In recent years, we have witnessed increasing publicity surrounding longevity risk. Valuation assumptions concerning mortality are no longer consigned to the dusty back room where a trusty number-crunching actuary resides. Longevity has crept up onto the agenda of executive committees wherever there is a final salary pension scheme, or an annuity book on the balance sheet. This article looks at the Actuarial Profession’s part in communicating the information about these liability portfolios to enable effective decision-making.

Imagine an actuary in a life company that sells annuities and sponsors final salary staff pensions, who is trying to explain to the new chief financial officer (CFO) about the allowance made for future mortality improvement in the embedded value and the IAS19 valuation. “Well,” the actuary starts off with the confidence in his technical abilities and the extensive modelling he has carried out, “our assumption is based on the average of medium and long-cohort projections with a 110%/90% scaling factor for males/ females, respectively, subject to a minimum improvement rate of 1.75% per annum.”

Seeing the look on the CFO’s face, the actuary feels the need for further clarification: “And it is supported by our stochastic P-spline model projections fitted to ONS data, 1961 to 1994, age cohort.”

While the importance of robust modelling of mortality is indisputable, surely actuaries can find a more effective way of communicating the results to people outside of the Profession? The first step is to consider the purpose for which they use the information.

**Digesting information**

The above-mentioned CFO needs to know what might affect the firm’s reported profits, embedded value and the balance sheet, as well as the volatility around the numbers. For example, it is important to ask:

>> How much will mortality improvement cost?

>> How will the firm pay for it?

>> How can it be put into perspective?

>> How much worse than expected can it get?

>> How much would it cost to hedge the risk?

Given the short time available to CFOs to digest the information, actuaries should aim to present the data in the simplest form possible, while retaining the features that are essential for decision-making.

An extreme example for many companies can be found in accounting disclosures concerning their final salary schemes, where mortality assumptions are typically expressed in terms of the average pensioner’s expected life in years. This approach matches most laymen’s perception of longevity, but it is too simplistic. Two sets of assumptions that translate to the same expected life are not necessarily equal in strength, because expected life does not capture the pattern of mortality improvement and the time value of money. Relying on this information alone, therefore, is not likely to lead to optimal business decisions.

Does this mean actuaries should revert to the communication style provided at the beginning of the article? Hopefully not. There is another alternative that some actuaries are using. In order to better understand the rationale behind this, it is useful to look at annuity contracts and pension provision in a slightly different light.

The single premium to purchase an annuity is a loan that the policyholder lends to the life office, and is repaid in regular instalments over the lifetime of the policyholder. The eventual repayments may not reflect the original loan for each individual contract, but they do, on average, for a large portfolio overall. Like any loan, the borrower incurs an interest charge. A ‘fair’ price may be based on gilt yields, in addition to the life office’s best estimate assumptions regarding mortality and expenses. There is likely to be a further margin for profit or risk, lowering the interest payable.

When dealing with loans, it is natural to think of the business in terms of interest rate margins. Consider a hypothetical book of new annuity business that has a fair value (based on gilt yields) of £100m, and the premiums amount to £103m. The duration or discounted-mean term of this portfolio is 12 years, based on best-estimate assumptions. In a low-interest-rate environment, an approximate profit margin can be gained by solving for x in the following equation:

*£100m*(1+x)^12 = £103m*

which gives 0.25% per annum. So the interest payable by the life office to service the loan is gilt yield minus 0.25% per annum. If all the premiums are invested in gilts matching the cash flows, and mortality experience turns out to be as expected, this margin will be banked.

The profit margin can be increased further by investing in, for example, corporate bonds. The corporate bond spread over gilts is often wider than justified by expected default risk. The excess spread is usually attributed to liquidity risk and supply and demand distortions. However, an annuity portfolio holding corporate bonds to maturity needs not worry about liquidity, and is therefore able to bank this additional yield. Assuming that the corporate bond portfolio generates a return of 0.5% per annum above gilts, after allowing for defaults, this means that the realistic cost of meeting the liabilities is not £100m, but rather:

*£100m*1.005^(-12) = £94m*

Now consider if the life office calculates the market-consistent European Embedded Value (EEV) based on best-estimate morality assumptions and gilt yields. On this basis, it will immediately capitalise the initial margin of 0.25% per annum, and the additional 0.5% per annum margin will be gradually released over the life of the policies.

So what about longevity? Assume the base-mortality assumptions are in line with past experience. In practice, the focus of management attention tends to be on the future improvement where most of the uncertainty resides. If we strip out the allowance for future mortality improvement, the total cost will reduce from £94m to, for example, £89m.

Again, this can be worked out to be equivalent to an interest rate margin of 0.46% per annum. It means that roughly 0.46% of the outstanding loan can be expected to pay for mortality improvement each year. Note that this does not eat into the profit margin above, because it has already been allowed for in the expected cash flows.

**Longevity-risk premium?**

In addition to the expected cost of mortality improvement, is it fair to charge a further longevity-risk premium? It may be argued that longevity risk deserves reward because:

>> There is no market consensus on best-estimate mortality assumptions

>> The inherent uncertainty in future mortality improvement cannot be diversified

>> Longevity risk adds to the life office’s reserving and capital requirement. The price should, therefore, reflect the appropriate cost of raising capital.

So does the profit margin reflect the fair compensation for longevity risk? There is no certain answer. In the absence of a deep and liquid market for this risk, the exact size of the longevity risk premium will depend on the views of the particular life office.

CFOs will be interested to know how durable these margins are, what kind of scenarios will erode the profit margin and how severe they need to be before the margin is completely spent. Again, any longevity stress scenario can be translated into an equivalent additional interest charge, which the life office has to pay. This would summarise the financial impact in a way that a CFO could easily grasp.

How will this information help CFOs? Figure 1 shows a hypothetical example of how this may be presented graphically. It will help to clarify where the total return on annuity business arises and how it is broken down, giving them an idea of the magnitude of longevity risk in relation to other risks. The interaction between market risk and longevity risk also becomes clear: the cost of longevity risk is met by excess investment returns over the expected interest charge on the loan.

To price new business, CFOs need to ask, “What minimum interest rate margin do I want in order to compensate for the longevity risk?” If they would like to transfer longevity risk away via reinsurance or hedging opportunities, the price and financial impact of such a deal could also be presented graphically and translated into an interest cost. The relevant question, therefore, is, “What maximum margin am I willing to give away in order to get rid of longevity risk?”

This approach effectively expresses mortality improvement in terms of the average rate of increase in the probability of survival, rather than the rate of decrease in the probability of death. This average rate is sensitive to the liability profile — for example, age, sex, cohorts and RPI index linkage — therefore, it should be presented together with the liability duration. Clearly, it is not only important to know the average annual interest charge, but also for how long this charge is to be applied.

**Application for pension schemes **

The above approach can also be applied to defined-benefit pension schemes. However, the interest charge on the ‘loan’, or deferred pay, is less clear-cut in this instance because, unlike annuity contracts, a present-day price is not agreed up-front. One argument is that it should reflect the interest charge on other corporate debts of similar term, ranking and collateralisation to the pension obligation.

What return does the employer earn from this loan? For an unfunded scheme, it is the marginal return on capital — in this case, the loan enables the employer to invest in its business rather than having to pay the full cost of employees’ services.

For a funded scheme, it is the weighted average of this return on capital relating to any deficit and the investment return on scheme assets. So the sponsor of a pension scheme shares a common goal with a life office and a high-street bank: to maximise the margin of what it earns on the loan over what it pays to service the loan.

In a similar fashion, the allowance for future mortality improvement, and any potential variance around the expected mean, can be translated into an interest rate margin required to meet the cost of increasing longevity.

Used alongside other tools — such as internal rates of return, return on capital and value at risk measures — expressing risk in terms of interest rate margins provides a way to present the risk-return dynamics in a simple form. It can also help to formulate important business decisions, such as pricing, risk appetite and risk-management strategies.