Functionally generated portfolios in stochastic portfolio theory

In this dissertation, we focus on constructing trading strategies through the method of functional generation. Such a construction is of great importance in Stochastic Portfolio Theory established by Robert Fernholz. This method is simplified by Karatzas and Ruf (Finance and Stochastics 21.3:753-787, 2017), where they also propose another method called additive functional generation. Inspired by their work, we first investigate the dependence of functional generation on an extra finite-variation process. A mollification argument and Komlós theorem yield a general class of potential arbitrage strategies. Secondly, we extend the analysis by incorporating transaction costs proportional to the trading volume. The performance of several portfolios in the presence of dividends and transaction costs is examined under different configurations. Next, we analyse the so-called leakage effect used to measure the loss in portfolio wealth due to renewing the portfolio constituents. Moreover, we further explore the method of additive functional generation by considering the conjugate of a portfolio generating function. The connection between functional generation and optimal transport is also studied. An extended abstract can be found before the first chapter of this dissertation

Leakage of rank-dependent functionally generated trading strategies

This paper investigates the so-called leakage effect of trading strategies generated functionally from rank-dependent portfolio generating functions. This effect measures the loss in wealth of trading strategies due to renewing the portfolio constituent stocks. Theoretically, the leakage effect of a trading strategy is expressed explicitly by a finite-variation term. The computation of the leakage is different from what previous research has suggested. The method to estimate leakage in discrete time is then introduced with some practical considerations. An empirical example illustrates the leakage of the corresponding trading strategies under different constituent list sizes.Comment: 13 pages, 2 figure

Impact of proportional transaction costs on systematically generated portfolios

The effect of proportional transaction costs on systematically generated portfolios is studied em- pirically. The performance of several portfolios (the index tracking portfolio, the equally-weighted portfolio, the entropy-weighted portfolio, and the diversity-weighted portfolio) in the presence of dividends and transaction costs is examined under different configurations involving the trading fre- quency, constituent list size, and renewing frequency. All portfolios outperform the index tracking portfolio in the absence of transaction costs. This outperformance is statistically significant for daily and weekly traded portfolios but not for monthly traded portfolios. However, when proportional transaction costs of 0.5% are imposed, most portfolios no longer outperform the market. Some exceptional cases include the entropy-weighted and the diversity-weighted portfolios under specific configurations. The only statistical significant difference appears for the relative underperformance of the equally-weighted portfolio

Generalised Lyapunov functions and functionally generated trading strategies

This paper investigates the dependence of functional portfolio generation, introduced by Fernholz (1999), on an extra finite variation process. The framework of Karatzas and Ruf (2017) is used to formulate conditions on trading strategies to be strong arbitrage relative to the market over sufficiently large time horizons. A mollification argument and Komlós theorem yield a general class of potential arbitrage strategies. These theoretical results are complemented by several empirical examples using data from the S&P 500 stocks