### Difference between Diversified and Undiversified SCR

**Difference between Diversified and Undiversified SCR –
Solvency II**

Before reading this article, kindly read the following 2 articles to make the most sense out of it:

- Solvency II SCR is a Value at Risk measure, it can be calculated via Standard formula as well as via Internal Model

- VaR is calculated for each component risk, then the diversified
SCR is determined with reference to the correlation between each component.
This is done by taking the sum over all risks of the square root of the product
of their SCRs multiplied by the correlation coefficient

- Broadly speaking, suppose you are a group Insurer with 4
entities across the globe named A,B,C and D

- All four of them
have SCR has $100 each. Then at Group Level your SCR is definitely less than
$400 because we have to allow for diversification via correlation matrices.

- Diversification occurs wherever the risks are not
perfectly correlated. (Hedging would occur where they were negatively
correlated.) In EIOPA's case they have defined a correlation matrix for each
risk type.

- A numerical example might help, say a company writes only
term insurance business and invests only in equity (with no default risk for
simplicity). Let their market risk component of SCR, SCR_m, be $20m and their
Life component of SCR, SCR_L, be $10m (which would have been calculated by the
company). The correlation between these two risks is defined by EIOPA to be
0.25.

The basic SCR before diversification is $30m i.e. 20+10

The diversified SCR is calculated as the sum over all (both)
risks as follows:

SCR = SQRT( Corr_m,m * SCR_m * SCR_m + Corr_m,L * SCR_m * SCR_L

+ Corr_L,m * SCR_L * SCR_m + Corr_L,L * SCR_L * SCR_L )

= SQRT( 1 * 20 * 20 + 0.25 * 20 * 10 + 0.25 * 10 * 20 + 1 *
10 * 10 )

= $24.5m

- So there is a diversification benefit of $5.5m as the
diversified SCR is that much lower than the undiversified SCR.

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