Abstract
The copula theory allows to easily model the probability distributions of random vectors by separately estimating the marginal distributions and the dependence structure of the components represented by the copula itself. Copula functions generally provide significant improvements to the financial portfolio allocation problem. However, being given the large spectrum of available copulas, the choice of the best model is rather complex. This paper investigates the copula misspecification impact on the portfolio allocation problem, which is an important risk model issue. We address this issue from the perspective of the behavioral portfolio theory through the Zakamouline (Quant Finance 14(4):699–710, 2014) approach by considering an investor allocating his wealth between a risk-free asset and a risky asset. Our main objective is to assess investors’ sensitivities to the choice of the probability of the random vector, namely both the marginal distributions and the copula function. This analysis is conducted with respect to their degrees of risk and loss aversions, for different compositions of the risky asset, and for different investment horizons.
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Notes
For this numerical case, we can also consider alternatively other copulas than the Student to define the “true” copula. We recover same qualitative results. In the empirical part, it is the Rotated Clayton that fits data better than the other ones (see goodness-of-fit tests) and thus is chosen as the “true” copula.
Further generalizations are straightforward but very time consuming from the numerical point of view.
Except for an investor with preferences of types \(\left( \alpha =0.1;\beta =0.8\right) \).
For more details see Patton (2012).
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Saida, A.B., Prigent, Jl. On the robustness of portfolio allocation under copula misspecification. Ann Oper Res 262, 631–652 (2018). https://doi.org/10.1007/s10479-016-2137-0
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DOI: https://doi.org/10.1007/s10479-016-2137-0