3.3 Equity

3.3 Equity risk

Equity risk is the risk of adverse change in the value of capital resources due to unexpected fluctuations in the level or volatility of market prices of equities.

A volatility stress.
Segments i., iii. and vi. are subject to a Neutral Adjusted Dampener (NAD) as described in section 3.3.3.6.
In terms of aggregation, equities in each of the six segments are first subject to a separate stress. The results of those stresses, i. and ii. under ‘Equity in developed markets’, iii. and iv. in ‘Equity in emerging markets’, ‘Hybrid debt/preference shares’, and ‘Other equity’ are aggregated using a correlation matrix. The result of the volatility stress is added to the aggregate result of the level scenarios.

The stress factors have been determined as the average result of the four methods described below:

The calibration for infrastructure equity was determined by reference to the calibration to listed equity, using a three-step approach:

a. Step 1: calculate relevant 99.5% VaR using the three methods described below, over a common time period, for infrastructure equity on the one hand, general equity on the other hand.
b. Step 2: determine a relativity factor for infrastructure, equal to the ratio between the 99.5% VaR for infrastructure and general equity as calculated in Step 1.
c. Step 3: apply the relativity factor determined in Step 2 to the stress factors applicable to listed equity, as calculated in section 3.3.3.1.

The three methods used under Step 1 are Methods 2, 3 and 4 described in section 3.3.3.1.1, adjusted to remove the effect of the drift. Those methods are specified below as Method 2 bis, 3 bis and 4 bis:

Since the inception of the ICS, a specific category has been created for hybrid debt and preference shares. Stress factors for these assets are determined with reference to credit risk stress factors for corporate and reinsurance bonds with a 10-11-year maturity, with a correction to account for a higher Loss Given Default assumed for hybrid debt (75% for investment grade hybrid debt – ICS RC 1 to 3 – and 90% for non-investment grade) than for senior debt (45%).
In addition, out of prudence, ICS RC 6 and 7 have been merged for hybrid debt and preference shares, attracting an equity-like stress factor (35%).

Stress factors are determined for three different asset classes, using the same methodology as used for listed equity, described in section 3.3.3.1.1.
The three asset classes chosen are:

The three stress factors are then combined into one using the following weights, which were chosen based on expert judgement:

Based on time series modelling of the VIX index (index of 1-month implied volatilities) with different combinations of ARMA and GARCH models, the 99.5% VaR of the relative increase in 1-month implied volatility has been determined to be 210%.
Separately, based on a random walk model, the shape of volatility 99.5% VaR stress factors depending on the tenor has been determined to be as follows:

Option term (months)	1	3	6	12	24	36	48	60	84	120	144	180
factor(t)/ factor(1)	1	0.653	0.533	0.437	0.382	0.350	0.332	0.314	0.288	0.261	0.233	0.221

Under the assumption of an initial flat term structure of volatility at 20%, the levels of absolute volatility upward stresses are as follows:

Option term (months)	1	3	6	12	24	36	48	60	84	120	144	180
Factor	42%	28%	22%	18%	16%	15%	14%	13%	12%	11%	10%	9%

The objective of the Neutral Adjusted Dampener (NAD) is to dampen the volatility of the solvency position of IAIGs resulting from market changes, reducing the risk of procyclical investment behaviour of the IAIGs, such as fire sales. Moreover, during periods of market exuberance, the increase of the equity risk charges is expected to increase the resilience with regard to future downturns.
The Neutral Adjusted Dampener is added to the raw level Equity risk charges for the following three level scenarios specified by segments of assets:

The NAD is calculated using the following formula, for each of the above three level scenarios:

NAD

\Big[a\times (\cfrac{CI_i-AI_i}{AI_i}-b) \Big]_{-c}^{+c}

a. $CI_i$ = Current Index value for category $i$
b. $AI_i$ = x years moving average index for category $i$
c. $c$ = This parameter provides a corridor to limit the impact of the NAD in extreme market conditions.
d. $a$ = This parameter has the impact of dampening the NAD and therefore prevents a binary behaviour (either $+c\%$ or $-c\%$ )
e. $b$ = This parameter aims to address the drawback whereby the NAD would always be positive and increasing in a positive accelerating market, even if the market change is a moderate/normal increase.

a, b, c and x are similar for the above three level scenarios and have been set based on expert judgement, in order to respond to the following targets:

a. The NAD should represent a positive and negative adjustment around the same number of times over a sufficiently long period of time, set between May 2000 and September 2022.
b. The average NAD value should be as close to zero as possible over a sufficiently long period of time, similarly set between May 2000 and September 2022.

The indices used for the purpose of the NAD calibration were the same as the ones used for determining the shocks of the raw level Equity risk charges.
As only one set of NAD parameters is defined for the above three level scenarios, the end- 2022 average equity allocation of IAIGs participating to the Monitoring Period data collection has been used for the purpose of the calibration, ignoring hybrid debt and preference shares:

3.3.3.7.1 Correlation between listed equity in developed and emerging markets

The empirical linear correlation between annual log-returns of the FTSE Developed index and FTSE Emerging index is 69%, based on time series between 1995 and 2015. This value has been rounded up to 75% in the Equity correlation matrix.