Mathematical and Statistical Methods for Actuarial Sciences and Finance

(Nora) #1

296 J. Roy


eventually select the methods to be applied. The two polar approaches in terms of ag-
gregation of data were implemented to obtain some form of cross-validation. Section
4 will document the aggregated approach, whereas Section 5 will describe the highly
disaggregated approach implemented through a Monte-Carlo simulation model. Sec-
tion 6 will compare the results of the two approaches, whereas Section 7 will report
on the several significant impacts of the study for the organisation. Section 8 will
provide the conclusion.


2 Context of the study


The context of this study had two main dimensions, one internal, namely the institu-
tional context, and the other external, namely the technical context. Both will now be
addressed.
The institution involved in this study is the “Fonds de securit ́ e Desjardins" or ́
Desjardins Guaranty Fund (DGF), which is a wholly owned incorporated affiliate of
the “Mouvement Desjardins". The Mouvement Desjardins is a federation of some 570
local “caissespopulaires" or credit unions. DGF acts as an internal mutual insurance
company. It collects annual premiums from the local credit unions and would provide
funds to any ot these credit unions in a situation of financial distress. In 2004, DGF
had a capital of 523 million CA$, whereas the insured credit unions had total assets
of 79 billion CA$, leading to a capitalisation ratio of 66.2 basis points. DGF had, at
that point, a capitalisation target of 100 basis points. However, management wanted a
formal evaluation of the solvency of the fund in order to confirm or review this target.
To perform the analysis, data for the 25 years of formal operation of the fund were
available. These showed that the fund had played a major role in keeping the local
credit unions solvent. Indeed, 964 subsidies were granted to 372 different credit unions
for a total of some 220 million un-indexed CA$ from 1980 to 2004. It also needs to
be mentioned that the federation played a key role in managing a consolidation of
the network, bringing the total number of credit unions down from its peak of 1465
credit unions in 1982 to 570 in 2004.
A first look at the data showed that the annual average subsidy rate, total subsidies
to credit unions divided by the total assets of these, was 3.245 basis points, such that
the current capital was equivalent to a 20.4-year reserve at the average rate. However,
a cursory analysis of the time series showed a high volatility (4.75 basis points) and
also high asymmetry and kurtosis. More precisely, two peaks could be identified in
the series: one at 20.8 basis points in 1982 and another one at 5.8 basis points in 1995.
Overall, five high values above 5 basis points could be observed during the period of
25 years. Aside from the historical data of the fund itself, extensive data were also
available on the insured credit unions over the latest period of seven years, allowing
contemplation of highly disaggregated models. At that point, a review of the literature
was conducted to survey the status of current practices for the solvency evaluation of
similar organisations.
DGF is an organisation that shares many similarities with public deposit insurers.
Thus the literature on the solvency evaluation of the US and Canadian deposit insurers

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