Solvency Analytics News

In a nutshell

Currently, standard fund reporting templates do not require aggregate figures on Solvency Capital Requirements (SCRs). We propose a conservative SCR aggregation that may be useful to insurance companies who are interested in a simple figure of a fund’s Solvency II risk profile.

The most widely used report, the Solvency II tripartite template, is designed to be on holding level and does not contain aggregate SCR figures at all. This is because SCRs are aggregated once all assets (and liabilities) of the insurer were ‘looked-through’. An SCR aggregation on fund level is difficult to interpret as its contribution to overal company SCR depends on the overall risk the insurance company is exposed to.
However, it is possible to caculate the upper bound or ‘worst-case’ SCR contribution that a fund can have to a company’s SCR. For further details refer to our working paper. We believe that SCR aggregation on fund level can be a useful information to insurance companies when screening funds from a broad universe. Moreover, it is likely not to require a non-disclosure agreement which would be necessary when reporting figures on holdings level.

We show that the maximum SCR contribution – independently from the risk exposure of an insurance commpany – is given by

$\text{Solvency II risk profile}= \begin{cases} \text{low},& \text{if } SCR_{maxcontr}\leq \lambda_1\\ \text{medium},& \text{if } \lambda_1 < SCR_{maxcontr}\leq \lambda_2\\ \text{high},& \text{if } \lambda_2 < SCR_{maxcontr}\\ \end{cases}$

with
$$SCR_{maxcontr} = \sqrt{\boldsymbol x’\boldsymbol C_{A=0.5}\boldsymbol x}$$

and
$$\boldsymbol C_{A=0.5} = \left[\begin{array}{cccccc} 1 & 0.5 & 0.5 & 0.5 & 0.25 \\ 0.5 & 1 & 0.75 & 0.75 & 0.25 \\ 0.5 & 0.75 & 1 & 0.5 & 0.25 \\ 0.5 & 0.75 & 0.5 & 1 & 0.25 \\ 0.25 & 0.25 & 0.25 & 0.25 & 1 \end{array}\right] \, .$$

The columns and rows of $\boldsymbol C$ represent Interest rate, Equity,
Property, Spread, and Currency and $\boldsymbol x$ is the vector of the fund’s market-value aggregated sub-SCRs.
The thresholds $\lambda_1$ and $\lambda_2$ define the levels that categorise SCR contributions into low, medium,
and high. For simplicity and transparency, we suggest to take round numbers, e.g. $\lambda_1$ equal to 10%, $\lambda_2$ equal to 30%.

Note that a fund’s effective SCR contribution is equal to the maximum SCR contribution if a company’s sub-SCRs are proportional to the sub-SCRs of the fund. This is intuitive as the fund does not provide additional diversification to the risk exposures of the insurance company.