The Term Structure of Interest Rates and its Impact on the Liability Adequacy Test for Insurance Companies in Brazil

Abstract

The Brazilian regulation for applying the Liability Adequacy Test (LAT) to technical provisions in insurance companies requires that the current estimate is discounted by a term structure of interest rates (hereafter TSIR). This article aims to analyze the LAT results, derived from the use of various models to build the TSIR: the cubic spline interpolation technique, Svensson's model (adopted by the regulator) and Vasicek's model. In order to achieve the objective proposed, the exchange rates of BM&FBOVESPA trading days were used to model the ETTJ and, consequently, to discount the cash flow of the insurance company. The results indicate that: (i) LAT is sensitive to the choice of the model used to build the TSIR; (ii) this sensitivity increases with cash flow longevity; (iii) the adoption of an ultimate forward rate (UFR) for the Brazilian insurance market should be evaluated by the regulator, in order to stabilize the trajectory of the yield curve at longer maturities. The technical provision is among the main solvency items of insurance companies and the LAT result is a significant indicator of the quality of this provision, as this evaluates its sufficiency or insufficiency. Thus, this article bridges a gap in the Brazilian actuarial literature, introducing the main methodologies available for modeling the yield curve and a practical application to analyze the impact of its choice on LAT.

Flow Correlations Within Time Intervals Of Variable Length: Spline Analysis

“…Limitations to the length of the investigated time series are eliminated by additional points of the rate interpolation curve between the 'nodes'. This enables more accurate identification of possible switches of 'modes' in economic flows and the study of sequential changes in correlation parameters (Duarte et al, 2015;Idrisov & Érlikh, 2002;Lipton & Rennie, 2012).…”

MAC: Uma Proposta para Metas Atuariais Consistentes em Fundos de Pensão

“…Adicionalmente, a evidência de que a rentabilidade futura não é capturada pela meta atuarial contraria Bertucci et al (2006), Silva et al (2007) Por outro lado, a presença da taxa-parâmetro no modelo confirma que os fundos de pensão estão optando, acolhidos na resolução 30, por metas atuariais baseadas em médias pretéritas de ETTJ, mas que estão distantes quase dez meses da data-base dos cálculos atuariais. Entendemos que esse fato corrobora Bicalho (2018), que identificou que o desempenho do patrimônio das EFPCs se assemelhou ao CDI, mas não podemos afirmar que a presença da taxaparâmetro no modelo significa que a meta atuarial representa rentabilidades prospectivas das taxas de título de baixo risco, como informado em Chapman et al (2001), Bader e Gold (2003), Varga (2009), Caldeira (2011), GAO (2014), Duarte et al (2015), Silva et al (2015) e Novy-Marx (2015). Já a presença do patrimônio líquido, no modelo, evidencia uma influência parcial do índice de solvência, defendida por Sousa e Costa (2015) no caso de déficits.…”

MAC: A Proposal for Consistent Actuarial Interest Rates in Pension Funds

“…The results produced in the models can often directly represent the rate and serve as an input for the future returns of part of the portfolio for ALM. Varga (2009) and Duarte, Silva, Oliveira, Weffort and Chan (2015) researched methods used by EFPCs in determining the rate, similar to those adopted in applying the liability adequacy test to technical provisions in the insurance market. Such methods consist of modeling a future yield curve, represented by the ETTJ, formed by a set of points in the zero-coupon spot interest rate space, i(t), versus the term, t, representing its maturity or duration.…”

“…We understand that this fact corroborates Bicalho (2018), who identified that the performance of the EFPC's asset was similar to the benchmark CDI rate. However, we cannot say that the presence of the parameter rate in the model means that the actuarial rate represents prospective returns of the rates observed in low-risk bonds, as reported in Chapman et al (2001), Bader and Gold (2003), Varga (2009), Caldeira (2011), GAO (2014), Duarte et al (2015), Silva et al (2015) and Novy-Marx (2015). The presence of the net asset in the model shows a partial influence by the solvency ratio, as advocated by Sousa and Costa (2015) in the case of deficits.…”