Abstract
Given a set of say m stocks (one of which may be “cash”), the online portfolio selection problem is to determine a portfolio for the ith trading period based on the sequence of prices for the preceding i – 1 trading periods. Competitive analysis is based on a worst case perspective and such a perspective is inconsistent with the more widely accepted analyses and theories based on distributional assumptions. The competitive framework does (perhaps surprisingly) permit non trivial upper bounds on relative performance against CBAL-OPT, an optimal offline constant rebalancing portfolio. Perhaps more impressive are some preliminary experimental results showing that certain algorithms that enjoy “respectable” competitive (i.e. worst case) performance also seem to perform quite well on historical sequences of data. These algorithms and the emerging competitive theory are directly related to studies in information theory and computational learning theory and indeed some of these algorithms have been pioneered within the information theory and computational learning communities. We present a mixture of both theoretical and experimental results, including a more detalied study of the performance of existing and new algorithms with respect to a standard sequence of historical data cited in many studies. We also present experiments from two other historical data sequences.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Blackwell, D.: An Analog of the Minimax Theorem for Vector Payoffs. Pacific J. Math. 6, 1–8 (1956)
Borodin, A., El-Yaniv, R.: Online Computation and Competitive Analysis. Cambridge University Press, Cambridge (1998)
Blum, A., Burch, C.: On-line Learning and the Metrical task System Problem. In: Proceedings of the 10th Annual Conference on Computational Learning Theory (COLT 1997), pp. 45–53 (1997); To appear in Machine Learning
Blum, A., Kalai, A.: Universal portfolios with and without transaction costs. Machine Learning 30(1), 23–30 (1998)
Bollerslev, T., Chou, R.Y., Kroner, K.F.: ARCH Modeling in Finance: A selective review of the theory and empirical evidence. Journal of Econometrics 52, 5–59
Bodie, Z., Kane, A., Marcus, A.J.: Investments. Richard D. Irwin, Inc. (1993)
Empirical Bayes Stock Market Portfolios. Advances in Applied Mathematics, 7, pp. 170-181 (1986)
Cover, T.M., Ordentlich, O.: Universal portfolios with side information. IEEE Transactions on Information Theory 42(2) (1996)
Cover, T.M.: Universal portfolios. Mathematical Finance 1(1), 1–29 (1991)
Cover, T.M., Thomas, J.A.: Elements of Information Theory. John Wiley & Sons, Inc., Chichester (1991)
Cross, J.E., Barron, A.R.: Efficient universal portfolios for past dependent target classes. DIMACS Workshop: On-Line Decision Making (July 1999)
Feder, M.: Gambling using a finite state machine. IEEE Trans. Inform. Theory 37, 1459–1465 (1991)
Feder, M., Gutman, M.: Universal Prediction of Individual Sequences. IEEE Trans. Inform. Theory 37, 1459–1465 (1991)
Green, W.: Econometric Analysis Collier. McMillan (1972)
Helmbold, D.P., Schapire, R.E., Singer, Y., Warmuth, M.K.: On-line portfolio selection using multiplicative updates. Mathematical Finance 8(4), 325–347 (1998)
Herbster, M., Warmuth, M.K.: Tracking the best expert. Machine Learning 32(2), 1–29 (1998)
Kalai, A., Chen, S., Blum, A., Rosenfeld, R.: On-line Algorithms for Combining Language Models. In: Proceedings of the International Conference on Acoustics, Speech, and Signal Processing, ICASSP (1999)
Kelly, J.: A new interpretation of information rate. Bell Sys. Tech. Journal 35, 917–926 (1956)
Krichevskiy, R.E.: Laplace law of succession and universal encoding. IEEE Trans. on Infor. Theory 44(1) (1998)
Langdon, G.G.: A note on the Lempel-Ziv model for compressing individual sequences. IEEE Trans. Inform. Theory IT-29, 284–287 (1983)
Markowitz, H.: Portfolio Selection: Efficient Diversification of Investments. John Wiley and Sons, Chichester (1959)
Merhav, N., Feder, M.: Universal prediction. IEEE Trans. Inf. Theory 44(6), 2124–2147 (1998)
Ordentlich, E.: Universal Investmeny and Universal Data Compression. PhD Thesis, Stanford University (1996)
Ordentlich, E., Cover, T.M.: The cost of achieving the best portfolio in hindsight. Accepted for publication in Mathematics of Operations Research (Conference version appears in COLT 1996 Proceedings under the title of On-line portfolio selection)
Rissanen, J.: A universal data compression system. IEEE Trans. Information Theory IT-29, 656–664 (1983)
Singer, Y.: Switching portfolios. International Journal of Neural Systems 84, 445–455 (1997)
Ziv, J., Lempel, A.: Compression of individual sequences via variable rate coding. IEEE Trans. Information Theory IT-24, 530–536 (1978)
Vovk, V., Watkins, C.: Universal Portfolio Selection, COLT (1998)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2000 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Borodin, A., El-Yaniv, R., Gogan, V. (2000). On the Competitive Theory and Practice of Portfolio Selection (Extended Abstract). In: Gonnet, G.H., Viola, A. (eds) LATIN 2000: Theoretical Informatics. LATIN 2000. Lecture Notes in Computer Science, vol 1776. Springer, Berlin, Heidelberg. https://doi.org/10.1007/10719839_19
Download citation
DOI: https://doi.org/10.1007/10719839_19
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-67306-4
Online ISBN: 978-3-540-46415-0
eBook Packages: Springer Book Archive