302 J. Roy
Ta b le 5 .Summary of solvency estimates under the two approachesApproach Probability of Probability of Implied S&P
solvency default (bp) rating
Statistical distribution
Weibull 99.9995 % 0.05 AAA
Gamma 99.9996 % 0.04 AAA
Log-normal 99.8142 % 18.58 BBB
Monte Carlo simulation
Base case and premiums at 1/14 % 99.9992 % 0.08 AAA
Base case and premiums at 1/17 % 99.9987 % 0.13 AAA
Stressed case and premiums at 1/14 % 99.9901 % 0.99 AAA
Stressed case and premiums at 1/17 % 99.9865 % 1.35 AAAbase case scenario. Then one observes that the probability of insolvency obtained
(0.08 bp) is quite consistent with the values obtained using the Weibull and Gamma
distributions (0.05 bp and 0.04 bp). This observation is quite comforting as we inter-
pret it as each result being reinforced by the other. It is striking indeed that the two
very different approaches did in fact converge to basically similar results. Overall, it
can be concluded that the solvency of the guaranty fund was excellent and that this
conclusion could be taken with a high level of confidence considering the duplication
obtained.
7 Financial impact of the study
The study led the management of the fund to take several significant actions. First,
the target capital ratio, which was previously set to 1% of the aggregate assets of the
credit unions, was brought down to an interval between 0.55% and 0.65%, basically
corresponding to the current level of capital of 0.62%. Secondly, management decided
to lower the premiums charged to the credit unions. Finally, the deposits made at any of
the credit unions of the Mouvement Desjardins are also guaranteed by a public deposit
insurer managed by the Financial Market Authority of Quebec (FMA) to which the
Mouvement Desjardins has to pay an annual premium. The solvency study that we
have described above was presented to the FMA to request a reduction of the premium
and after careful examination the FMA granted a very significant reduction. Thus,
one could argue that the study achieved its goals. First, it provided management of the
guaranty fund with the information it requested, that is a well grounded estimation of
the solvency of the fund. Secondly, the very favourable assessment of the solvency
allowed management to take several actions to reap the benefits of the excellent state
of solvency of the fund.