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On the impact of conditional expectation estimators in portfolio theory

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Abstract

In this paper, we investigate the implications for portfolio theory of using conditional expectation estimators. First, we focus on the approximation of the conditional expectation within large-scale portfolio selection problems. In this context, we propose a new consistent multivariate kernel estimator to approximate the conditional expectation and it optimizes the bandwidth selection of kernel-type estimators. Second, we deal with the portfolio selection problem from the point of view of different non-satiable investors, namely risk-averse and risk-seeker investors. In particular, using a well-known ordering classification, we first identify different definitions of returns based on the investors preferences. Finally, for each problem, we examine several admissible portfolio optimization problems applied to the US stock market. The proposed empirical analysis allows us to evaluate the impact of the conditional expectation estimators in portfolio theory.

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Notes

  1. See, among others, Branda and Kopa (2012, 2014, 2016).

  2. We define the ith gross return between time t and time \(t+1\) as \(z_{i,t}=\frac{P_{t+1,i}}{P_{t,i}}\), where \(P_{t,i}\) is the price of the ith asset at time t.

  3. Typical positive risk measures are deviation measures (see Rockafellar et al. 2006) or CVaR at lower percentiles for returns (\(R_{i,t}=z_{i,t}-1\)) or for log returns (ln\((z_{i,t})\)).

  4. Heavy-tailed distributions have been observed in many applications in economics and finance. Some basic references are Mandelbrot (1963) and Rachev and Mittnik (2000).

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Acknowledgements

This paper has been supported in part by the Italian funds ex MURST 60% 2016 and in part through the Czech Science Foundation (GACR) under the Project 15-23699S and through SP2017/32, an SGS Research Project of VSBTU Ostrava.

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Authors and Affiliations

  1. Department of Management, Economics and Quantitative Methods, University of Bergamo, Via dei Caniana 2, Bergamo, Italy

    Sergio Ortobelli & Noureddine Kouaissah

  2. Department of Finance, VSB-TU Ostrava, Sokolská tr. 33, Ostrava, Czech Republic

    Sergio Ortobelli, Noureddine Kouaissah & Tomáš Tichý

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  1. Sergio Ortobelli
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  2. Noureddine Kouaissah
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  3. Tomáš Tichý
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Correspondence to Noureddine Kouaissah.

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Ortobelli, S., Kouaissah, N. & Tichý, T. On the impact of conditional expectation estimators in portfolio theory. Comput Manag Sci 14, 535–557 (2017). https://doi.org/10.1007/s10287-017-0282-9

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