Two new mean–variance enhanced index tracking models based on uncertainty theory

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.

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

Brazilian Review of Finance ◽

10.12660/rbfin.v8n4.2010.1534 ◽

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.

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An analysis of a mean-variance enhanced index tracking problem with weights constraints

Investment Management and Financial Innovations ◽

10.21511/imfi.15(4).2018.15 ◽

2018 ◽

Vol 15 (4) ◽

pp. 183-192

Author(s):

Wanderlei Lima de Paulo ◽

Marta Ines Velazco Fontova ◽

Renato Canil de Souza

Keyword(s):

Asset Allocation ◽

Global Minimum ◽

Minimum Variance ◽

Index Tracking ◽

Tracking Problem ◽

Market Index ◽

Satisfactory Performance ◽

Minimum Variance Portfolio ◽

Global Minimum Variance Portfolio ◽

Mean Variance

In this paper, the authors deal with a mean-variance enhanced index tracking (EIT) problem with weights constraints. Using a shrinkage approach, they show that constructing the constrained EIT portfolio is equivalent to constructing the unconstrained EIT portfolio. This equivalence allows to study the effect of weights constraints on the covariance matrix and on the EIT portfolio. In general, the effects of weights constraints on the EIT portfolio are different from those observed in the case of global minimum variance portfolio. Finally, the authors present a numerical asset allocation example, where the S&amp;P 500 index is used as the market index to be tracked using a portfolio composed of ten stocks, in which the constrained EIT portfolio shows a satisfactory performance when compared to the unconstrained case.

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