Empirical Behavior of a World Stock Index from Intra-Day to Monthly Time Scales

Research Paper Number: 250, Quantitative Finance Research Centre, University of Technology, Sydney

27 Pages Posted: 9 Nov 2012

See all articles by Wolfgang Breymann

Wolfgang Breymann

affiliation not provided to SSRN

David Lüthi

affiliation not provided to SSRN

Eckhard Platen

University of Technology, Sydney (UTS) - Finance Discipline Group; University of Technology Sydney, School of Mathematical and Physical Sciences; Financial Research Network (FIRN)

Date Written: June 1, 2009

Abstract

Most of the papers that study the distributional and fractal properties of financial instruments focus on stock prices or foreign exchange rates. This typically leads to mixed results concerning the distributions of log-returns and some multi-fractal properties of exchange rates, stock prices, and regional indices. This paper uses a well diversified world stock index as the central object of analysis. Such index approximates the growth optimal portfolio, which is demonstrated under the benchmark approach, it is the ideal reference unit for studying basic securities. When denominating this world index in units of a given currency, one measures the movements of the currency against the entire market. This provides a least disturbed observation of the currency dynamics. In this manner, one can expect to disentangle, e.g., the superposition of the two currencies involved in an exchange rate. This benchmark approach to the empirical analysis of financial data allows us to establish remarkable stylized facts. Most important is the observation that the repeatedly documented multi-fractal appearance of financial time series is very weak and much less pronounced than the deviation of the mono-scaling properties from Brownian-motion type scaling. The generalized Hurst exponent H(2) assumes typical values between 0.55 and 0.6. Accordingly, autocorrelations of log-returns decay according to a power law, and the quadratic variation vanishes when going to vanishing observation time step size. Furthermore, one can identify the Student t distribution as the log-return distribution of a well-diversified world stock index for long time horizons when a long enough data series is used for estimation. The study of dependence properties, finally, reveals that jumps at daily horizon originate primarily in the stock market while at 5 min horizon they originate in the foreign exchange market. These results are contrasted with the behavior of foreign exchange rates. The principal message of the empirical analysis is that there is evidence that a diffusion model without multi-scaling could reasonably well model the dynamics of a broadly diversified world stock index.

Suggested Citation

Breymann, Wolfgang and Lüthi, David and Platen, Eckhard, Empirical Behavior of a World Stock Index from Intra-Day to Monthly Time Scales (June 1, 2009). Research Paper Number: 250, Quantitative Finance Research Centre, University of Technology, Sydney, Available at SSRN: https://ssrn.com/abstract=2173022 or http://dx.doi.org/10.2139/ssrn.2173022

Wolfgang Breymann

affiliation not provided to SSRN ( email )

David Lüthi

affiliation not provided to SSRN ( email )

Eckhard Platen (Contact Author)

University of Technology, Sydney (UTS) - Finance Discipline Group ( email )

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HOME PAGE: http://datasearch.uts.edu.au/business/finance/staff/StaffDetails.cfm?UnitStaffId=90

University of Technology Sydney, School of Mathematical and Physical Sciences ( email )

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Financial Research Network (FIRN)

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Queensland
Australia

HOME PAGE: http://www.firn.org.au

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