In previous articles, we have discussed the relative merits of the Point-in-Time (PIT) and the Through-the-Cycle (TTC) views of risk and capital; in a new research report, we analyse these approaches from the perspective of policyholder protection. This entry summarises the main findings, namely that PIT capital regimes can in principle simultaneously provide a higher degree of policyholder protection and a lower long-run average capital requirements than the TTC approach, although there are practical difficulties which must be considered.

Figure 1: Comparison of TTC and PIT Value-at-Risk at 99.5% over one day for the S&P 500

PIT capital takes account of all available current information to assess capital requirements for the current period. By contrast, TTC capital aims to set  capital requirements for a typical year.  These two approaches turn out to deliver both different levels of average capital and potentially different levels of protection for policyholders. In our report we develop and illustrate three key results as follows.

Result 1:  The long-term average capital requirement using the PIT approach is typically lower than the capital requirement using a TTC approach.

We know that the average of a function of a random variable is not the same as the function of the average of that random variable. In a similar manner, the capital required for average risk is not the same as the average capital for time-varying risk. In fact, we have observed that long-term average PIT capital requirements are typically lower than TTC capital requirements. This is not always the case but in all the realistic examples we have investigated we have found this result to hold.

To illustrate this we can use real data on equity returns. Figure 1 shows daily S&P 500 losses (negative returns) from 1990 to 2011, along with TTC and PIT “capital requirements” of 99.5% Value-at-Risk over a one-day horizon. The frequency of losses exceeding available capital is 0.5% per day in both cases. The TTC case holds a constant level of capital, while the PIT case dynamically adjusts capital requirements according to forecasts of volatility. The average PIT capital requirement is 2.94%, significantly lower than the TTC capital requirement of 4.17%.

Intuitively this can be thought about using the following analogy: if you were flying a jumbo jet through a mountain range, how low would you dare fly? The chances are you’d want to fly at, or about, the height of the highest mountain in the range. How about if you were flying in a nimble fighter jet? You could fly lower through most of the range, and pull up over the high peaks whennecessary (Figure 2). Your average height would be lower in the second case than the first (although the ride might be more nail-biting!).

Figure 2: TTC is like a jumbo jet, PIT is like a fighter jet. You can fly lower on average with PIT, although at times you may fly higher.

Result 2: The PIT approach using Value-at-Risk provides the optimum protection to policyholders, in terms of the Expected Policyholder Deficit, for a given average level of capital support over time.

The Expected Policyholder Deficit (EPD) is the expected value of policyholders’ losses through insolvency. The EPD is often used as a measure of policyholder protection, as it considers both the severity and the frequency of insolvency. It turns out that, for any given long-term average level of capital support, the policyholders’ total expected deficit is minimised if this capital is held on a PIT basis, using Value-at-Risk as a risk measure.  

This says that if an insurance company wishes to maintain a long-term average level of capital support of $100 million, say, then it is much more beneficial to policyholders for the insurer to hold more capital when riskiness is high, and less when riskiness is low, such that the average level of capital is $100 million, than to hold $100 million at all times. This is a very general result which does not make strong assumptions about the particular distributional form of the model.

In the example of equity returns above, if we scaled up the PIT capital requirement so that the average PIT capital is the same as the TTC capital requirement of 4.17%, the Expected Policyholder Deficit in the PIT case is 0.0011% per day while in the TTC case it is over 7 times higher at 0.0078% per day.

Result 3: The PIT approach can simultaneously give a higher degree of policyholder protection and lower long-run average capital requirements compared to the TTC approach.

What is the outcome of combining Result 1 and Result 2? Do the costs and benefits associated with the different approaches to capital just cancel out? If TTC capital requirements are higher than average PIT capital, does this offset the lower Expected Policyholder Deficit for PIT for the same average level of capital? The answer is no, not in general. Even when TTC capital requirements are higher than average PIT capital requirements, the Expected Policyholder Deficit tends to be lower in the PIT case than the TTC case.

To achieve the same degree of policyholder protection, in terms of Expected Policyholder Deficit, TTC capital requirements may have to be substantially higher than long-run average PIT capital requirements.

Table 1 summarises the average capital requirement, probability of insolvency and EPD for the following four cases in our S&P 500 example:

• TTC(I): Through-the-Cycle VaR at the 99.5% level
• PIT(I): Point-in-Time, scaled to match the same average capital requirement as TTC(I)
• PIT(II): Point-in-Time VaR at the 99.5% level
• TTC(II): Through-the-Cycle, scaled to match the same EPD as PIT(II)

Table 1: Comparison of results of different capital approachesapplied to daily S&P 500 returns

Summary

Our analysis and investigations suggests that, in principle, the PIT approach to capital requirements provides a higher level of policyholder protection than the TTC approach. To put it simply, with TTC, when policyholders lose, they tend to lose big. Further, PIT capital requirements tend to be lower in the long-run average sense than TTC capital requirements – capital is committed when it is needed most. Capital has an opportunity cost and so shareholders will prefer a company to operate at lower capital levels if they can achieve the same objectives. In practice, however, we do acknowledge that there are a number of operational difficulties in carrying out the PIT approach. In particular, PIT capital requirements can be very volatile, and a company could find itself having to raise significant levels of capital at certain points in the “cycle”.  Thought needs to be given to how a company could manage these variations in capital requirements i.e. how the costs of raising and distributing capital influence the optimal strategy and how the volatility in capital requirements may enforce cyclicality.

Finally, these results do not incorporate the impact of model risk (i.e. the possibility of mis-forecasting risk) which would both tend to dampen the movements in PIT capital. In terms of our airplane analogy, if it is foggy, or if the instruments in the cockpit of the plane are faulty, the PIT pilot may be wise to fly higher to give themselves more of a buffer should a mountain suddenly appear.

Contrasting the differing requirements of the various stakeholders in an insurance company, there turns out to be a direct conflict between policyholder protection and the commercial difficulties of implementing a PIT capital management strategy in practice. We believe that the framework summarised here and presented in detail in our research note provides an important reference point for firms and policymakers in respect of a fundamental question in the capital management debate.

Many have expressed concern regarding possible implementation of the draft proposals contained in these documents. Speaking in his capacity as chair of the NAPF, Lindsay Tomlinson voiced concerns that a Solvency II regime applied to pension schemes will have the effect of restricting pension schemes’ freedom to invest, suggesting that pension schemes should be growth investors.  Many have interpreted this ‘restriction’ as having the effect of prompting an exodus from equities to bonds. Another concern is the burden of potentially yet another funding basis – no doubt prompted by the reports of spiralling Solvency II costs in the life sector - allegedly some companies have already spent  over £150 million on Solvency II implementation.

While this debate continues, we should perhaps pause and ask ourselves -- are we already approaching a theoretical Solvency II regime on pensions?

Mapping Solvency II onto the existing pensions framework

In order to understand how far we are currently from a possible Solvency II regime, let’s summarise what Solvency II for insurers looks like, and how that potentially maps onto the pensions world.

A high level summary comparing an insurance regime and a pension regime are set out in the diagram below:

• Pillar I – covers the quantitative requirements – in essence, what is the value of your pension liabilities and how much risk is there in the scheme?
• Pillar II – covers the qualitative requirements which will require a clear robust governance structure as well as a risk management process in place.  In pensions language, this translates into pension scheme trustee governance, trustee knowledge and understanding and the risk register, to name a few.
• Pillar III – covers disclosure requirements to regulators and members. This translates into disclosure of pension scheme’s annual Trustee Report & Accounts and Annual Summary Funding Statement to all members.

Comparing the current DB pension system in the UK with the insurance sector, one may even be convinced that the two sectors are not really under a very different regime. Most of the contentious points about applying a Solvency II type regime on DB pensions are about Pillar I and not about Pillars II and III.  

The devil is in the detail

Pillar I has caused most controversy as on the face of it,  a Solvency II approach will require pension schemes to operate on a much stronger funding basis as well as holding additional capital against investment risks and other unhedgeable risks.  However, this scenario might not arise as the Call for Advice has made a clear distinction between the schemes which are underwritten by a sponsoring employer and those which are not. The implication is that schemes with a sponsoring employer (which apply to almost all schemes in the UK) will be able to allow for the recourse to the employer as a backing asset. In addition, it may be possible for credit to be taken for the presence of the PPF in some form. We are of course far from getting the details on paper, but for the sponsors who are worried about the funding implications of Solvency II on pensions, the reality of the situation might not be  as grim as it sounds.

What’s changing: the wider implications

Apart from the IORP directive, other regulatory bodies continue to move forward in the area of deriving a platform which better reflects risks taken by pension schemes.

One such change is the PPF levy framework for 2012/2013. Within this framework, part of the PPF’s main objectives in respect of measuring investment risk is as follows:

1. to reflect the potential volatility of a scheme’s investment strategy in thelevel of risk-based levy charged; and
2. to give schemes that have adopted de-risking strategies the opportunity to obtain appropriate credit for these risk reduction measures.

Practically, this means that for the 2012/2013 levy year, schemes with liabilities above £1.5 billion will have to carry out a Bespoke Stress Calculation on a mandatory basis. But adopting a more risk-based approach is very much in line with the principles of Solvency II and the PPF’s levy framework will hopefully act as a catalyst to better risk management practice for pension schemes without the bureaucratic burden of onerous legislation.

Conclusion

With the other changes, driven by different authorities coupled with the review of the IORP directive, it is not a matter of lobbying against whether Solvency II should be applied to pensions; one would argue, it is already in place, simply badged up under a different name.

A constructive way to deal with the possibility of applying Solvency II to pensions is to learn our lessons from how Solvency II implementation on insurance is working and select the elements which have worked well and avoid the pitfalls for pensions.

Different parties within the pensions industry are currently lobbying about (mostly against) Solvency II on pensions. If we are not careful, some of the strong messages may get lost in politics as a result of highly negative voices about the IORP directive. Initiatives such as the PPF levy framework to include investment risks are good practice to ensure that schemes are rewarded for managing risks. As we see from the current financial crisis, a system whereby institutions are treated equally regardless of the level of risks they run means that the good ones will forever have to bail out the bad ones.

When thinking about the probability that should be attached to the Fed’s scenario, it is worth saying that there are many other scenarios that could play out over the coming years. Whilst central bankers are clearly smart people, even they would not claim to have perfect foresight.  Past attempts by economists to forecast financial and economic circumstances have been fairly unsuccessful and are naturally constrained by the practical challenge of forecasting the behavior of a complex, dynamic social system which we do not (and probably never will) fully understand. In other words, I think we should be sceptical of any forecast.  Uncertainty about what will and can happen to asset prices is one of the reasons that stochastic models can offer significant insights. There is little doubt that, with S&P’s credit downgrade of the US and the intensification of the Euro area debt crisis, the future of the global economy is especially uncertain and investor confidence is unusually fragile. This leaves policymakers in a weak position when it comes to making rhetorical guarantees or promises.

The announcement by the Fed is best interpreted – by the sceptic – as a fairly clear (and worryingly impotent) attempt to calm the markets as opposed to an unshakeable commitment to a certain monetary policy stance. The clear internal wrangling that was behind the decision (signalled by the split in the vote 7-3) and the fairly slippery language used to make the announcement (“[The Federal Open Market Committee] will continue to assess the economic outlook in the light of incoming information and is prepared to employ these tools as appropriate.”) doesn’t really inspire belief that a low rate environment is something that policymakers will enforce ‘come hell or high water’. If, for example, inflation rates continue to tick up and expectations lose anchor there will be pressure to respond. The question we need to ask is how much attention should we pay to this announcement when thinking about yield curve projections for the coming years? As is so often the case, market instruments offer an important source of information.

How have participants in the market for US treasuries reacted to the announcement?

Source: http://www.treasury.gov/resource-center/data-chart-center/interest-rates/Pages/TextView.aspx?data=yield

The falling prices of risky assets and the corresponding flight to safety depressed yields between August 1^st and 8^th across all maturities. Subsequently, as might be expected, longer yields have not reacted (much) to the Fed statement, although at shorter maturities curves appear to have become slightly more depressed. Whether this will persist remains to be seen.

So, how does the Fed signal feed through to our views on the potential outcomes for yield curves over the coming two years? To the extent that the market would be calmed by the news and to the extent that the market believes the announced rate paths, our calibrations and views should naturally adjust to reflect this (whilst also weighting some longer term fundamental views). From the market reaction so far the implication is that the Fed announcement is being treated with an understandable degree of scepticism by investors.

Stochastic projection methods are implicitly sceptical but don’t provide explicit explanations for the scenarios generated. We can tell stories around some of these scenarios and debate probabilities – Rumsfeld’s known unknowns – for example, the inflation surprise that triggers a response from the Fed. Other scenarios – the unknown unknowns – are more elusive and therefore can, ultimately have a bigger impact on future prices. It is easy to forget this important source of risk.

ifaonline.co.uk

"John Higgins and David Campbell believe the at- retirement space is currently underserved by financial planning tools. Advisers are provided with plenty of options for which tools to use in the accumulation of their pension funds but have little to help decide the most effective approach to managing the transition to retirement and how to optimise their income in retirement."

Comment: Practical considerations are compromising Solvency II methodology

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"A number of politically-inspired compromises have led the Solvency II directive away from its market-consistent routes – so much so that according to Barrie & Hibbert’s Craig Turnbull and John Hibbert, the final confidence level for some liabilities is not one in 200, but one in 12."

Pensions: Value at Risk

The Actuary

"Celene Lee looks at the implications of new reporting standards for the measurement of risk in pension schemes and asks if there is a better means of communicating VaR."

Policymakers, regulators, firms, actuaries and accountants have belatedly focussed on a number of difficult questions including the choice of risk-free asset, the method for extending valuation beyond traded maturities and the possible impact of market liquidity premia on the way the valuation question is answered. This comment focuses on one specific aspect of the extrapolation – the reliability of forward rate estimates and whether we should switch focus from the liquidity of assets to the reliability of forward rates derived from market prices.

It’s apparent that there is considerable discomfort with potential variation in yield curves and their impact on the balance sheet where firms are exposed to large duration mismatches. Putting aside the rights and wrongs of exposing the economic mismatch between assets and liabilities (and I’m in the accounting camp here), I think there is a lack of appreciation of the difficulty and estimation error in establishing a reliable forward interest rate curve even where markets are Active and meet the ‘Deep/Liquid/Transparent’ (DLT) requirement (if we could decide what ‘DLT’ really means).  This is important because I think the preference for a reduced longest liquid point (‘LLP’) is driven by the desire to stabilise the forward curve between valuation dates rather than any objective view on liquidity. This objective is not unreasonable given that, in practice, for durations beyond 15-years there can be a reasonably wide range of credible forward rates that will closely fit market prices. So, if your objective is not simply to produce the best fit to market prices at a single point in time but to produce a good fit and manage changes between valuation dates in a credible fashion, it may be more useful to think in terms of a ‘longest reliable point’ (LRP). Here, we might choose to extend the curve from 15 or 20 years, not because of liquidity considerations but because we can better manage the trade-off between providing a good fit to market instruments out to – say – 30 years and, additionally, ensuring that the behaviour of the curve beyond the LRP is credible through time.

Here’s an example. This compares the government forward curves produced by Barrie & Hibbert and the US Fed for end-December 2008:

A few points to note:

• Both curves provide an extremely close fit to bond prices
• The Fed (in common with other central banks) use methods which focus only on the traded part of the curve (why would they do otherwise?)
• Generally, the spline approach allows for a richer description of the market and provides a marginally better fit
• However, the B&H curve is additionally influenced by what we want to happen in the extrapolated part of the curve (which is not shown) and so the terminal gradient is managed, but this does not have a material impact on the overall fit to observed prices.

My conclusion is that we may want to think about shifting the discussion from a narrow focus on liquidity (which could be argued is a ‘red herring’) to a longest reliable observation on forward rates and management of the trade-off between fitting instruments beyond this LRP with stability of the curve over time.
 

Consider a very basic example. Suppose an insurer holds a single unhedged position in a written 10-year put option with a strike at 90% of the current (total return) index level. We assume that the only source of uncertainty is equity risk and calculate some alternate measures of capital as follows:

• VAR measures at 1, 2 and 3 year horizons
• A run-off capital requirement (the PV of the shortfall at the specified confidence level)
• A conditional tail expectation (CTE) 

All measures are calculated at various confidence levels between 90% and 99.9%. The results plotted below are for the PV of capital in excess of the basic value of the option. I have highlighted 3 points which represent measures commonly used in different parts of the world:

• 1-year 99.5% VAR measure (14.9%)
• 95% run-off measure (15.9%)
• 90% CTE measure (17.6%)

You can see that, for this example, the capital requirements are broadly similar. Now, the quantity of capital required to support a risk exposure of this type will be critically dependent on the assumptions made about equity risk. For the 1-year VAR measure, the tail of the distribution of equity returns at the end of the first year of projection will be important. For the two alternative measures, the tail of the terminal 10-year distribution will be of most importance. For the analysis below we have assumed that equity returns follow a process where volatility is stochastic (i.e. it varies through time) but it is initialised at a neutral level. However, there are other assumptions we might make which, as you will see, have a material impact on absolute and relative capital requirements.

Consider the following alternatives:

• Volatility is stochastic but its initial value is set to be LOW
• Volatility is stochastic but its initial value is set to be HIGH
• Equity returns are assumed to incorporate some ‘mean reversion’ which will limit the tails of long-horizon equity distributions.

The chart below plots the results from the first chart in the first column. You can see that the capital requirements are pretty consistent assuming constant equity volatility. Now consider the additional columns. When initial volatility is reduced (year 1 volatility falls from 20.5% to 17.6%) the 1-year VAR capital is reduced by nearly 20% to 12.3%. The run-off measure is very slightly affected by the lower year-1 volatility. In much the same way, an elevation in initial volatility lifts the 1-year VAR measure to around 25% and modestly raises the run-off measures. Finally, the ‘bubble’ plot assumes mean reversion so that the annualised volatility of the 10-year return falls to 16.4% and the 95^th percentile total return is moved from -42% (under the base case) to -26%. Unsurprisingly, this has a material impact on the run-off capital measures reducing them both to 3.9% (95% run-off) and 6.6% (98% CTE).

The story is a familiar one. 1-year VAR capital is very sensitive to initial market conditions. ‘Point-In-Time’ (i.e. conditional) estimates for the returns distribution will deliver far more variable (and pro-cyclical) capital requirements than ‘Through-The-Cycle’ (i.e. unconditional) measures. VAR capital will be sensitive to short-term movements in asset prices driven by changing risk and liquidity premia. By contrast, run-off capital measures will tend to be less sensitive to initial market conditions but very sensitive to the sources to which the modeller attributes volatility. If short-term price changes are attributed to transitory changes in risk and liquidity premia these assumptions will have a material impact on the run-off measures of capital requirements.

Consider (again) savings accumulation over a long horizon – 30 years – where we assume an individual saves €1000 each month. Now, let’s assume that we have a fixed set of returns available for the 30 years. The returns have an (arithmetic) average of 7% pa and a volatility of 16.5% so they are in line with the sort of assumptions that practitioners might make for a financial planning exercise.  Suppose we now experiment with the order in which the returns are delivered but leave the magnitude of returns unchanged. What difference does this make to results – to the sum accumulated at the end of the 30-year period?

The chart below plots some possibilities for the growth in the underlying investment asset price. You can see that all paths start and finish in the same place for a unit investment. The top (green) profile shows the path where we place returns in order from best to worst. The bottom (red) profile shows the reverse with returns ordered from worst to best. As we have already seen (see blog part I) accumulation strategies benefit from ‘late returns’ as under the red path. In this case, for the same set of returns, the ‘late return’ red path delivers a final fund of €3.7M (IRR of 12.7% pa) whilst the worst ordered outcome (‘late damage’) produces €0.3M (IRR of -1.4% pa). These striking differences are exactly reversed for de-accumulation problems.

Two additional random-ordered paths are also plotted on the chart. In the chart below the full distribution of possibilities is shown for the accumulated fund where we randomise the order of the same fixed set of 30 returns and simulate a large number of possibilities. There turns out to be a 1-in-5 probability of achieving either more than €1280K or less than €680K. Given how much investors focus on both returns and measures of asset volatility it is striking how, when we nail down both these properties for a fixed set of returns, the outcomes for accumulated fund fall over such a wide range.

The lesson is that the path really matters and so advisers and savers need tools and strategies in order to understand and control these risks.

Choices over which prices may be used (and why) will have a material impact on valuation and risk management actions. A topical example is the choice of ‘longest liquid point’ in the extrapolation of swap curves for SII valuations. The value of long-term cash flows and the connection between balance sheet assets and liabilities will depend on how the quality of individual instrument markets is judged.

The diagram provides a crude comparison of the terminology in use among European insurance regulators, accountants and European firms (CRO forum). The CRO forum and accountants’ definitions of Active markets and Hedgeable market risks look aligned.

..quoted prices are readily and regularly available from an exchange, dealer, broker, industry group, pricing service or regulatory agency, and those prices represent actual and regularly occurring market transactions on an arm's length basis.

For non-hedgeable risk (no Active markets), accountants make a distinction between model-based valuations based on the observability of the model’s inputs. Although this is a useful distinction, in practice its application will be rather grey. I would view the extrapolated price of a cash flow falling only 1 year beyond the liquid market as qualifying for level-2 whereas a 50-year extrapolation clearly falls under the level-3 definition. Most of us would struggle to say where the cut-off lies. More problematic is the additional layer of analysis applied by European regulators in defining reliable prices which additionally must trade in ‘deep’, ‘liquid’ and ‘transparent’ markets. Taking these definitions at face value suggests only a small set of instruments may pass the ‘DLT’ test. Where market prices are observable, but fail the DLT requirement, it is not clear how much weight should be placed on them in valuations. Strictly speaking, any non-DLT price will require the addition of a risk margin under Solvency II. The QIS 5 technical specification suggests that it is possible that non-DLT prices could be completely ignored (which creates a worrying potential disconnect between non-DLT assets on the balance sheet and liability valuations). A further requirement for ‘permanence’ which appeared in early versions of technical guidance has been removed (for the time being at any rate). Whilst the DLT definitions could be clarified further, the basic properties of an instrument market they seek to measure are:

• Depth. The ‘normal market size’ (NMS) of trades. You might easily ask whether qualification as ‘deep’ require an absolute or relative amount?
• Liquidity. This can be interpreted as a measure of the impact of abnormal trade sizes i.e. if an insurer aims to trade 10 x NMS, what impact on the price is expected.
• Transparency. What information makes a market transparent? When must it be disclosed and how?

These words are somewhat different to the SII definitions but aim to convey the intention of the regulator. To help understanding of these properties of a market price, consider the chart below. It shows offers to buy and sell in a market where the amounts offered (or bid) are indicated by the size of the circles. It happens to be a market for bets on a tennis tournament. It is interesting because this ‘public order book’ provides a clear view of dealing intentions in a market so that a trader can understand the likely impact of a trade of a specific size. You can see that for Federer, it is possible to buy or sell relatively large amounts (of the bet) across a narrow price range. The market for Federer is both deep (large size) and liquid (low impact). Markets for Nadal and Djokovic are less liquid and, although there are bids and offers for Murray, only small trades are feasible and they will suffer a large impact cost.

In their report on the ‘Flash Crash’ of May 6 2010, the US CFTC provide a useful description of ‘depth’ as follows:

We use the term market depth.. to refer to resting orders that market participants place to express their willingness to buy or sell at prices equal to, or outside of .. current market levels. These orders are referred to as “buy interest” and “sell interest”, and the number of shares of each type of order interest represent “buy-side market depth” and “sell-side market depth.” Collectively, buy-side and sell-side resting orders form a “liquidity pool” against which incoming sell or buy orders can be executed.

Of course, you need to remember that this picture excludes the hidden intentions of dealers or investors who would offer liquidity but either do not bother to advertise through the order book or prefer to keep their dealing intentions secret. Dealers are notoriously cagey about revealing information to other market participants. The picture above gives an ideal view of what a market – where dealing intentions are publicly available – could look like. In practice, few markets offer this level of transparency. However, this view is useful because it can help us understand what we would like to measure.

So where are we now? To summarise:

• Some clarification of language would be helpful.
• The divergence between accounting and insurance terminology and emerging practice is worrying and has the potential to create an inconsistency between accountants’ fair vales and Solvency II technical provisions.
• Whatever the result, firms will need to gather evidence on the reliability of the prices used in their valuations.
• An informed discussion requires the development of objective, operationally-feasible measures of the various characteristics discussed in this article.

It’s a big job. We should start soon.

The obvious answer (to many of us at least) turns out to be a poor choice. For the profiles illustrated below, the particular paths shown would produce final accumulated sums of €758,000 for the green (6.1%) path and €1,016,000 for the red (3.7%) path. Of course, when you think about the timing of the cash flows, it’s no real surprise. For the red path, many of the poor returns fall in the early years when there is little contributed to the fund so they do little damage. By contrast, on the green profile the early strong returns are wasted since only a few contributions have been committed to the fund. Notice that for de-accumulation problems these effects would be exactly reversed so the poor early returns along the red path would be hugely damaging to a withdrawal strategy.

The lesson is pretty clear – for the purposes of understanding financial goals, the path really matters. It isn’t enough simply to focus on returns and their volatility. The sequence of returns will have quite different implications for different savers depending on their own pattern of contributions and withdrawals.

Finally, investment analysts often quote a ‘money-weighted’ or internal rate of return. This is the fixed return over the entire period that would produce the same cash flows. Of course, this depends on the returns and the timing, size and sign of cash flows. In this case the IRR is 4.5% for the upper path and 6.1% for the lower path.

Under the proposed Solvency II framework this standard assumption is adjusted using a ‘dampener’ in order to avoid procyclicality. The stress test may be modified up or down depending on the where global equity prices are trading relative to their recent average. For QIS5, the dampener was calculated based on market prices relative to their 3-year moving average. At end-2009, equity prices were 9% below their 3-year moving average and so the equity stress was reduced by 9% to 30% for QIS5. At end-2010, equity prices were 11% above the 3-year moving average (MA) and so the equity stress would be adjusted up (by a capped 10%) to 49% on the same basis. The chart below plots the differences of the MSCI World Index used in CEIOPS’ studies to its 3-year MA and the resulting modified stress on the right-hand scale.

So, capital requirements to support equity risk would have been raised substantially over the year for those using a standard formula approach modified using the dampener. It is worth noting the contrast with market-based measures of equity risk. During the year, option implied volatilities (for a broad range of maturities) were broadly unchanged. Of course, we have argued in the past that a truly objective stress test following a stress test would be more severe not less severe as under the dampener. This is because – following equity stress – although risk premia tend to rise, this effect is offset by the typical increase in uncertainty and volatility (see link). In practice, it seems considerations of procyclicality outweigh cold analysis.  

It is also worth noting another property of the dampener. The adjustment to the equity capital charge is described in both the Solvency II directive and guidance as being ‘symmetric’. Of course, it is symmetric in the sense that it can raise or reduce the capital charge by equal amounts. However, you can see from the chart that it certainly is not symmetric in the frequency of adjustment i.e. the adjustment upwards is applied far more frequently than the downward adjustment because equity markets tend to rise over the long term. The table below shows the proportion of time at the floor and ceiling for the equity capital charge and compares results with the CEIOPS ‘majority’ view where the dampener is based on 1-year MA and centred on a basic charge of 45%.

This is no mere accident of history. A very simple simulation of price paths shows virtually identical results:

I have no fundamental difficulty with the notion of procyclicality or the desire of regulators to limit its damaging impact. However, in an environment where equity values are reduced, it seems we are unable to face the economic reality and say the words: “policyholder security is reduced to x%; firms will rebuild their capital base to meet the 99.5% requirement over the next N years”.

If as for end-2009, the averaging period is to be selected to produce the answer firms can live with, perhaps regulators should just say so. Pretending the averaging is the result of objective analysis won’t help improve transparency or build faith in the insurance industry’s emerging capital measures.