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

INVESTMENT PORTFOLIO REBALANCING DECISION MAKING

Nowadays financial markets’ volatility and significant stock prices’ fluctuations allow improving investment return actively managing investment portfolio, rather than choosing long term investment strategy. Active portfolio management also allows personal investor’s development and gives opportunity to avoid losses in terms of market instability. However active portfolio management is more risky. Rebalancing the investment portfolio investor incurs real costs for expected return, so actively managing the investment portfolio it is crucial to use a good, investor needs meeting portfolio rebalancing method. Dealing with mentioned problem scientific information sources analysis is made and a new portfolio rebalancing method is suggested in the article

A memetic algorithm for cardinality-constrained portfolio optimization with transaction costs

This is the author’s version of a work that was accepted for publication in Applied Soft Computing. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Applied Soft Computing, Vol 36 (2015) DOI 10.1016/j.asoc.2015.06.053A memetic approach that combines a genetic algorithm (GA) and quadratic programming is used to address the problem of optimal portfolio selection with cardinality constraints and piecewise linear transaction costs. The framework used is an extension of the standard Markowitz mean–variance model that incorporates realistic constraints, such as upper and lower bounds for investment in individual assets and/or groups of assets, and minimum trading restrictions. The inclusion of constraints that limit the number of assets in the final portfolio and piecewise linear transaction costs transforms the selection of optimal portfolios into a mixed-integer quadratic problem, which cannot be solved by standard optimization techniques. We propose to use a genetic algorithm in which the candidate portfolios are encoded using a set representation to handle the combinatorial aspect of the optimization problem. Besides specifying which assets are included in the portfolio, this representation includes attributes that encode the trading operation (sell/hold/buy) performed when the portfolio is rebalanced. The results of this hybrid method are benchmarked against a range of investment strategies (passive management, the equally weighted portfolio, the minimum variance portfolio, optimal portfolios without cardinality constraints, ignoring transaction costs or obtained with L1 regularization) using publicly available data. The transaction costs and the cardinality constraints provide regularization mechanisms that generally improve the out-of-sample performance of the selected portfolios

Combining Alpha Streams with Costs

We discuss investment allocation to multiple alpha streams traded on the same execution platform with internal crossing of trades and point out differences with allocating investment when alpha streams are traded on separate execution platforms with no crossing. First, in the latter case allocation weights are non-negative, while in the former case they can be negative. Second, the effects of both linear and nonlinear (impact) costs are different in these two cases due to turnover reduction when the trades are crossed. Third, the turnover reduction depends on the universe of traded alpha streams, so if some alpha streams have zero allocations, turnover reduction needs to be recomputed, hence an iterative procedure. We discuss an algorithm for finding allocation weights with crossing and linear costs. We also discuss a simple approximation when nonlinear costs are added, making the allocation problem tractable while still capturing nonlinear portfolio capacity bound effects. We also define "regression with costs" as a limit of optimization with costs, useful in often-occurring cases with singular alpha covariance matrix.Comment: 21 pages; minor misprints corrected; to appear in The Journal of Ris

Arbitrage and Control Problems in Finance. Presentation.

The theory of asset pricing takes its roots in the Arrow-Debreu model (see,for instance, Debreu 1959, Chap. 7), the Black and Scholes (1973) formula,and the Cox and Ross (1976) linear pricing model. This theory and its link to arbitrage has been formalized in a general framework by Harrison and Kreps (1979), Harrison and Pliska (1981, 1983), and Du¢e and Huang (1986). In these models, security markets are assumed to be frictionless: securities can be sold short in unlimited amounts, the borrowing and lending rates are equal, and there is no transaction cost. The main result is that the price process of traded securities is arbitrage free if and only if there exists some equivalent probability measure that transforms it into a martingale, when normalized by the numeraire. Contingent claims can then be priced by taking the expected value of their (normalized) payo§ with respect to any equivalent martingale measure. If this value is unique, the claim is said to be priced by arbitrage and it can be perfectly hedged (i.e. duplicated) by dynamic trading. When the markets are dynamically complete, there is only one such a and any contingent claim is priced by arbitrage. The of each state of the world for this probability measure can be interpreted as the state price of the economy (the prices of $1 tomorrow in that state of the world) as well as the marginal utilities (for consumption in that state of the world) of rational agents maximizing their expected utility.arbitrage, control problem

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