# Equity investments, symmetric adjustment updates, and Solvency II ratio stability

In early 2024, the European Council and the European Parliament published their agreed amendments to the Solvency II Directive. This briefing note summarizes the amendment to the symmetric adjustment (SA) of the Standard Formula equity risk module and provides insights into the Solvency II ratio stabilizing effects of the symmetric adjustment.

## Introduction

In this note, we analyze the impact of equity shocks on the Solvency II ratio for insurers with equity investments operating under Standard Formula. We demonstrate that for such an insurer an equity allocation can be selected that keeps the Solvency II ratio approximately stable under small and medium-sized equity shocks, given a certain target level for the Solvency II ratio. We elaborate on additional conditions needed to obtain this stability and identify when unintuitive behavior may be triggered. The analysis focuses on typical risk profiles of Dutch non-life insurance companies.

We also explain that the symmetric adjustment’s wider corridor, as agreed in the amendments to the Solvency II Directive, has limited impact on our observations compared to the current Solvency II framework.

## Background on symmetric adjustment

The symmetric adjustment (SA), often referred to as the equity dampener, was introduced to mitigate the impact of sharp decreases in stock markets on the Solvency II ratio, avoiding potential “fire sales.” The mechanism ensures that the impact of changing equity markets on own funds is offset by changes in the Solvency Capital Requirement (SCR) for equity investments under the Standard Formula. This is accomplished by adding the symmetric adjustment to the equity shock used for equity risk SCR computations. The value of the SA is derived from the relative deviation of the current European Insurance and Occupational Pensions Authority (EIOPA) equity index value from its three-year average.^{1} The underlying justification is the mean reversion that, to a certain degree, has been observed historically.

In the published amendments to the Solvency II Directive, the corridor for the symmetric adjustment is expanded from the existing range of [-10%, 10%] to a broader range of [-13%, 13%]. The rationale behind this change is to enhance the ability of the adjustment to further mitigate pro-cyclical effects in the ratio by allowing for larger variations in the standard equity capital charge. In recent years the lower bound was for example reached during the initial outbreak of the COVID-19 pandemic.

## Background on Dutch non-life insurers’ equity allocation

In examining the equity allocations within the non-life insurance sector of the Netherlands, a pattern emerges. Insurers with less total assets display a diverse range of equity allocations. Larger insurers typically allocate well below 20% of their assets to equities. This is visible in Figure 1, which compares the equity allocation^{2} against total assets for selected Dutch non-life insurers per year-end 2023 using Solvency and Financial Condition Report (SFCR) data. This signals that larger insurers seem to adopt a more cautious approach to equity investments, where larger asset pools are diversified across a spectrum of other investment options. Overall, we conclude that a wide range of viewpoints on equity allocation sizes appears to exist across non-life insurers.

### Figure 1: Equity allocation for selected Dutch non-life insurers

## Equity investments and Solvency II ratio stability

Equity investments are a strategic instrument for insurers, with a key trade-off being the balancing of return versus risk and volatility. In practice, a varying range of additional factors will influence equity investment decisions. A high-level constraint or risk appetite for equities can be formed by considering their impact on solvency ratio volatility. The SA aims to mitigate exactly this volatility. To get further insight into the SA’s stabilizing effects, we will analyze consequences of various equity allocations on equity-driven ratio volatility.

As a starting point of our analysis, we optimize the equity allocation for local ratio stability. More specifically, starting with an assumed target Solvency II ratio level, we can determine the equity allocation for which the Solvency II ratio is immune to small equity shocks.^{3} This happens when own funds and the SCR move together in the right proportion under equity shocks. Indeed, on the one hand, equity shocks impact own funds through decreases in the value of the equity portfolio. On the other hand, equity shocks influence the equity risk SCR through changes in equity portfolio size and changes in the symmetric adjustment. The equity risk SCR movements cause total SCR movements, but in a dampened way due to diversification effects with other risks.

A key assumption that we will make going forward is that the actual equity investments are closely aligned with the EIOPA equity index underlying the symmetric adjustment. Without this condition the ratio stabilizing effect of the SA can be significantly different, as we will show below.

Figure 2 illustrates the relationship between the target ratio and the equity allocation needed to maintain local stability. To achieve this initial target ratio, sufficient own funds are needed to support the capital strain attached to the equity risk and, in practice, it might take time to build up this amount of own funds. The graph in Figure 2 presents three types of non-life insurer risk profiles with varying relative levels of non-life underwriting risk.^{4} The graph reveals an inverse relationship: as the target ratio increases, a lower equity allocation is necessary to sustain a stable ratio.

For example, point (1) on the middle line shows that, for a target ratio of 155%, an equity allocation of 53% is adequate for stability. However, at a target ratio of 210% the equity allocation must be significantly reduced to 18% to maintain stability, as indicated by point (3).

Intuitively, higher target ratios allow for larger equity allocations because more buffer is available to absorb equity volatility. Our analysis demonstrates that aiming for ratio stability creates an opposite incentive, that is, lower equity allocations at higher ratio levels. Without a symmetric adjustment, the incentive for ratio stability would still be in the same direction, but the adjustment helps to achieve ratio stability for lower equity allocations.

Additionally, Figure 2 shows an inverse relation between the proportion of non-life underwriting risk and the required equity allocation needed for ratio stability. The reason is that ratio stability requires “matched” sensitivities of own funds and SCR. As a result, a lower equity allocation is needed for ratio stability when the SCR becomes less sensitive to equity, and vice versa. For example, an increase in non-life underwriting risk SCR ensures equity risk SCR diversifies better, leading to a lower SCR sensitivity to equity. This drives the inverse relationship. Typically, risks that diversify well are candidates for increased exposure. Again, aiming for ratio stability provides an incentive in the opposite direction.

### Figure 2: Required equity allocation given target ratio level ensuring stable ratio sensitivity under small equity shocks

## Understanding equity sensitivities

Figure 3 shows ratio sensitivities for a range of equity shocks, corresponding to the starting ratio positions labelled as points (1), (2), and (3) in Figure 2. These sensitivities provide more insight into the meaning of Figure 2, which focuses on ratio stability for small equity shocks. We observe that for small equity shocks the ratio is indeed approximately stable. The ratio impacts are limited and almost symmetric up to shock sizes of approximately 23% in either direction. However, there is a steep drop and increase in the ratio when the shock exceeds 23% down and up, respectively. This effect occurs because the equity shocks have surpassed the limits of the SA corridor. The symmetry in the SA effect is driven by our assumption of a starting SA of 0%^{5} and using the amended SA corridor of [-13%, 13%]. We will return to the SA corridor below.

### Figure 3: Ratio sensitivity under equity shocks under varying starting positions for balance sheet with medium non-life SCR vs. other SCR

To illustrate ratio sensitivities for different equity allocations, but with the same starting ratio,^{6} we included Figure 4. The yellow line in Figure 4 aligns with the yellow line in Figure 3, which corresponds to the situation where the equity allocation is optimized for ratio stability under small equity shocks. The other equity allocations in Figure 4 reveal the consequences of different starting equity allocations, resulting in increased variability of the ratio in response to equity shocks. Interestingly, with higher equity allocations, an asymmetrical countercyclical effect can appear, where the ratio increases under certain equity down shocks. This is caused by an SCR that reduces “faster,” due to the SA in particular, than the own funds reduce.

The black line represents a scenario without the SA, where equity shocks would have a more linear and pro-cyclical impact on the ratio. Due to the time decay of the weighted average in the SA, if equity markets stay constant after the initial shock, then the ratio will gradually interpolate from the yellow line toward the black line. This also shows that ratio sensitivity can be considerably different without SA effects. Differences in SA effects can, for example, be caused by basis risk between the own portfolio and the benchmark portfolio underlying the SA.

### Figure 4: Equity ratio sensitivities for various equity allocations and fixed starting ratio

## Equity sensitivities under wider SA corridor

In summary, widening the symmetric adjustment corridor from [-10%, 10%] to [-13%, 13%] has a reasonably limited impact on equity sensitivities compared to the current situation. This is illustrated in Figure 5, with the yellow line aligning across Figures 3 to 5. Additionally, we included SA values under various equity shocks. The analysis reveals that the 10% corridor is breached at equity shock sizes beyond approximately 20% up and down, whereas the new corridor is breached at shock sizes of approximately 23% up and down. The most notable difference for the ratio sensitivity is a delayed increase for strong positive returns. For equity downturns the difference is limited. Reflecting on the purpose of this amendment to the SA, it becomes apparent that the adjusted corridor makes a limited contribution to its intended goal of enhancing the adjustment's capacity to mitigate countercyclical effects.^{7}

### Figure 5: SCR ratio sensitivities for equity and SA with different corridors

## Conclusion

We conclude that symmetric adjustment mechanics can narrow down the possible equity investment strategy considerably, depending on insurers’ appetite for ratio volatility. Indeed, our analysis shows that the symmetric adjustment allows for limited equity sensitivities of the ratio for common risk profiles and target ratio levels. This means that the mechanism can promote equity investments while avoiding pro-cyclicality.

However, the symmetric adjustment comes with caveats. First, the volatility dampening only works for equity investments close to the EIOPA equity index driving the symmetric adjustment. Otherwise, it can even increase volatility of the ratio due to basis risk between the own portfolio and the index. Second, the dampening of volatility is effective up to shock sizes of approximately 20%. Beyond that point it creates a “cliff effect" in the ratio sensitivity, especially for larger equity allocations. Third, if equity markets remain stable for a longer period after a shock, the SA dampening will disappear over time and the larger undampened ratio impact still realizes. The last two points can only be managed by restricting the maximum equity allocation.

If you have any questions or comments on the information above or want to discuss further balance sheet management or asset-liability management (ALM) solutions, please contact your usual Milliman consultant.

^{1}
More specifically, the symmetric adjustment is calculated as *SA = 0.5 * ((CI - AI) / AI) - 8%)*, where *CI* represents the current level of the EIOPA equity index and *AI* denotes the weighted average of the daily levels of the index over the last 36 months. EIOPA’s equity index consists of an average of various common equity indices from across the world.

^{2}
We show equity allocations excluding collective investment undertakings, which sometimes also include equity investments but are not split out as equity in SFCR data. Also, a split between equity type 1 and equity type 2 is not made available in SFCR data.

^{3}
This is computed by solving for the type 1 equity allocation that results in a zero derivative of the Solvency II ratio with respect to instantaneous equity shocks, where we assume that the starting ratio position aligns with the target ratio level. The considered equity exposure relates to general account, non-equity derivative investments, so analytic expressions are available. A zero derivative of the Solvency II ratio with respect to equity level shock requires (*OF/SCR) = (OF'/SCR')*, where the prime refers to taking the derivative with respect to equity. The *OF'* is driven by the equity portfolio size. The expression for *SCR'* is somewhat lengthy. Key drivers are the size of the equity portfolio size, the marginal equity diversification benefit, and the sensitivity of the SA to equity shocks.

^{4}
The average ratio between non-life SCR and other SCR for the low, medium, and high curves in the plot is given by 0.6, 0.8, and 1.1, respectively. This ratio varies across each plotted curve as all non-equity SCRs are kept constant, while the equity exposure is chosen such that a stable ratio sensitivity to small equity shocks is obtained. In the numbers shown, we assumed that effects of the loss-absorbing capacity of deferred taxes (LAC DT) are captured by taking 80% of the applicable tax rate.

^{5}
For non-zero starting SA, the equity sensitivity profile remains the same, but then the starting point would be shifted to the left or right of the horizontal middle of the graph.

^{6}
The different equity allocations result in different SCR levels. To ensure that the starting ratio is the same, the own funds also need to vary across the curves shown in Figure 4.

^{7}
Alternative changes to the symmetric adjustment could have been considered to address some of its key caveats, like the basis risk between the own portfolio and the EIOPA equity index, and the sudden impact of reaching the boundary of the SA corridor. For example, the basis risk for the volatility adjustment is partly mitigated by a Solvency II review proposal to allow for the own investment portfolio in its computation. This could also be effective for reducing basis risk for the SA. Moreover, the likelihood of reaching an SA threshold in case of very volatile equity markets could be decreased if the halving factor in the SA computation would be reduced.

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