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Portfolio choice with high frequency data: CRRA preferences and the liquidity effect

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Abstract

This paper suggests a new approach for portfolio choice. In this framework, the investor, with CRRA preferences, has two objectives: the maximization of the expected utility and the minimization of the portfolio expected illiquidity. The CRRA utility is measured using the portfolio realized volatility, realized skewness and realized kurtosis, while the portfolio illiquidity is measured using the well-known Amihud illiquidity ratio. Therefore, the investor is able to make her choices directly in the expected utility/liquidity (EU/L) bi-dimensional space. We conduct an empirical analysis in a set of fourteen stocks of the CAC 40 stock market index, using high frequency data for the time span from January 1999 to December 2005 (seven years). The robustness of the proposed model is checked according to the out-of-sample performance of different EU/L portfolios relative to the minimum variance and equally weighted portfolios. For different risk aversion levels, the EU/L portfolios are quite competitive and in several cases consistently outperform those benchmarks, in terms of utility, liquidity and certainty equivalent.

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Notes

  1. In alphabetic order, the stocks are: AIR LIQUIDE; AXA; CARREFOUR; DANONE; ESSILOR INTL; FRANCE TELECOM; L’OREAL; LVMH; MICHELIN; PERNOD RICARD; SAINT GOBAIN; SANOFI AVENTIS; TOTAL; UNIBAIL

  2. The most critical co-moment, in terms of possible rounding errors, is cokurtosis, since it involves summing returns raised to the fourth power. Concerning this co-moment, we start by noticing that, in the dataset, we have double digit stock prices (no higher). With double digit stocks prices and ticks of 1c, high frequency returns can be as low as 10−4 and their fourth power can be of the 10−16 order. In turn, the highest value that the realized cokurtosis takes is of the 10−4 order. Therefore, since we work with a 16 digit precision, in the computation of the realized cokurtosis at least 4 significant digits of the fourth power of the high frequency returns are preserved.

  3. This solver is public and available by request at http://www.mat.uc.pt/dms/.

  4. The same pattern was found for two different choices of the relative risk aversion parameter (γ = 1 and γ = 10).

  5. A turnover constraint can be formulated as \({\sum }_{i=1}^{N}|x_{i,t+1}-x_{i,t}^{0}|\leq h\), where \(x_{i,t}^{0}\) is the reference portfolio and h is the turnover upper bound.

  6. When the numerator was negative, the ratio was refined in order to achieve a correct rank of the portfolios. In this paper we used the methodology proposed by Israelsen (2005).

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Authors and Affiliations

  1. CeBER, Faculty of Economics, University of Coimbra, 3004-512, Coimbra, Portugal

    R. P. Brito, H. Sebastião & P. Godinho

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  1. R. P. Brito
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  2. H. Sebastião
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  3. P. Godinho
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Correspondence to R. P. Brito.

Additional information

Support for R. P. Brito was provided by FCT under the scholarship SFRH/BD/94778/2013.

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Brito, R.P., Sebastião, H. & Godinho, P. Portfolio choice with high frequency data: CRRA preferences and the liquidity effect. Port Econ J 16, 65–86 (2017). https://doi.org/10.1007/s10258-017-0131-3

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