Growth optimal investment in discrete-time markets with proportional transaction costs

We investigate how and when to diversify capital over assets, i.e., the portfolio selection problem, from a signal processing perspective. To this end, we first construct portfolios that achieve the optimal expected growth in i.i.d. discrete-time two-asset markets under proportional transaction costs. We then extend our analysis to cover markets having more than two stocks. The market is modeled by a sequence of price relative vectors with arbitrary discrete distributions, which can also be used to approximate a wide class of continuous distributions. To achieve the optimal growth, we use threshold portfolios, where we introduce a recursive update to calculate the expected wealth. We then demonstrate that under the threshold rebalancing framework, the achievable set of portfolios elegantly form an irreducible Markov chain under mild technical conditions. We evaluate the corresponding stationary distribution of this Markov chain, which provides a natural and efficient method to calculate the cumulative expected wealth. Subsequently, the corresponding parameters are optimized yielding the growth optimal portfolio under proportional transaction costs in i.i.d. discrete-time two-asset markets. As a widely known financial problem, we also solve the optimal portfolio selection problem in discrete-time markets constructed by sampling continuous-time Brownian markets. For the case that the underlying discrete distributions of the price relative vectors are unknown, we provide a maximum likelihood estimator that is also incorporated in the optimization framework in our simulations

Optimal Investment Under Transaction Costs: A Threshold Rebalanced Portfolio Approach

We study optimal investment in a financial market having a finite number of assets from a signal processing perspective. We investigate how an investor should distribute capital over these assets and when he should reallocate the distribution of the funds over these assets to maximize the cumulative wealth over any investment period. In particular, we introduce a portfolio selection algorithm that maximizes the expected cumulative wealth in i.i.d. two-asset discrete-time markets where the market levies proportional transaction costs in buying and selling stocks. We achieve this using "threshold rebalanced portfolios", where trading occurs only if the portfolio breaches certain thresholds. Under the assumption that the relative price sequences have log-normal distribution from the Black-Scholes model, we evaluate the expected wealth under proportional transaction costs and find the threshold rebalanced portfolio that achieves the maximal expected cumulative wealth over any investment period. Our derivations can be readily extended to markets having more than two stocks, where these extensions are pointed out in the paper. As predicted from our derivations, we significantly improve the achieved wealth over portfolio selection algorithms from the literature on historical data sets.Comment: Submitted to IEEE Transactions on Signal Processin

On the Measurement of financial market integration.

The paper presents sorne vector optimization problems to measure arbitrage and integration of financial markets. This new approach may be applied under static or dynamic asset pricing assumptions and leads to both, numerical and stochastic integration measures. Thus, the paper provides a new methodology in a very general setting, allowing many instruments in each market to test optimal arbitrage portfolios depending on the state of nature and the date. Markets with frictions are also analyzed, and sorne empirical results are presented.El artículo aplica la optimización vectorial para introducir nuevos procedimientos que miden el nivel de arbitraje e integración de mercados financieros. Las técnicas son aplicables tanto bajo supuestos estáticos, como bajo supuestos dinámicos de valoración de activos. Por consiguiente el nivel de generalidad es alto, y se proporcionan instrumentos que permiten determinar estrategias de arbitraje óptimas de carácter dinámico y estocástico. Finalmente, también se analizan los mercados con fricciones y se presentan los resultados de algunas contrastaciones empíricas.Vector optimization; Arbitrage portfolio; Dual problem; Pricing rule;

Migration, credit markets, moral hazard, interlinkage.

A fast numerical algorithm is developed to price European options with proportional transaction costs using the utility maximization framework of Davis (1997). This approach allows option prices to be computed by solving the investor's basic portfolio selection problem, without the inser- tion of the option payo into the terminal value function. The properties of the value function can then be used to drastically reduce the number of operations needed to locate the boundaries of the no transaction region, which leads to very e cient option valuation. The optimization problem is solved numerically for the case of exponential utility, and comparisons with approximately replicating strategies reveal tight bounds for option prices even as transaction costs become large. The computational tech- nique involves a discrete time Markov chain approximation to a continuous time singular stochastic optimal control problem. A general de nition of an option hedging strategy in this framework is developed. This involves calculating the perturbation to the optimal portfolio strategy when an option trade is execute

Efficient option pricing with transaction costs

A fast numerical algorithm is developed to price European options with proportional transaction costs using the utility-maximization framework of Davis (1997). This approach allows option prices to be computed by solving the investor’s basic portfolio selection problem without insertion of the option payoff into the terminal value function. The properties of the value function can then be used to drastically reduce the number of operations needed to locate the boundaries of the no-transaction region, which leads to very efficient option valuation. The optimization problem is solved numerically for the case of exponential utility, and comparisons with approximately replicating strategies reveal tight bounds for option prices even as transaction costs become large. The computational technique involves a discrete-time Markov chain approximation to a continuous-time singular stochastic optimal control problem. A general definition of an option hedging strategy in this framework is developed. This involves calculating the perturbation to the optimal portfolio strategy when an option trade is executed

Optimal portfolio control with trading strategies of finite variation

We propose a method for portfolio selection where the trading strategies are constrained to have a finite variation. A simulation example shows a significant reduction in trasaction costs as compared to log-optimal portfolio, for almost same final wealth

Testing Affine Term Structure Models in Case of Transaction Costs

In this paper we empirically analyze the impact of transaction costs on the performance of affine interest rate models. We test the implied (no arbitrage) Euler restrictions, and we calculate the specification error bound of Hansen and Jagannathan to measure the extent to which a model is misspecified. Using data on T-bill and bond returns we find, under the assumption of frictionless markets, strong evidence of misspecification of one- and two-factor affine interest rate models. This is in line with earlier research. However, we show that the pricing errors of these models are reduced considerably, if relatively small transaction costs are taken into account. The average transaction costs for T-bills, due to the bid-ask spread, are around 1.5 basis points. At this size of transaction costs and for monthly holding periods, the misspecification of one- and two-factor affine interest rate models becomes statistically insignificant and economically very small. For quarterly holding periods, higher transaction costs of around 3 basis points are required to avoid misspecification.