Solvency II: The conventions of the standard model and possible adverse effects

The Solvency II framework will change the way insurance companies address the investments performance in risky assets, by adding a new parameter to the traditional risk / reward tradeoff ....

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What is the SCR ?

Solvency II requires a rigorous control of extreme risks, via a capital requirement to cover the various risks faced by European insurance companies.
This capital requirement or SCR (Solvency Capital Requirement) is given by a 1-year VaR 99.5%: It is the minimum amount of capital that the insurer should have to cover potential losses over a one-year period with a probability of 99.5% (even though commitments may be for 10 years ...)
The SCR covers all the risks faced by the insurance company: market risk, but also the counterparty risk, operational risk, death risk, survival risk...

The SCR is an asset-liabilities directive: here we focus only on assets, thus before any liabilities effects that are unique to each company insurance. Moreover, we focus on the Market SCR which is the regulatory capital required to cover the impact on investments in risky assets, and whose main components are given by shocks on rates, spreads, equities and currencies. For simplicity we will call them thereafter Rate SCR, Spread SCR, Equity SCR and FX SCR. Those intermediary SCR do not constitute regulatory capital but are used for the calculation of the final SCR after reintegration of liabilities.

What SCR consumption per asset class?

For each asset class, the SCR is calculated by applying instantaneous shocks on underlying and estimating the impact of these shocks on the valuation of financial instruments of the given asset class. The methodology presented here is the standard model, but insurers may choose to use an internal model.
For rate instruments, we need to compute two SCR, one for the rising rates scenario and another one for the falling rates scenario.
Upward and downward shocks on the yield curve are expressed in percentage of the level of rates and change according to maturity.
These shocks are applied to the zero coupon swap curve of the base currency. For example, for a 10-year zero-coupon euro swap rate of 3.46%, the shock to be applied in the scenario of rising interest rates is 42% * 3.46% = 1.45%.

As the shock is applied to the swap curve, it is the same for all the states of the euro area. Thus, a German bond and an Irish bond with the same maturity will have very close SCR!

The SCR of a bond in case of rising rates is given by the difference between the bond price and the price recalculated from the curve with upward shock.
For example, the Rate UP SCR of a 10-years bond is 11%.

Equities are split into two groups: "Global" equities (European Union or OECD) and so-called "others" equities including equities not belonging to OECD, unlisted equities, private equity, commodities and alternative investments. The historical study which uses data starting in 1970 estimated an annual stress of 39% for the "global" and 49% for the "others ". This shock is supplemented by an adjustment mechanism based on the position in the cycle in order to reduce the SCR around the bottom of the cycle where the likelihood of an increase is significant, and to increase the SCR around the top of the cycle where the probability of falling is important. The equity shock is thus adjusted by + / -10% (from 29% to 49% for "global" equities, from 39% to 59% for "others" equities) given the position within the cycle. This adjustment is computed using the MSCI World. Since mid-November, the "global" equities SCR is at 49% - highest value -

The total Equity SCR is computed by aggregating the "global" SCR and "others" SCR assuming a correlation of 0.75

The Credit SCR depends on the sensitivity and the rating of credit positions. There is neither credit SCR for European Union’s states, nor for the AAA-rated, provided they issue debt in their local currency. Shocks applied to credit spreads are not the same for investment in physical securities and CDS. As shown in the table below, there is a scenario for upward and downward shocks on derivate spreads whereas there is only a scenario for upward shock on physical securities spreads.

Upward spread shocks on CDS are much higher than those on physical securities. The lower the rating is, the more important is the gap.

The Credit SCR is computed by multiplying the shock in spread by the sensitivity of the instrument. For example, for a paper with sensitivity equals to 8 and BBB rating, the SCR is 8 * 2.50% = 20%, whereas the same investment using CDS exhibits a SCR of 8 * 4.50% = 36%.
We can see here that long-term credit held by insurers’ portfolios is strongly penalized by Solvency II

Let’s Note also that shocks on investment grade are more aggressive than those on High Yield. The current shock on the iTraxx Main 5Y is around 350bp, the one on the iTraxx Xover is around 900bp. The level has already been seen on the Xover, but not the one on the Main!

The floor in sensitivity for physical securities penalizes short-term investments. As this shock is not applied to credit derivatives, for short maturities it may be cheaper to invest using CDS. For instance, for an AAA-rated issuer of 6 months maturity, even if the derivative shock (130bp) is greater than the securities shock (90bp), it is cheaper, in terms of SCR consumption, to invest using CDS. This is not the case for a B-rated - or less - issuer

How do SCRs of various asset classes change given market conditions?

Shocks applied to the yield curve are expressed in percentage of rates level. The lower the rates are, the lower the impact will be. The chart below shows the change in rate "UP" SCR given the market environment.

In the current environment of low rates, a potential rise in rates implies a double risk: losses on bond portfolios and an increase of the SCR. Of course this point depends also on the ability to absorb liabilities.

The Equity SCR changes given differences between the MSCI World and its 3-years moving average (mechanism called "dampener"): this very important point can still be updated by the authorities.

In 2004-2005, the increase in SCR occurred in a context of bull markets (the deviation from the moving average gets lower, thus increasing the adjustment factor and therefore the SCR). However, since the beginning of 2010, the MSCI World performs while the Euro Stoxx 50 underperforms. The increase of SCR for European equities comes in the context of a bear market. The lack of stability of the Equity SCR is constraining, beyond its already penalizing level. However, the Credit SCR is much more stable because the shocks are expressed in absolute level of spreads: for a given rating, the volatility of the Credit SCR is almost zero.

How to compute the SCR of a portfolio?

For each portfolio, we first compute intermediate SCR (Rates up, Rates down, Credit, Equity, Fx etc.) by aggregating the intermediate SCR of the various positions (transparency approach as far as possible).

The market SCR is calculated by aggregating the intermediate SCR of different assets classes included using correlation matrices in both rising and falling rates regimes. Here again, extreme levels of correlations are used and diversification is limited as the correlation levels suggested by CEIOPS are much higher than those observed. For instance, the correlation between bond and equity may go up to 0.5, a level never reached even in 1994. Finally, the portfolio market SCR is the maximum between the market SCR assuming rising rates and the one assuming falling rates.

What are the research topics related to Solvency II?

The Solvency II framework will change the way insurance companies address the investments performance in risky assets, by adding a new parameter to the traditional risk / reward tradeoff. It leads to two research topics: Updates of asset allocation models to take into account the SCR and the search for investment solutions that optimize the SCR constraint. We are working closely with both management teams and sales on these two topics.

Noémie Hadjadj-Gomes , February 2011

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