Application of the Kelly Criterion to Ornstein-Uhlenbeck Processes

In this paper, we study the Kelly criterion in the continuous time framework building on the work of E.O. Thorp and others. The existence of an optimal strategy is proven in a general setting and the corresponding optimal wealth process is found. A simple formula is provided for calculating the optimal portfolio for a set of price processes satisfying some simple conditions. Properties of the optimal investment strategy for assets governed by multiple Ornstein-Uhlenbeck processes are studied. The paper ends with a short discussion of the implications of these ideas for financial markets.Comment: presented at Complex'2009 (Shanghai, Feb. 23-25

Rebalancing Frequency Considerations for Kelly-Optimal Stock Portfolios in a Control-Theoretic Framework

In this paper, motivated by the celebrated work of Kelly, we consider the problem of portfolio weight selection to maximize expected logarithmic growth. Going beyond existing literature, our focal point here is the rebalancing frequency which we include as an additional parameter in our analysis. The problem is first set in a control-theoretic framework, and then, the main question we address is as follows: In the absence of transaction costs, does high-frequency trading always lead to the best performance? Related to this is our prior work on betting, also in the Kelly context, which examines the impact of making a wager and letting it ride. Our results on betting frequency can be interpreted in the context of weight selection for a two-asset portfolio consisting of one risky asset and one riskless asset. With regard to the question above, our prior results indicate that it is often the case that there are no performance benefits associated with high-frequency trading. In the present paper, we generalize the analysis to portfolios with multiple risky assets. We show that if there is an asset satisfying a new condition which we call dominance, then an optimal portfolio consists of this asset alone; i.e., the trader has "all eggs in one basket" and performance becomes a constant function of rebalancing frequency. Said another way, the problem of rebalancing is rendered moot. The paper also includes simulations which address practical considerations associated with real stock prices and the dominant asset condition.Comment: To appear in the Proceedings of the IEEE Conference on Decision and Control, Miami Beach, FL, 201

Well-temperate phage: optimal bet-hedging against local environmental collapses

Upon infection of their bacterial hosts temperate phages must chose between lysogenic and lytic developmental strategies. Here we apply the game-theoretic bet-hedging strategy introduced by Kelly to derive the optimal lysogenic fraction of the total population of phages as a function of frequency and intensity of environmental downturns affecting the lytic subpopulation. "Well-temperate" phage from our title is characterized by the best long-term population growth rate. We show that it is realized when the lysogenization frequency is approximately equal to the probability of lytic population collapse. We further predict the existence of sharp boundaries in system's environmental, ecological, and biophysical parameters separating the regions where this temperate strategy is optimal from those dominated by purely virulent or} dormant (purely lysogenic) strategies. We show that the virulent strategy works best for phages with large diversity of hosts, and access to multiple independent environments reachable by diffusion. Conversely, progressively more temperate or even dormant strategies are favored in the environments, that are subject to frequent and severe temporal downturns.Comment: 26 pages, 3 figure

The Viability of Trade Union Organisation: A Bargaining Unit Analysis

The paper develops a model of trade union behaviour based on the concept of the viable bargaining unit. Bargaining unit viability rests on five conditions; membership level, service level, membership participation, employer recognition and facilities. Viability is achieved by mobilisation of both members and employers. Trade unions may be seen as portfolios of viable and inviable bargaining units. From this, six propositions about trade union structure and behaviour are derived, concerning scale, growth, the impact of statutory recognition provisions, the emergence of conglomerate unions, governance structures and relations with employers. Employer dependence is a crucial element in the model and a simple game theoretic approach is used to discuss employer co-operation. A key conclusion is that viability at the union level is achieved by diversifying portfolios of bargaining units and securing co-operative relations with employers.Unions, structure, strategy

Practical implementation of the Kelly criterion: optimal growth rate, number of trades, and rebalancing frequency for equity portfolios

We develop a general framework to apply the Kelly criterion to the stock market data, and consequently, to portfolio optimization. Under few conditions, using Monte Carlo simulations with different scenarios we prove that the Kelly criterion beats any other approach in many aspects. In particular, it maximizes the expected growth rate and the median of the terminal wealth. We also show that, under a normal distribution of returns, the Kelly criterion has the best performance in the long run. Next, we optimize a portfolio with the Kelly criterion with no leverage and no short selling conditions and show that this portfolio lays in the mean-variance efficient frontier and has higher expected return and higher variance, although it is less diversified, respect to the tangent portfolio optimized under the Markowitz approach. Finally, we implement a dynamic strategy applied on the European stock market data and compare the results between the tangent and the optimal Kelly portfolios. In a dynamic setting, the rolling Kelly portfolio outperforms competitors particularly in the case of rebalanced portfolios optimized with a 2-years window width

The Kelly Criterion : An empricial study of the growth optimal Kelly portfolio, backtested on the Oslo Stock Exchange

This study analyzes the performance of the growth optimal Kelly portfolio on the Norwegian stock market from February 2003 through December 2022. To measure the strategy’s alpha, we employ the Capital Asset Pricing Model, Fama French’s three-factor model and Carhart’s four-factor model. The Kelly portfolio generates a higher annual growth rate than the benchmark, and consequently a higher ending wealth level. Our results indicate that the strategy generates an annualized alpha of 16.8%, significant on a 1% level. However, the models show very poor explanatory power, prohibiting us from drawing a meaningful conclusion. Furthermore, when accounting for transaction costs, the portfolio no longer achieves a higher wealth level than the benchmark, and the corresponding alpha is only significant on a 10% level, indicating that the strategy is unable to generate risk-adjusted excess returns in the real world.nhhma