especially the ‘tail risk’ correlation. Unfortunately, the validity of even elegant models and estimating techniques will never be known due to the probabilistic nature of the outcomes. An associated confounding issue is the purpose of the estimate. If the interest is ‘normal’ market conditions, then detailed specificity of tail risk correlations is not necessary. If extreme events are the concern, then standard ‘normal’ models are inappropriate.
Table 5 displays the two VaR/T-VaR metrics predicated upon ‘normal’
markets for the low leverage scenario. The Normal Markets column relies upon historic correlations. The Armageddon column eliminates all diversifi cation and hedging benefi ts by setting all correlations to unity. Essentially, this is a stress test showing the estimated consequences of adverse tail risk. The Normal Markets scenario readily demonstrates the difference between VaR and T-VaR, indicating sensitivity to tail risk, and between end-of-period and intra-period estimates, the latter being more relevant unless one believes capital impairment coincides with Julian calendar dates.
AN ASYMMETRIC WORLD AND
CAPITAL CHARGES Another approach to focus on tail risk outcomes is to use asymmetric
return distributions such as Levy alpha-Stable (Levy). In Chart 2 we contrast hypothetical differences between normal and Levy outcomes. The question of greatest importance is, ‘what happens in the tails?’. In a ‘normal’ world, the answer is, ‘not so much’. When it matters the most, the standard Solvency II model approach provides slight value.
In Table 6 we contrast the 99.5 VaR and T-VaR as a percentage of
capital and dollar amount scaled to the industry’s 2010 year-end capital base of $540 billion. The 99.5 T-VaR derived from ‘normal’ markets is 30.26 percent (Tables 4 and 5) of capital, or $163.4 billion, in contrast to $419.9 billion accounting for more extreme asymmetric outcomes. This amount is comparable to the Armageddon result shown in Table 5.
SUMMARY The extrapolation of the global banking industry’s Basel II accords to
the insurance industry’s Solvency II requirements demonstrates a zealous fervour to achieve uniform international fi nancial reporting across disparate industries.
The proposed applications to the insurance industry might serve to
reduce transparency, mask underlying economics and change business practices for the worse.
In contrast to either the Solvency II standard model prescription or possible simulation approaches we prefer an asymmetric closed form approach, for several reasons. First, it is essential that the methodology accommodates extreme events that are potentially common fare to the industry. If the issue is ‘solvency’, then an approach that accounts for
CHART 2: NORMAL VERSUS LEVY 1.2
Normal vs -Stable Distribution
0.2 0.4 0.6 0.8 1
0 -3.5
-Stable Distribution Normal Distribution
-2.5 Source: GR-NEAM Analytics
TABLE 6: VAR/T-VAR SCALED TO 2010 LOW LEVERAGE AND $540B CAPITAL
Metric
Normal Markets Asymmetric World
99.5% VaR
% Capital $B 27.20 39.11
Source: GR-NEAM Analytics
adverse consequences rather than ignores them is the logical choice. ‘Normal’ markets’ pedestrian volatility is not a relevant consideration.
Second, the allure of complex simulations masks their inherent defi ciency,
ie, their outcomes cannot be replicated, especially at the confi dence levels required to assure targeted solvency standards. This further compounds the issue of transparency fl owing from the lack of a robust standardised approach.
Third, already there is the desire for cross-border uniform capital
requirements. Allowing individual company ‘modelling’ of enterprise risk certifi ed by independent regulatory bodies attempting adherence to broad-based principles will circumvent this quest. The overriding goal of accounting for the inter-connectedness of systemic risk will be handicapped.
‘Principles’ appear to have trumped ‘rules’ in the prospective regulatory
and accounting schemes. That is an interesting phenomenon. For if the failures of the recent fi nancial debacle were a failure to ‘adhere to the rules’, imagine the largesse permitted by ‘adhering to principles’, and will tomorrow’s guardians of the faith prove more effective than yesterday’s protector of the script? That remains an unanswered dilemma.
Jim Bachman is vice president, capital management, and Tobias Gummersbach is a quantitative analyst at GR-NEAM. This article was originally published by GR- NEAM in November 2011. It is not an offer to conduct business in any jurisdiction in which General Re-New England Asset Management, Inc. and its subsidiaries are not registered or authorised to conduct business. Please contact authors for references.
Spring 2012 | INTELLIGENT INSURER | 33
$146.9 211.19
99.5% T-VaR
% Capital $B 30.26 77.75
$163.40 419.85
-1.5
-0.5 (%) Total Return
0.5
1.5
Density
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