Mathematical and Statistical Methods for Actuarial Sciences and Finance

Solvency evaluation of the guaranty fund at a large

financial cooperative

Jean Roy

Abstract.This paper reports on a consulting project whose objective was to evaluate the

solvency of the guaranty fund of the Mouvement Desjardins, a large federation of financial

cooperatives based in Quebec, Canada. The guaranty fund acts as an internal mutual insurance

company; it collects premiums from the 570 local credit unions of the federation and would

provide funds to any of these local credit unions facing financial difficulties. At the time of the

study, the assets of the insured credit unions totalled 79 billion CA$ and the fund had a capital of

523 million CA$. The purpose of the study was to estimate the probability of insolvency of the

fund over various horizons ranging from one to 15 years. Two very different approaches were

used to obtain some form of cross-validation. Firstly, under the highly aggregated approach,

three theoretical statistical distributions were fitted on the 25 historical yearly rates of subsidy.

Secondly, a highly disaggregated Monte-Carlo simulation model was built to represent the

financial dynamics of each credit union and the guaranty fund itself, taking into account some

150 parameters for each credit union. Both approaches converged to similar probabilities of

insolvency for the fund, which indicated that the fund was well within an implicit AAA rating.

The study had several significant financial impacts both internally and externally.

Key words:solvency analysis, financial cooperatives, guaranty fund, Monte Carlo method,

credit risk

1 Introduction

The regulatory context brought by the Basel IIaccord has given a new impetus to the

evaluation of the solvency of financial institutions. Although internationally active

commercial banks have been at the forefront, other financial institutions, such as large

financial cooperatives, are also strongly involved. The decentralised nature of financial

cooperatives brings new challenges to the process, as the case study presented here

will show. Specifically, this paper will report on a consulting project whose objective

was to evaluate the solvency of the guaranty fund of the Mouvement Desjardins, a

large federation of credit unions based in Quebec, Canada. The paper will proceed as

follows. Section 2 will describe the institutional and technical context of the study.

Section 3 will present the preliminary analysis that was conducted to identify and

M. Corazza et al. (eds.), Mathematical and Statistical Methodsfor Actuarial Sciencesand Finance
© Springer-Verlag Italia 2010