UK: Report for the ABI on Key Correlation Assumptions in ICA for Life Offices (Part 2 of 3)

Last Updated: 18 July 2005
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This article is part of a series: Click Report for the ABI on Key Correlation Assumptions in ICA for Life Offices - Executive Summary for the previous article.


Terms of reference

This report has been prepared in accordance with terms of business dated 16 May 2005. The report considers risk correlations in individual capital assessment of life insurance firms.

Purpose of report

The purpose of the report is to:

a) outline risk capital aggregation techniques based on the application of correlation matrices;

b) give background on the use of correlation matrices in practice, including a discussion of internal consistency conditions;

c) outline alternative techniques that could be used to allow for dependencies between risks;

d) identify a range of diversification benefits that has been seen to arise due to correlation between risk drivers;

e) discuss in detail instances of correlation between risk drivers in life insurance business, including correlations between:

  • market risk and lapse & surrenders;
  • market risk and mortality;
  • annuitant and assured lives mortality;
  • intra-market correlations.

Use of this report and legal responsibility

The matters discussed in this report are by their nature technical. The intended recipient of the report, the ABI, is familiar with the issues, facts and other matters addressed and the report was written with that in mind.

This report was prepared for the sole and confidential use of the Association of British Insurers (ABI) and for the purposes set out in the terms of reference and outlined above. It was not prepared for or in contemplation of any other purpose or for the use of any other person. In preparing this report our only responsibility and duty of care was to the ABI. We did not, and do not by consenting to publication of this report, assume or accept or owe any responsibility or duty of care to any other person. Our report was prepared on the basis that, except with the written consent of Deloitte the report, any written or oral information or advice provided by Deloitte must not be reproduced, distributed or communicated in whole or in part to any other person, or be relied upon by any other person.

The ABI has asked for our consent to making this report publicly available by posting it on their web-site. We have agreed to provide such consent on the following understanding and conditions:

  • This report will not be suitable for the use of any person other than the ABI. The work performed in producing the report was not carried out in the knowledge or context of any specific requirements which any third party may have. Accordingly, publication of this report to persons other than the ABI is for information purposes only and no person other than the ABI should place any reliance on this report.
  • We do not assume or accept or owe any responsibility or duty of care to any person other than the ABI. Accordingly, any person other than the ABI who, contrary to the above, chooses to rely on this report, does so at their own risk and we will not be responsible for any losses of any such person caused by their reliance on this report. Such parties should carry out their own independent investigations and obtain independent professional advice on all matters covered (or which ought to have been covered) by this report.
  • This report is not intended by Deloitte to form the basis of any decision by any third party.
  • No representation, warranty, promise or undertaking, express or implied is or will be made or given in relation to the truth, accuracy or completeness of the report.

The Report must be considered in its entirety as individual sections, if considered in isolation, may be misleading. 

If reliance is placed contrary to the guidelines set out above, Deloitte disclaims any and all liability which may arise.


Deloitte & Touche LLP retains copyright over the report. Findings should not be quoted without explicit reference to the report.

Reliance and limitations

The report is issued under the assumption that no legal reliance is placed on the results by the intended audience or any other parties. Findings presented in the report may not be viewed as advice given by Deloitte to the parties in receipt of the report.

Details of individual capital assessment calculations are strongly dependent on the individual circumstances of a particular life assurance company. Judgement needs to be exercised in interpreting the report, as it is possible that not all of the points are applicable to the circumstances of individual firms in practice. Deloitte can give no assurance as to the applicability of the findings of the report to individual members’ ICA calculations. 

For individual firms suitable correlation values will vary and must be determined with reference to the composition of their individual businesses, including asset/liability management and the risk profile of the company.

The results of our analysis should not be taken as applying to any specific firm as our work will be based upon the consideration of a generalised insurance operation, which may not be appropriate for any one individual firm.

Our analysis should not be used outside the scope of work as described above.

Best practice in carrying out ICA calculations is still materialising. Therefore any assistance we provide will be on the basis of our experience to date.

The scope of our work and our responsibilities has not involved us in performing the work necessary for the purpose of providing, neither shall we provide, any opinion as to the reliability, proper compilation or clerical accuracy of any prospective financial information supplied to us, nor the reasonableness of the underlying assumptions. Since any prospective financial information relates to the future, it may be affected by unforeseen events. Actual results are likely to be different from those projected because events and circumstances frequently do not occur as expected, and those differences may be material.

The realisation of any prospective financial information depends in part upon the effectiveness of management’s actions in its implementation and execution of the underlying business plans. We can give no assurance as to whether or how closely the actual results ultimately achieved will correspond to those projected or forecast. Any views we may express as to the basis for any prospective financial information or possible future outcomes is made in good faith on the basis of the information available to us at the time but does not constitute a representation, undertaking or warranty of any kind.

In preparing this report, we have used information and data extracted from published surveys and papers, which we believe to be reliable, to produce the findings shown. Several sources have been used and are detailed in the back of this report. We have relied upon such information and data as being true, correct and complete and have not audited, tested or checked any such information or data.

This report was based on data available to Deloitte at, or prior to 31 December 2004, and takes no account of developments after that date. Deloitte is under no obligation to update or correct inaccuracies which may become apparent in the Report.

This report is subject to the terms and limitations, including limitation of liability, set out in the conditions of contract for professional services agreed with the ABI and signed on 16 May 2005.

This report will be governed by and construed in accordance with English Law and the parties submit to the exclusive jurisdiction of the English courts in connection with all disputes and differences arising out of, under or in connection with this report. If any part of a provision of this report is held invalid, illegal or unenforceable then the remainder of such provision shall remain valid and enforceable to the fullest extent permitted by law.


Description of ICA calculation

Following several years of development and shadow operation, a new framework of prudential regulation for the UK insurance industry was introduced by the Financial Services Authority (FSA) on 31 December 2004. Amongst the changes introduced is a requirement that all life insurance firms undertake their own assessment of the capital needed to support the business they write. The Individual Capital Assessment (ICA) determines the level of capital required to ensure that the probability of insolvency over a set time horizon is acceptably low and in a wider sense the ICA fits clearly into Pillar II of the Basel framework for capital management.

In the UK context, the ICA process operates as follows:

a) FSA communicates common standards expected of life insurance firms;

b) FSA reviews firms’ ICA submissions; and

c) Firm and FSA engage in dialogue on the ICA, the underlying assumptions and the overall capital assessment.

FSA emphasises the need for transparency at all stages of the process, which underlines the importance of firms being able to justify the assumptions underpinning their ICA and the techniques applied in its calculation, including those used in stress testing, scenario testing and risk capital aggregation.

Following the firm’s ICA submission, the dialogue and consultation undertaken between the firm and the FSA may result in formal Individual Capital Guidance (ICG) being given to the firm by the FSA. This effectively implements Pillar II of the Basel approach to capital management.

Typically, the target used by life insurance firms is to remain solvent over the next year with 99.5% probability. In other words, to hold sufficient capital to reduce the likelihood of insolvency over the next 12 months to a 1 in 200 year event. However, a firm may use a different measure or time horizon if it believes this to be more appropriate. Where a longer time horizon is used, (for instance to run off the whole book) then a lower level of confidence of solvency would normally apply. However, if this approach is adopted, it is necessary for the firm to be able to demonstrate solvency at intermediate points, for example once every year, which can result in a challenging computational exercise.

In preparing their ICA, firms will identify the main risks in carrying out their business and will quantify the amount and quality of capital required to mitigate these risks. There will be areas where capital is not an appropriate risk mitigation tool and so companies may look to change processes and practices in an effort to mitigate these risks. 

As a matter of good practice, companies are in any event advised to retain a buffer of capital over the ICA or ICG amount.

Scope of risks covered by ICA

Firms are required to understand and quantify the impact of risk events which may crystallise in all major categories including:

  • credit risk;
  • liquidity risk;
  • market risk;
  • operational risk;
  • insurance risk;
  • group risk.

Typically this is achieved by carrying out scenario and stress testing. It is recognised that in some areas this will be more challenging than in others. Analysis of credit risk, operational risk and measurement of the degree of association between the risks, in particular, may not be easy. Of course, the ultimate responsibility for ensuring adequate capital provision remains with the directors and managers of the firm.

Detailed information on the scope of risks covered in the ICA framework is provided in section 2.3 of the Integrated Prudential Sourcebook for Insurers.

Stress tests versus scenario testing

Stress and scenario testing may be applied to the business model of a life firm to quantify the amount of capital required to meet projected liabilities as they fall due, with the required degree of confidence.

Stress testing involves the analysis of individual risk factors, for example, changes in yield curve or the level of product lapses. Having isolated and assessed the impact of all the individual risk factors, the results must then be aggregated to derive an overall measure of required capital.

Scenario testing is based on simultaneous assessment of mutually consistent worst-case realisation of risks. The overall amount of capital required is determined as the amount needed to withstand the worst combination of events with a required degree of confidence. 

Given the complexity of insurance business and the nature of the risks, one of the major challenges for life companies is simply to be able to model their business in a sufficiently robust way to fully understand the firm’s capital requirements. This area will continue to develop in complexity as firms upgrade their modelling capability.


Stand-alone capital calculations

Life insurance companies are exposed to many risks, which need to be reflected in the ICA. These risks would usually include movements in interest rates, equity and property markets, lapse rates, mortality, inflation and other uncertain variables.

Offices will try to determine a level of capital to cover a "worst case" scenario. However, in determining this worst case it is not the absolute worst combination of events conceivable that is assessed, but rather a selected severe outcome with a large confidence level that reality will turn out to be better.

The overall amount of capital required depends on the time horizon used the confidence level selected by management and importantly, the degree of diversification between the risks.

Given the complexity of modelling, understanding the individual risks and the interaction between these risks, offices may determine their required capital in two stages:

  • Estimate the amount of capital required for each risk on a stand-alone basis.
  • Combine these stand-alone amounts into an aggregate amount.

Allowance for diversification

A very conservative approach would be simply to add up the stand-alone capital amounts for each risk, to produce a total. This is probably excessively cautious because it assumes that all the worst cases for each risk factor occur simultaneously. This would be the same as assuming 100% correlation between all the risk factors.

It is highly unlikely that all risks will be perfectly correlated. For example, given a sharp fall in the stock market, we should not necessarily expect a simultaneous sharp improvement in annuitant longevity expectations. It would therefore be unreasonable to expect a company to hold risk capital equal to the sum of all the amounts calculated for each of the individual risks.

Allowing for imperfect correlation between risks is therefore important in achieving a realistic assessment of the capital required to support the business. For most companies, this will result in overall capital requirements being substantially below the amount obtained by simply summing the capital for the separate risks.

The reduction in required capital relative to the sum of standalone capital requirements is referred to as the diversification benefit. A high correlation implies a low diversification benefit. Offices arguing for large diversification benefits must therefore offer evidence of low correlations.

Correlation matrices

The benefits arising from diversification may be derived in a number of ways. Given the complexity of the task and the need for a pragmatic and understandable approach, many companies have calculated their initial ICA using one-year stress tests for the various risks and then combined these results using a correlation matrix.

A correlation matrix contains all the correlations between the various pairs of risks. This method is reliable provided that the individual risk factors all have Normal distributions. 

For example, consider an office with the following stand-alone capital requirements: 

Table 1


Risk capital requirement (£m)













Table 2


They might construct the following correlation matrix:


















































The diversified capital can be calculated through matrix multiplication which has the following form:

Take the sum of: 

• square of the capital required for each risk factor; 

• twice the product of the capital required for each pair of risk factors, multiplied by the relevant correlation; 

and then take the square root of the sum.

In our example, the overall capital requirement is £135.8 million. This can be contrasted with £204 million obtained by a simple sum of stand alone capital amounts. Applying the correlation matrix yields the diversification benefit of approximately 33%.

To illustrate how aggregate risk capital requirements relate to the correlation assumptions we consider a simplified example of combining the capital requirement of insurance and market risks. If there were no diversification benefit the capital requirement would be the sum of the individual capital requirements, (£137 million). The following graph shows the capital requirement as the correlation factor changes.

Here the diversification benefit ranges from 0 under the correlation assumption of 100% to approximately 79% under the correlation assumption of -100%.

Correlation consistency

For this approach to work a correlation matrix needs to be internally consistent. For example, if an investigation suggest that:

  • The 2-year spot rate has a 90% correlation with the 5-year spot rate.
  • The 5-year spot rate has a 95% correlation with the 10-year spot rate.

Then for our correlation matrix to be internally consistent without any further analysis we can use standard mathematical techniques to imply that the 2-year spot rate and the 10-year spot rate are at least 70% correlated. A correlation of less than 70% would not produce an internally consistent matrix. In mathematical terms the matrix ought to be "positive definite". In addition to verifying that individual correlations are appropriate, offices should ensure that any proposed matrix is positive definite2

The positive-definite condition can easily be checked by regulators.

Simple algorithms, for example the Jacobi algorithm can identify a positive definite matrix close to a specified first estimate matrix. See, for example, Press, Teukolskly, Vetterling and Flannery (1992).

Limits on correlations

Correlations must lie between -100% and +100%. A correlation of 100% occurs when two variables are perfectly aligned with the same pattern of occurence. This will often involve a causal link between two factors. However, few variables are perfectly matched in this way. To give a simple example, let us suppose equity returns have a Normal distribution. If we also assume mortality has its own discrete distribution where mortality remains unchanged 90% of the time, improves 5% of the time by a given amount and deteriorates 5% of the time by the same amount, then these two variables cannot be perfectly aligned.

Since equity return and mortality have different distributions, they cannot possibly have a 100% correlation. In fact, the maximum achievable mathematical correlation is 65% in the example above.

Tail correlations

Put simply, under extreme conditions established relationships between factors may change. When we are considering the highly unusual circumstances which could give rise to the possible financial failure of a firm, the correlations which exist under these extreme conditions, the "tail correlations", are highly significant.

Historic data often suggests low correlations between, for example, equity market and interest rates, or between capital markets and mortality. Assumptions of zero correlation frequently give rise to large stated diversification benefits.

However, these low correlations are based on observations in normal market conditions and it is possible that extreme events, such as natural catastrophes, liquidity crises or political upheaval, could cause all markets to move downward simultaneously, even when these markets show low historic correlations. This is a scenario cited in connection with the failure of the Long Term Capital Management hedge funds and the 2001 World Trade Centre attacks.

Understanding the tail correlation arguments

The tail correlation argument has two elements:

  • Historic data may underestimate the prospective correlations.
  • The use of correlation matrices may be unsound because the underlying distributions do not combine as multivariate Normal distributions. To address this point more general measures of association, such as the use of "copulas" which can join univariate distribution functions to form multivariate distribution functions are sometimes proposed.

Tail correlations do not necessarily lead to higher capital requirements and there are several counter-arguments. These include:

  • Large events may well affect all markets at once, but not necessarily all in an adverse direction. For example, equity market crises are frequently accompanied by a rise in bond markets as equity sellers move their cash to a perceived safe haven.
  • It is impossible for all currency markets to fall simultaneously. If the dollar falls relative to the pound, then the pound must rise in value against the dollar.
  • Extreme events may be mitigated by stakeholder actions. For example, some funds have switched wholly or partly into bonds, mitigating the effect of falling equity markets on guarantees.
  • An erosion of insurer solvency may cause a decline in policyholder confidence, triggering surrenders which in turn relieve the insurer of the very guarantees which caused the original solvency problem.

Many of the tail correlation arguments are speculative and have scant basis in objective data. There is seldom sufficient data to reject Normal correlations in favour of more exotic copular approaches.

The fact that we can imagine very extreme and damaging scenarios does not justify the selective inclusion of extreme events into capital models which would lead to inappropriately high levels of capital.

Allowing for tail correlations in practice

It may be possible to account for tail correlations by adjusting the correlation matrix assumptions. However, the magnitude, or even the direction in which the correlation assumptions need to be adjusted, may not be clear.

This effect is driven by the fact that for the aggregation of risk by application of a correlation approach to work, the multivariate distribution of the underlying risks must be Normal. If the resulting distribution is non-Normal we will need to make adjustments to the correlation matrix to achieve the correct result.

For example, suppose that two risks X and Y have a joint non-Normal multivariate distribution. For example, X may be the annuitant mortality risk and Y may be the assured lives mortality risk and these have liability weightings of 30% and 70%. To measure the overall risk capital requirement of the insurer we need to determine the 0.5th percentile of the combined risk distribution, that is of the distribution of 0.3X + 0.7Y. There are two alternative approaches.

First, we could compute the percentile directly; however, this is often difficult or impossible in practice. In our example below we have chosen distributions that allow us to calculate the analytic result directly.

Second, we could calculate the 0.5th percentile of 0.3X and the 0.5th percentile of 0.7Y, then add these up, subtracting a diversification benefit. This is the ICA correlation matrix approach.

Suppose that for the purposes of the diversification calculation, 0.3X and 0.7Y are Normally distributed. Making sure that the means and 0.5th percentiles for the stand-alone risks are fitted correctly, we may ask ourselves: "what is the correlation assumption that captures the true underlying ICA value?".

Depending on the weighting of individual risks in the liabilities portfolio the correlation assumption between these risks may have to be varied significantly in order to reproduce the true ICA value as derived from the analytic distribution.

We can see this in Figure 2 where the red line is the implied correlation between the risks based on the correlation matrix approach whilst the blue line is the theoretically correct underlying correlation based on the analytic solution of the multivariate non-Normal distribution.

We have chosen a relatively simple example but in practice fitting this exposure will require significant effort and if possible a simple and pragmatic parallel model should help calibrate the matrix

Reference to PRU

The FSA guidance on ICA contains relatively little on correlations. Firms are required to document the key assumptions used in performing the stress and scenario tests, including those assumptions made in aggregating the results. The FSA has also stated that companies must be prepared to justify the correlations, or the equivalent diversification benefits, claimed in the determination of their ICA.

In the Basel Pillar II framework, correlations are analysed primarily as a measure of risk concentration in the assessment of investment risks. Little information is provided about diversification benefits, or risk capital aggregation techniques. However, given that under Pillar II financial institutions are allowed a degree of flexibility in performing their own capital assessment, it may be possible to claim some offset for the correlation between separate risk drivers. The appropriateness of the diversification credit taken is ultimately judged by a regulator. It remains to be seen how this will work in practice.

Diversification and hedging

Considering correlation between assets in capital markets, or between an asset and the market is important in portfolio management theory. The Prudential Sourcebook for Insurers emphasises the need to account for correlation between assets in the process of market risk quantification.

In a market where the number of available assets is sufficiently large, an investor can diversify all of the asset-specific risk, leaving only pure market risk by investing in a large number of uncorrelated assets. This is one of the fundamental tenets of modern financial theory.

By analogy, the volume of capital necessary to maintain solvency would be at its lowest if the capital requirement was driven by a large number of uncorrelated risks. This can be contrasted with risk aggregation by simple summation of the capital required for all individual risks, which would imply a 100% correlation, in other words assuming that all (negative) risk events which could occur in any circumstances will in fact all occur at the same time. As described above, we know that in many instances this is either highly unlikely or in fact impossible.

Range of diversification benefits seen in practice

The diversification benefit obtained from imperfect correlation between risks depends on two factors, the correlations assumed and the relative magnitude of the individual risks. If a company has a large exposure to one risk, whilst all other risk exposures are relatively small, then the aggregate capital requirement will be relatively insensitive to the correlations assumed. Conversely, if a company is exposed to several risks of comparable magnitude, then the correlation assumptions between these risks will have a significant bearing on the overall ICA result.

The diversification benefit obtained in any one company is therefore critically dependent on the mix of risks within that company. Those risks will reflect the differing mixes of product types and the different risk management policies adopted by companies. It is therefore almost impossible to benchmark diversification benefits between companies. It would be better to focus on comparing correlation assumptions and possibly the allowance for risk practices and corresponding management actions.

We have observed that the typical effect of diversification is to reduce the amount of capital required by between 25% and just over 50% from the notional position assuming all risks are perfectly correlated.

Why we are focussing on the following correlations

We have been asked to concentrate on the following correlations, as these are regarded as among the most material in most companies’ ICA calculations:

  • Market risk and lapse & surrender rates.
  • Market risk and mortality.
  • Annuitant mortality and term assurance mortality.
  • Intra-market correlations.

Techniques other than correlations

An alternative to the use of correlations is to allow for specified dependencies between some of the risks in a projection model.

This may be achievable for certain risk combinations but it is unlikely that an all encompassing series of formulae could be determined.

Examples of where dependencies could be used are GAO take up rates, and surrender and lapse rates. In the former case, we might expect that GAO take up rates increase as interest rates fall. A rule or formula could then in principle be developed to link take up rates to the level of interest rates. The details of such a rule are likely to be subjective, since there may not be sufficient data to fully support the formula and future experience may differ from the past. However, such rules should be relatively straightforward to model and test, and to compare with results obtained through the use of correlations.

Similarly, surrender and lapse rates might be expected to depend on economic conditions (see relevant section below), and for lapses on contracts with guarantees to depend on the value of those guarantees. Again, it may be possible to develop some rules for testing. This would be a relatively straight forward extension of the functionality which companies are building in to their models to represent policyholder and management actions. No matter which approach is used, companies will need to ensure they have a good understanding of the methodology used and how the risks are modelled to avoid any double counting of capital requirements.

Relevant results from Deloitte RBS/ICA survey

A recent survey by Deloitte indicated that the most common method of achieving risk aggregation was through the use of a ‘correlation matrix’ applied to the capital required for each separate risk. This is not surprising given the technical simplicity of the method on the one hand and the ability to derive diversification benefits explicitly on the other hand.

Where risk aggregation by application of a correlation matrix is adopted sizeable diversification benefits have been demonstrated. Figure 3 suggests reduction in the capital requirement of between 20% and 60% for firms completing the survey.

We understand that in addition to the simple application of the correlation matrix approach a number of firms have used a hybrid approach to improve the accuracy and reliability of the calculation.

It remains to be seen whether the ICA consultation process, following submission of the first set of ICA results, will affect risk aggregation techniques used by firms.


Lapse & surrender rate drivers

In considering our findings it is important to differentiate between the correlation of rates, such as interest rates and lapse rates, and the correlation between the associated risks which may not move in the same way.

Lapse & surrender rates vary considerably by company, product type, duration in force, age, sex, sale channel, policy size, quality of risk and method of premium payment. See for example figures 5 and 6 below for variation by sales channel.

Lapse & surrender rate variations are the result of differences in the underlying drivers of policyholders’ commitment such as:

  • Continuing ability to pay.
  • Duration in force.
  • Company reputation and creditworthiness.
  • The extent to which the product meets personal financial needs.
  • Perceived value of the policy, including understanding of guarantees.
  • Performance of the policy fund.
  • Product design, including surrender penalties and frequency of premium payment.
  • Market Value Adjusters or MVA’s.
  • Type of policy and restrictions e.g. life vs. pensions.
  • Quality of advice given at the point of sale.

To the extent that the above commitment factors may be dependent either on the same sources of uncertainty as the capital markets or, alternatively directly dependent on the markets themselves, we would expect to see a degree of simultaneous movement in lapse & surrender rates and the capital markets.

Empirical studies

A recent report on the calibration of the risk capital margin (RCM) commissioned by the FSA considered the historical evidence for correlation between market risks and lapse & surrender rates. The evidence suggested that lapse and surrender rates increased as stock markets performed poorly, but it was felt that this may be more representative of policies with short in force durations. The report suggested that a rational policyholder should take the value of these guarantees into account and so would not normally surrender the policy where these valuable guarantees existed. However, there may in fact be circumstances where the optimal decision would still be to lapse.

In his paper on valuation of life business Mehta (1992) analysed lapse data from several insurance companies, concluding that a 15% fall in equity markets resulted in, approximately, a 3% increase in lapse rates. That is, lapses and equity markets are negatively correlated. However, this study predates many recent developments in the life insurance market in particular the increased public awareness of the value of guarantees embedded in their insurance contracts. As policyholders become more informed about the value of guarantees in their contracts perceptions of the value of contracts in varying economic conditions may change over time. Furthermore, we need to consider the question of whether past aggregate data is a reliable guide to the future, given the varying mix of products sold and in force, (for example, we might distinguish unit linked contracts with no guarantees).

FSA consumer survey results

A policyholder survey commissioned by FSA in 2000 identifies the main reasons for life insurance policy discontinuances.

The results suggest that the affordability of premium payments is the single most important factor in making a decision to surrender or lapse followed closely by disappointment with policy performance.

Those reasons would support the historical evidence of a negative correlation between market performance and lapse and surrender rates. We understand that the FSA has concluded that the market decline in 2001 caused an increase in lapse rates. On the other hand some of the surrendering policyholders have commented on the perceived opportunity cost associated with having to forego potentially more favourable investment returns by locking capital in the policies. This suggests a possibility of positive correlation between lapses and market performance.

Further studies by the FSA have concentrated on finding out whether policyholders understand the features of the product they hold. In many cases the research suggests that they do not and consumers often find it difficult to decide what to do with their policies.

Approximate ranges of correlations

The correlation between market risk and lapse & surrender risks typically falls in the range between zero and 75%, with many companies sitting within a narrower range between 25% and 50%.

These correlations should be interpreted as being positive between the capital required for the two risks. However, we understand that some companies, (particularly those with a predominance of guaranteed with-profits business) have experienced negative correlations between these risks.

Likely variation by product type

As discussed earlier there is a great deal of variation in behaviour depending on the product type concerned. In this section we look at product specific points. We consider separately:

  • Unit linked products without guarantees.
  • With profits and unit linked with guarantees.
  • Contracts with Guaranteed Annuity Options (GAOs).
  • Term assurances and protection policies.

Conventionally, in adverse conditions, surrender rates have tended to increase on unit linked contracts with no guarantees (quite likely for the reasons discussed above). It seems plausible to assume this relationship will continue in the future.

With-profits policies and a small proportion of linked contracts contain guarantees. Rational policyholders should take into account the value of these guarantees when deciding whether to surrender or continue their policies. As guarantees become more valuable (as would happen in adverse market conditions) and policyholders become more aware of the value of these guarantees, we would expect to see declining lapse and surrender rates leading to a higher capital requirement. Normative behaviour would therefore suggest that surrender rates (at least for policies with guarantees) should decline in adverse stock market conditions and so for these types of policy we might expect a fairly high positive correlation between market risk and lapse rates, although clearly there is room for further debate around the degree to which policyholders will act rationally and the extent to which past behaviour provides an accurate guide to the future.

For contracts with GAOs similar normative arguments would point to lapse rates being positively correlated with interest rates i.e. lapse rates should fall as interest rates fall, and the value of the GAOs rise. This is similar to the effect on GAO take up rates discussed earlier.

For term assurances and other protection policies payable by level annual premiums lapses early on in a contract generally result in reduced profits or even losses as the policies have not been in force long enough to cover initial costs. Lapses later on in the term of these contracts can boost profitability, as reserves are released and by then the annual premium may be insufficient to cover the current risk cost and expenses. There are also lapse and re-entry options to consider, especially in times of falling premium rates, though these options are more likely to arise in the early stages of a policy’s life. This effect is likely to be more dominant for protection business than market risk.

Clearly, correlations between market risk and lapse & surrender rates will vary by contract type and this should be reflected in the aggregation of the capital requirement for these different risks.

Persistency in a macroeconomic perspective

Annual UK life insurance industry persistency data has been collated by the FSA since 1993 and the following figures illustrate some salient features of that data.

The small data set means that statistical analysis is not conclusive, but it is instructive to compare first policy year persistency rate pattern with the shape of certain economic series. Year one persistency is a useful measure as we would expect any correlation to be at its strongest at this point. However from a risk perspective longer durations are likely to weigh heaviest in any analysis and the correlations here are likely to be less pronounced.

On the basis of the limited data available, it appears that the earnings index and unemployment appear to have little bearing on the persistency rate. Persistency on three out of four product lines forms a humped pattern, with a peak in 1996-1998. By contrast, the unemployment rate consistently decreases and the earnings index consistently increases through out the period.

As we would expect, household spending on life insurance has a closer degree of association with persistency patterns, to the extent that the spending on insurance shows a degree of variation in 1993-2000, peaking in 1998.

However, it is the consumer confidence index that is more closely aligned with historic persistency. This may be because consumer confidence is a better proxy for current disposable income than either of the other two measures. It may also be better at capturing future expectations regarding personal economic prospects and changes in disposable income.

Low and/or declining consumer confidence may be associated with higher or rising lapse rates because insurance, both investment contracts and protection insurance, are often seen as discretionary items of expenditure, areas that may be cut back when times are hard. By contrast, when people have confidence in the future and, more importantly, have money in their pocket they are more likely to continue with their policies.

High and rising consumer confidence would normally be associated with positive real economic performance, making the consumer confidence index not only a barometer of general economic optimism, but also perhaps some composite measure of economic performance as viewed from the household’s perspective.

Obviously the consumer confidence index is perception based, so there will not be a mechanical linkage with actual economic performance. However it is this perception and more generally the sense of confidence both in personal circumstances and in the expected performance of the insurance contract which are likely to be significant influences upon behaviour with regard to persistence or lapsing of policies.

Arguments for negative correlation between lapse and surrender rates and equity markets


The continuing ability of policyholders to contribute regular premiums depends on the state of economy. The earnings index, unemployment levels, and inflation affect the disposable income of policyholders and are therefore likely to affect lapse and surrender rates. Premium payments will be affordable to more policyholders, and therefore fewer will lapse or surrender their policies if earnings growth exceeds inflation and unemployment rates are low or falling. In these economic circumstances (low inflation, low unemployment rates, earnings underpinned by strong economic growth) equity markets will tend to be strong. We may therefore expect that lapse rates are negatively correlated with equity markets.

Smoothing of payouts

Smoothing mechanisms applied to the fund value may influence the propensity to surrender. Payouts on with-profits policies are normally smoothed, with the result that in times of rising markets, the payouts are usually less than underlying asset values, with the reverse being true in times of falling markets. In the past this may have lead to surrender rates being higher in depressed markets as policyholders perceived that their policies were of a higher value than the market level due to smoothing. This effect is mitigated by the now quite widespread application of Market Value Adjusters (MVAs). The magnitude of any effect caused by smoothing will depend on the smoothing parameters and MVAs employed by the life company concerned.

Product performance

Strong equity markets will generate good returns for life insurance contracts with a high equity backing ratio. Policyholders that experience good returns on the policy fund will be less likely to surrender or lapse their policies, provided returns compare favourably with results achieved by competing offices. A further consideration will be the policyholder’s perception of the opportunity cost of holding an insurance contract and if appropriate the impact of smoothing.

Argument for negative correlation between lapse and surrender rates and the performance of the life company

Negative publicity

Negative coverage in the press, whether as the result of mismanagement, miscommunication or industry-wide issues, could have seriously damaging consequences for the reputation of a life company.

For proprietary companies this is likely to have the simultaneous effects of increasing lapse & surrender rates and driving down the company’s shares price.

Therefore we may expect that the share price of a proprietary life company and the lapse & surrender experience of the company to be negatively correlated although this is likely to be a second order effect. Further, the share price may be impacted by other wider factors such as market sentiment towards the sector which would not necessarily impact on the behaviour of individual policyholders.

Argument for positive correlation between lapse and surrender rates and equity markets

Opportunity cost perception

If equity markets are rising rapidly some policyholders might conclude that higher returns could be achieved by surrendering life insurance policies and investing directly in the stock market. This will depend on the degree of smoothing employed by the company and the resulting impact on performance.

Guaranteed maturity values or MVA free periods

These guarantees will become more valuable if equity markets are low. Provided that policyholders understand product features, they will be more likely to hold the policy to maturity. This applies to both conventional with-profits policies with guaranteed sums assured and reversionary bonuses, as well as unitised with-profits contracts which have MVA free encashment dates. The magnitude of this effect and the resulting capital impact will depend on the nature of the guarantee provided.

Argument for positive correlation between lapse and surrender rates and equity market volatility

Policyholder risk-aversion

Policyholders tend to buy insurance contracts for protection and dislike excessively volatile policy values. This is an issue of particular concern in falling equity markets where there is no form of smoothing to protect policy values. Accordingly, policyholders are more likely to surrender in times of high equity market volatility and falling prices where there is no smoothing mechanism.

Arguments for negative correlation between lapse and surrender rates and equity market volatility in the presence of guarantees

Value of guarantees

To policyholders, the value of minimum fund value guarantees and smoothing mechanisms will increase if equity market volatility is high. Therefore policies containing such guarantees are more likely to persist to maturity.

Argument for negative correlation between lapse and surrender rates and interest rates

Product performance

If interest rates are high, the income return on fixed interest instruments will also be high. Fixed interest instruments now typically make up a sizeable part of insurers’ asset portfolios. The exact effect of high interest rates will depend on the asset mix of the company. Policyholders experiencing good returns on the policy fund will be less likely to surrender or lapse their policies, provided returns compare favourably with results achieved by competitors.

Argument for positive correlation between lapse and surrender rates and interest rates


High interest rates typically reduce household disposable income by increasing the cost of servicing consumer debt. Therefore premium payments become less affordable and so lapse & surrender rates may increase.

Guaranteed annuity options

A guaranteed annuity option is in effect an option on annuity rates in the open market, which are themselves a function of interest rates, life expectancy and credit spreads. All else being equal, if interest rates are relatively low, the guarantee may be ‘in the money’ and therefore policyholders may be more likely to hold on to the policy until vesting date, reducing surrenders. However, there is some evidence which suggests that in many cases policyholders do not act in a rational fashion, maintaining their policy and taking advantage of the GAO. It is unclear, particularly under a stressed scenario, how policyholders would behave in the future, and past experience may not be a reliable guide owing to changes in the marketplace, with greater flexibility now available and increased policyholder awareness. In this area again, the impact is likely to be heavily influenced by the specific circumstances of the life company and the products they offer.

Argument for positive correlation between lapse and surrender rates and interest rate volatility

Policyholder risk-aversion

Policyholders generally dislike excessively volatile fund values. They will therefore tend to surrender in times of high interest rate volatility if this leads to high levels of fund volatility. However, if this volatility does not translate through to fund values, because of guarantees and smoothing, the effect will be less marked

Argument for negative correlation between lapse and surrender rates and interest rate volatility in the presence of guarantees

Value of guarantees

The value of minimum guaranteed annuity options will tend to increase if interest rate volatility is high. Therefore, policyholders will be more likely to persist to maturity in times of high interest rate volatility if guaranteed annuity options are attached to the policy.

Argument for positive correlation between property prices and mortgage endowments surrenders

Effect of a strong property market

If property prices rise, activity in the residential property market may increase. This may be a result of a number of factors. First, increasing perceptions of personal wealth fuelling consumer confidence. Second, the experience of rising prices producing an expectation that prices will continue to rise in future, making property a ‘good investment’. Third, the leveraging effect of rising house prices providing consumers with rapidly rising levels equity in their homes, which may be used to underpin the purchase of a larger property or a second property. When a policyholder moves home, this is often a trigger for surrender as an entirely new policy may be taken out rather than amending or adding to existing policies. This may be for convenience, for simplicity, or because the consumer expects to find a better deal. Consequently, rising property markets may be associated with an increase in surrenders or lapses on mortgage endowments and mortgage protection policies.

Market risk and lapse and surrender rate correlations: 


Lapse & surrender rates and Equity markets

Why positive: Opportunity cost perception, Minimum fund value guarantees. 

Why negative: Affordability, Smoothing of payouts, Fund performance.

Lapse & surrender rates and Own share price

Why negative: Negative publicity.

Lapse & surrender rates and Equity volatility

Why positive: Policyholder risk-aversion.

Why negative: Value of guarantees.

Lapse & surrender rates and Interest rates

Why positive: Affordability, Guaranteed annuity options, Product performance capital value of bond holdings.

Why negative: Product performance – income return on fixed interest instruments.

Lapse & surrender rates and Interest rate volatility

Why positive: Policyholder risk-aversion.

Why negative: Value of guarantees.

Endowment mortgage lapse & surrender rates and Property prices

Why positive: Property moves leading to lapses.


2 As an ideal the matrix should be positive definite but, owing to rounding errors, a matrix which for all practical purposes is internally consistent might fail a strict positive definite constraint. However, the broader point of principle stands.

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This article is part of a series: Click Report for the ABI on Key Correlation Assumptions in ICA for Life Offices - Executive Summary for the previous article.
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