Actuarial Risk Matrices: The Nearest Positive Semidefinite Matrix Problem

The manner in which a group of insurance risks are interrelated is commonly presented via a correlation matrix. Actuarial risk correlation matrices are often constructed using output from disparate modeling sources and can be subjectively adjusted, for example, increasing the estimated correlation between two risk sources to confer reserving prudence. Hence, while individual elements still obey the assumptions of correlation values, the overall matrix is often not mathematically valid (not positive semidefinite). This can prove problematic in using the matrix in statistical models. The first objective of this article is to review existing techniques that address the nearest positive semidefinite matrix problem in a very general setting. The chief approaches studied are Semidefinite Programming (SDP) and the Alternating Projections Method (APM). The second objective is to finesse the original problem specification to consider imposition of a block structure on the initial risk correlation matrix. This commonly employed technique identifies off-diagonal subsets of the matrix where values can or should be set equal to some constant. This may be due to similarity of the underlying risks and/or with the goal of increasing computational efficiency for processes involving large matrices. Implementation of further linear constraints of this nature requires adaptation of the standard SDP and APM algorithms. In addition, a new Shrinking Method is proposed to provide an alternative solution in the context of this increased complexity. “Nearness” is primarily considered in terms of two summary measures for differences between matrices: the Chebychev Norm (maximum element distance) and the Frobenius Norm (sum of squared element distances). Among the existing methods, adapted to function appropriately for actuarial risk matrices, APM is extremely efficient in producing solutions that are optimal in the Frobenius norm. An efficient algorithm that would return a positive semidefinite matrix that is optimal in Chebychev norm is currently unknown. However, APM is used to highlight the existence of matrices close to such an optimum and exploited, via the Shrinking Method, to find high-quality solutions. All methods are shown to work well both on artificial and real actuarial risk matrices provided under collaboration with Tokio Marine Kiln (TMK). Convergence speeds are calculated and compared and sample data and MATLAB code is provided. Ultimately the APM is identified as being superior in Frobenius distance and convergence speed. The Shrinking Method, building on the output of the APM algorithm, is demonstrated to provide excellent results at low computational cost for minimizing Chebychev distance.     

Purchasing power parity in Brazil: a test for fractional cointegration

The purpose of this paper is to test the validity of the purchasing power parity (PPP) doctrine in Brazil. Historical data for the period 1855–1996 are considered. The period 1855–1990 is also analysed in order to compare the results with those obtained by Zini and Cati (1993) using the conventional cointegration analysis. This article uses fractional cointegration analysis, a flexible methodology which allows for more subtle forms of mean reversion. The tests performed are those of Geweke and Porter-Hudak (1983), and of Hurvich and Ray (1995). The critical values for both tests are generated by simulation because they are non-standard. The empirical results do not support the absolute PPP hypothesis but the relative PPP holds in the long run.     

The importance of education for the reallocation of labor: Evidence from Swedish linked employer–employee data 1986–2002

Using Swedish employer–employee data we study job and worker flows for different educational groups, as well as the cyclicality of such flows. Due to the long period studied, from 1986 to 2002, and the widely fluctuating business cycle during this period, we have a unique opportunity to analyze the cyclical pattern of job and worker flows. We especially look at the big downturn in the Swedish economy in the beginning of the 1990s. When workers are treated as homogenous, we find job reallocation to be countercyclical. However, when we estimate correlations for different educational groups, we find job reallocation to be countercyclical for the lowest educated, and acyclical for higher educated workers. Contrary to job flows, we find worker flows to be acyclical, with a strong procyclical pattern in hiring rates, and an acyclical pattern in separation rates. When decomposing worker flows into educational groups, the acyclical pattern is prevalent for all groups, except for the highest educated. For the highest educated, worker reallocation is strongly pro-cyclical due to both more hirings and separations during up-turns.     

Consumers’ response to the EU Quality policy allowing for heterogeneous preferences

Using dry-cured ham as an anchor product, consumers’ preferences for EU Quality Certification schemes, region of origin and price have been investigated with conjoint analysis. In order to achieve this aim, a mixed rank-ordered logit which allows for the investigation of heterogeneous preferences and their sources has been estimated. In particular, we have analysed to what extent consumers’ socio-demographic traits affect their price-sensitiveness and whether consumers’ sensory (hedonic) valuations and attitudes towards ham with a Protected Designation of Origin (PDO) affect the preferences for specific attributes. Results show that consumers with a low-medium age and income are more price sensitive. Consumers more inclined sensorially towards the regional specialty (with or without PDO) are more likely to purchase this product, and consumers with a more favourable attitude towards PDO ham are also more prone to purchase cured ham with quality certification. Findings also suggest that although the PDO scheme attracts a segment of consumers, the origin by itself is still a more powerful signal of quality, and more specifically the region of origin.     

Green supply chains and the missing link between environmental information and practice

Within the field of green supply chain management (GSCM), an interest in supply chain cooperation to create sustainable competitive advantage, i.e. the collaborative paradigm, has made researchers turn their attention to information related aspects of the supply chain. This study contributes to an understanding of a suboptimal use of environmental information, which is critical for all collaborative efforts aiming at sustainable competitive advantage. The aim of this article is to describe the use of environmental information at different stages of the Swedish food supply chain. The results from this case study of the Swedish food supply chain indicate that environmental information is perceived and used differently by purchasers in the supply chain depending on where (in the supply chain) they are situated in relation to other chain actors. The main contribution of this study is the suggestion of a stage‐dependent connection between perceived environmental cost and perceived environmentally informed consumer demand, which are barriers to GSCM practice discussed in recent GSCM literature. The missing link between information sharing and (environmental) performance of supply chains is explained as distance to end‐consumer in terms of supply chain stages. Implications for GSCM practice and theory are discussed. Copyright © 2009 John Wiley & Sons, Ltd and ERP Environment.     

Do stress tests matter? A study on the impact of the disclosure of stress test results on European financial stocks and CDS markets

During the recent sovereign debt crisis, the European Banking Authority conducted two stress tests on European banks in order to gauge their capital needs, core Tier-1 ratios and ratios of resilience to adverse shocks. We assess the informational content of the disclosure of the stress test outcomes. We conclude that the stress tests conveyed new information and that the outcomes were not anticipated by the stock market but were partially anticipated by the credit default swap (CDS) market. However, while the stock market reacted to the disclosure of the stress test outcomes, in the CDS market there is some evidence of a ‘reverse’ reaction. Moreover, the publication of the outcomes of the stress tests had a stronger impact on the stock prices of riskier financial institutions. A similar pattern is evident in the CDS market, albeit narrowed to one of the stress tests and amid the financial institutions with higher perceived credit risk.     

Economic Benefits of Gender Equality in the EU

To analyse how gender equality measures can contribute to economic growth in the EU, the European Institute for Gender Equality studied the impacts of reducing gender inequalities in areas relevant from a macroeconomic perspective: STEM education, labour market activity and pay. It also considered the demographic changes that would take place if these gender gaps are reduced and a more equal distribution of unpaid care work between women and men is achieved. The study is the first of its kind to use a robust econometric model to estimate a broad range of macroeconomic benefits of gender equality at the EU level. The results of the modelling show that improved gender equality would have a largely positive effect on GDP per capita and on employment of women. The positive impacts are due to an increase in productivity and an improvement to the potential productive capacity of the economy.     

Institutional Investors’ Reaction to SEC Concerns about IFRS and US GAAP Reporting

For the period of 2006 to 2008, we collect Comment Letters issued by the SEC that question the application of US GAAP by US firms or the application of IFRS by European firms registered with the SEC. We investigate whether institutional investors react to the letters by changing their holdings and whether their responses vary for US registrants and European registrants. We do this via a treatment‐effects model in which we test the hypothesis that institutional investors rebalance their portfolio holdings because they view Comment Letters as informative public signals. We find that institutional investors reduce their equity holdings when firms receive SEC Comment Letters, and their negative reactions are most marked for low turnover institutional investors, who we use to represent those informed investors most prepared to incur costs to closely monitor firms. Next, while noting that the number of Letters questioning application of IFRS are smaller in number relative to those questioning application of US GAAP, we investigate whether there are different reactions to Comment Letters questioning different standards. We show that there is a higher probability of the SEC questioning the application of IFRS as compared to US GAAP. After controlling for firm‐specific conditions that impact the issuance of a Comment Letter, we show that this higher probability has economic significance because institutional investors’ react more negatively to Comment Letters that question the application of IFRS as compared to US GAAP. A content analysis confirms the economic importance of the Comment Letters. We find that in almost half of all IFRS cases the Comment Letters request amendments to financial statements.