[PDF]     http://dx.doi.org/10.3952/lithjphys.52204

Open access article / Atviros prieigos straipsnis

Lith. J. Phys. 52, 102114 (2012)

S. Esipov
Quant Isle LTD., Scarsdale, New York, USA
E-mail: sergei.esipov@gmail.com

Received 5 March 2012; accepted 7 June 2012

Market participants who capitalize on high-frequency price dynamics and rely on automated trading are responsible, along with market makers, for the observed level of market efficiency. The remaining inefficiency is usually measured as the ratio of expected P&L, derived from the price signals, to its standard deviation. Such signals are also termed alpha in market slang. Signals and their volatility depend on time in a different manner, leading to temporal diversification and rise of multi-step strategies. It is shown that the coexistence of small market inefficiencies, multi-step strategies, and market impact lead to price randomization. In other words, high-frequency strategies redefine prices in their attempt to amplify weak price signals, and make markets more effective. In this paper we identify and explore discrete and continuous strategies. We further demonstrate that strategies within the domain of weak inefficiency are stable when incorporated into regular risk-return framework. In the presence of market impact we show how an efficiency edge propagates towards smaller time scales.
Keywords: econophysics, financial markets
PACS: 89.65.Gh

References / Nuorodos

[1] E. Fama, The behavior of stock market prices, The Journal of Business 38, 34–105 (1965),
[2] P. Samuelson, Proof that properly anticipated prices fluctuate randomly, Industrial Management Review 6, 41–49 (1965)
[3] E. Fama, Efficient capital markets: A review of theory and empirical work, Journal of Finance 25(2), 383–417 (1970),
[4] A.W. Lo, Hedge Funds: an Analytic Perspective (Princeton University Press, Princeton and Oxford, 2008)
[5] On its web site Thomson Reuters advertises a set of data and tools to help their clients in developing and deploying strategies for generating alpha and controlling risk (Thomson Reuters, 2010),
[6] J. Keehner, Milliseconds are focus in algorithmic trades (2007),
[7] T. Yamamoto and Y. Ikebe, Inversion of band matrices, Linear Algebra and its Applications 24, 105–111 (1979),
[8] G. Meurant, A review on the inverse of symmetric tridiagonal and block tridiagonal matrices, SIAM Journal on Matrix Analysis and Applications 13(3), 707–728 (1992),
[9] S. Esipov and I. Vaysburd, On the profit and loss distribution of dynamic hedging strategies, International Journal of Theoretical and Applied Finance 2, 131–153 (1999),
[10] S. Esipov and I. Vaysburd, Dynamic investment strategies: Portfolio insurance versus efficient frontier, available at SSRN (1999),
http://ssrn.com/abstract=170574 or
[11] A. Kyle, Continuous auctions and insider trading, Econometrica 53(6), 1315–1335 (1985),
[12] R. Almgren and N. Chriss, Optimal execution of portfolio transactions, Journal of Risk 3, 5–39 (Winter 2000/2001)
[13] R. Almgren, Optimal execution with nonlinear impact functions and trading-enhanced risk, Applied Mathematical Finance 10, 1–18 (2003),