ORSA and Economic Modeling Choices Bert Kramer, André van Vliet, Wendy Montulet OFRC Applied Paper No. 2011-04 May 2011
OFRC WORKING PAPER SERIES ORSA and Economic Modeling Choices Bert Kramer, André van Vliet, Wendy Montulet 1,2 OFRC Applied Paper No. 2011-04 May 2011 Ortec Finance Research Center P.O. Box 4074, 3006 AB Rotterdam Boompjes 40, The Netherlands, www.ortec-finance.com ABSTRACT With the Solvency I rules, supervisors only look at the current solvency level of an insurance company. No prospective long-term analysis is required. As a consequence, decision making is generally based on short horizons. In contrast, within Solvency II insurance companies are required to perform an Own Risk and Solvency Assessment (ORSA), which is a prospective analysis with a three to five year horizon. This forces insurance companies to shift their focus to longer horizons. The prospective nature of the ORSA also implies that insurance companies have to apply risk models to generate prospective scenarios for possible developments of the relevant risk factors. A major risk factor for insurance companies is economic or market risk. In this paper, we will discuss the influence of economic modeling choices on the ORSA within Solvency II. Keywords: Solvency II, ORSA, economic modeling, risk analysis 1 All authors work for Ortec Finance in Rotterdam. Bert Kramer is team manager and senior researcher at the Ortec Finance Research Center, André van Vliet is Head of Insurance Risk Management and Wendy Montulet is team manager and senior consultant Insurance Risk Management.. Please e-mail comments and questions to Bert.Kramer@ortec-finance.com. 2 Copyright 2011 Ortec Finance bv. All rights reserved. No part of this paper may be reproduced, in any form or by any means, without permission from the authors. Shorts sections may be quoted without permission provided that full credit is given to the source. The views expressed are those of the individual author(s) and do not necessarily reflect the views of Ortec Finance bv. 2
Table of Contents 1 Introduction... 4 2 ORSA and ALM... 5 3 Economic modeling within ORSA... 6 4 ORSA example... 8 References... 9 3
1 Introduction The introduction of the new European Solvency II regulation for insurance companies is expected at the end of 2012. These new rules are markedly different from the current Solvency I rules. Therefore, insurance companies started preparing for these changes long before the introduction date. The current Solvency I rules are only based on the characteristics of the liabilities where the technical reserves are based on book value accounting. Furthermore, the Solvency I requirements do not depend on the risks taken. In contrast, the forthcoming Solvency II requirements are based on a total balance sheet approach with all relevant balance sheet items valued at economic (market) value. Furthermore, Solvency II looks at a wide range of risks and applies a Value at Risk approach to determine capital requirements. With the Solvency I rules, supervisors only look at the current solvency level of an insurance company. No prospective long-term analysis is required. As a consequence, decision making is generally based on short horizons. In contrast, within Solvency II insurance companies are required to perform an Own Risk and Solvency Assessment (ORSA), which is a prospective analysis with a three to five year horizon. This forces insurance companies to shift their focus to longer horizons. The prospective nature of the ORSA also implies that insurance companies have to apply risk models to generate prospective scenarios for possible developments of the relevant risk factors. A major risk factor for insurance companies is economic or market risk. In this paper, we will discuss the influence of economic modeling choices on the ORSA within Solvency II. But before we come to that, we will first discuss the link between ORSA and Asset Liability Management (ALM). Ortec Finance May 2011 4/10
2 ORSA and ALM Under Solvency II Pillar 2, all insurance companies are required to undertake an ORSA. The ORSA should provide a forward-looking perspective of the long-term solvency development based on the integral strategy of the company. The time horizon of the ORSA must be identical to the time horizon used in the business planning process, which is usually three to five years. The focus is not (only) on the expected solvency development, but specifically on the uncertainty and risks with respect to the solvency development. That is, a risk-based view is expected. Furthermore, all balance sheet projections should be on market value. The ORSA should take into account the insurer s business plans and projections; and all material risks that may impact the insurer s ability to meet its obligations under the insurance contracts should be evaluated. Therefore, an integrated stress and scenario testing framework should be used. The recommended frequency is (at least) annually, with an update if the risk and solvency profile has changed significantly. Performing an ORSA is very similar to performing an ALM study. Both have a long-term perspective and take into account all material risks. Both include a forward-looking balance sheet (Capital and Solvency) projection over the business planning period. Both look at future capital and solvency levels under different (base, best and worst case) scenarios. The main difference is, that an ORSA also requires more qualitative descriptions of issues like the governance processes, the legal and organizational structure, risk management strategy, risk appetite, risk management process, etceteras. Therefore, in our opinion, ALM software can be used to perform the quantitative analyses required within an ORSA. So within an ORSA, an insurance company can use ALM software to monitor whether given the current integral strategy and business projections their own funds held are adequate given the policy horizon, given the risks they face and given their risk tolerance and risk limits. Ortec Finance May 2011 5/10
3 Economic modeling within ORSA One of the main risk categories for insurance companies is that of market risk. This includes risk related to the uncertain return on investments (equity, bonds, credits, real estate ) and risk related to changing interest and discount rates. Within an ORSA, scenarios have to be generated and analyzed for these and other risk factors. Scenarios are future trajectories modeling the external insecurities that decision makers must take into account in their policy determination and evaluation. With the use of a corporate model of the insurance company we can calculate, for every year and each scenario, what the consequences of the policy intentions are. The scenarios used within an ORSA can be obtained from a scenario model. The scenarios generated by such a model should be realistic. That is, scenarios generated by the model should contain all known real world features and dynamics. Examples of well known real world features as reported by the academic literature are: Term structure of risk and return: Risk and return properties such as means, volatilities, correlations and distributions vary with the investment horizon. For instance: the correlation between equity returns and inflation is around zero for short horizons, but it increases to over 0.5 on a 30 year horizon. Business cycle dynamics: For example, stock prices tend to lead the business cycle (in GDP) while unemployment typically lags the business cycle. Volatility dynamics: Volatility itself is volatile and shows dynamics and correlations. Typically, the correlation between the actual return and volatility is negative for equity (high volatility and bad returns tend to happen together). Tail risk: Correlations increase in the left tails of the distribution. Consequently, the benefits of diversification disappear during crises at times when it is needed most. Non-normal distributions: Distributions typically do not resemble the Normal distribution, but are skewed and have fatter tails. Ignoring one or more of these real world features may impact the outcome of an ORSA, resulting in incorrect conclusions and actions. To consistently model the economic risks within an ORSA, we propagate the use of frequency domain techniques as described in, for example, Steehouwer (2010); combined with (non-normal) factor models for high dimensional processes. The frequency domain methodology consists of a number of statistical and econometric techniques such as spectral analysis, frequency decomposition (filtering) and frequency restricted stochastic processes. The aim is to describe all the aspects of the time series behavior of economic variables at the same time, rather than focusing on a subset of aspects (e.g. only the long term properties). The basic idea underlying the methodology and frequency decomposition in particular is illustrated in Figure 3.1. Figure 3.1 illustrates how a long term interest rate series can be decomposed into a long term (low frequency) and short term (business cycle) component using filtering techniques. The filtered components are orthogonal (uncorrelated) and add up to the original series. Spectral analysis techniques can be used to further analyze the (multivariate) dynamic behavior of the filtered time series. A frequency based decomposition has the following advantages: There is no loss or suppression of long term information (as happens when modeling based on returns): both long and short term fluctuations are visible. Appropriate data can be used for the relevant aspects of the series behavior: for example, long term (annual) series for long term behavior and higher frequency (monthly, weekly or even daily) short term series for short term behavior. Empirical behavior at all horizons can be modeled simultaneously due to separate modeling of the various components. Because they are uncorrelated, separate models for the various components can be devised. In the end the results from the component models can then be brought together again. Time varying (i.e., stochastic) volatility can also integrated in this decomposition framework by using long term realized volatility time series. This enables high dimensional modeling of long and short term volatility dynamics including mutual and return correlations. Ortec Finance May 2011 6/10
Figure 3.1: Frequency decomposition of the Dutch long interest rate With this methodology it is possible to construct time series models that give a better joint description of the empirical long term behavior of economic and financial variables, bring together the empirical behavior of these variables at different horizons and get insight in and understanding of the corresponding dynamic behavior. In the next section we will show an example of the impact of different economic modeling choices on ORSA outcomes. Ortec Finance May 2011 7/10
4 ORSA example We will show the impact of different economic modeling choices on the ORSA results for the stylized case of a Dutch healthcare insurer without supplementary health insurance. That is, this insurance company only sells the standard package of essential healthcare as determined by the Dutch government (i.e., the mandatory basic health insurance). Due to a settlement system via a central fund, the insurance risk run by Dutch health insurance companies is relatively low. Therefore, the main risk factor is investment risk. The return on investment should at least keep up with medical inflation. The asset mix of this insurance company consists of 12.5% worldwide equity, 50% Euro government bonds, 10% Euro credits, 25% cash and 2.5% commodities. We use the Ortec Finance ALM model to generate and analyze 1,000 scenarios for the relevant economic and financial variables. These scenarios are generated using the frequency domain techniques as described above, taking into account the real world features of these variables as reported by the academic literature. We will compare the results for two different scenario sets: Scenario set 1 is based on annual data with constant volatility and no explicit modeling of tail risk; Scenario set 2 is based on monthly data with stochastic volatility and explicit modeling of tail risk (via non-normal factors). Both sets are based on data up to 31 December 2010 and have the same expected (average) values for all variables. The results are summarized in Figure 4.1 and Table 4.1. Figure 4.1: 1,000 scenarios for the solvency ratio. Left panel: set 1; right panel: set 2. In Figure 4.1, the differences are not very clear, but at least you can see that in set 2 the downside risk is somewhat larger that in set 1, especially for the first year (2011). That is, taking into account stochastic volatility and tail risk increases the total risk in this case. Ortec Finance May 2011 8/10
Table 4.1: Numerical results ORSA based on 1,000 scenarios Set 1 (no stochastic vol. and no tail risk) 2011 2012 2013 P(solvency ratio SCR < 120%) 3.8 2.2 0.8 P(solvency ratio SCR < 125%) 22.7 11.8 5.1 VaR 95% solvency ratio SCR 120.7 122.4 125.0 VaR 97.5% solvency ratio SCR 118.9 120.3 123.3 VaR 99% solvency ratio SCR 117.0 117.5 120.5 Set 2 (stochastic vol. and tail risk) 2011 2012 2013 P(solvency ratio SCR < 120%) 6.8 3.3 0.7 P(solvency ratio SCR < 125%) 27.1 14.2 5.1 VaR 95% solvency ratio SCR 119.0 121.3 124.9 VaR 97.5% solvency ratio SCR 117.9 119.2 122.8 VaR 99.0% solvency ratio SCR 115.9 117.1 120.3 The differences between the two sets become clearer when one looks at Table 4.1. Here we see that the probability that the solvency ratio drops below 120% within one year significantly increases from 3.8% to 6.8% when stochastic volatility and tail risk are taken into account. The second year (2012) also shows higher risks with Set 2. By 2013, the differences are negligible. So the modeling choices shown in this example mainly influence the ORSA results for short horizons. However, these differences in the first two years can significantly impact the conclusions for the company and for the supervisor. These differences can lead to risk limits being violated in one case and not in the other. Therefore, in our opinion this example reemphasizes the need to carefully consider how economic risks are and should be modeled when performing an ORSA. References Steehouwer, H. (2010), A Frequency Domain Methodology for Time Series Modeling, in Interest Rate Models, Asset Allocation and Quantitative Techniques for Central Banks and Sovereign Wealth Funds, edited by Berkelaar, A., J. Coche and K. Nyholm, Palgrave Macmillan. Ortec Finance May 2011 9/10