This article proposes a new method for the estimation of the parameters of a simple linear regression model which is based on the minimization of a quartic loss function. The aim is to extend the traditional methodology, based on the normality assumption, to also take into account higher moments and to provide a measure for situations where the phenomenon is characterized by strong non-Gaussian distribution like outliers, multimodality, skewness and kurtosis. Although the proposed method is very general, along with the description of the methodology, we examine its application to finance. In fact, in this field, the contribution of the co-moments in explaining the return-generating process is of paramount importance when evaluating the systematic risk of an asset within the framework of the Capital Asset Pricing Model. We also illustrate a Monte Carlo test of significance on the estimated slope parameter and an application of the method based on the top 300 market capitalization components of the STOXX® Europe 600. A comparison between the slope coefficients evaluated using the ordinary Least Squares (LS) approach and the new Least Quartic (LQ) technique shows that the perception of market risk exposure is best captured by the proposed estimator during market turmoil, and it seems to anticipate the market risk increase typical of these periods. Moreover, by analyzing the out-of-sample risk-adjusted returns we show that the proposed method outperforms the ordinary LS estimator in terms of the most common performance indices. Finally, a bootstrap analysis suggests that significantly different Sharpe ratios between LS and LQ yields and Value at Risk estimates can be considered more accurate in the LQ framework. This study adds insights into market analysis and helps in identifying more precisely potentially risky assets whose extreme behavior is strongly dependent on market behavior.
The problem related to the identification of a change in time series trajectories plays a crucial role in many contexts. In this paper, we propose a flexible and computationally efficient procedure for turning point identification based on hypothesis testing applied to the difference between two consecutive slopes in a rolling regression framework. Along with the description of the methodology, to measure the performance of the method we have applied it to the S&P 500 Stock Index and its subsector indices. By using an in‐sample/out‐of‐sample approach we compare results with the profit/losses we could obtain by using the moving average crossover strategy. Results show that the operating signals obtained by our proposal may better enable financial analysts to make profitable decisions. Finally we present an extensive simulation study to show the weaknesses and strengths of the proposal under different expected returns and volatility scenarios.
We propose a model to extract significant risk spatial interactions between countries adopting the Graphical Lasso algorithm, used in graph theory to sort out spurious conditional correlations. In this context, the major issue is the definition of the penalization parameter. We propose a search algorithm aimed at the best separation of the variables (expressed in terms of conditional dependence) given an a priori desired partition. The case study focuses on Credit Default Swap (CDS) returns over the period 2009-2017. The proposed algorithm is used to estimate the spatial systemic risk relationship between Peripheral and Core Countries in the Euro Area.
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