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November 2007
Tim Wilkins looks at the challenges involved in modelling and managing guarantees on variable annuities.
Variable annuities have been successful in the US and Japan and now a number of European insurers have recently introduced, or are considering introducing, a similar product. In a previous issue of the Insurance and financial services review, Mark Joannes concluded that variable annuities may become a significant part of the UK retirement market if certain obstacles can be overcome, such as current pension regulations. This article looks at another challenge for insurers launching these products: how to model and manage the risks involved.
The term variable annuity typically describes a unit-linked product with some or all of a range of guaranteed benefits (see Figure 1). Offering these guarantees without some form of risk mitigation would lead to onerous capital requirements and expose insurers to large potential losses (at least one US insurer lost several hundred million dollars during the equity market declines in 2002) and so most insurers choose to pass on at least some of the risks. Reinsurance may be one option (although market capacity has been limited at times), but in this article we will concentrate on direct hedging of the liabilities.
Hedging programmes can be divided broadly into static and dynamic approaches. A static hedge involves buying and holding a portfolio of assets that is expected to be a close match to liabilities and is rebalanced infrequently. As publicly traded assets are not always a sufficiently good match, a static hedging strategy often involves structured derivatives purchased over-the-counter from an investment bank.
In contrast, a dynamic hedging strategy would involve buying a liquid portfolio of assets that is expected to match movements in liabilities only over a short period. The portfolio is rebalanced frequently to maintain the match, where the rebalancing period is chosen to balance trading costs with the accuracy of the hedge.
In the US, where large volumes of variable annuities are sold each year, many of the larger insurers have opted for a dynamic hedging strategy. This is different from the situation in the UK, where the majority of insurers have tended to look for longer-term, more static hedges to de-risk their businesses. This may reflect the fact that much UK hedging activity has focused on mature books of withprofits business, whereas in the US the greater weight of recent new business makes the static hedging approach less practical but creates sufficient scale to make dynamic hedging attractive. Most insurers who have launched variable annuity products in UK and European markets to date have been able to draw on the experience of US companies within their groups and some have made use of their existing dynamic hedging capabilities. Below we will look at the dynamic hedging process in a little more detail.
Before embarking on any hedging programme it is important to be clear on the objectives. A key decision is what measure will be hedged, for example economic value, statutory liabilities, economic earnings or GAAP earnings. Decisions also need to be made at the outset about which risks should be hedged and what level of retained risk is acceptable. Ideally discussions about hedging will be held at the product design stage as there is an inevitable tension between the desire, from a marketing perspective, to increase the range of funds and product features available and, from a risk management/hedging perspective, the pressure to keep everything as simple as possible. For example, it is not unusual to impose asset allocation restrictions so that policyholders can select only limited amounts of funds for which it would be difficult to find suitable hedging assets.
Dynamic hedging is typically based on calculating the sensitivity of the liabilities to changes in underlying variables. These sensitivities are sometimes referred to as the ‘greeks’ (see Figure 2). Delta risk would always be hedged but other greeks may also be included depending, amongst other things, on the desired accuracy of the hedge portfolio, the nature of the underlying guarantees and the rebalancing period. For example, GMIB and GMWB may have significant interest rate exposure (rho) but this may be less significant for other guarantees. Companies using a longer rebalancing period may want to hedge second-order effects such as gamma risk. Some US companies are starting to hedge second-order and cross-greeks such as the sensitivity of vega to changes in the underlying assets.
Having calculated the desired liability sensitivities, the next step is to identify a portfolio of assets that will offset these exposures. There is a wide range of assets with different maturities and other characteristics, each one with its own set of greeks. Identifying the optimal hedging portfolio can therefore become a complex optimisation problem and other factors are likely to influence the choice. Where frequent rebalancing is used the preference is likely to be for relatively simple, liquid, possibly exchange-traded assets. If rebalancing is less frequent then less liquid but potentially better-matching assets might be considered.
A dynamic hedging strategy implies frequent asset trading and relies on complex underlying calculations so it is clearly vital to set up robust risk management systems and controls. Dynamic trading is exposed to liquidity and ‘gap’ risk (the risk that markets move too quickly to execute the necessary trades). A very important element of the control process is an attribution analysis. This analyses the contribution to profit and loss of items such as basis risk between policyholder funds and indices underlying the hedging assets, movements in unhedged risk factors, policyholder behaviour and deviations between other assumptions and actual experience. However this is no easy task; a Society of Actuaries survey of US life insurers rated this as the most difficult implementation challenge for variable annuity hedging (see Figure 3).
The full survey can be found at: http://www.soa.org/research/research-finance.aspx
The modelling underlying dynamic hedging is not only complex but needs to be sufficiently quick, accurate and robust to be used to drive an active trading strategy. Rebalancing may be done weekly or even daily. Processes such as extracting, formatting and verifying policy data, and calibrating an economic scenario generator (ESG) need to be automated as there is unlikely to be scope for much manual intervention.
Run times can create difficulties unless modelling short cuts are taken. Grouping policies into model points might help, but may mis-estimate the liability cost by, for example, averaging across policies with in- and out-of-the-money guarantees. This is risky when the results are used to determine daily trading, so using full policy data is preferable. Unit funds, however, will tend to be grouped for modelling purposes by using regression techniques to map them onto a smaller number of representative funds, which would typically consist of linear combinations of market indices.
This approach may also help with the selection of hedging assets as these are usually based on market indices so it is necessary to identify the most appropriate index for each fund. Finally, there are a number of variance reduction methods, such as antithetic variables and control variates (discussed in Feifei Zhang’s article), which can help to reduce the number of simulations to a manageable scale without unacceptable loss of accuracy.
Variable annuities offer policyholders a wide range of options, such as switching assets between funds and when to start GMWB withdrawals and at what level. Unlike with-profit policies, policyholders have some control over the underlying assets on which the guarantees are written and have relatively transparent surrender values so the assumed policyholder behaviour can have a significant impact on the modelled cost of guarantees.
When deriving suitable assumptions ‘economically rational’ behaviour (which seeks to maximise the value of the options) is a guide, but policyholders do not always follow this principle. The complexity and interaction of the guarantees means it may not even be clear which actions maximise their value. Predicting policyholder behaviour is also made difficult by the lack of suitable past data, so the assumption-setting process is somewhat subjective and it is prudent to test the effect of different assumptions.
In theory, a perfect hedging strategy would remove all market risk and lock in a guaranteed profit. In practice, however, no hedging strategy is completely effective and so an insurer will need to be able to understand and project any mis-match for economic capital and business planning purposes. This leads to another level of modelling complexity as the market value of hedging assets and the value of guarantees needs to be calculated at each time step. Simple assets can often be valued using formulae, but this is unlikely to be feasible for the guarantees embedded in the liabilities or for any more exotic hedging assets, and so nested stochastic loops may be required.
Variable annuities offer complicated guarantees with significant scope for policyholder behaviour to affect the cost, and modelling these guarantees is highly challenging. An insurer seeking to instigate a dynamic hedging strategy would generally have to perform this modelling frequently and to sufficient accuracy to drive a robust asset-trading programme.
This can introduce significant operational risk and therefore requires not only actuarial modelling skills but also expertise in risk management and derivatives trading, and so substantial investment IT systems and personnel is likely to be needed. Clearly this route is not suitable for all insurers but experience in the US shows that it is possible and can be an effective way to manage risks.
For further information, please contact Tim Wilkins
+44 (0) 1737 274152
tim.wilkins@watsonwyatt.com
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