## Can we learn to beat the best stock (2004)

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Venue: | Journal of Artificial Intelligence Research |

Citations: | 16 - 0 self |

### BibTeX

@ARTICLE{Borodin04canwe,

author = {Allan Borodin and Ran El-yaniv and Vincent Gogan},

title = {Can we learn to beat the best stock},

journal = {Journal of Artificial Intelligence Research},

year = {2004},

volume = {21},

pages = {579--594}

}

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### Abstract

A novel algorithm for actively trading stocks is presented. While traditional universal algorithms (and technical trading heuristics) attempt to predict winners or trends, our approach relies on predictable statistical relations between all pairs of stocks in the market. Our empirical results on historical markets provide strong evidence that this type of technical trading can “beat the market ” and moreover, can beat the best stock in the market. In doing so we utilize a new idea for smoothing critical parameters in the context of expert learning. 1

### Citations

8567 |
Elements of Information Theory
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- 1991
(Show Context)
Citation Context ...exponential returns in a “no-growth market”. Under the assumption that the daily market vectors are observations of identically and independently distributed (i.i.d) random variables, it is shown in (=-=Cover & Thomas, 1991-=-) that CBAL ∗ performs at least as good (in the sense of expected total return) as the best online portfolio selection algorithm. However, many studies (see e.g. Lo & MacKinlay, 1999) argue that stock... |

649 |
Online computation and competitive analysis
- Borodin, El-Yaniv
- 1998
(Show Context)
Citation Context .... . , 2 )) (Cover & Ordentlich, 1996).7 Somewhat surprisingly, as noted in (Cover & Ordentlich, 1996) the algorithm is equivalent to a static weighted average (given by µ(b)) over all CBALs (see also =-=Borodin & El-Yaniv, 1998-=-, p. 291). This equivalence helps to demystify the universality result and also shows that the algorithm can never outperform CBAL ∗ . 5. Helmbold et al. show how to eliminate the need to know xmin an... |

541 | Portfolio selection: Efficient diversification of investments - Markowitz - 1959 |

314 | How to use expert advice
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- 1997
(Show Context)
Citation Context ...g the ANTICORw algorithms as experts, we can try to learn the best expert. But the windows, like individual stocks, induce a rather volatile set of experts and standard expert combination algorithms (=-=Cesa-Bianchi et al., 1997-=-) tend to fail. 13 Alternatively, we can adaptively learn and invest in some weighted average of all ANTICORw algorithms with w less than some maximum W . The simplest case is a uniform investment on ... |

214 | Simple technical trading rules and the stochastic properties of stock returns - Brock, Lakonishok, et al. - 1992 |

160 |
A universal data compression system
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(Show Context)
Citation Context ...). As a prediction algorithm, LZ is provably powerful in various senses. First it can be shown that it is asymptotically optimal with respect to any stationary and ergodic finite order Markov source (=-=Rissanen, 1983-=-; Ziv & Lempel, 1978). Moreover, Feder shows that LZ is also universal in a worst case sense with respect to the (offline) benchmark class of all finite state prediction machines. To summarize, the co... |

150 | Universal portfolios
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(Show Context)
Citation Context ...ctive (in computational finance) is to develop online trading strategies that are in some sense always guaranteed to perform well. 4 Within a line of research pioneered by Cover (Cover & Gluss, 1986; =-=Cover, 1991-=-; Cover & Ordentlich, 1996) one attempts to design portfolio selection algorithms that can provably do well (in terms of their total return) with respect to some online or offline benchmark algorithms... |

85 | Universal portfolios with side information
- Cover, Ordentlich
- 1996
(Show Context)
Citation Context ... as a special case of portfolio selection, and perhaps more surprisingly, from a certain worst case minimax criterion, portfolio selection is not essentially any harder (than prediction) as shown in (=-=Cover & Ordentlich, 1996-=-) (see also Lugosi, 2001, Thm. 20 & 21). But there seems to be a qualitative difference between the practical utility of “universal” sequence prediction and “universal” portfolio selection. Simply sta... |

77 | On-line portfolio selection using multiplicative updates - Helmbold, Schapire, et al. - 1996 |

55 | Universal portfolios with and without transaction costs, Machine Learning 35(3
- Blum, Kalai
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(Show Context)
Citation Context ... or near optimal choice. Of course, it is possible to adaptively set η throughout the trading period, but that is beyond the scope of this paper. 7. The papers (Cover, 1991; Cover & Ordentlich, 1996; =-=Blum & Kalai, 1998-=-) consider a simpler version of this algorithm where the (Dirichlet) prior is uniform. This algorithm is also universal and achieves a ratio Θ(n m−1 ). Experimentally (on our datasets) there is a negl... |

43 |
A Non-Random Walk down Wall Street
- Lo, MacKinlay
- 1999
(Show Context)
Citation Context ..., it is shown in (Cover & Thomas, 1991) that CBAL ∗ performs at least as good (in the sense of expected total return) as the best online portfolio selection algorithm. However, many studies (see e.g. =-=Lo & MacKinlay, 1999-=-) argue that stock price sequences do have long term memory and are not i.i.d. A non-traditional objective (in computational finance) is to develop online trading strategies that are in some sense alw... |

31 | A Statistical Adversary for On-line Algorithms - Raghavan - 1992 |

21 | The Statistical Adversary Allows Optimal Money-making Trading Strategies - Chou, Cooperstock, et al. - 1995 |

20 |
Gambling using a finite state machine
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(Show Context)
Citation Context ...ons made using the prediction component of the well-known Lempel-Ziv (LZ) lossless compression algorithm (Ziv & Lempel, 1978). This prediction component is nicely described in (Langdon, 1983) and in (=-=Feder, 1991-=-). As a prediction algorithm, LZ is provably powerful in various senses. First it can be shown that it is asymptotically optimal with respect to any stationary and ergodic finite order Markov source (... |

13 |
Empirical bayes stock market portfolios
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- 1986
(Show Context)
Citation Context ... non-traditional objective (in computational finance) is to develop online trading strategies that are in some sense always guaranteed to perform well. 4 Within a line of research pioneered by Cover (=-=Cover & Gluss, 1986-=-; Cover, 1991; Cover & Ordentlich, 1996) one attempts to design portfolio selection algorithms that can provably do well (in terms of their total return) with respect to some online or offline benchma... |

12 | On the competitive theory and practice of portfolio selection (extended abstract
- Borodin, El-Yaniv, et al.
- 2000
(Show Context)
Citation Context ...ts of the asymptotically optimal algorithm. 582Can We Learn to Beat the Best Stock A different type of “winner learning” algorithm can be obtained from any sequence prediction strategy, as noted in (=-=Borodin, El-Yaniv, & Gogan, 2000-=-). For each stock j, a (soft) sequence prediction algorithm provides a probability p(j) that the next symbol will be j ∈{1, . . . , m}. We view this as a prediction that stock j will have the best rel... |

9 |
Adjusting for risk in portfolio performance measurement
- SHARPE
- 1975
(Show Context)
Citation Context ...is the standard deviation of these daily returns multiplied by √ 252 where 252 is the assumed standard number of trading days per year. These calculations are standard. The (annualized) Sharpe ratio (=-=Sharpe, 1975-=-) is the ratio of annualized return minus the risk-free return (taken to be 4%) divided by the (annualized) standard deviation. 590Can We Learn to Beat the Best Stock ˆbt = 1 bt·xt (bt(1)xt(1), . . .... |

7 |
A note on the Lempel–Ziv model for compressing individual sequences
- Langdon
- 1983
(Show Context)
Citation Context ...000) considers predictions made using the prediction component of the well-known Lempel-Ziv (LZ) lossless compression algorithm (Ziv & Lempel, 1978). This prediction component is nicely described in (=-=Langdon, 1983-=-) and in (Feder, 1991). As a prediction algorithm, LZ is provably powerful in various senses. First it can be shown that it is asymptotically optimal with respect to any stationary and ergodic finite ... |

5 | Portfolio Selection: E#cient Diversification of Investments - Markowitz - 1959 |

2 |
Lectures on prediction of individual sequences. URL:http://www.econ.upf.es/∼lugosi/ihp.ps
- Lugosi
- 2001
(Show Context)
Citation Context ...xpert learning. 1. Introduction The portfolio selection (PS) problem is a challenging problem for machine learning, online algorithms and, of course, computational finance. As is well known (e.g. see =-=Lugosi, 2001-=-) sequence prediction under the log loss measure can be viewed as a special case of portfolio selection, and perhaps more surprisingly, from a certain worst case minimax criterion, portfolio selection... |