Robust asset allocation with conditional value at risk using the forward search

Abstract

The well‐known Markowitz approach to portfolio allocation, based on expected returns and their covariance, seems to provide questionable results in financial management. One motivation for the pitfall is that financial returns have heavier than Gaussian tails, so the covariance of returns, used in the Markowitz model as a measure of portfolio risk, is likely to provide a loose quantification of the effective risk. Additionally, the Markowitz approach is very sensitive to small changes in either the expected returns or their correlation, often leading to irrelevant portfolio allocations. More recent allocation techniques are based on alternative risk measures, such as value at risk (VaR) and conditional VaR (CVaR), which are believed to be more accurate measures of risk for fat‐tailed distributions. Nevertheless, both VaR and CVaR estimates can be influenced by the presence of extreme returns. In this paper, we discuss sensitivity to the presence of extreme returns and outliers when optimizing the allocation, under the constraint of keeping CVaR to a minimum. A robust and efficient approach, based on the forward search, is suggested. A Monte Carlo simulation study shows the advantages of the proposed approach, which outperforms both robust and nonrobust alternatives under a variety of specifications. The performance of the method is also thoroughly evaluated with an application to a set of US stocks.

Robust portfolio optimization for banking foundations: a CVaR approach for asset allocation with mandatory constraints

“…Grossi and Laurini (2011) propose a robust estimator which weights data using a forward search approach (see also Grossi and Laurini 2009). In this paper we use an optimal portfolio allocation method, developed by Grossi and Laurini (2019), which is based on the robust estimation of the input parameters through a forward search with the allocation conducted minimizing the CVaR and which shows many advantages and outperforms both robust and non-robust alternatives. We compare this approach with the Markowitz model, using a B&H strategy.…”

“…Since we also use the budget allocation constraint (i.e., sum of the weights equal to one), all allocations should be "rescaled" suitably. Since we aim to suggest an innovative asset allocation strategy for risk averse investors who operate on very long-time horizons, such as Italian FBOs, we first identify an optimal portfolio asset allocation by using Markowitz's model and the R-CVaR approach developed by Grossi and Laurini (2019). Indeed, the well-known Markowitz portfolio allocation model, based on expected returns and their covariance, has been criticized for many reasons (e.g.…”

“…Our analysis aims to compare the Markowitz model (Markowitz 1959) and a R-CVaR approach (Grossi and Laurini 2019) in order to identify an efficient asset allocation strategy for Italian FBOs. The optimal portfolio allocation method (R-CVaR) we adopt is based on the robust estimation of the input parameters through a forward search with the allocation conducted minimizing the CVaR.…”

“…Following Grossi and Laurini (2019), this paper makes some substitutions in meanvariance optimization: we use CVaR as a measure of risk instead of variance and we express the optimization problem using the risk aversion formulation, in order to explore the results for a variety of values of λ. This is an important innovation compared to other studies; the very recent work of Kremer et al (2020), for example, uses minimum variance portfolios, which makes any comparison of little practical relevance.…”

“…Although the role of FBOs is growing internationally (Lecy and Van Slyke 2013), to our knowledge few studies have to date investigated their portfolio construction strategies. In the light of the importance of social value creation, and stakeholder and community management of FBOs, we use Markowitz's model (Markowitz 1959) and a robust portfolio optimization procedure minimizing the Conditional VaR (CVaR) proposed by Grossi and Laurini (2019) to examine a possible asset management solution which takes the need to preserve capital into account. The classical Markowitz model and the Robust CVaR (R-CVaR) are compared under the constraints imposed by the "Protocollo ACRI-MEF" and the particular asset management characteristics of FBOs.…”