Transaction costs and resampling in mean-variance portfolio optimization

Transaction costs and resampling are two important issues that need great attention in every portfolio investment planning. In practice costs are incurred to rebalance a portfolio. Every investor tries to find a way of avoiding high transaction cost as much as possible. In this thesis, we investigated how transaction costs and resampling affect portfolio investment. We modified the basic mean-variance optimization problem to include rebalancing costs we incur on transacting securities in the portfolio. We also reduce trading as much as possible by applying the resampling approach any time we rebalance our portfolio. Transaction costs are assumed to be a percentage of the amount of securities transacted. We applied the resampling approach and tracked the performance of portfolios over time, assuming transaction costs and then no transaction costs are incurred. We compared how the portfolio is affected when we incorporated the two issues outlined above to that of the basic mean-variance optimization

A two-stage stochastic mixed-integer program modelling and hybrid solution approach to portfolio selection problems

In this paper, we investigate a multi-period portfolio selection problem with a comprehensive set of real-world trading constraints as well as market random uncertainty in terms of asset prices. We formulate the problem into a two-stage stochastic mixed-integer program (SMIP) with recourse. The set of constraints is modelled as mixed-integer program, while a set of decision variables to rebalance the portfolio in multiple periods is explicitly introduced as the recourse variables in the second stage of stochastic program. Although the combination of stochastic program and mixed-integer program leads to computational challenges in finding solutions to the problem, the proposed SMIP model provides an insightful and flexible description of the problem. The model also enables the investors to make decisions subject to real-world trading constraints and market uncertainty. To deal with the computational difficulty of the proposed model, a simplification and hybrid solution method is applied in the paper. The simplification method aims to eliminate the difficult constraints in the model, resulting into easier sub-problems compared to the original one. The hybrid method is developed to integrate local search with Branch-and-Bound (B&B) to solve the problem heuristically. We present computational results of the hybrid approach to analyse the performance of the proposed method. The results illustrate that the hybrid method can generate good solutions in a reasonable amount of computational time. We also compare the obtained portfolio values against an index value to illustrate the performance and strengths of the proposed SMIP model. Implications of the model and future work are also discussed

The misconception of the option value of deposit insurance and the efficacy of non-risk-based capital requirements in the literature on bank capital regulation

This study shows how the misconception of the option value of deposit insurance by Merton (1977) and its later misuse by Keeley and Furlong (1990), among others, have led some literature supporting the adoption of binding non-risk-based capital requirements to derive incorrect conclusions about their efficacy. This study further shows that what Merton defines as the option value of deposit insurance is actually a component of a bank?s limited liability option under a third-party deposit guarantee. As such, it is already included in the value of the bank?s equity capital, and the flawed definition makes the Keeley-Furlong model internally incoherent.Capital requirements, Credit risk, Deposit insurance, Prudential regulation, Portfolio approach

Is portfolio rebalancing good for investors?

Our study seeks to examine the value of various portfolio rebalancing strategies using historical data for 20-years period for U.S. which includes business cycles - expansion and contractions, our study is based on hypothetical of portfolio asset allocations - 60/40 (stock fund), 50/50 (balanced fund), and 40/60 (bond fund). We combine both periodical rebalancing (daily, monthly, quarterly, semi-annually, annually, 2nd-yearly, 3rd-yearly, 4th-yearly, and 5th-yearly) and threshold rebalancing (0%, 5%, 10%, 15%, 20%, 25% and 30%) in our study. We investigate for the whole 20-years period contraction and expansion periods. In the 20-years period, our findings show that: a) rebalancing strategies improve return of a portfolio as compared with buy-and-hold strategy, b) the rebalancing strategies results is slightly lower risk than buy-and-hold strategy, c) periodic rebalancing leads to better risk-return outcome than buy-and-hold strategy, and d) portfolio rebalancing based on certain threshold choice perform better buy-and-hold strategy in the long run. Based on the results of the study, we recommend the optimal rebalancing strategy for investors to be threshold rebalancing 25 percent/annually or 30 percent/annually. In addition, our results also indicate that the returns of rebalancing strategies during business cycles perform better than buy-and-hold strategy. However, the difference in portfolio performance of various rebalancing strategies vis-~\u2020-vis buy and hold strategy is not substantial to warrant a definitive recommendation of a particular portfolio rebalancing strategy. --Leaf iii.The original print copy of this thesis may be available here: http://wizard.unbc.ca/record=b195067

Fairness and optimality in trading

Thesis (S.M.)--Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2010.Cataloged from PDF version of thesis.Includes bibliographical references (p. 50-51).This thesis proposes a novel approach to address the issues of efficiency and fairness when multiple portfolios are rebalanced simultaneously. A fund manager who rebalances multiple portfolios needs to not only optimize the total efficiency, i.e., maximize net risk-adjusted return, but also guarantee that trading costs are fairly split among the clients. The existing approaches in the literature, namely the Social Welfare and the Competitive Equilibrium schemes, do not compromise efficiency and fairness effectively. To this end, we suggest an approach that utilizes popular and well-accepted resource allocation ideas from the field of communications and economics, such as Max-Min fairness, Proportional fairness and a-fairness. We incorporate in our formulation a quadratic model of market impact cost to reflect the cumulative effect of trade pooling. Total trading costs are split fairly among accounts using the so-called pro rata scheme. We solve the resulting multi-objective optimization problem by adopting the Max-Min fairness, Proportional fairness and a-fairness schemes. Under these schemes, the resulting optimization problems have non-convex objectives and non-convex constraints, which are NP-hard in general. We solve these problems using a local search method based on linearization techniques. The efficiency of this approach is discussed when we compare it with a deterministic global optimization method on small size optimization problems that have similar structure to the aforementioned problems. We present computational results for a small data set (2 funds, 73 assets) and a large set (6 funds, 73 assets). These results suggest that the solution obtained from our model provides a better compromise between efficiency and fairness than existing approaches. An important implication of our work is that given a level of fairness that we want to maintain, we can always find Pareto-efficient trade sets.by Van Vinh Nguyen.S.M

Portfolio optimisation with transaction cost

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.Portfolio selection is an example of decision making under conditions of uncertainty. In the face of an unknown future, fund managers make complex financial choices based on the investors perceptions and preferences towards risk and return. Since the seminal work of Markowitz, many studies have been published using his mean-variance (MV) model as a basis. These mathematical models of investor attitudes and asset return dynamics aid in the portfolio selection process. In this thesis we extend the MV model to include the cardinality constraints which limit the number of assets held in the portfolio and bounds on the proportion of an asset held (if any is held). We present our formulation based on the Markowitz MV model for rebalancing an existing portfolio subject to both fixed and variable transaction cost (the fee associated with trading). We determine and demonstrate the differences that arise in the shape of the trading portfolio and efficient frontiers when subject to non-cardinality and cardinality constrained transaction cost models. We apply our flexible heuristic algorithms of genetic algorithm, tabu search and simulated annealing to both the cardinality constrained and transaction cost models to solve problems using data from seven real world market indices. We show that by incorporating optimization into the generation of valid portfolios leads to good quality solutions in acceptable computational time. We illustrate this on problems from literature as well as on our own larger data sets

Enhanced index tracking with CVaR-based ratio measures

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Fuzzy portfolio optimization with tax, transaction cost and investment amount: a developing country case

The socioeconomic or political structures of countries and investment costs play a crucial role in investor decisions, especially in developing countries where the environment is unstable. In this regard, fuzzy models that consider the investment amount and cost may enable making more realistic decisions rather than the deterministic models used in portfolio optimization (PO). Hence, the objective of this paper is to examine the effects of the environment, investment amount and cost on PO in a politically, socially and economically unstable environment. Konno-Yamazaki PO model was fuzzified by adopting fuzzy linear programming (FLP) approaches of Verdegay and Werners for this purpose. Afterward, extended models were created. To do that, investment amount, tax and transaction costs were integrated into the return constraint of the fuzzified models. Mean-Variance Model (MVM) of Markowitz was also used for comparatively interpreting the results of the optimization. Results show that the fuzzified models based on Verdegay and Werners FLP approaches can be suggested as a decision-making tool, respectively for risk-averse and risk-taker investors. The extended models provide much better results compared to the fuzzified models. On the other hand, they are not more successful than the MVM in an unstable environment but the stable environment. The main contributions are onsidering political, social and economic events in the optimization, comparatively analyzing fuzzified Konno-Yamazaki model with its extended versions and the MVM, investigating the relationship between optimization models and investor types.</p

MULTIPERIOD PORTFOLIO OPTIMIZATION WITH TRANSACTION COSTS

Ph.DDOCTOR OF PHILOSOPH