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The Actuary The magazine of the Institute & Faculty of Actuaries

Insurance: Crunch decisions

Over the past 18 months, the big story in the European life insurance world has been the rise of variable annuities (VAs). More recently, this has been overshadowed by the credit crunch and falling markets. Just when the power of the VA proposition to the customer has been vividly demonstrated, so has the risk that VAs can pose to the insurer. In this article we explore the impact of the credit crunch, and ask whether we should see this as an unforeseeable ‘black swan’ event, or a risk that VA insurers should have had on the horizon all along.

A black swan?
Recently, we have seen market conditions make life difficult for VA insurers. Longer term implied volatilities have increased dramatically in recent months, leading to an increase in the price of long-dated put options of three times or more. And of course, no matter what the hedging strategy, the mark to-market or mark-to-model value of liability guarantees has suffered a similar impact, leading both to a dramatic fall in the market consistent value of VA businesses globally, and a significant reduction in profitability of new business priced at ‘old’ rates.

So, is this a black swan event — an event so unlikely that no one should reasonably have anticipated it? No hedging programme is designed to be perfect in all conditions. If economic conditions are beyond reasonable levels, we should accept that some hedging programmes will fail and live with the consequences. After all, when we set a risk appetite, or capitalise on a certain degree of confidence, we are effectively saying that outside this limit we accept failure.

We think not. Both the implied and observed level of equity volatilities are themselves volatile. In fact current volatilities, while historically high, are not even close to a one-in-200-year event. Additionally, it is hard to argue that current economic conditions in general are unprecedented, or even very far into the tail — they were much worse than this less than 100 years ago. Indeed a naive comparison of today with the Great Depression of the late 1920s and 1930s would suggest there is still a lot more downside potential in the market.

A risk management failure?
If current conditions are not a black swan, we should expect hedging programmes to cope. To date, most have. While some companies have disclosed losses arising from increased tracking error, so far they appear to be contained. However, this is surely a good time to think harder about the effectiveness of dynamic hedging programmes and the risk management processes that sit around them. In particular, do insurers fully understand the effectiveness of their hedges in this environment, and have they put in place the broader management infrastructure, including simply holding capital, to protect against those situations where hedging isn’t as effective?

The most common approach to dynamic hedging of VA guarantees is the ‘two-greek’ approach. This typically involves dynamically rebalancing a portfolio of equity and interest rate futures to track the behaviour of the guarantees for small movements in the underlying funds and in interest rates. It is well known that such an approach can be less effective when the fund is more volatile. This is illustrated in Figure 1.

Where to from here?
More useful than trying to unpick the reasons why insurers have taken the approach they have, is to decide what to do now, given the circumstances we are in. Assuming the ‘hit and hope’ strategy of shutting down hedging all together and waiting for markets to recover is not an option, we see three possible courses of action:

1 The insurer could maintain a two-greek hedging programme, with rebalancing triggered by market movements. This keeps tracking error down at the cost of more frequent rebalancing, which increases the trading costs of hedging.

2 It could maintain a two-greek hedging programme, without increasing the frequency of rebalancing. This keeps trading costs down but leaves the company open to the risk of markets ‘gapping’ — i.e. significant falls in the underlying between rebalancing periods. To some extent the attractiveness of this strategy depends on whether you view the current volatility as mostly noise (movement around a stable value) or momentum (a falling trend in the underlying). Either way, insurers taking this approach need to understand the risks associated with it, have the ability to monitor it, and hold sufficient capital to cover the gapping risk.

3 The insurer could move to a more sophisticated ‘three-greek’ hedging programme. This deals with the risk associated with larger jumps in underlying (gamma) by introducing options into the hedge asset portfolio. However, it should not be taken lightly, as buying options has the side effect of complicating the delta and rho characteristics of the portfolio, which may undo some of the effectiveness of the basic hedge.

This can be seen in Figure 2, where complex product features such as ratchets and resets can cause a naive three-greek hedging strategy to produce unexpected losses in favourable market conditions. This happens because the gamma of the liabilities switches sign as a ratchet point approaches, whereas the gamma of an option is always the same sign. Adding the correct gamma exposure to the hedge asset portfolio is complex and the dynamics of doing so must be fully understood.

Safe variable annuities
For European insurers, the VA portfolio will not be big enough to do real damage. However, the current turmoil certainly gives pause for thought. Insurers need to understand better their hedging strategy, and the risks associated with it. They need to understand how their strategy will behave in different tail events, and the impact on their risk profile. They need to be close to the full risk management programme, from measurement through to executing hedges, so that they can react as the unexpected happens. Our advice is to start with three things:

>> Whether or not you hedge a particular greek, measure it, be explicit about your tolerance to it, and hold capital against it to the extent your hedge is not perfect (it won’t be)
>> Don’t just rely on a single stochastic model. Use multiple scenarios and stress tests to understand and manage the hedging and risk management programme
>> Use a dedicated and fast system that enables you to understand your risk position in (nearly) real time, so that you can react immediately as the market fluctuates. Waiting weeks for results is not an option.

Today’s market conditions have given some indication of the damage that a weak hedging programme can do to the balance sheet. Equally though, they have shown how valuable this product is for customers. The memory of the credit crunch will live for a long time in the minds of consumers: if insurers can offer VAs safely, their customers and shareholders alike will thank them for it.


The greeks provide a measure of the sensitivity of the guarantee value to movements in the market. Mathematically, the greeks are different partial derivatives of the guarantee price.
Delta represents the rate of change between the guarantee’s price and the underlying asset’s price.
Gamma represents the rate of change between a guarantee portfolio’s delta and the underlying asset’s price.
Rho represents the rate of change between a guarantee portfolio’s value and the interest rate, or sensitivity to the interest rate.
Vega represents the rate of change between a guarantee portfolio’s value and the underlying asset’s volatility.
Put option
An option contract that provides the holder with the right to sell a certain quantity of the underlying to the writer of the contract at a specified price (‘the strike price’) at a specified up to (American option) or on (European option) a specified date (expiration date).
Ratchet options allow the policyholder to ratchet/increase the guaranteed benefit amount to the higher of the account value and the current guarantee amount on the ratchet date without resetting the contract term.
A reset option or shout option allows the contract holder to reset/restart the option term. Upon reset, the benefit base will be reset to equal the account value on the date of reset.

Andrew Rear is head of Oliver Wyman’s European Insurance Practice
Emma Gosland is senior consultant in Oliver Wyman’s Insurance Practice