inter-period (DIP) and Levy inter-period (Levy). In addition to location (mean) and dispersion (variance), the Levy method accounts for skewness and kurtosis (tail behaviour statistics). These metrics yield significantly different solvency estimates.
The difference between SNEOP and DIP is simply the time frame. The
former considers the shortfall at the end of the period, ie, one calendar year, whereas the latter focuses upon the shortfall at any time during the year. Both methods are based upon multivariate normal distributions and correlations. Both metrics are compatible with Solvency II technical requirements and are predicated upon ‘normal market conditions’.
In the standard normal framework, risk is the sum of each asset’s
(and product’s) volatility and the covariance among assets and products, amplified by firm asset and product leverage. Covariance is dependent upon the underlying assets’ returns and products’ margins correlations. We can further stress-test the initial SNEOP and DIP VaR estimates by eliminating all diversification benefits.
The Levy method is used to account for the asymmetric outcomes of
extreme capital market returns and underwriting margins. However, the observed returns have an underlying correlation structure, ie, how events actually did unfold. In the Levy framework it is not possible to stress-test correlations. And, indeed, that might not be needed given Levy is an extreme event estimation method, ie, its characterisations are anything but ‘normal’.
By way of caveat we must note that the calculated differences among
the methods are quite large and need to be matched carefully to the intended objectives. Also, as in all capital calculations there is no explicit recognition of management’s (owners’) ability to adjust to emerging market conditions. The models do not ‘learn’. They blindly follow their calculation logic. This caveat emphasises the need not to rely overly upon any model or method, even those we seem to favour.
US PROPERTY/CASUALTY SCALING Chart 1 displays proforma historic results for the US P&C industry for
the period 1980 to 2010. We show annual product margins (one minus the combined ratio) and pre-tax investment total returns on the left-hand y-axis. Historic product (premium:capital ratio) and investment (invested asset:capital ratio) leverage are shown on the right-hand y-axis.
Product margins are based upon industry-wide reported calendar year combined ratios. Investment returns are based upon the industry’s 2010 asset allocation proxied by 45 indices reflecting annual marked-to-market valuations over the period. In the analysis we use both the lowest (those ending in 2010) and highest (those ending in 1984-85) leverage values to demonstrate their significance in enterprise rate of return and VaR calculations.
In Table 1 we scale the product margins, investment returns, their
respective volatilities and correlations for the low and high leverage scenarios. The product margin was arbitrarily set to 1.0 (a 99 combined ratio) and the total return on assets is the after-tax embedded yield of the fixed income portfolio and a 7 percent return on equities. We assume current full rate taxes. Leverage has a major impact upon the total return on equity and earnings risk.
TABLE 1: PROFORMA ENTERPRISE AFTER-TAX TOTAL RETURN ON EQUITY AND EARNINGS RISK
Enterprise Results
Total Return on Equity Earnings Risk (Std Dev) Total Return on Assets Investment Leverage Product Margin Product Leverage
Source: GR-NEAM Analytics CHART 1: PROFORMA PRODUCT MARGINS, INVESTMENT RETURNS AND LEVERAGE 1980 TO 2010
10 15 20 25 30
-25 -20 -15 -10 -5 0 5
1980 Source: GR-NEAM Analytics Spring 2012 | INTELLIGENT INSURER | 31 1985 Product Margin 1990 Investment Return 1995 2000 Product Leverage 2005 2010 Investment Leverage
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
Low leverage 9.29
15.27 3.72 2.37 1.00 0.74
High Leverage 15.45 25.36 3.72 3.82 1.00 1.92
Product Margin and Investment Return %
Product and Investment Leverage
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