## Universal Portfolios With and Without Transaction Costs (1997)

Venue: | Machine Learning |

Citations: | 59 - 3 self |

### BibTeX

@INPROCEEDINGS{Blum97universalportfolios,

author = {Avrim Blum and Adam Kalai},

title = {Universal Portfolios With and Without Transaction Costs},

booktitle = {Machine Learning},

year = {1997},

pages = {309--313},

publisher = {ACM Press}

}

### Years of Citing Articles

### OpenURL

### Abstract

A constant rebalanced portfolio is an investment strategy which keeps the same distribution of wealth among a set of stocks from period to period. Recently there has been work on on-line investment strategies that are competitive with the best constant rebalanced portfolio determined in hindsight (Cover, 1991; Helmbold et al., 1996; Cover and Ordentlich, 1996a; Cover and Ordentlich, 1996b; Ordentlich and Cover, 1996; Cover, 1996). For the universal algorithm of Cover (Cover, 1991), we provide a simple analysis which naturally extends to the case of a fixed percentage transaction cost (commission), answering a question raised in (Cover, 1991; Helmbold et al., 1996; Cover and Ordentlich, 1996a; Cover and Ordentlich, 1996b; Ordentlich and Cover, 1996; Cover, 1996). In addition, we present a simple randomized implementation that is significantly faster in practice. We conclude by explaining how these algorithms can be applied to other problems, such as combining the predictions of statis...

### Citations

321 | How to use expert advice
- Cesa-Bianchi, Freund, et al.
- 1997
(Show Context)
Citation Context ...) log n=n bits per word is a small overhead as n gets large. It also helps to explain a relationship between portfolios and weighted-average-type algorithms for making predictions from expert advice (=-=Cesa-Bianchi et al., 1993-=-; DeSantis et al., 1988; Foster and Vohra, 1993; Haussler et al., 1994; Kivanen and Warmuth, 1994; Vovk, 1990; Vovk, 1995). Acknowledgments We thank the anonymous referees for their helpful comments. ... |

260 |
Aggregating strategies
- Vovk
- 1990
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Citation Context ...weighted-average-type algorithms for making predictions from expert advice (Cesa-Bianchi et al., 1993; DeSantis et al., 1988; Foster and Vohra, 1993; Haussler et al., 1994; Kivanen and Warmuth, 1994; =-=Vovk, 1990-=-; Vovk, 1995). Acknowledgments We thank the anonymous referees for their helpful comments. This research was supported in part by NSF National Young Investigator grant CCR-9357793, a grant from the AT... |

187 |
Portfolio selection with transaction costs
- Davis, Norman
- 1990
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Citation Context ... 2 , thus increasing total worth by a factor of 9=8 every two periods. We extend this model by adding a fixed percentage commission cost c ! 1 to each transaction, as is common in financial modeling (=-=Davis and Norman, 1990-=-). To fully define the commission model, in addition to specifying the cost of each transaction, we must also specify how a CRP pays this overhead. In Section 2, we give three natural properties of su... |

109 |
Mistake Bounds and Logarithmic Linear-threshold Learning Algorithms
- Littlestone
- 1989
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Citation Context ...f)(1 \Gamma cff) times an investor who starts and ends the period with distribution b . This is (4). It is easy to establish that 1 \Gamma cffs(1 \Gamma ff) c for 0sc; ffs1 (see, e.g. Lemma 3.4.1 of (=-=Littlestone, 1989-=-)). Combining this with (4), wealth of CRPbs(1 \Gamma ff) (1+c)n (wealth of CRPbs): Since (2) is the only use of n in the previous proof, we can replace n by (1 + c)n in the final guarantee. This algo... |

91 | Universal portfolios with side information
- Cover, Ordentlich
- 1996
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Citation Context ... to period. Recently there has been work on on-line investment strategies that are competitive with the best constant rebalanced portfolio determined in hindsight (Cover, 1991; Helmbold et al., 1996; =-=Cover and Ordentlich, 1996-=-a; Cover and Ordentlich, 1996b; Ordentlich and Cover, 1996; Cover, 1996). For the universal algorithm of Cover (Cover, 1991), we provide a simple analysis which naturally extends to the case of a fixe... |

80 | Portfolio selection using multiplicative updates
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- 1998
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Citation Context ...t of stocks from period to period. Recently there has been work on on-line investment strategies that are competitive with the best constant rebalanced portfolio determined in hindsight (Cover, 1991; =-=Helmbold et al., 1996-=-; Cover and Ordentlich, 1996a; Cover and Ordentlich, 1996b; Ordentlich and Cover, 1996; Cover, 1996). For the universal algorithm of Cover (Cover, 1991), we provide a simple analysis which naturally e... |

51 | Tight worst-case loss bounds for predicting with expert advice
- Haussler, Kivinen, et al.
- 1995
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Citation Context ... to explain a relationship between portfolios and weighted-average-type algorithms for making predictions from expert advice (Cesa-Bianchi et al., 1993; DeSantis et al., 1988; Foster and Vohra, 1993; =-=Haussler et al., 1994-=-; Kivanen and Warmuth, 1994; Vovk, 1990; Vovk, 1995). Acknowledgments We thank the anonymous referees for their helpful comments. This research was supported in part by NSF National Young Investigator... |

34 |
Learning probabilistic prediction functions
- DeSantis, Markowsky, et al.
- 1988
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Citation Context ...a small overhead as n gets large. It also helps to explain a relationship between portfolios and weighted-average-type algorithms for making predictions from expert advice (Cesa-Bianchi et al., 1993; =-=DeSantis et al., 1988-=-; Foster and Vohra, 1993; Haussler et al., 1994; Kivanen and Warmuth, 1994; Vovk, 1990; Vovk, 1995). Acknowledgments We thank the anonymous referees for their helpful comments. This research was suppo... |

34 | A comparison of new and old algorithms for a mixture estimation problem
- Helmbold, Singer, et al.
- 1995
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Citation Context ...mma ffi , the approximation achieves a wealth at least 1 \Gamma ffl times as large as the universal algorithm. For a given market with no commission, one can determine, in hindsight, the optimal CRP (=-=Helmbold et al., 1995-=-) and then estimate R. In the worst case R grows like n m\Gamma1 . However, experiments on stock market data, presented in (Cover, 1991; Helmbold et al., 1996), all have a ratio R ! 2 for various comb... |

33 |
A randomization rule for selecting forecasts
- Foster, Vohra
- 1993
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Citation Context ...ets large. It also helps to explain a relationship between portfolios and weighted-average-type algorithms for making predictions from expert advice (Cesa-Bianchi et al., 1993; DeSantis et al., 1988; =-=Foster and Vohra, 1993-=-; Haussler et al., 1994; Kivanen and Warmuth, 1994; Vovk, 1990; Vovk, 1995). Acknowledgments We thank the anonymous referees for their helpful comments. This research was supported in part by NSF Nati... |

20 | The cost of achieving the best portfolio in hindsight
- Ordentlich, Cover
- 1998
(Show Context)
Citation Context ...e a ratio R ! 2 for various combinations of two stocks, making this approach especially efficient. This same observation can be used to implement the Dirichelet(1=2; : : : ; 1=2) universal algorithm (=-=Cover and Ordentlich, 1996-=-a). In this case, it is an improvement because R grows, at worst, like n (m\Gamma1)=2 . 4. Analysis With Commission In this section, we introduce a slight modification of UNIVERSAL, UNIVERSAL c , whic... |

11 |
On-line portfolio selection
- Ordentlich, Cover
- 1996
(Show Context)
Citation Context ... that are competitive with the best constant rebalanced portfolio determined in hindsight (Cover, 1991; Helmbold et al., 1996; Cover and Ordentlich, 1996a; Cover and Ordentlich, 1996b; Ordentlich and =-=Cover, 1996-=-; Cover, 1996). For the universal algorithm of Cover (Cover, 1991), we provide a simple analysis which naturally extends to the case of a fixed percentage transaction cost (commission), answering a qu... |

9 |
Universal data compression and portfolio selection
- Cover
- 1996
(Show Context)
Citation Context ... that are competitive with the best constant rebalanced portfolio determined in hindsight (Cover, 1991; Helmbold et al., 1996; Cover and Ordentlich, 1996a; Cover and Ordentlich, 1996b; Ordentlich and =-=Cover, 1996-=-; Cover, 1996). For the universal algorithm of Cover (Cover, 1991), we provide a simple analysis which naturally extends to the case of a fixed percentage transaction cost (commission), answering a qu... |

6 |
A new interpretation of information rate, Bell Sys
- Kelly
- 1956
(Show Context)
Citation Context ...analogy between stocks and language models which shows how the UNIVERSAL algorithm can be applied to language models and other predictors. This analogy is more general than Kelly's racehorse analogy (=-=Kelly, 1956-=-) because it covers price relatives and probabilities other than just f0; 1g. A statistical language model is a probability distribution over sequences of words. A language model is generally represen... |