Optimal Index Tracking Under Transaction Costs and Impulse Control

1998 ◽  
Vol 01 (03) ◽  
pp. 315-330 ◽  
Author(s):  
I. R. C. Buckley ◽  
R. Korn
Keyword(s):  
Transaction Costs ◽  
Optimal Strategy ◽  
Impulse Control ◽  
Tracking Error ◽  
Management Problem ◽  
Index Tracking ◽  
Cash Management ◽  
Proportional Transaction Costs ◽  
Control Techniques ◽  
Mean Variance

We apply impulse control techniques to a cash management problem within a mean-variance framework. We consider the strategy of an investor who is trying to minimise both fixed and proportional transaction costs, whilst minimising the tracking error with respect to an index portfolio. The cash weight is constantly fluctuating due to the stochastic inflow and outflow of dividends and liabilities. We show the existence of an optimal strategy and compute it numerically.

A Simulation Analysis on the Tradeoff Between Cost and Risk in Replicating ELS (Equity-Linked Securities) with Transactions Costs: The Early Redeemable Case

2009 ◽  
Vol 17 (2) ◽  
pp. 1-47
Author(s):  
Jun Young Park ◽  
Chongseok Hyun
Keyword(s):  
Transaction Costs ◽  
Simulation Analysis ◽  
Transactions Costs ◽  
Proportional Transaction Costs ◽  
Underlying Asset ◽  
Trade Off ◽  
Computational Burden ◽  
Considerable Impact ◽  
The Right ◽  
Mean Variance

The trade-off between cost and risk of discretely rebalanced ELS hedges is analyzed under the proportional transaction costs. The analysis shows that the transaction costs have a considerable impact on the hedging performance. The trade-off, or mean-variance graphs move in the right and lower directions in cases that the drift or the volatility of the underlying asset increases, the redemption level of the ELS decreases, or the maturity of the ELS gets longer. The underlying asset move-based strategy (UAMB) reveals better performances than the time-based strategy (TS), while the delta move-based strategy (DMB) shows worse results. However, as the volatility of the underlying asset grows, the time-based strategy shows worse performances than the other two strategies does. The difficulty of computational burden in simulating the hedge procedure is alleviated using the vectorized scheme, which makes the simulation analysis in feasible time.

scholarly journals SCALED AND STABLE MEAN-VARIANCE-EVAR PORTFOLIO SELECTION STRATEGY WITH PROPORTIONAL TRANSACTION COSTS

2017 ◽  
Vol 18 (4) ◽  
pp. 561-584 ◽  
Author(s):  
Ebenezer Fiifi Emire ATTA MILLS ◽  
Bo YU ◽  
Jie YU
Keyword(s):  
Transaction Costs ◽  
Portfolio Selection ◽  
Downside Risk ◽  
Estimation Risk ◽  
Expected Return ◽  
Proportional Transaction Costs ◽  
Portfolio Returns ◽  
L2 Norm ◽  
The Mean ◽  
Mean Variance

This paper studies a portfolio optimization problem with variance and Entropic Value-at-Risk (evar) as risk measures. As the variance measures the deviation around the expected return, the introduction of evar in the mean-variance framework helps to control the downside risk of portfolio returns. This study utilized the squared l2-norm to alleviate estimation risk problems arising from the mean estimate of random returns. To adequately represent the variance-evar risk measure of the resulting portfolio, this study pursues rescaling by the capital accessible after payment of transaction costs. The results of this paper extend the classical Markowitz model to the case of proportional transaction costs and enhance the efficiency of portfolio selection by alleviating estimation risk and controlling the downside risk of portfolio returns. The model seeks to meet the requirements of regulators and fund managers as it represents a balance between short tails and variance. The practical implications of the findings of this study are that the model when applied, will increase the amount of capital for investment, lower transaction cost and minimize risk associated with the deviation around the expected return at the expense of a small additional risk in short tails.

scholarly journals Estratégia Long-Short, Neutra ao Mercado, e Index Tracking Baseadas em Portfólios Cointegrados

2010 ◽  
Vol 8 (4) ◽  
pp. 469
Author(s):  
João Frois Caldeira ◽  
Marcelo Savino Portugal
Keyword(s):  
Ad Hoc ◽  
Tracking Error ◽  
Covariance Matrices ◽  
Return Level ◽  
Index Tracking ◽  
Optimal Portfolios ◽  
The Mean ◽  
Efficient Allocations ◽  
Mean Variance ◽  
Tracking Portfolios

The traditional models to optimize portfolios based on mean-variance analysis aim to determine the portfolio weights that minimize the variance for a certain return level. The covariance matrices used to optimize are difficult to estimate and ad hoc methods often need to be applied to limit or smooth the mean-variance efficient allocations recommended by the model. Although the method is efficient, the tracking error isn’t certainly stationary, so the portfolio can get distant from the benchmark, requiring frequent re-balancements. This work uses cointegration methodology to devise two quantitative strategies: index tracking and long-short market neutral. We aim to design optimal portfolios acquiring the asset prices’ co-movements. The results show that the devise of index tracking portfolios using cointegration generates goods results, replicating the benchmark’s return and volatility. The long-short strategy generated stable returns under several market circumstances, presenting low volatility.

scholarly journals Hereditary Portfolio Optimization with Taxes and Fixed Plus Proportional Transaction Costs—Part II

2007 ◽  
Vol 2007 ◽  
pp. 1-25 ◽  
Author(s):  
Mou-Hsiung Chang
Keyword(s):  
Transaction Costs ◽  
Portfolio Optimization ◽  
Impulse Control ◽  
Stock Price ◽  
Optimization Problem ◽  
Proportional Transaction Costs ◽  
Infinite Dimensional ◽  
Hereditary Nature ◽  
Portfolio Optimization Problem ◽  
The Value Function

This paper is the continuation of the paper entitled “Hereditary portfolio optimization with taxes and fixed plus proportional transaction costs I” that treats an infinite-time horizon hereditary portfolio optimization problem in a market that consists of one savings account and one stock account. Within the solvency region, the investor is allowed to consume from the savings account and can make transactions between the two assets subject to paying capital-gain taxes as well as a fixed plus proportional transaction cost. The investor is to seek an optimal consumption-trading strategy in order to maximize the expected utility from the total discounted consumption. The portfolio optimization problem is formulated as an infinite dimensional stochastic classical impulse control problem due to the hereditary nature of the stock price dynamics and inventories. This paper contains the verification theorem for the optimal strategy. It also proves that the value function is a viscosity solution of the QVHJBI.

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