Abstract
Most of previous work on robust equity portfolio optimization has focused on its formulation and performance. In contrast, in this paper we analyze the behavior of robust equity portfolios to determine whether reducing the sensitivity to input estimation errors is all robust models do and investigate any side-effects of robust formulations. Therefore, our focus is on the relationship between fundamental factors and robust models in order to determine if robust equity portfolios are consistently investing more in the factors opposed to individual asset movements. To do so, we perform regressions with factor returns to explain how robust portfolios behave compared to portfolios generated from the Markowitz’s mean-variance model. We find that robust equity portfolios consistently show higher correlation with the three fundamental factors used in the Fama-French factor model. Furthermore, more robustness among robust portfolios results in a higher correlation with the Fama-French three factors. In fact, we show that as equity portfolios under no constraints on portfolio weights become more robust, they consistently depend more on the market and large factors. These results show that robust models are betting on the fundamental factors instead of individual asset movements.
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Notes
Data obtained from the online data library of Kenneth R. French (http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html).
For the estimation error covariance matrix Σ μ in the robust models with ellipsoidal uncertainty sets, we use the diagonal matrix containing the estimation variances, which is known to work well in practice for robust optimization. For further details, see Stubbs and Vance (2005).
The values of λ are chosen to represent five portfolios with standard deviation less than 0.3 that are equally spread-out when plotted on the mean-variance efficient frontier.
The value of δ does not directly represent confidence levels (90 %, 95 %, etc.). Asset returns are assumed to follow a normal distribution when setting the confidence interval. For example, a 95 % confidence level for the box model uses \(\delta_{i}=1.96\sigma_{i}/\sqrt{T}\), where T is the sample size (Fabozzi et al. 2007a, 2007b, 2010). For the ellipsoid model, we assume the square of estimation error δ 2 follows a χ 2 distribution with degrees of freedom as the number of assets in the portfolio (Fabozzi et al. 2007a, 2007b, 2010).
The first curve uses return data from 1970 to 1974, the second curve uses return data from 1975–1979, and so on.
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Kim, W.C., Kim, J.H., Ahn, S.H. et al. What do robust equity portfolio models really do?. Ann Oper Res 205, 141–168 (2013). https://doi.org/10.1007/s10479-012-1247-6
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DOI: https://doi.org/10.1007/s10479-012-1247-6