T. Cover
Selected Papers on Portfolio Theory

  1. Robert M. Bell and Thomas M. Cover. Competitive Optimality of Logarithmic Investment. Mathematics of Operations Research, 5(2):161--166, May 1980.

  2. Thomas M. Cover. An Algorithm for Maximizing Expected Log Investment Return. IEEE Transactions on Information Theory, IT-30(2):369--373, March 1984.

  3. Thomas M. Cover and David H. Gluss. Empirical Bayes Stock Market Portfolios. Advances in Applied Mathematics, (7):170-181, 1986. Summary of this paper appears in: Proceedings of Conference Honoring Herbert Robbins, Springer-Verlag, 1986. Abstract and Summary appears in ``Adaptive Statistical Procedures and Related Topics,'' IMS Lecture Notes Monograph Series, Vol. 8, ed. by J. Van Ryzin.

  4. Thomas M. Cover. Log Optimal Portfolios. Chapter in Gambling Research: Gambling and Risk Taking, Seventh International Conference, Vol 4: Quantitative Analysis and Gambling, ed. by W.E. Eadington, 1987, Reno, Nevada.

  5. Robert Bell and Thomas M. Cover. Game-Theoretic Optimal Portfolios. Management Science, 34(6): 724-733, June 1988.

  6. Andrew R. Barron and Thomas M. Cover. A Bound on the Financial Value of Information. IEEE Transactions of Information Theory., 34(5): 1097-1100, September 1988.

  7. Paul H. Algoet and Thomas M. Cover. Asymptotic Optimality and Asymptotic Equipartition Properties of Log-Optimum Investment. The Annals of Probability, 16(2): 876-898, 1988.

  8. T. Cover and J. Thomas. Information Theory and the Stock Market. chapter in Elements of Information Theory, pp.459-481, Wiley & Sons, New York, 1991.

  9. Thomas M. Cover. Universal Portfolios. Mathematical Finance, 1(1): 1-29, January 1991.

  10. Thomas M. Cover and Erik Ordentlich. Universal Portfolios with Side Information. IEEE Transactions on Information Theory, 42(2):348-363, March 1996.

  11. Elza Erkip and Thomas M. Cover. The Efficiency of Investment Information. IEEE Transactions on Information Theory, 4(3):1026-1040, May 1998.

  12. Erik Ordentlich and Thomas M. Cover. The Cost of Achieving the Best Portfolio in Hindsight. Mathematics of Operations Research, 23(4):960-982, November 1998.

  13. Garud N. Iyengar and Thomas M. Cover. Growth Optimal Investment in Horse Race Markets with Costs, IEEE Transactions on Information Theory, 46(7):2675-2683, November 2000.

  14. Charles Mathis and Thomas Cover. A Statistic for Measuring the Influence of Side Information in Investment. Proceedings of the IEEE International Symposium on Information Theory, pp.1156-1157, September 2005.

Competitive optimality

Bell and Cover [1980], Bell and Cover [1988]. These papers solve the two-person zero-sum game in which one player wishes to outperform the other. One should choose a randomized version of the log optimal portfolio for each of the players. Gives different approach to the St. Petersburg paradox.

Kelly and the value of side information

Here the paper Barron and Cover [1988] generalizes Kelly's statement that the mutual information I(X;Y) between a horse race market X and side information Y gives the increase in the growth rate of wealth in repeated investments. The mutual information is always an upper bound on the increase in growth rate, for any market distribution F(x,y), with equality if and only if the stock market is a horse race market.

Growth rate optimality

The paper Algoet and Cover [1988] finds the optimal growth rate of wealth for arbitrary stationary markets. The optimal investment at any given time maximizes the conditional expected log wealth factor given the past. This turns out to be a generalization of the Shannon-MacMillan-Breiman theorem that states for any ergodic process that -(1/n) log p(X_1,...,X_n)--> H, where H is the entropy rate.

Universal portfolios

"Universal Portfolios," Cover [1991] introduces a portfolio that does as well to first order in the exponent as the best constant rebalanced portfolio. This paper contains graphs of the performance of the portfolio on real stock market sequences. The paper Cover and Ordentlich [1996] finds precise upper and lower bounds on the ratio of universal portfolio wealth to the best wealth achievable by a constant rebalanced portfolio given hindsight. It also makes optimal use of side information by using the side information states to break the market sequence into subsequences labeled by the state. And the culminating paper, Ordentlich and Cover [1988], "The Cost of Achieving the Best Portfolio in Hindsight," gives an exact minimax result for the value of a game with fixed horizon n in which the player must announce some causal portfolio strategy and his opponent is allowed to choose any stock market sequence and the best constant rebalanced portfolio for that sequence. Here the payoff is the ratio of player 1's wealth to the wealth of his opponent at time n. Mathis and Cover [2006], Information Theory Conference Proceedings, shows that if one compares the wealth achievable with side information to that achievable by a constant rebalanced portfolio, one can see whether the increase in wealth is illusory or not and therefore whether side information is valuable. The improvement due to random side information is simply of the form e^1/2 Z^2 where Z is a standard normal random variable and show how to use it.