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

Standard treatment of market and mortality risks When performing actuarial analysis, it is conventionally assumed that there is a zero correlation between mortality rates and the capital markets. This is generally supported by historic data since mortality rates have steadily and fairly smoothly decreased, whilst equity markets have behaved erratically in the short term, grown exponentially in the long-term, and interest rates have tended to revert to the mean. So there seems little prospect of identifying a meaningful connection between mortality across the general population and financial risk drivers.

On the other hand, even if correlation between mortality rates and market risk may not be observed in the data, the two are not necessarily unrelated. It is possible to argue that significant correlation between mortality experience and market risk could exist for certain population types, or under certain sets of conditions.

For instance, for some lines of morbidity business such as income protection, claim experience shows there to be a clear correlation between economic slow down leading to an increase in unemployment rates and an increase in the number of claims being made. This is predominantly driven by policyholder anti-selection but can be traced back to physical manifestations which may satisfy policy claim conditions. This is largely an issue for those insurers who write substantial amounts of business in these classes.

Similarly, if we consider a specialist insurer who concentrates solely on key man insurance for high net worth individuals, a sizeable correlation between market risk and mortality rates may be observed if a substantial share of policyholders’ wealth is tied to the performance of the capital markets.

A link between mortality and wealth is illustrated by Figure 12, tracking life expectancy at birth in the UK by social group.

The significance of this dependency will be high if the insurer specialises in a given socioeconomic group or industry exposure, however if it holds a diversified liability portfolio, the impact of one line of business on the correlation between insurance risk and investment risk for the entire operation may be negligible.

Market and mortality risk may exhibit correlation under extreme conditions. A catastrophic event causing extensive loss of life may simultaneously have a significant adverse impact on the capital value of investments held in an insurer’s portfolio.

The severity of reaction will depend on the views held by investors concerning the impact and gravity of the consequences of the catastrophic event, although past experience suggests that the reaction is not inevitably negative.

One of the best documented cases is described in Table 4 which shows stock prices quoted on the Buenos Aires exchange between 1917 and 1920. During this period the world suffered from the great influenza pandemic often referred to as "Spanish Flu" which it is estimated killed 3% of the world population between June 1918 and April 1919. If we consider the All Stocks Index we can see that it grew steadily over the period.

Source: Nakamura and Zarazaga (2000)

In the United Kingdom over the same period Spanish Flu killed nearly 250,000 people. However, gross annual total return on equities in the year of the pandemic maintained its positive performance and achieved a level of 5% according to the Barclays Equity Gilt Study. A much more recent scare was the SARS outbreak in February 2003. Despite concerns over accelerated transmission of the disease, with over 8,000 people infected and 774 deaths, the market reaction was very limited.

The extent of a market’s reaction to emerging health threats may depend on the population groups affected. A disease spreading among more economically significant or active groups within the population may be perceived as a greater threat to the economy. So increased mortality amongst younger age groups will be more heavily correlated with market risk than pensioners’ mortality.

Similarly, the capital markets have largely failed to register the Indian Ocean tsunami as reported in the China Daily on 3 January 2005, "Tsunami has little impact in Europe". Whilst the number of deaths was large, at over 100,000, the event was seen as a one-off natural phenomenon – an event falling at the far end of the statistical tail of probability and described by some as a one in two hundred year type event.

Indeed the simple fact of location, in the Indian Ocean, also meant that there was no direct impact upon Europe, Japan or the US and the effect on international trade and world economic output was expected to be very modest, with no material impact on global economic confidence and stability. Indeed, even at a more local level, the long term economic impact was expected to be limited and in the weeks following the Tsunami the Indonesian stock market actually rose.By contrast, the September 11th terrorist attack on the World Trade Centre triggered a sharp decline in equity markets, even though the official death toll was much lower than for the Tsunami. In this instance, the event could not be rationalised as a one-off natural disaster but instead it raised the prospect of further such atrocities, striking at the heart of the Western World's economic centres. This would result in not only a direct effect on output from the direct loss of life and physical damage to buildings and infrastructure, but would also have a much wider impact on general economic confidence affecting investment, consumption, employment and hence output in all the major economies.

So, it is clear that market movements are not driven simply by the number of deaths resulting from a catastrophe or disaster, but rather the underlying cause of these deaths and the probability of re-occurrence.

For firms writing specialist group life and health business, taking account of the correlation between capital markets and mortality rates in catastrophic scenarios will be important. For instance, a terrorist attack targeting the City of London may cause both deterioration of mortality experience of insurers providing group cover for City firms on the one hand, and a significant instantaneous reduction in value of their stock holdings on the other. A similar dependency may be experienced by an insurer underwriting occupational schemes for frontline emergency services staff.

Whether such shocks have a lasting effect on the capital market is debatable but depending on the profile of an individual firm there may be a significant impact.

A protracted economic recession is likely to both increase long term mortality rates and have a significant impact on the capital markets. Higher mortality would be expected to result from a deterioration of the standard of living due to higher unemployment rates, lower earnings, higher cost of living and lower healthcare spending. However, the extent to which this would affect the self selected insured population is open to question. The impact is likely to manifest itself in a long term trend rather than a short term shock.

An extreme example to demonstrate the concept was the demographic situation in Russia arising from economic difficulties rapidly translating into a significant deterioration of mortality experience. The effect is disproportionate to the actual reduction in healthcare spending and may largely be attributed to stress-related conditions. Male mortality has risen particularly sharply, exacerbated by the rise of violence and alcoholism. For an analysis of Russian mortality trends see Men, Brennan, Boffetta and Zaridze (2003). In the context of insured business in the UK this effect would be most likely to manifest itself in increased claims on income protection policies rather than necessarily increased claims on life insurance. To illustrate the long term effect in a more stable economy, in the UK, between 1928 and 1929 ("the Great Depression"), life expectancy at birth of males decreased by more than two years. Over the same period female life expectancy at birth decreased by a year and four months.

On this evidence we might expect male mortality to be disproportionately affected in an event of economic recession.

Middle aged males and the elderly are the two groups most likely to experience hardship during an economic downturn, since the first group is under the most pressure to adjust successfully, while the second has the least means to do so. We may therefore expect to see an impact on male term assurance mortality and annuitant mortality experience. The impact of term assurance experience deterioration will be complicated by policy lapses due to the reduced affordability of premiums being off set by the increase in selective withdrawals where only the poorer risks remain in the portfolio. Conversely we may in fact see an increase in deaths in the annuitant portfolio which would reduce exposure. Whether a 1 in 200 year recession can be extreme enough to lead to a significant deterioration of mortality experience is uncertain. The key issue in formulating justifiable assumptions is data availability and the difficulty in accurately estimating extreme events.

It is useful as part of our analysis to consider the long term demographic trends and the resulting impact on the investment markets. This will not impact the ICA in the way that a 1 in 200 year event would by causing a step change in experience rather it may cause a long term re-appraisal of likely future experience which would lead to a change in the reserving basis.

When projecting mortality rates into the future it is useful to consider the impact of demographic trends on the balance of net borrowers and lenders in the economy and the demand structure for certain type of assets.

A relationship between age structure of population and investment/dis-investment patterns has been commented on by a number of authors. See for example Herbertsson and Zoega (2001), who identify a link between unemployment, investment and age structure in a cross-section of OECD countries.

A commonly projected demographic scenario combines low fertility rates with increasing longevity, resulting in a gradual but radical shift of population composition by age. It is reasonable to expect that older people will play an increasingly significant role in the economy. The increase in aggregate wealth will be accompanied by the growth of wealth concentration in older age bands.

Since older people tend to be net lenders, while younger people tend to be net borrowers, the lending supply will increase relative to borrowing demand. This could result in downward pressure on interest rates, particularly when combined with the impact of increased longevity upon the annuity market and the consequent pattern of investment increasing demand for bonds. However, low interest rates may also support strong growth of equity markets and high property prices.

It is expected that despite lower fertility rates, the UK population will continue to increase, recent government forecasts suggesting the total will reach 65 million by 2051. If, as has been the case in more recent times, the increased demand for residential housing cannot be met by the building industry, population growth will be another factor contributing to high property prices. Finally, the ageing population may prove to be a burden on the UK economy. The cost of pension and health care provision may impact on both government finances and private companies, both directly and indirectly via high taxation. As a consequence, the attractiveness of the UK economy may decrease relative to countries with a younger population structure.

A sudden improvement of mortality, in excess of the pricing basis projections, possibly due to a revolutionary treatment becoming available for cardio-vascular diseases or cancer, will have significant implications for the insurance industry. Annuity-focused insurance companies and pension companies might find their capital positions compromised and may need to raise capital whilst re-aligning their investment portfolios to match significantly longer liabilities, which in turn may have an impact on the markets.

Correlation between market risk and mortality may be triggered by: existence of a link between policyholders’ wealth and the markets, a catastrophic event causing extensive loss of life, economic recession, long-term demographic factors, and an unanticipated mortality improvement.

Non-linear effects include: greater deterioration of male mortality in adverse economic conditions and stronger market reaction to increased mortality at economically active ages. If correlation effects are triggered we would generally expect to see negative correlation between mortality rates and equity markets and positive correlation between mortality rates and interest rates. However, the opposite may be the case if mortality rates suddenly improve owing to the discovery of a revolutionary medical treatment for cardiovascular disease or cancer. In the long run, negative correlation between mortality rates and equity markets and positive correlation between mortality rates and interest rates may arise due to long term demographic trends. The influence of demographic trends may also manifest itself in negative correlation between mortality rates and property prices.

As a rule, market and mortality risks are assumed to be uncorrelated.

Prospective policyholders tend to opt for products that they expect to get the most benefit out of. A prospective policyholder has better health-related information than a life insurance firm underwriting the risk. Individuals will try to use this asymmetry to their advantage and will buy products which they consider under-priced relative to the market. This gives rise to the adverse selection.

Mortality of annuitants tends to be lighter than mortality of assured lives at similar ages and the populations have different age profiles. Consequently, annuity and protection products are priced and reserved on different bases. Insurers protect themselves through pricing and underwriting this risk to ensure an appropriate charge is made for this effect. In addition, if a relationship between the two bases exists it may impact capital assessment calculations if a diversification effect can be identified.

Insurance risk affects the capital required to support annuity business and term assurance business in opposing ways. For annuity business, the risk is that mortality improves faster than assumed whilst for term assurance the reverse is true.

Given that in general insurers do not have the opportunity to re-price these products then the actual experience relative to the pricing basis will have a direct impact on profitability. A similar argument applies to the management of reserves. In the short term, the significance of realised mortality losses will not be as high as the impact of capital movement resulting from adjustment of reserves as the reserving impact capitalises the future effect of the change. A reserve adjustment may be necessary to reflect not only actual changes in experience but the company’s view of future mortality trends. Additional capital will have to be found to increase reserves on annuity business if mortality assumptions in the reserving basis have been made lighter. If mortality assumptions have been made heavier, additional capital will be needed to provide for assurance contracts.

In practice, annuitant and assured lives mortality risks are rarely considered separately at the risk capital aggregation stage. It is usual to have these risks incorporated in the overall insurance risk measure.

In the past, mortality rate projections both for annuitants and to a certain extent assured lives have underestimated the extent of the mortality improvement. An under priced improvement of mortality rates for annuitants constitutes a significant risk to the long term savings industry. While the mortality losses on the annuity business may in part be offset by the corresponding gains on the term assurance business, the size of this offset depends on the correlation between assured and annuitant lives mortality and the relative exposure to the risks. A high correlation implies a large offset.

However, given the different nature of these contracts the impact on the business will be very different for annuity and assurance business. Given that term assurance business can be lapsed without financial penalty for the policyholders, this means improvements in mortality may in fact lead to policyholders chasing the best rates in the market and surrendering their polices to move to another lower cost provider who has factored these improvements into their pricing. Indeed this effect has been quite apparent from the mid to late 1990s when there was a very significant fall in the retail price of term assurance and a corresponding increase in lapse rates.

Annuity business on the other hand is generally less portable and will tend to stay with the company. Since generally there is no opportunity to review rates the impact of lighter mortality will crystallize as a cost to the office.

As discussed earlier the issue in the ICA will be the cost to the company in increasing reserves over a one year period rather than a substantial deterioration in experience. It is not unreasonable to expect that annuitant and assured lives mortality rates will continue to have broadly similar dynamics. However, the correlation may not be perfect. There is some evidence to suggest that annuitant mortality and assured lives mortality improve at different rates. This is illustrated by Figures 14 and 15 which use CMI experience to show patterns of improvement for assured lives and life pensioners respectively.

One of the possible explanations for the differences in observed rates of improvement of assured lives mortality rates and annuitant mortality rates is the cohort effect. This was first described in detail by the CMI Mortality sub-Committee in their working paper 1 in 2002. The cohort effect describes the situation where discernable groups of lives can be seen to experience different rates of mortality improvement. For example, it has been observed that those born in the mid to late 1920s experienced a particularly fast rate of mortality improvement in the 1980s.

Since assured lives and annuitants tend to belong to different age groups, namely pre- and post-retirement, the cohort effect will be a factor affecting relative rates of improvement of the two groups.

A stochastic approach to modelling mortality may help insurers to improve the understanding of risks contained in their liability portfolios and in turn help in setting their ICA. If term assurance and annuitant mortality are calibrated on the basis of relevant data, it may be possible to quantify the correlation between assured lives mortality risk and annuity mortality risk by incorporating stochastic mortality into the model office and measuring the correlation between the corresponding projections of risk capital amounts.

Annuitant mortality rates and assured lives mortality rates are positively correlated. The correlation may be strong, but imperfect, in part due to selection and cohort effects. The corresponding mortality risks are negatively correlated.

The degree of correlation between the mortality risks may be different from the degree of correlation between the corresponding mortality rates, and will depend on the product mix. This is because the measure of capital may be a complicated function of mortality rates. To take a simple example, annuitant and assured lives mortality are positively correlated, but the risks are negatively correlated. In practice, deriving a correlation between the capital requirements of individual risks will involve some judgement. Alternatively, if a stochastic model of the relevant risk parameters and their correlations can be developed, then that model can be used to determine the capital requirements for the combined risks.

A suitably calibrated stochastic model of mortality can be used to gauge the correlation between the mortality risks for a particular portfolio of business. This approach will partly address the modelling concerns discussed in the section on Tail Correlations.

Commonly, the correlation of these risks falls in the range -20% to -75%. Many life insurance firms have assumed a correlation close to -50%. A suitable assumption for an individual firm has to be determined with reference to the nature of its insurance liabilities and the mix of business. 

Capital required for market risks can itself be broken down into several constituent risks. These risks include:

• Interest rate risks of various terms or equivalently, bond prices of various terms.

• Equity market risk.

• Property market risk.

• Risk from change in credit spreads or in default experience.

• Currency risks.

• Risk from changes in real yields or inflation expectations.

• Various forms of basis risks or tracking errors.

The correlation between these different risk classes determines the degree of diversification

that may be claimed. The key correlations in most ICA calculations are:

• Between equities and bonds.

• Between interest rates of different terms.

• Property with equities and bonds.

• Credit spreads with interest rates and equity markets.

It is important in considering correlations and the ICA calculations that we look at the issues from the right perspective. For instance, the correlations required for ICAs must relate to financial gains or losses – that is, they must be based on arithmetic means. Asset modelling, particularly in the field of option pricing, more often specifies means, standard deviations and correlations between the logarithm of asset prices, or equivalently, based on geometric means. The following example illustrates the same set of assumptions expressed in these two ways:

For capital calculation purposes, the distinction between arithmetic and geometric parameters can be important when considering means and variances, but is generally less significant when considering correlation coefficient values, as illustrated by the example above. For the process of calibrating our models it is also important to distinguish between:

• longitudinal correlations, which describe one historic outcome path but are sampled over many years; and

• cross sectional correlations, which describe the correlation over a single year but many possible future outcomes.

Historical data analysis produces longitudinal correlations. Simulation models produce cross sectional correlations, and these are required for capital assessments. In the simplest random walk models, these two should be equivalent.

It is important to remember that the structure of any asset model used imposes a relationship between longitudinal and cross sectional correlations. This will be important if we try to use an asset model to help us understand the likely profile of correlations. Typically, longitudinal correlations in asset returns are higher than cross sectional returns. This means that a simple extrapolation of historic longitudinal correlations may understate the benefits available from diversification.

The difference between longitudinal and cross sectional correlation may be explained as follows. In many models, asset returns are expressed as a risk free (one year) bond return plus a risk premium plus a residual error term. A longitudinal study covers many years with a series of one year interest rates. A large part of the historical correlation may be due to changes in one year rates from year to year. This generates a positive longitudinal correlation between risky asset classes because the same risk free rate sets the baseline for all risky assets.

On the other hand, a cross sectional investigation observes many simulations, across which the risk free rate is maintained at a single common value. The observed cross sectional correlation relates only to the residual terms, and is not influenced by movements over time in risk-free rates.

A number of research papers, including Smith (1995) and Wilkie and Lee (2000), compare the output of available asset models. Wilkie and Lee collate the following comparison of correlations. It should be remembered that we are observing the correlations generated by running these models based on different calibrations based on the economic conditions over a similar period of time.

These tables serve to illustrate the wide range of assumptions which might legitimately be selected. The models shown should all have been calibrated to similar historic data sets and all calibrations were first published between 1995 and 2000. Typically, most of these models would allow the one-year correlations to be set by parameter choices, while the emerging time behaviour of correlations is a function of the model structure.

It is interesting to observe not only the relative levels of correlation, but also the time structure of the correlations, which will be affected by the type of model used. So, for instance, it is not surprising that models based on a random walk show a relatively flat time structure whilst ‘jump-‘ or ‘multi-state’ models have a less predictable term structure.

Using 10 years of weekly UK data we have estimated the following matrix at the end of 2004. Correlations observed may vary where a different holding period or time horizon is chosen.

Source: DataStream

This estimate has also been used as part of the calibration of our proprietary economic scenario generator called The Smith Model or TSM. We can then observe the cross-sectional correlations of annual returns, measured on the TSM output and these are shown in Table 8.

Source: TSM Streamline Calibration Report, Historic Calibration 31.12.2004. UK Economy.

The time period used for the observations is likely to have a significant effect on the measured correlation. This should be linked to the period over which capital adequacy is being assessed, or perhaps to the period over which management action can be agreed and implemented, if such action is to be reflected in the assessment of the ICA. When considering the correlation between equities and bonds (or interest rates), it should be remembered that the past ten years or so has been a period of sustained reduction in interest rates in contrast to long term historic experience, so this period may not be reliable for the formulation of a conditional assumption going forward.

Unlike equity and bond data, reliable and uniform property data is not readily available. This makes it difficult to produce accurate calibrations for property asset class in economic scenario generators.

A number of institutions, mainly mortgage lenders, construct indices aiming to measure performance of the property market. The indices suffer from problems, including heterogeneity of properties in the index basket and transaction reporting lags. The observed correlation figures vary depending on the index chosen, as well as by holding period and time horizon.

To illustrate we have measured correlation between property and equity as well as property and interest rates for returns on two different property indices.

Source: Halifax and Nationwide.

The correlations have been measured on monthly data, over the past eight years. A different choice of time period and observation frequency can significantly change correlation estimates.

There is clear economic logic relating market interest rates to bond prices. Market interest rates are calculated directly from bond prices. A downward move in interest rates necessarily implies a rise in bond prices and vice versa.

The smoothness of the yield curve creates further correlations. A five year bond yield is, usually, close to the average between four year and six year yields, which in turn are usually fairly close to each other. Empirical studies inevitably report strong positive correlations between neighbouring points of the yield curve.

There are also powerful theoretical reasons to expect a negative correlation between yield spreads on corporate bonds and equity markets. The yield spread on a corporate bond reflects, among other things, the likelihood of a bond default. At the point of default, a company’s control passes to bondholders and equity holders can expect to see little more of their investment. For this reason, we would expect to see a positive correlation between the performance of shares and corporate bonds when these relate to the same underlying company. As the yield spread moves in the opposite direction to the bond price this same argument should generate negative correlations between credit spreads and equity prices. Although this effect is seen in market indices, the correlation is not as strong as might at first be expected. This is largely because the available equity indices do not necessarily contain the same companies and in the same proportions as the corporate bond indices. There are some superficially appealing arguments for a negative correlation between interest rates and equity prices. These arguments construct share valuations via a discounted cash flow model, observing that an increase in the discount rate causes a fall in the share price. However, this relation is not evident in many historic studies, probably because changes in interest rates have a wider impact not only on the discount rate but also on the dividend estimates themselves and these two effects have historically offset each other to some degree.

The property market dynamics may exert a significant influence on the overall state of economy. Firstly, a large proportion of household wealth is held in property. This implies that the level of property prices impacts consumer perceptions of prosperity, and therefore affects the level of spending.

Secondly, property is widely accepted as collateral in the banking world. Davis and Zhu (2004) argue that the level of commercial property prices is strongly linked to the lending behaviour of banks, and therefore may be seen to affect inter-bank interest rates. Thirdly, the Bank of England bases its interest rate decisions in part on the residential property market, with a view to prevent overheating of that market and of domestic demand more generally.

Finally, in many cases acquisition of residential property is a highly leveraged investment, financed by fixed interest borrowing. A sudden rise in interest rates may therefore induce a decline of residential property prices, by increasing supply due to forced sales on the one hand, and restricting demand due to higher cost of borrowing on the other hand.

Property and equity have been generally assumed to be positively correlated and this tends to fall in 0-40% band. Interest rate and equity correlation will typically be in the range of -25% to 10%.

Barclays Equity Gilt Study. 2003

Basel Committee on Banking Supervision. Pillar 2 (Supervisory Review Process). 2001. Retrieved from http://www.bis.org/publ/bcbsca08.pdf

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Continuous Mortality Investigation. Mortality sub-committee. Working Paper 1: An interim basis for adjusting the "92" Series mortality projections for cohort effects. 2002

DataStream http://www.datastream.com/product/has/

Davis, E. and Zhu, H. Commercial Property Prices and Bank Performance. 2004. Retrieved from http://www.brunel.ac.uk/depts/ecf/research/papers/04-19.PDF

Herbertsson, T. and Zoega, G. The Modigliani Puzzle. 2001 HBOS. Halifax Property Price Index. Retrieved from http://www.hbosplc.com/economy/historicaldataspreadsheet.asp

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FSA. Calibration of Enhanced Capital Requirement for With-Profit life Insurers http://www.fsa.gov.uk/pubs/policy/04_16/ww_report.pdf

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FSA. Persistency of life and pensions policies. 8th Survey. 2002. Retrieved from http://www.fsa.gov.uk/pubs/other/persistency_8.pdf

FSA. Persisting: why consumers stop paying into policies. Consumer Research Series. 2000. Retrieved from http://www.fsa.gov.uk/pubs/consumer-research/crpr06.pdf

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Men, T., Brennan, P., Boffetta, P. and Zaridze, D. Russian mortality trends for 1991-2001: analysis by cause and region. BMJ, 327: 964.2003.

Mehta, S.J.B., Allowing for Asset, Liability and Business Risk in the Valuation of a Life Office, Journal of the Institute of Actuaries, 119: 385-455. 1992

Nakamura, L. and Zarazaga, C. Banking and Finance in Argentina in the period 1900-35. 2000.

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Society of Actuaries website. Electronic Library of Mortality Tables http://library.soa.org:8080/xtbml/jsp/index.jsp

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