The calibration of bond risk under Solvency II could undermine the financial stability and financing of businesses and sovereigns. Philippe Foulquier and Liliana Arias at Edhec explore the asset-liability mechanisms and long-term guarantee assessments.
Asset-liability mechanisms (ALM) are not taken into account by the Solvency II Directive for life insurance companies and this means increased volatility for prudential balance sheets – a fact highlighted by the European Insurance and Occupational Pensions Authority Quantitative Impact Study 5 (QIS5).
The Omnibus II Directive will amend certain provisions of Solvency II and long-term guarantee assessments (LTGA) have been conducted to test a variety of measures with the aim of integrating ALM into long-term insurance activities, such as life insurance and pensions.
These measures relate to the valuation of insurance liabilities – the extrapolation of long-term rates, implementation of a counter-cyclical premium and a matching adjustment – as well as to new risk calibrations, particularly that of spread risk.
To better reflect ALM strategies, measures specific to the valuation of long-term liabilities were put forward in the LTGA impact study:
- Extrapolation of the long-term rate beyond 20 years: convergence periods of ten and 40 years were tested as underlying assumptions.
- The counter-cyclical premium: a measure applied by EIOPA during volatile market conditions.
The matching adjustment adjusts the discount rate for certain liabilities so that the impacts of spread movements, which affect the value of assets are accounted for on the liability side.
It also tested some new risk calibrations, particularly in relation to spread risk.
In recent research, supported by Russell Investments as part of the Solvency II research chair at Edhec-Risk Institute, we concentrate on the effect of the new spread risk calibration on bond management for activities that are not subject to LTGA measures related to the valuation of long-term liabilities.
Based on the LTGA impact study, the risk factors of the spread risk module depend on rating and now also depend on bond duration.
On comparison of spread risk calibrations of QIS5 and LTGA, and once we conducted an analysis of rating-maturity ratios, we observed that for the majority of these pairings, there was a reduction in the SCR spread under LTGA – in some cases a reduction of up to 50% when compared to QIS5. We thus showed that, under LTGA, the solvency capital requirement spread capital requirement is:
- lower for bonds with durations of less than one, regardless of rating
- lower for investment grade bonds and of substantial benefit for A-rated bonds
- lower for average duration non-investment grade bonds
- higher for long duration non-investment grade bonds and BBB-rated bonds with a duration above 25
However, the findings show that the application of these formulas to our sample results in considerable dilution of the bond regulatory capital requirements because of:
- the weak concentration of AAA highly-rated bonds with durations above ten, for which the reduction in the solvency capital requirement spread is greatest
- the strong concentration of highly-rated bonds with a durations inferior to nine and which have a less significant reduction in the solvency capital requirement spread
- the weak concentration of weakly-rated bonds with long durations for which the capital requirements rise
- the dilution effect linked to the weight of the solvency capital requirement spread
The second part of our research analysed the adequacy of bond solvency capital requirement as a measure of risk. The first analysis we conducted related to the sensitivity of this against nine intrinsic bond characteristics. Our tests conducted under the LTGA guidelines for the spread risk calibration led to similar results and conclusions as those reached under QIS5. Duration emerges as the variable most correlated to solvency capital requirement.
This sensitivity study on rating and maturity showed that the longer the maturity, the higher the capital requirements, regardless of the credit rating in question. As regards the sensitivity of based solely on rating, the study shows that bonds rated AAA, AA and A, consume significantly less capital than bonds with inferior ratings.
These poorly-rated bonds could end up being neglected if the marginal cost brought on by Solvency II is deemed excessive, which could consequently lead to financing difficulties for the companies concerned.
Third, we analysed LTGA bond risk based on the traditional measures of risk, namely value at risk and volatility. The first step, which involved calculating the capital overrun rate, based on a 99.5% value at risk as set by the regulator, showed that for 1.373% of our observations, historical losses exceeded the capital requirements set under LTGA. This indicates that solvency capital requirement was underestimated for the period in question.
This LTGA calibration produced a slightly higher overrun rate than that obtained under QIS5 (1.228%), which can be explained by the overall decrease in capital requirements for investment grade bonds, as well as for medium-duration bonds even if, as previously mentioned, this impact is diluted due to the composition of our sample and due to the weight of the SCR spread in the overall bond SCR.
When looking solely at crisis periods (between 2007 and 2009, 2009 and 2011), capital overrun rates were at their highest (3.481% and 0.737%, respectively), indicating that capital requirements were underestimated. However, in non-crisis periods, the overrun rates are lower or even nil, thus implying that capital requirements are overestimated, as was the case under QIS5.
We also carried out overrun analyses by geography, by rating and by maturity. Our overall results show that the LTGA calibration does not produce any real changes when compared to the trends observed under QIS5, even if the LTGA rates overrun rates are generally slightly higher.
The analysis by rating, in particular, showed that capital overrun rates tended to rise inversely to credit ratings, as we also observed with the QIS5 calibration. Only AAA-rated and unrated bonds satisfy the 99.5% value at risk condition.
The analysis by maturity showed that overrun rates fell as maturities increased. This is due to the fact that long maturity issuances typically only involve highly-rated bonds, which tend to have better-estimated capital requirements.
In the final part of our research we looked at the impact of bond solvency capital requirement on the asset allocation of insurance companies, based on the LTGA’s new spread risk calibration.
To do this, we studied bond return pairings by rating to determine if all risk taken was rewarded or not. Bond return curves expressed in terms of solvency capital requirement keep their quasi-concave shape as identified under QIS5.
Returns increase as long as the requirement is between 0% and 10%; beyond this level they stagnate and even decline. Risk-taking is only rewarded up to a certain level, depending on the credit rating. It should be noted that above 25%, the correlation between return and solvency capital requirement is rather weak. This level of risk generally relates to investment grade bonds with an average duration of 19.62, high yield bonds with an average duration of seven, and unrated bonds with an average duration of 16.
Last, we conducted an analysis on the efficiency of risk-taking based on the bond return-solvency capital requirement ratio. The results show that maximum efficiency is achieved for low durations (between one and three), which corresponds to risk levels of between 3% and 15%, depending on rating. The changes introduced by LTGA in terms of spread shocks do not affect the results in terms of ratings-based maximum efficiency because the capital requirements for low durations (between one and five) remain unchanged from QIS5. The calibration put forward by LTGA continues to favour short-duration bonds (one to three).
To conclude, based on the LTGA impact study, along with QIS5, the solvency capital requirement is, overall, an appropriate measure of risk for fixed-rate debt instruments.
However, it can still be improved by taking into account the following:
- incorporating a Dampener mechanism for bonds in order to integrate the effects of economic cycles and possibly and adjustment that factors in the geographical area in which the bonds were issued
- a revamp of the way in which risk is measured for long-maturity investment grade bonds which are subject to ALM, particularly given their heavy penalisation under Solvency II. They could be treated using a similar approach to that used for equity-backed ring-fenced pension liabilities
- reformulating the risk approach of high yield bonds. These bonds, which are picked by insurers to obtain additional performance, are sensitive to risk factors different from other bonds. As their valuation is sensitive to loss estimation in the event of default, a model in which default risk is paramount should be used by the European regulator.
The calibration of bond risk under Solvency II could very well undermine the financial stability and financing of both businesses and sovereigns. Our assessment of the new calibration of bond risk as defined by the LTGA impact study does not necessarily bring us to the conclusion that it is an improvement on the calibration under QIS5.
Philippe Foulquier is a professor of finance at Edhec Business School and a director at Edhec Financial Analysis and Accounting Research Centre. Liliana Arias is a research engineer at Edhec Financial Analysis and Accounting Research Centre
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