bayesian estimation, Bayesian filters, Wiener filtering theory, Stratonovich optimal non-linear filtering theory, Stratonovich – Kalman – Bucy filtering algorithm, Hodrick-Prescott filter, Hirose - Kamada filter, particle filtering methods, particle filters, multivariate filters, Gaussian linear distribution, non-Gaussian nonlinear distribution, Monte-Carlo simulation, Brownian motion, diffusion process, econophysics, econometrics, global capital markets.
• Subjects: C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C11 - Bayesian Analysis: General; C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C13 - Estimation: General; ; C - Mathematical and Quantitative Methods > C3 - Multiple or Simultaneous Equation Models ; Multiple Variables; C - Mathematical and Quantitative Methods > C3 - Multiple or Simultaneous Equation Models ; Multiple Variables > C32 - Time-Series Models ; Dynamic Quantile Regressions ; Dynamic Treatment Effect Models ; Diffusion Processes ; State Space Models; C - Mathematical and Quantitative Methods > C3 - Multiple or Simultaneous Equation Models ; Multiple Variables > C35 - Discrete Regression and Qualitative Choice Models ; Discrete Regressors ; Proportions; C - Mathematical and Quantitative Methods > C3 - Multiple or Simultaneous Equation Models ; Multiple Variables > C38 - Classification Methods ; Cluster Analysis ; Principal Components ; Factor Models; C - Mathematical and Quantitative Methods > C4 - Econometric and Statistical Methods: Special Topics; C - Mathematical and Quantitative Methods > C4 - Econometric and Statistical Methods: Special Topics > C46 - Specific Distributions ; Specific Statistics; C - Mathematical and Quantitative Methods > C5 - Econometric Modeling; C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C51 - Model Construction and Estimation; C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C53 - Forecasting and Prediction Methods ; Simulation Methods; C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C58 - Financial Econometrics; C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C61 - Optimization Techniques ; Programming Models ; Dynamic Analysis; C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C63 - Computational Techniques ; Simulation Modeling; C - Mathematical and Quantitative Methods > C8 - Data Collection and Data Estimation Methodology ; Computer Programs; C - Mathematical and Quantitative Methods > C8 - Data Collection and Data Estimation Methodology ; Computer Programs > C87 - Econometric Software; D - Microeconomics > D8 - Information, Knowledge, and Uncertainty; D - Microeconomics > D8 - Information, Knowledge, and Uncertainty > D84 - Expectations ; Speculations

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187. Engle R F 1974 Band spectrum regression International Economic Review Department of Economics University of Pennsylvania and Osaka University Institute of Social and Economic Research Association vol 15 (1) pp 1 - 11.

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195. Engle R F 1983 Estimates of the variance of US inflation based upon the ARCH model Journal of Money, Credit, and Banking 15 pp 286–301.

196. Engle R F, Watson M 1983 Alternative algorithms for the estimation of dynamic factor, MIMIC and varying coefficient regression models Journal of Econometrics vol 23 pp 385-400.

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198. Engle R F, Hendry D F, Trumble D 1985 Small-sample properties of ARCH estimators and tests Canadian Journal of Economics Canadian Economics Association vol 18 (1) pp 66- 93.

199. Engle R F, Lilien D M, Watson M 1985 A Dynamic model of housing price determination Journal of Econometrics vol 28 pp 307-326.

200. Watson M W, Engle R F 1985 Testing for regression coefficient stability with a stationary AR(1) alternative The Review of Economics and Statistics MIT Press vol 67 (2) pp 341 - 346.

201. Bollerslev T, Engle R F, Nelson D B 1986 Arch models in Engle R F, McFadden D editors Handbook of Econometrics Elsevier edition 1 vol 4 chapter 49 pp 2959-3038.

202. Engle R F, Yoo B S 1987 Forecasting and testing in co-integrated systems Journal of Econometrics Elsevier vol 35 (1) pp 143 - 159.

203. Engle R F, Granger C W J 1987 Co-integration and error correction: Representation, estimation, and testing Econometrica Econometric Society vol 55 (2) pp 251 - 276.

204. Engle R F, Lilien D M, Robins R P 1987 Estimating time varying risk premia in the term structure: The ARCH-M model Econometrica 55 pp 391–407.

205. Bollerslev T, Engle R F, Wooldridge J M 1988 A capital asset pricing model with time-varying covariances Journal of Political Economy University of Chicago Press vol 96 (1) pp 116-131.

206. Engle R F 1988 Estimates of the variance of US inflation based upon the ARCH model: Reply Journal of Money, Credit and Banking Blackwell Publishing vol 20 (3) pp 422 - 423.

207. Engle R F 1990 Stock volatility and the crash of '87: Discussion Review of Financial Studies Society for Financial Studies vol 3 (1) pp 103-106.

208. Engle R F, Ito T, Lin W L 1990 Meteor-showers or heat waves – Heteroskedastic intradaily volatility in the foreign-exchange market Econometrica 58 pp 525 – 542.

209. Engle R F, Ng V K, Rothschild M 1990 Asset pricing with a factor-ARCH covariance structure: Empirical estimates for treasury bills Journal of Econometrics 45 pp 213 – 237.

210. Engle R F, Granger C W J editors 1991 Long-run economic relationships: Readings in Cointegration Oxford University Press UK OUP catalogue number 9780198283393.

211. Engle R F, Gonzalez-Rivera G 1991 Semiparametric ARCH models Journal of Business & Economic Statistics American Statistical Association vol 9 (4) pp 345-359.

212. Chou R, Engle R F, Kane A 1992 Measuring risk-aversion from excess returns on a stock index Journal of Econometrics 52 pp 201 – 224.

213. Ng V, Engle R F, Rothschild M 1992 A multi-dynamic-factor model for stock returns Journal of Econometrics Elsevier vol 52 (1-2) pp 245 - 266.

214. Engle R F, Navarro P, Carson R 1992 On the theory of growth controls Journal of Urban Economics Elsevier vol 32 (3) pp 269 - 283.

215. Engle R F, Mustafa Ch 1992 Implied ARCH models from options prices Journal of Econometrics Elsevier vol 52 (1-2) pp 289 - 311.

216. Ding Zh, Granger C W J, Engle R F 1993 A long memory property of stock market returns and a new model Journal of Empirical Finance Elsevier vol 1 (1) pp 83 - 106.

217. Engle R F, Ng V K 1993 Measuring and testing the impact of news on volatility Journal of Finance American Finance Association vol 48 (5) pp 1749 -1778.

218. Engle R F, Hendry D F 1993 Testing superexogeneity and invariance in regression models Journal of Econometrics Elsevier vol 56 (1-2) pp 119 - 139.

219. Engle R F, Kozicki Sh 1993 Testing for common features Journal of Business & Economic Statistics American Statistical Association vol 11 (4) pp 369 - 380.

220. Vahid F, Engle R F 1993 Common trends and common cycles Journal of Applied Econometrics John Wiley & Sons Ltd vol 8 (4) pp 341 - 360.

221. Engle R F, Susmel R 1993 Common volatility in international equity markets Journal of Business & Economic Statistics American Statistical Association vol 11 (2) pp 167 - 176.

222. Engle R F, Ng V K 1993 Time-varying volatility and the dynamic behavior of the term structure Journal of Money, Credit and Banking Blackwell Publishing vol 25 (3) pp 336 - 349.

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225. Engle R F 1994 Bayesian analysis of stochastic volatility models: Comment Journal of Business & Economic Statistics American Statistical Association vol 12 (4) pp 395-396.

226. Engle R F, Kroner K F 1995 Multivariate simultaneous generalized ARCH Econometric Theory Cambridge University Press UK vol 11 (01) pp 122 - 150.

227. Engle R F, Issler J V 1995 Estimating common sectoral cycles Journal of Monetary Economics Elsevier vol 35 (1) pp 83 - 113.

228. Engle R F editor 1995 ARCH: Selected readings Oxford University Press UK OUP Catalogue number 9780198774327.

229. Engle R F, Russell J R 1997 Forecasting the frequency of changes in quoted foreign exchange prices with the autoregressive conditional duration model Journal of Empirical Finance Elsevier vol 4 (2-3) pp 187 - 212.

230. Vahid F, Engle R F 1997 Codependent cycles Journal of Econometrics Elsevier vol 80 (2) pp 199 - 221.

231. Engle R F, Russell J R 1998 Autoregressive conditional duration: A new model for irregularly spaced transaction data Econometrica 66 pp 1127–1162.

232. Burns P, Engle R F, Mezrich J 1998 Correlations and volatilities of asynchronous data Journal of Derivatives pp 1–12.

233. Engle R F, White H editors 1999 Cointegration, causality, and forecasting: Festschrift in honour of Clive W J Granger Oxford University Press UK OUP Catalogue number 9780198296836.

234. Engle R F, Smith A D 1999 Stochastic permanent breaks The Review of Economics and Statistics MIT Press Cambridge USA vol 81 (4) pp 553 - 574.

235. Engle R F 2000 The econometrics of ultra-high-frequency data Econometrica 68 (1) pp 1 – 22.

236. Alfonso D, Engle R F 2000 Time and the price impact of a trade Journal of Finance American Finance Association vol 55 (6) pp 2467 - 2498.

237. Engle R F 2001a GARCH 101: The use of ARCH/GARCH models in applied econometrics Journal of Economic Perspectives American Economic Association vol 15 (4) pp 157 - 168.

238. Engle R F 2001b Financial econometrics - A new discipline with new methods Journal of Econometrics Elsevier vol 100 (1) pp 53 - 56.

239. Engle R F, Lange J 2001 Predicting VNET: A model of the dynamics of market depth Journal of Financial Markets Elsevier vol 4 (2) pp 113 - 142.

240. Engle R F, Patton A J 2001 What good is a volatility model? Quantitative Finance Taylor and Francis Journals vol 1 (2) pp 237 - 245.

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242. Engle R 2002a Dynamic conditional correlation: A simple class of multivariate generalized autoregressive conditional heteroskedasticity models Journal of Business & Economic Statistics 20 (3) pp 339 – 350.

243. Engle R 2002b New frontiers for ARCH Journal of Applied Econometrics 17 (5) pp 425 – 446.

244. Engle R, Ishida I 2002 Forecasting variance of variance: The square-root, the affine, and the CEV Garch models Department of Finance Working Papers New York University NY USA.

245. Rosenberg J V, Engle R F 2002 Empirical pricing kernels Journal of Financial Economics 64 (3) pp 341 – 372.

246. Engle R F 2003 Risk and volatility: Econometrics models and financial practice Nobel Lecture www.nobel.org pp 326 - 349.

247. Engle R F, Lunde A 2003 Trades and Quotes: A Bivariate Point Process Journal of Financial Econometrics Society for Financial Econometrics vol 1 (2) pp 159 - 188.

248. Engle R F, Manganelli S 2004 CAViaR: Conditional autoregressive value at risk by regression quantiles Journal of Business & Economic Statistics American Statistical Association vol 22 pp 367 - 381.

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254. Engle R F, Gallo G M 2006 A multiple indicators model for volatility using intra-daily data Journal of Econometrics Elsevier vol 131 (1-2) pp 3 - 27.

255. Diebold F X, Engle R F, Favero C, Gallo G M, Schorfheide F 2006 The econometrics of macroeconomics, finance, and the interface Journal of Econometrics Elsevier vol 131 (1-2) pp 1 - 2.

256. Engle R F, Marcucci J 2006 A long-run pure variance common features model for the common volatilities of the Dow Jones Journal of Econometrics Elsevier vol 132 (1) pp 7 - 42.

257. Engle R F, Colacito R 2006 Testing and valuing dynamic correlations for asset allocation Journal of Business & Economic Statistics American Statistical Association vol 24 pp 238 - 253.

258. Engle R F 2006a Private communications on the modern portfolio, risk management and nonlinear dynamic chaos theories in finances Rotman School of Management University of Toronto Ontario Canada.

259. Engle R F 2006b Private communications on the Stratonovich – Kalman – Bucy filtering algorithm Rotman School of Management University of Toronto Canada.

260. Barone-Adesi G, Engle R F, Mancini L 2007 A GARCH option pricing model in incomplete markets Swiss Finance Institute Research Paper Series 07-03 Swiss Finance Institute Switzerland.

261. Engle R F, Rangel J G 2008 The Spline-GARCH model for low-frequency volatility and its global macroeconomic causes Review of Financial Studies Society for Financial Studies vol 21 (3) pp 1187 - 1222.

262. Easley D, Engle R F, O'Hara M, Wu L 2008 Time-varying arrival rates of informed and uninformed trades Journal of Financial Econometrics Society for Financial Econometrics vol 6 (2) pp 171 - 207.

263. Giovanni B-A, Engle R F, Mancini L 2008 A GARCH option pricing model with filtered historical simulation Review of Financial Studies Society for Financial Studies vol 21 (3) pp 1223 - 1258.

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348. Amin G, Kat H 2003b Stocks, bonds, and hedge funds: Not a free lunch! The Journal of Portfolio Management 29 (4) pp 113-120.

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