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Life insurance convexity
(2023)
Life insurers sell savings contracts with surrender options, which allow policyholders to prematurely receive guaranteed surrender values. These surrender options move toward the money when interest rates rise. Hence, higher interest rates raise surrender rates, as we document empirically by exploiting plausibly exogenous variation in monetary policy. Using a calibrated model, we then estimate that surrender options would force insurers to sell up to 2% of their investments during an enduring interest rate rise of 25 bps per year. We show that these fire sales are fueled by surrender value guarantees and insurers’ long-term investments.
Life insurance convexity
(2021)
Life insurers massively sell savings contracts with surrender options which allow policyholders to withdraw a guaranteed amount before maturity. These options move toward the money when interest rates rise. Using data on German life insurers, we estimate that a 1 percentage point increase in interest rates raises surrender rates by 17 basis points. We quantify the resulting liquidity risk in a calibrated model of surrender decisions and insurance cash flows. Simulations predict that surrender options can force insurers to sell up to 3% of their assets, depressing asset prices by 90 basis points. The effect is amplified by the duration of insurers' investments, and its impact on the term structure of interest rates depends on life insurers' investment strategy.
This paper documents that the bond investments of insurance companies transmit shocks from insurance markets to the real economy. Liquidity windfalls from household insurance purchases increase insurers' demand for corporate bonds. Exploiting the fact that insurers persistently invest in a small subset of firms for identification, I show that these increases in bond demand raise bond prices and lower firms' funding costs. In response, firms issue more bonds, especially when their bond underwriters are well connected with investors. Firms use the proceeds to raise investment rather than equity payouts. The results emphasize the significant impact of investor demand on firms' financing and investment activities.
Common systemic risk measures focus on the instantaneous occurrence of triggering and systemic events. However, systemic events may also occur with a time-lag to the triggering event. To study this contagion period and the resulting persistence of institutions' systemic risk we develop and employ the Conditional Shortfall Probability (CoSP), which is the likelihood that a systemic market event occurs with a specific time-lag to the triggering event. Based on CoSP we propose two aggregate systemic risk measures, namely the Aggregate Excess CoSP and the CoSP-weighted time-lag, that reflect the systemic risk aggregated over time and average time-lag of an institution's triggering event, respectively. Our empirical results show that 15% of the financial companies in our sample are significantly systemically important with respect to the financial sector, while 27% of the financial companies are significantly systemically important with respect to the American non-financial sector. Still, the aggregate systemic risk of systemically important institutions is larger with respect to the financial market than with respect to non-financial markets. Moreover, the aggregate systemic risk of insurance companies is similar to the systemic risk of banks, while insurers are also exposed to the largest aggregate systemic risk among the financial sector.
A tontine provides a mortality driven, age-increasing payout structure through the pooling of mortality. Because a tontine does not entail any guarantees, the payout structure of a tontine is determined by the pooling of individual characteristics of tontinists. Therefore, the surrender decision of single tontinists directly affects the remaining members' payouts. Nevertheless, the opportunity to surrender is crucial to the success of a tontine from a regulatory as well as a policyholder perspective. Therefore, this paper derives the fair surrender value of a tontine, first on the basis of expected values, and then incorporates the increasing payout volatility to determine an equitable surrender value. Results show that the surrender decision requires a discount on the fair surrender value as security for the remaining members. The discount intensifies in decreasing tontine size and increasing risk aversion. However, tontinists are less willing to surrender for decreasing tontine size and increasing risk aversion, creating a natural protection against tontine runs stemming from short-term liquidity shocks. Furthermore we argue that a surrender decision based on private information requires a discount on the fair surrender value as well.
Under Solvency II, corporate governance requirements are a complementary, but nonetheless essential, element to build a sound regulatory framework for insurance undertakings, also to address risks not specifically mitigated by the sole solvency capital requirements. After recalling the provisions of the second pillar concerning the system of governance, the paper is devoted to highlight the emerging regulatory trends in the corporate governance of insurance firms. Among others, it signals the exceptional extension of the duties and responsibilities assigned to the Board of directors, far beyond the traditional role of both monitoring the chief executive officer, and assessing the overall direction and strategy of the business. However, a better risk governance is not necessarily built on narrow rule-based approaches to corporate governance.
Depending on the point of time and location, insurance companies are subject to different forms of solvency regulation. In modern regulation regimes, such as the future standard Solvency II in the EU, insurance pricing is liberalized and risk-based capital requirements will be introduced. In many economies in Asia and Latin America, on the other hand, supervisors require the prior approval of policy conditions and insurance premiums, but do not conduct risk-based capital regulation. This paper compares the outcome of insurance rate regulation and riskbased capital requirements by deriving stock insurers’ best responses. It turns out that binding price floors affect insurers’ optimal capital structures and induce them to choose higher safety levels. Risk-based capital requirements are a more efficient instrument of solvency regulation and allow for lower insurance premiums, but may come at the cost of investment efforts into adequate risk monitoring systems. The paper derives threshold values for regulator’s investments into risk-based capital regulation and provides starting points for designing a welfare-enhancing insurance regulation scheme.
We study the impact of estimation errors of firms on social welfare. For this purpose, we present a model of the insurance market in which insurers face parameter uncertainty about expected loss sizes. As consumers react to under- and overestimation by increasing and decreasing demand, respectively, insurers require a safety loading for parameter uncertainty. If the safety loading is too small, less risk averse consumers benefit from less informed insurers by speculating on them underestimating expected losses. Otherwise, social welfare increases with insurers’ information. We empirically estimate safety loadings in the US property and casualty insurance market, and show that these are likely to be sufficiently large for consumers to benefit from more informed insurers.
Tail-correlation matrices are an important tool for aggregating risk measurements across risk categories, asset classes and/or business segments. This paper demonstrates that traditional tail-correlation matrices—which are conventionally assumed to have ones on the diagonal—can lead to substantial biases of the aggregate risk measurement’s sensitivities with respect to risk exposures. Due to these biases, decision-makers receive an odd view of the effects of portfolio changes and may be unable to identify the optimal portfolio from a risk-return perspective. To overcome these issues, we introduce the “sensitivity-implied tail-correlation matrix”. The proposed tail-correlation matrix allows for a simple deterministic risk aggregation approach which reasonably approximates the true aggregate risk measurement according to the complete multivariate risk distribution. Numerical examples demonstrate that our approach is a better basis for portfolio optimization than the Value-at-Risk implied tail-correlation matrix, especially if the calibration portfolio (or current portfolio) deviates from the optimal portfolio.
Historical evidence like the global financial crisis from 2007-09 highlights that sector concentration risk can play an important role for the solvency of insurers. However, current microprudential frameworks like the US RBC framework and Solvency II consider only name concentration risk explicitly in their solvency capital requirements for asset concentration risk and neglect sector concentration risk. We show by means of US insurers’ asset holdings from 2009 to 2018 that substantial sectoral asset concentrations exist in the financial, public and real estate sector, and find indicative evidence for a sectoral search for yield behavior. Based on a theoretical solvency capital allocation scheme, we demonstrate that the current regulatory approaches can lead to inappropriate and biased levels of solvency capital for asset concentration risk, and should be revised. Our findings have also important implications on the ongoing discussion of asset concentration risk in the context of macroprudential insurance regulation.
This paper documents that the bond investments of insurance companies transmit shocks from insurance markets to the real economy. Liquidity windfalls from household insurance purchases increase insurers’ demand for corporate bonds. Exploiting the fact that insurers persistently invest in a small subset of firms for identification, I show that these increases in bond demand raise bond prices and lower firms’ funding costs. In response, firms issue more bonds, especially when their bond underwriters are well connected with investors. Firms use the proceeds to raise investment rather than equity payouts. The results emphasize the significant impact of investor demand on firms’ financing and investment activities.
Testing frequency and severity risk under various information regimes and implications in insurance
(2023)
We build on Peter et al. (2017) who examined the benefit of testing frequency risk under various information regimes. We first consider testing only severity risk, and whether the principle of indemnity, i.e. the usual contract term that excludes claims payments above the resulting insured loss, affects the insurance contracts offered and purchased. Under information regimes which are less restrictive (in terms of obtaining and using customer information), it is possible for the insurer to offer different contracts for tested and untested individuals. In the absence of the principle of indemnity, individuals will test their severity risk and a separating equilibrium ensues. With the principle of indemnity, given an actuarially fair pooled contract, individuals will not test for severity under less restrictive information regimes; a pooling equilibrium thus ensues. Under more restrictive information regimes, the insurer offers separating contracts. Individuals will test for severity and purchase appropriate contracts. We also consider testing for both frequency and severity risk. The results here are more varied. The highest gain in efficiency from testing results from one of the more restrictive information regimes. Generally under all information regimes, there is a greater gain in efficiency without the principle of indemnity than with the principle of indemnity.
Gradient capital allocation, also known as Euler allocation, is a technique used to redistribute diversified capital requirements among different segments of a portfolio. The method is commonly employed to identify dominant risks, assessing the risk-adjusted profitability of segments, and installing limit systems. However, capital allocation can be misleading in all these applications because it only accounts for the current portfolio composition and ignores how diversification effects may change with a portfolio restructuring. This paper proposes enhancing the gradient capital allocation by adding “orthogonal convexity scenarios” (OCS). OCS identify risk concentrations that potentially drive portfolio risk and become relevant after restructuring. OCS have strong ties with principal component analysis (PCA), but they are a more general concept and compatible with common empirical patterns of risk drivers being fat-tailed and increasingly dependent in market downturns. We illustrate possible applications of OCS in terms of risk communication and risk limits.
Most insurers in the European Union determine their regulatory capital requirements based on the standard formula of Solvency II. However, there is evidence that the standard formula inaccurately reflects insurers’ risk situation and may provide misleading steering incentives. In the second pillar, Solvency II requires insurers to perform a so-called “Own Risk and Solvency Assessment” (ORSA). In their ORSA, insurers must establish their own risk measurement approaches, including those based on scenarios, in order to derive suitable risk assessments and address shortcomings of the standard formula. The idea of this paper is to identify scenarios in such a way that the standard formula in connection with the ORSA provides a reliable basis for risk management decisions. Using an innovative method for scenario identification, our approach allows for a simple but relatively precise assessment of marginal and even non-marginal portfolio changes. We numerically evaluate the proposed approach in the context of market risk employing an internal model from the academic literature and the Solvency Capital Requirement (SCR) calculation under Solvency II.
I measure the effects of workers’ mobility across regions of different productivity through the lens of a search and matching model with heterogeneous workers and firms estimated with administrative data. In an application to Italy, I find that reallocation of workers to the most productive region boosts productivity at the country level but amplifies differentials across regions. Employment rates decline as migrants foster job competition, and inequality between workers doubles in less productive areas since displacement is particularly severe for low-skill workers. Migration does affect mismatch: mobility favors co-location of agents with similar productivity but within-region rank correlation declines in the most productive region. I show that worker-firm complementarities in production account for 33% of the productivity gains. Place-based programs directed to firms, like incentives for hiring unemployed or creating high productivity jobs, raise employment rates and reduce the gaps in productivity across regions. In contrast, subsidies to attract high-skill workers in the South have limited effects.
Between 2016 and 2022, life insurers in several European countries experienced negative longterm interest rates, which put pressure on their business models. The aim of this paper is to empirically investigate the impact of negative interest rates on the stock performance of life insurers. To measure the sensitivities, I estimate the level, slope, and curvature of the yield curve using the Nelson-Siegel model and empirical proxies. Panel regressions show that the effect of changes in the level is up to three times greater in a negative interest rate environment than in a positive one. Thus, a 1ppt decline in long-term interest rates reduces the stock returns of European life insurers by up to 10ppt when interest rates are below 0%. I also show that the relationship between the level and the sensitivity to interest rates is convex, and that life insurers benefit from rising interest rates across all maturity types.
Homeownership rates differ widely across European countries. We document that part of this variation is driven by differences in the fraction of adults co-residing with their parents. Comparing Germany and Italy, we show that in contrast to homeownership rates per household, homeownership rates per individual are very similar during the first part of the life cycle. To understand these patterns, we build an overlapping-generations model where individuals face uninsurable income risk and make consumption-saving and housing tenure decisions. We embed an explicit intergenerational link between children and parents to capture the three-way trade-off between owning, renting, and co-residing. Calibrating the model to Germany we explore the role of income profiles, housing policies, and the taste for independence and show that a combination of these factors goes a long way in explaining the differential life-cycle patterns of living arrangements between the two countries.
In crisis times, insurance companies might feel the pressure to present an investment portfolio performance that is superior to the market, since investment portfolios back the claims of policyholders and serve as a signal for the claims’ safety. I investigate how a stock market crisis as experienced over the course of the Covid-19 pandemic influences insurance firms’ decisions on the allocation of their corporate bond portfolio. I find that insurers shift their portfolio holdings towards lower credit risk assets as financial market conditions tighten. This tendency seems to be restricted by the liquidity risk of high-yield assets, and the credit risk of lower-rated investment grade assets. Both effects lead to an increase in the fraction of less liquid assets during the crash and the recovery.
The capital requirements of Solvency II allow insurers to make discretionary choices. Besides extensive possibilities regarding the choice of a risk model (ranging between a regulatory prescribed standard formula to a full self-developed internal model), insurers can make use of transitional measures and adjustments, which can have a substantial impact on their reported solvency level. The aim of this article is to study the effect of these long-term guarantee measures and to identify drivers of the discretionary decisions. For this purpose, we first assess the risk profile of 49 European insurers by estimating the sensitivities of their stock returns to movements in market risk drivers, such as interest rates and credit spreads. In a second step, we analyze to what extent insurers’ risk profiles influence their discretionary decisions in the capital requirement calculation. We gather information on discretionary decisions based on hand-collected Solvency II data for the years 2016 to 2020. We find that insurers optimize their reported solvency situation by making discretionary decisions in such a way that capital requirements for material risk drivers are clearly reduced. For instance, we find that the usage of the volatility adjustment is positively related to the interest rate risk as perceived by financial markets, even when controlling for the portion of life insurance in technical provisions. Similarly, the matching adjustment is linked to significantly higher credit risk sensitivities. Our results point out that due to discretionary decisions Solvency II figures can substantially deviate from a market-oriented, risk-based view on insurance companies’ risk situation.
In times of crisis, insurance companies may invest into riskier assets to benefit from expected price recoveries. Using daily stock market data for 34 European insurers, I investigate how a stock market contraction, as experienced during the Covid-19 pandemic, affects insurers’ decision on the allocation of their corporate bond portfolio. I find that insurers shift their portfolio holdings pro-cyclically towards lower credit risk assets in the first month of the market contraction. As the crisis progresses, I find evidence for counter-cyclical investment behavior by insurers, which can neither be explained by credit rating downgrades of held bonds nor by hedging with CDS derivatives. The observed counter-cyclical investment behavior of insurers could be beneficial for the financial system in attenuating price declines, but excessive risk-taking by insurance companies over longer periods can also reinforce stress in the system.