Economic Capital – a common currency of risk

This is the paper which provides the background behind a presentation on economic capital which I made to the Institute of Actuaries of Australia’s Biennial Convention.

How and why should we measure it?

Economic capital means different things to different people. But for this presentation, the purpose of economic capital is to assist companies in appropriately measuring the rate of return a company is getting in proportion to the risk it is taking.

Economic capital is not:

• Regulatory capital – regulatory capital is the amount of capital a regulator has determined an institution needs to hold, but is generally not as specific to the institution as economic capital would be. The capital for particular risks would be calculated more broadly, and the definition of risk would be a systemic one, rather than an institutional one.
• Value of the organisation – the value of an organisation (in the long term) should be the discounted value of future distributable profits. There is no reason for economic capital (which is a measure of extreme risk) and discounted value of future profits to have any defined relationship. Companies should, however, be earning adequate return on the capital they hold – the purpose of economic capital is to help them work out what that return should be.
• A capital resource – economic capital measures a capital requirement, not how much capital a company might have available. Net assets (below) are a capital resource

In working out what to do with economic capital, the capital resources available to the company can include net assets, future value of profits, and some other assets which may not be recognised for accounting purposes. On the flip side, some accounting assets (such as the goodwill paid for a recent acquisition) may be valueless in an economic capital scenario.

What is the point of economic capital?

There are two main points to economic capital. The first is about solvency. A company needs to have a degree of comfort in its ability to withstand extreme events. It is not efficient for a company to hold enough capital for every conceivable contingency, but neither is it efficient to run the risk of insolvency with too frequent events. The importance of economic capital for this purpose will, to some degree, depend on the regulatory environment. In a strong regulatory environment, where substantial regulatory capital is required to operate, most companies will choose their level of capital to reduce the risk of breaching regulatory requirements, rather than based on the underlying risks of not meeting liabilities. However, in an environment with very light regulatory requirements for capital (which is more likely to occur in the insurance industries, or in countries with less developed regulatory frameworks, or both), economic capital is important for a company in understanding the solvency position of the company.

The second purpose of economic capital is the main purpose for most large financial services institutions. Economic capital enables a company to make decisions which involve quantitative risk reward trade-offs. If each part of the economic entity is required to make an appropriate return on economic capital, and economic capital is appropriately allocated between the lines of business in proportion to their risks (all risk, including operational and strategic), then the high risk parts of the company will naturally require a higher return to compensate for the risks they are taking with the firms money. Effectively economic capital enables a company to have a common currency of risk. This will mean that decisions across many different business and risk types can be made with the intention of making the same return on a given unit of risk.

This process helps with many decisions:

• Is it worth investing in systems to reduce operational risk?
• The treasury operation is making a high contribution to profit – does this adequately reward the company for the risks taken?
• Adding a general insurance operation adds diversification. Is the extra margin (which is lower than mortgage business) adequate, given the overall reduction in average risk?

These decisions may be characterised more broadly as the major decisions taken in a diversified institution:

• pricing for risk, enabling an understanding of the relative returns on risks across the institution
• portfolio optimisation – ensuring a good understanding of the mix of return for risk across different business types, and which business lines support each other in risk terms, as well as returns (diversification effects across different risks, for example)
• investment assessment for new decisions  – looking not just at the return on the investment decision, but the risk adjusted return

To make good decisions on this basis, the whole organisation must be managed on that basis. Which means regular measurement (monthly reporting) must be occurring, and all KPIs that are based on a measure of return should be based on a measure of return for risk – ie economic capital. In effect, the control cycle for the organisation must include economic capital at all stages – forecasting, measuring actual experience, and then reviewing risk appetite and key assumptions.

For good decision making on this basis, however, there must be a substantial degree of trust in the economic capital calculation process, from those who are going to be measured by it. This means that in a large, diversified financial institution, it is worth thinking through the differences between the types of risks, balance sheets, and modelling methods – trying to make sure that the methodology works for all the various types of risks and businesses.

So how do you calculate it?

To calculate a number for economic capital, the theory is quite simple.

First, determine your required level of confidence, which is linked to your risk appetite. Risk appetite is the subject of a whole other paper – how to define it, and how to express it. But for the moment, let’s take the simple route. At its simplest, a level of confidence can be expressed as the probability of not meeting your liabilities. For example, the Basel regulatory capital requirement (for advanced measurement status for a bank) is a probability of not meeting liabilities of 1 in 1000 (over a one year period). For general insurance companies in Australia, the requirement for internal models to be used to determine minimum capital requirements (MCR) is 1 in 200. There is no internal model standard for life insurers in Australia, but the Capital Adequacy Standard requires the Appointed Actuary to provide a level of reserves “able to cover a combination of adverse circumstances that would arise once every 400 years”.

Why does the measure of confidence vary across industries?

Consequences of failure: These very varied probabilities reflect quite a few philosophical differences between the way in which risk is measured across these different institutions. First, they reflect differences in the importance of the institutions to the financial system. The global experience of the last nine months (and counting) has made anyone who works in the financial system acutely aware of the importance of banks to a functioning financial system. While life and general insurers are also important (as anyone in Australia would have noticed when HIH failed), they are not the backbone to the same degree.

Shareholder expectations: A bank is generally expected to be more conservative than a life or general insurer in its management of capital, given its importance to the financial system.

Ratings agencies: Ratings agencies do not necessarily have absolutely equivalent ratings across industries. For example, many banks choose a measure of economic capital defined by a risk of default – say AA for a risk of 0.03-0.05% or so. But ratings agencies generally only require general insurers to hold catastrophe cover up to a lower level than that very extreme risk – say around 0.4% for an AA rating.

Confidence in models: But also, and potentially more controversially, the differences in probabilities outlined above reflect differences in confidence in modelling approaches. For most (not all) general insurers, the extreme events that need to be modelled for regulatory capital purposes are natural disasters. For example, take a personal lines insurer in Australia. The recent Victorian bushfires, while extreme, were not the biggest natural disaster insurance event in Australia’s history(after adjusting for inflation, the Newcastle Earthquake, the Sydney Hailstorms in ‘99 and Cyclone Tracey were bigger). We probably haven’t had a 1 in 200 year event in Australia in the last 50 years (at least based on the modelling I have seen for my own company).

Very few general insurers will place much confidence in models beyond around the 1 in 250 level. APRA, for example, only requires reinsurance up to a 1 in 250 Maximum Probable Loss. Beyond 1 in 250, the natural disaster is quite rare. And while catastrophe modellers can use a combination of weather models and patterns of insured risk to provide the probability of an event with an economic loss that hasn’t happened yet (for example a Cyclone Tracey intensity cyclone hitting today’s city of Cairns head on, or an earthquake in the centre of Botany Bay, Sydney), the less likely the event, the harder it is to work out the probability of a specific monetary loss).

It’s not hard to find, though, commentary throughout the global financial crisis from various banks (particularly investment banks) suggesting that the various impacts on different markets were very extreme – far greater than included in their models. A topical (and typical) quote:

August 5, 2007: During a conference call with investors, various high-ranking AIG officials stressed the near-absolute security of the credit-default swaps. “The risk actually undertaken is very modest and remote,” said AIG’s chief risk officer.

The key to this kind of modelling is always the tail of the model. In order to get a measure of a fairly extreme level of risk (anything beyond 1 in 100) modelling will be needed of events which haven’t happened recently. While other markets, and other timeframes can be used as proxies (for example there are several world wide databases of operational risk events, and credit cycles have had different timeframes and severity around the world during the last 100 years) , most models used for economic capital effectively extrapolate the extreme tail of the distribution based on the more known, central distribution.

Most credit risk models were based on as much detailed history as was available. And for most banks, although records of credit risk went back much further than the last 20 years, records in the level of detailed needed to create an economic capital model was not easy to find. So to value complex instruments which, at heart depended on credit risk (the notorious collateralized debt obligations, or CDOs), tractable mathematical solutions were needed. This article from Wired magazine describes the way in which a tractable mathematical solution to the valuation of very complex instruments, which depended on understanding underlying correlations drove the dramatic increase in the market for these instruments.

In my view, it doesn’t matter all that much what you are modelling – once you get beyond around 1 in 100, proceed with caution. And the less symmetrical the distribution, the more caution required. Even the actuaries’ most predictable risk, mortality risk, requires caution beyond that point because of the risk of pandemics of various types. Nassim Nicholas Taleb, outlines this very eloquently in his book Fooled by Randomness: the Hidden Role of Chance in Life and in the Markets. He talks about how difficult it is to express probability about extreme events – because they are generally outside our own experience. So careful distribution fitting is likely to miss them, or worse, ignore them as being outliers, and therefore not credible.

What to do with a confidence level?

Once you have some expression of the confidence level required, economic capital is a way of quantifying that risk. However different industries often make that translation differently. In both banking, and general insurance, there is an understanding that the tail of the distribution – where you calculate economic capital – is uncharted territory. But the culture of dealing that appears different in the two industries.

In general insurance, most economic capital models do not choose a very extreme point of the distribution. Instead, they choose a moderately extreme point (say 1 in 250) and then hold economic capital as a multiple of that point, or as a multiple of the TailVaR at that point. Swiss Re, for example, defines economic capital as a 150-200% of the 99% TailVaR of their economic capital calculation. TailVaR is defined as the average loss beyond the 99% point of the distribution. So it does depend on understanding the distribution at that point, but does not define it in terms of a single point.

While in banking, most companies choose a very extreme point of the distribution – 1 in 2,000, or 1 in 3,333 are popular numbers. These have historically been chosen as the probability of default of an AA security – ie the level of capital that would be required to stay AA. More recently, the nexus between a rating, and a probability, is disappearing, but the very extreme used seems to remain (at least so far).

Life insurance is generally somewhere in between – few life insurers trust the very extremes of their distributions (when points like 1 in 1,000 or 1 in 2,000 are mentioned, many life insurers start talking about the black death, in the 1340s, where somewhere between 25% and 50% of Europeans died).

The issue with the way in which a confidence level is defined is that it does change the relativities of different decisions.

Confidence levels and decision making

The point on a distribution that is chosen will tend to change the relativities between different risky portfolios, and hence the relative returns that might be needed for them. In general insurance, for example, home and contents insurance often has a longer tail than motor vehicle insurance – earthquakes being risks that will damage a home portfolio much more than a hailstorm might, but wouldn’t have the same extreme effect on a motor portfolio. So the more extreme the probability chosen (in the absence of reinsurance) the higher the return the home portfolio will require compared with the motor portfolio.

Many companies, though, would also want to ensure that more frequent risks require substantial returns in compensation. A portfolio that has a relatively high loss level at the 1 in 250 level, should have some return required to compensate for that loss, even if it doesn’t get any worse at the 1 in 2,000 level.

So in choosing the way in which economic capital is measured, you are choosing which risks are compensated. Is it the risks that would bring a company down? Or if a risk would not bring the company down, but creates substantial profit volatility short of that, should it also be required to make a high level of return? Or is it both?

What about the balance sheet? What is the starting point?

In order to understand the economic capital required for each part of an organisation, we need to understand the balance sheet of that organisation. Although IFRS has been designed to be as comparable as possible across different types of products, countries and regulatory structures, there are substantial differences between the accounts of different financial services entities. These differences can mean that one entity might have a balance sheet where the net assets are the statistically best estimate of the gross assets and liabilities. And another entity might have liabilities or assets which have been estimate with a considerable degree of conservatism.

So it is quite common for the level of hidden reserves in the different balance sheets to be quite different across different financial services entities, or even product lines. For example:

• general insurance outstanding claims liabilities are required to be at least at the 75% confidence level
• life insurance liabilities are set such that there is no profit to the company on the initial sale – which means that if the business sold is very profitable, the liabilities held are likely to be quite conservative, particularly in the early years of a contract. But if the business is sold at a barely break even point, there will be no margins in the accounting liabilities at all.

So if the differences between balance sheets reflect substantial differences in the risks of those organisations (in the above example, the general insurance company has a 25% chance of having to dip into the net assets, while the life insurer might have a 50% chance of having to dip into the net assets), then the risk implied in the balance sheet should be incorporated in some way in the economic capital calculation.

Details of measurement

The traditional way of measuring economic capital in a bank is risk by risk – looking at the separate risks (credit, market, operational, strategic), and then combining them using correlations. For insurance companies, the measurement tends to be by product – combining the risks within a product, and then combining the products as a whole. In many cases, for both insurance and banking, separate regional or structural entities are calculated independently and then combined at a very high level using a correlation approach. Both these methods have issues. Both methods are trying to calculate the impact of a full model of all risks for the entire enterprise. And in both cases, they will miss some subtle interactions – between types of risk – credit risk and market risk generally go bad somewhat in tandem, but the detail of that will get lost in an overall correlation of risks approach used by banks –  and between different product lines – the interactions between annuity business and traditional term life insurance will not be well modelled if a product by product analysis is done in the insurance model.

Diversification benefits

In many entities, there can be substantial benefit from diversification. Even though much of the last 12-18 months shows how correlated markets are, particularly on the downside, insurance, particularly general insurance, has less correlation with economic indicators than most other financial services products. It is important to appropriately allocate that diversification benefit. Most companies allocate it proportionately, but some have more sophisticated approaches, such as looking at the marginal contribution of each unit of risk, and allocating economic capital on a marginal basis. The process generally depends upon the proportions. If one part of the entity dwarfs other parts, it is probably not appropriate for the smaller entities to have a full diversification allocation.

And the revenue side?

If the main purpose of economic capital is to measure the appropriate return for risk, we also need to make some attempt at consistency between the different measures of profit (before the cost of risk is taken into account). Some differences between the different profit and loss accounts (even if the underlying contracts are quite similar) would emerge from the following questions:

• Should the profit of a long term contract be recognised up front?
• Should the expenses of acquiring a long term asset be recognised up front (to create a loss), or deferred over its life?
• If an entity holds a credit asset with the aim of holding it to maturity, should the movements in credit spreads in the secondary market be recognised?
• What about the effects of tax? Should profits be recognised before or after tax? And if after tax, whose – the corporation or the ultimate shareholder?

Economic Capital as part of Enterprise Risk Management

Economic capital must be part of the management of a company, to be useful. Every major decision made needs to effectively understand the risk and reward tradeoffs inherent in that decision. Economic capital can be, if measured consistently, a common currency of risk. Reviewing the performance of each year needs to review the risks taken, and their rewards, as well as the profit performance. This will help the business more deeply understand the risks taken, compared with the risk appetite, and the rewards that were available. And once reviewed, the cycle starts again – with a new plan, new assumptions about risk and reward.

So why measure economic capital?

I’ve just spent the best part of 3,000 words explaining how difficult it is to measure economic capital in a consistent way across a diversified financial services group. So why would you bother? The answer is that the future of the institution may depend on doing it well. The last 18 months have shown us how important it is to measure risk well enough to understand how much risk the institution is exposed to. But we’ve also seen just how important it is that models are not just back room tools that are blindly followed.

So an institution that is attempting to implement or improve an economic capital measurement process as part of an enterprise risk management framework will need to take into account the different languages and measurement approaches that have been used in different parts of the financial services industry. But in the end, a robust economic capital framework that combines the measure of risk and return as the main measurement of value added in the group is the best way to match the management of risk and return in a financial services institution.

Jennifer Lang

Disclaimer:

The opinions in this post are my own. They do not necessarily represent the opinions of my employer, Commonwealth Bank, or any of my previous employers. In writing this post, I have received valuable feedback from many friends and colleagues, both on the post itself, and as they listed to my half-formed opinions on this topic. In particular, I thank Tim Gorst, Andrew Reynolds and John Evans, for taking the time to read in detail and provide valuable feedback. Nevertheless any errors or omissions remain my own responsibility.

Further reading:

Books:

Enterprise Risk Analysis for Property and Liability Insurance Companies, Edited by Brehm, Perry, Venter, Witcraft

Managing Bank Capital: Capital Allocation and Performance Measurement, by Chris Matten

Fooled by Randomness: the Hidden Role of Chance in Life and in the Markets, by Nassim Nicholas Taleb

Papers:

Recognising Risk in Financial Decision Making, by Tim Gorst and Anton Kapel (Institute of Actuaries of Australia Convention, 2007)