Restricted Kalman filter applied to dynamic style analysis of actuarial funds

Abstract

We use dynamic style analysis to unveil the strategies followed by Brazilian actuarial funds from January 2004 to August 2008 and investigate whether managers' decisions were compatible with the intention of protecting the investor against the negative effects of inflation. The main goal of this paper is to show that this methodology is suitable for allowing insurance companies to increase their capacity to monitor the behavior of portfolios and to control the amount of risk they assume. The basic steps of the method are to build and/or choose market indexes capable of characterizing the returns of the main securities available and to apply restricted linear state space models estimated with a Kalman filter with exact initialization. The main conclusions of this paper are the following: (1) the use of exact initialization of the Kalman filter promotes numerical stability; (2) there is no need to consider the entire set of market indicators because a subset containing only three indexes spans the relevant space of investment opportunities; and (3) the actuarial funds' resources were primarily invested in inflation-indexed bonds, but fund managers also left room to adjust their exposure to other assets not directly related to the objective of providing protection against inflation. a Inflation-indexed assets or liabilities are those with returns protected against inflation, which means that their purchasing power does not decrease over time. b Loosely speaking, an exposure (or an allocation) is the proportion of total investment resources that is directed to a specific market or asset class. For instance, equity funds invest the bulk of their resources in buying shares; therefore, they have a higher exposure to some indexes that follow the returns provided by this kind of asset (such as the Dow Jones or the S&P 500 indexes in the US financial market). From a statistical point of view, they are nothing more than the coefficients of the time series regression models considered within. In our framework, a time-varying exposure is a random coefficient of a time series regression model. Bus. Ind. 2012, 28 558-570 d The acronym WN stands for 'White Noise', a term used for (possibly multivariate) second-order stochastic processes with uncorrelated components with zero mean and common variance. Because the covariance matrices H t and Q t can be time-varying, the use of the term here is perhaps inappropriate. Appl. Stochastic Models

Private pension funds: passivity at active fund prices

“…More speci cally in Brazil, we may cite some major works, such as: Amaral (2013), Linhares (2003), Marques (2006), Nunes (2015), Varga and Valli (1998), and Yoshinaga, Castro Jr., Oda and Lucchesi (2009). Among the authors who have used variations and improvements of the RBSA in Brazil, we may mention Marques, Pizzinga and Vereda (2012), Pizzinga, Vereda, Azevedo and Fernandes (2012), and Schutt and Caldeira (2014), who used a more advanced methodology: the Kalman lter, applied to style analysis to determine how fund exposures to asset classes of vary over time. is methodology is detailed below, since it is used by this study.…”

“…Next, such a window is 'rolled' a time interval forward and the analysis for this period is replicated, repeating this procedure to the end. Among the authors who have used this technique in their studies there are Gibson and Gyger (2007), Holmes and Fa (2008), Linhares (2003), Marques (2006), Marques, Pizzinga and Vereda (2012), and Varga and Valli (1998).…”

Testing for structural breaks in return-based style regression models

“…When shift in manager style is assumed to occur continuously and gradually over time, such smoothing time variation can be captured by "time-varying parameter models" such as state-space models usually estimated by the Kalman filter method. Several studies including Swinkels and Van Der Sluis (2006), Bodson et al (2010), Darolles and Vaissie (2012), and Marques et al (2012) proposed such modeling methods to incorporate smoothing time variation in style analysis. Although these studies opened a path toward a more general framework for style analysis, their methodology is not fully general as their time-varying models can only be applicable to either the weak style analysis or semi-strong style analysis according to the terminology of DeRoon et al (2004).…”

Análise de estilo baseada em retornos: um estudo aplicado aos fundos de previdência complementar oferecidos pelo instituto Agros

“…A estimação dos parâmetros do modelo ou das sensibilidades, 𝜷 = (𝛽 1 , 𝛽 2 , … , 𝛽 𝐾 ) ′ , quando nenhuma restrição for imposta (o que também é conhecido como RBSA fraca), pode ser realizada via método dos Mínimos Quadrados Ordinários (MQO), pois nesse caso trata-se de um modelo convencional de regressão linear múltipla. Já quando a restrição de igualdade ou de portfólio é imposta (RBSA semiforte), pode-se ainda utilizar o método dos MQO com uma reparametrização do modelo (Marques et al, 2012) ou então o método dos Multiplicadores de Lagrange (Gross, 2012).…”

“…Por isso, as estimativas obtidas representam apenas as sensibilidades médias dos retornos do fundo em estudo aos fatores de risco ou classes de ativo, ao longo do período de tempo avaliado. Para mais detalhes sobre variações recentes da RBSA consultar os trabalhosde Dor et al (2005),Holmes e Faff (2008),Weng e Truck (2011),Swinkels e Sluis (2006),Mamaysky et al (2008),Marques et al (2012),Schutt e Caldeira (2016),Campani e Brito (2018).…”