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

Competitive portfolio selection using stochastic predictions

We study a portfolio selection problem where a player attempts to maximise a utility function that represents the growth rate of wealth. We show that, given some stochastic predictions of the asset prices in the next time step, a sublinear expected regret is attainable against an optimal greedy algorithm, subject to tradeoff against the \accuracy" of such predictions that learn (or improve) over time. We also study the effects of introducing transaction costs into the model

Growth optimal investment with threshold rebalancing portfolios under transaction costs

We study how to invest optimally in a stock market having a finite number of assets from a signal processing perspective. 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. This is achieved by 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. © 2013 IEEE

Message passing algorithms - methods and applications

Algorithms on graphs are used extensively in many applications and research areas. Such applications include machine learning, artificial intelligence, communications, image processing, state tracking, sensor networks, sensor fusion, distributed cooperative estimation, and distributed computation. Among the types of algorithms that employ some kind of message passing over the connections in a graph, the work in this dissertation will consider belief propagation and gossip consensus algorithms. We begin by considering the marginalization problem on factor graphs, which is often solved or approximated with Sum-Product belief propagation (BP) over the edges of the factor graph. For the case of sensor networks, where the conservation of energy is of critical importance and communication overhead can quickly drain this valuable resource, we present techniques for specifically addressing the needs of this low power scenario. We create a number of alternatives to Sum-Product BP. The first of these is a generalization of Stochastic BP with reduced setup time. We then present Projected BP, where a subset of elements from each message is transmitted between nodes, and computational savings are realized in proportion to the reduction in size of the transmitted messages. Zoom BP is a derivative of Projected BP that focuses particularly on utilizing low bandwidth discrete channels. We give the results of experiments that show the practical advantages of our alternatives to Sum-Product BP. We then proceed with an application of Sum-Product BP in sequential investment. We combine various insights from universal portfolios research in order to construct more sophisticated algorithms that take into account transaction costs. In particular, we use the insights of Blum and Kalai's transaction costs algorithm to take these costs into account in Cover and Ordentlich's side information portfolio and Kozat and Singer's switching portfolio. This involves carefully designing a set of causal portfolio strategies and computing a convex combination of these according to a carefully designed distribution. Universal (sublinear regret) performance bounds for each of these portfolios show that the algorithms asymptotically achieve the wealth of the best strategy from the corresponding portfolio strategy set, to first order in the exponent. The Sum-Product algorithm on factor graph representations of the universal investment algorithms provides computationally tractable approximations to the investment strategies. Finally, we present results of simulations of our algorithms and compare them to other portfolios. We then turn our attention to gossip consensus and distributed estimation algorithms. Specifically, we consider the problem of estimating the parameters in a model of an agent's observations when it is known that the population as a whole is partitioned into a number of subpopulations, each of which has model parameters that are common among the member agents. We develop a method for determining the beneficial communication links in the network, which involves maintaining non-cooperative parameter estimates at each agent, and the distance of this estimate is compared with those of the neighbors to determine time-varying connectivity. We also study the expected squared estimation error of our algorithm, showing that estimates are asymptotically as good as centralized estimation, and we study the short term error convergence behavior. Finally, we examine the metrics used to guide the design of data converters in the setting of digital communications. The usual analog to digital converters (ADC) performance metrics---effective number of bits (ENOB), total harmonic distortion (THD), signal to noise and distortion ratio (SNDR), and spurious free dynamic range (SFDR)---are all focused on the faithful reproduction of observed waveforms, which is not of fundamental concern if the data converter is to be used in a digital communications system. Therefore, we propose other information-centric rather than waveform-centric metrics that are better aligned with the goal of communications. We provide computational methods for calculating the values of these metrics, some of which are derived from Sum-Product BP or related algorithms. We also propose Statistics Gathering Converters (SGCs), which represent a change in perspective on data conversion for communications applications away from signal representation and towards the collection of relevant statistics for the purposes of decision making and detection. We show how to develop algorithms for the detection of transmitted data when the transmitted signal is received by an SGC. Finally, we provide evidence for the benefits of using system-level metrics and statistics gathering converters in communications applications

Turnover, account value and diversification of real traders: evidence of collective portfolio optimizing behavior

Despite the availability of very detailed data on financial market, agent-based modeling is hindered by the lack of information about real trader behavior. This makes it impossible to validate agent-based models, which are thus reverse-engineering attempts. This work is a contribution to the building of a set of stylized facts about the traders themselves. Using the client database of Swissquote Bank SA, the largest on-line Swiss broker, we find empirical relationships between turnover, account values and the number of assets in which a trader is invested. A theory based on simple mean-variance portfolio optimization that crucially includes variable transaction costs is able to reproduce faithfully the observed behaviors. We finally argue that our results bring into light the collective ability of a population to construct a mean-variance portfolio that takes into account the structure of transaction costsComment: 26 pages, 9 figures, Fig. 8 fixe

Semi-universal portfolios with transaction costs

Ministry of Education, Singapore under its Academic Research Funding Tier

Liquidity risks, transaction costs and online portfolio selection

The performance of online (sequential) portfolio selection (OPS), which rebalances a portfolio in every period (e.g. daily or weekly) in order to maximise the portfolio's expected terminal wealth in the long run, has been overestimated by the ideal assumption of unlimited market liquidity (i.e. no market impact costs). Therefore, a new transaction cost factor model that considers both market impact costs, estimated from limit order book data, and proportional transaction costs (e.g. brokerage commissions or transaction taxes in a fixed percentage) has been proposed in this paper to measure existing OPS strategies performance in a more practical way as well as to develop a more effective OPS method. Backtesting results from the historical limit order book (LOB) data of NASDAQ-traded stocks show both the performance deterioration of existing OPS methods by the market impact costs and the superiority of our proposed OPS method in the environment of limited market liquidity

Time-series and cross-sectional price momentum: Applying the Dual Momentum strategy from a Norwegian perspective

Master's thesis in Business Administration: Executive MBATime-series and cross-sectional price momentum have been observed in the majority of asset classes around the globe. This thesis investigates and replicates the Dual Momentum strategy created by Antonacci (2014) from a Norwegian perspective. The Dual Momentum strategy combines both time-series and cross-sectional price momentum and applies the price momentum to indexes. Using indexes simplifies and reduces the transaction cost compared to momentum strategies that involve large stock portfolios. The Dual Momentum strategy uses the current price and the historical price less the risk-free rate to determine if an asset’s momentum is positive over the last twelve months. The asset with the highest momentum is held, unless the momentum is negative, then high-quality bonds are held until the momentum returns to positive. In this thesis OBX and ST5X serve as the Norwegian assets, and 39 different foreign indexes have been tested as the third asset of the Dual Momentum strategy. The results show impressive risk-adjusted returns, lower standard deviations, higher sharpe ratio and lower maximum drawdowns than holding OBX as a passive index investment in the same period. The vast majority of the Dual Momentum portfolios return significant positive alphas after the CAPM model, Fama-French and Carhart factors are applied in regression analysis. The thesis validates the Dual Momentum strategy from the Norwegian perspective in the tested sample period of 21 years. The strategy produces higher risk-adjusted returns in the sample period than the benchmark, and the findings are in line with the current price momentum literature