# The standard (but not-so-simple) formula

Ciara Russell contributed to the writing of this blog.

###### Standard formulae are common among mathematicians and scientists and serve a key purpose – to simplify a problem. Nowadays the phrase ‘standard formula’ doesn’t infer memories of how to calculate the area of a triangle or how to work out the speed of sound. Today standard formula goes hand in hand with Solvency II but is this standard formula simple?

In this blog we explore the difficulties that can arise under the standard formula approach.

## It started off simple

The evolved thinking towards risk measures led to the need for replacing Solvency I. The standard formula started as a factor based formula approach that was based on a percentage of reserves or another risk measure. Although this was definitely simple, it was not fit for purpose and failed to account for the specific risks that the insurance industry faces. Nowadays the standard formula has evolved into a more complicated structure.

## But they tell you how to do it?

Taking a layman’s view, there may not appear to be a problem – Solvency II requires insurance companies to calculate capital based on a formula approach for which there are thousands of pages of documentation explaining to the user how to use the formula. How hard can it be? Yes, this does make it sound easy in theory but anyone who has tried to read all of the documentation available will know that this is a challenge in its own right.

## The not-so-simple stuff

There are a number of aspects that can cause difficulties when using the standard formula, as summarised below.

### Data

The amount of data needed for Solvency II calculations is much greater than under the current regime. At a basic level, more data requires more validation and could increase the chance of data errors. Processes for collating data will need to be more robust.

For the market risk module, the lookthrough approach requires firms to gain access to line-by-line asset data from their fund managers rather than asset summaries. This is likely to be a new process for many firms, requiring changes to how asset data is handled and managed. Solvency II will require firms to move from using a single data point for each fund to potentially having over 100 fields for each asset in the fund – a colossal amount of information, especially for those with multiple funds.

### Calculations

The ICA has been a logical starting point for firms developing Solvency II models. However the approach under the standard formula is more complex than firms are currently familiar with in their ICAs. This requires new or re-worked systems and checking procedures, having obvious implications on the bottom line, costing time and resources. Here we have highlighted areas of the calculation that are a change to some insurers.

"Credit spread risk is the most complicated market risk calculation with the amount of capital depending on bond type, duration and credit rating."

The traditional ICA approach is to apply an upward or downward stress to the lapse and mortality/longevity assumptions. Under the standard formula, firms are required to apply the more onerous stress at each future point. The more onerous stress can change over time, requiring dynamic stressing on a per policy basis. For many, this requires developing a model that calculates reserves at frequent intervals, e.g. weekly or monthly, and adjusts the stress depending on which is more onerous. Calculations of this sort are likely to increase model run times.

Credit spread risk is the most complicated market risk calculation with the amount of capital depending on bond type, duration and credit rating. Derivative positions add an additional layer of complexity as further consideration needs to be given to their impact under the shock scenarios. Firms will need to have a deeper understanding of the type of instruments they are holding so that the correct credit shocks can be applied.

In addition, counterparty risk is particularly difficult to assess as exposures to single entities are not always obvious from asset listings. The problem is compounded when multiple asset managers are used or where a pension scheme needs to be included. Firms will need to develop a means of identifying the same counterparty both within and across funds.

The calculation of the risk margin is complicated and circular. With five possible methods of calculation to choose from, which in principle range from simple to a more complex calculation, it can be difficult to choose which one is best and how to justify it. At the more complex level, firms are required to project their risk margin for current business into run off, a difficulty in itself if they are struggling to calculate it at the valuation date. It is likely to require more run time of systems and thorough checking.

The need to value the risk of a pension scheme on the balance sheet is a new area. Keep a look out for our blog on pension scheme risk under Solvency II which will be released soon.

### Understanding the numbers

Understanding the full standard formula calculation and the drivers behind the SCR requires the calculation to be viewed holistically. Collating the information, including additional input data and calculations will require more robust audit procedures.

A key requirement under the internal model approach is meeting the use test. Although this is not a formal requirement for firms using the standard formula approach, the ORSA and general best practice is likely to mean insurers want to embed the standard formula calculations into their business planning and decisions. The Board and management will be interested in what the numbers mean for their strategy and the drivers behind the SCR. For this purpose, the outputs of the calculation need to be user friendly. Data visualisation techniques may be useful and these will need to be developed.

### Is it simple?

We agree that in principle the standard formula approach should be simple and usable for many UK firms. It is cheaper to build and run than an internal model and likely easier implemented, with less justification of the parameters required.

As noted, there are many practical considerations to the approach including collating data, increased modelling and the need for user friendly outputs. All of these take time and resources however these are limited. Firms face tight reporting deadlines during the preparatory phase, when reporting alongside Solvency I, and in 2016 onwards when reporting timescales are set to reduce each year by 1 week until 2019. Having systems in place now and having a run through will help to smooth out any issues at an earlier date.

The insurance team at Barnett Waddingham has developed a user-friendly tool, SIIMPLIFY. This performs SCR calculations using the standard formula approach, making capital calculations and reporting easier. SIIMPLIFY makes data entry clearer, collates calculations into one place and offers both numerical and visual user friendly results.