Trading strategies generated by Lyapunov functions

Functional portfolio generation, initiated by E.R. Fernholz almost twenty years ago, is a methodology for constructing trading strategies with controlled behavior. It is based on very weak and descriptive assumptions on the covariation structure of the underlying market model, and needs no estimation of model parameters. In this paper, the corresponding generating functions G are interpreted as Lyapunov functions for the vector process μ(⋅) of market weights; that is, via the property that G(μ(⋅)) is a supermartingale under an appropriate change of measure. This point of view unifies, generalizes, and simplifies several existing results, and allows the formulation of conditions under which it is possible to outperform the market portfolio over appropriate time-horizons. From a probabilistic point of view, the present paper yields results concerning the interplay of stochastic discount factors and concave transformations of semimartingales on compact domains

Diversifying an Index

In July 2023, Nasdaq announced a `Special Rebalance' of the Nasdaq-100 index to reduce the index weights of its large constituents. A rebalance as suggested currently by Nasdaq index methodology may have several undesirable effects. These effects can be avoided by a different, but simple rebalancing strategy. Such rebalancing is easily computable and guarantees (a) that the maximum overall index weight does not increase through the rebalancing and (b) that the order of index weights is preserved

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

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

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

Trading Strategies Generated Pathwise by Functions of Market Weights

Almost twenty years ago, E.R. Fernholz introduced portfolio generating functions which can be used to construct a variety of portfolios, solely in the terms of the individual companies' market weights. I. Karatzas and J. Ruf recently developed another methodology for the functional construction of portfolios, which leads to very simple conditions for strong relative arbitrage with respect to the market. In this paper, both of these notions of functional portfolio generation are generalized in a pathwise, probability-free setting; portfolio generating functions are substituted by path-dependent functionals, which involve the current market weights, as well as additional bounded-variation functions of past and present market weights. This generalization leads to a wider class of functionally-generated portfolios than was heretofore possible, and yields improved conditions for outperforming the market portfolio over suitable time-horizons.Comment: 45 pages, 3 figure