Portfolio management with background risk under uncertain mean-variance utility
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Portfolio management with background risk under uncertain mean-variance utility Xiaoxia Huang1 · Guowei Jiang1 Accepted: 24 September 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract This paper studies comparative static effects in a portfolio selection problem when the investor has mean-variance preferences. Since the security market is complex, there exists the situation where security returns are given by experts’ estimates when they cannot be reflected by historical data. This paper discusses the problem in such a situation. Based on uncertainty theory, the paper first establishes an uncertain meanvariance utility model, in which security returns and background asset returns are uncertain variables and subject to normal uncertainty distributions. Then, the effects of changes in mean and standard deviation of uncertain background asset on capital allocation are discussed. Furthermore, the influence of initial proportion in background asset on portfolio investment decisions is analyzed when investors have quadratic mean-variance utility function. Finally, the economic analysis illustration of investment strategy is presented. Keywords Portfolio selection · Mean-variance utility · Background risk · Uncertain variable · Uncertain programming
1 Introduction Mean-variance utility framework is an important method for rational portfolio investment choice under risk. The mean-variance utility decision criterion hypothesizes that an investor’s optimal choice is made by ranking alternatives through a preference function defined over the first and second moments of random payoff. Since the studies of Tobin (1958) and Chipman (1973), this decision-making framework has received prominent attention and been widely applied in theoretical and empirical research.
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Xiaoxia Huang [email protected] Donlinks School of Economics and Management, University of Science and Technology Beijing, Beijing 100083, China
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X. Huang, G. Jiang
The mean-variance utility framework is impressive because of its simplicity and ease of handling. In recent years, a large number of research results have been presented based on mean-variance utility framework. For example, Lajeri-Chaherli (2003) solves a portfolio problem with a risk free asset and a risky asset by using the partial derivatives of mean-variance utility. However, these research only considers the risks of financial assets themselves. When investors make portfolio investment in financial assets, they often face additional sources of risk, such as exogenous and unhedged risks brought by labor income, health and real estate. These sources of risk are often referred to as background risks and the sources background assets. Therefore, some research based on mean-variance utility with background risk is done. For example, Eichner and Wagener (2003) study the influence of standard deviation increase in a mean-zero background risk on an investor’s willingness to take risk when the investor adopts mean-variance utility framework. Eichner and
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