Actuarial Sciences
Equity Risk under Solvency II
by: Hans Heintz & Timo van der Veen
All regulations induce both intended and unintended effects. The aim of Solvency II is clear, but certain
consequences of the regulation may lead to an undesirable situation. This article illustrates that regulations
imposed by Solvency II may not lower the risk for policyholders as much as intended. This is particularly true
with respect to the treatment of equity risk. The analysis of CEIOPS to measure equity risk, neglects a variety of
factors that are important for analyzing portfolio risk in the long-term. This article argues that the duration of
liabilities plays an important role in insurance companies’ risk profile, and that the requirements for equity risk
should explicitly incorporate this. Literature shows that as the investment horizon increases, stocks become less
risky while providing relatively high returns. This implies that capital requirements on equity must be decreasing
with the duration of liabilities of a life insurance company.
Introduction
The main objective of Solvency II is policyholder
protection by ensuring financial soundness of insurance
companies. The insolvency risk of an insurance company
must be reduced to at most 0.5 percent for the coming
year, leading to the requirement of holding a minimum
amount of capital. Investments in risky assets require
higher amounts of capital than less risky investments.
As the (1 year) volatility of stocks is higher than the
volatility on bonds, Solvency II considers equity to be
riskier than bonds.
Solvency II defines risk as the probability that
assets will be insufficient to cover liabilities during the
following year. This definition, however, does not take
the duration of the liabilities into account. This can be
problematic for life insurance companies with long term
liabilities. Solvency II requires them to use a mark to
market valuation of assets and liabilities. Mark to market
valuation introduces swings in their solvency ratios
as equity prices are volatile. But there is no reason to
liquidate investments in the short term if liabilities lay
in the far future. It therefore seems more reasonable to
require a life insurance company to meet its (future)
liabilities with a probability of 99.5 percent. This seems
like a nuance in formulation, but it is not. The difference
will become clear at the end of this article.
In his book ‘Stock for the Long Run’ Jeremy Siegel
argues that in the long run stocks bear less risk than bonds,
while they have a higher return. If true, Solvency II does
not only introduce adverse side effects, it also misses
its goal to decrease the risk for insurance companies.
Solvency II might bring the insolvency risk for insurance
companies to 0.5 percent for the year ahead, but this
could lead to a suboptimal asset allocation if a longer
time span is taken into consideration.
Multiple institutions saw their capital evaporate
during the financial crises of 2008. Regulators responded
by increasing the capital requirements. Low supply of
capital, combined with a high demand, makes capital
expensive as a mean for funding. However, if capital
is expensive and the capital requirements for equities
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AENORM vol. 19 (75) May 2012
are high, equity becomes unaffordable for insurance
companies. Accordingly, by implementing high capital
requirements for equity, Solvency II stimulates insurance
companies to reduce their investments in equity. The
change of asset allocation increases several risks in the
economy. The problem is that this increase in risk is not
measurable, but surely affects the policyholders.
Capital Requirements of Solvency II
The high capital requirements do not only make equity
unaffordable, they also incentivize insurance companies
to change their product mix. Products with a defined
benefit scheme become too expensive under the new
Hans Heintz
After graduating in business econometrics in
1995, Hans joined ING Barings to work within
the Trading Risk department. In 2000, Hans became account manager large corporate relations
at Deutsche Bank Corporate Finance. In 2006
Hans moved back to ING, where he helped to
establish a new model validation department.
In 2008 Hans together with three other partners
founded RiskQuest, an Amsterdam based consultancy firm specialized in mathematical models for financial solutions.
Timo van der Veen
In August 2012 Timo graduated with a bachelors degree in econometrics and operational research at the University of Amsterdam.
In September 2012 Timo started the master
financial econometrics at the UvA. In the
same month he joined RiskQuest to acquire
empirical competence in Risk management
and to write his thesis.
Actuarial Sciences
regulations. The market-consistent approach of Solvency
II values assets at current market prices. The liabilities
of defined benefit products are fixed for sometimes more
than 30 years, while the assets covering these liabilities
bear the risk of a sharp decline in prices every day. It
therefore seems attractive to transfer this risk to the
policyholder. Defined benefit products become rarer and
defined contribution products may be the new norm.
Danielsson et al. (2012) state that “market-consistent
valuation induces excessive volatility in solvency ratios
for insurers with matched long-term liabilities. Solvency
II should introduce measures recognizing the possibility
of temporary adjustments in required solvency ratios, to
facilitate carrying matched long-term promises.”
Solvency II does introduce a symmetric adjustment
mechanism1, which should cover the risk arising from
changes in the level of equity prices. If the equity
index (MSCI World developed index) is smaller than a
weighted average level of this index, the equity capital
charge will be lower than the standard capital charge.2
But according to Danielsson et al. (2012) “The proposed
countercyclical premium adjustment defines a valuation
concept with no economic foundations, and is thus easily
manipulated. It even fails to be countercyclical, as it
adjusts reserve requirements only in distress.” Although
the adjustment mechanism indeed discourages fire sales
of equities during an equity crash and thus pro-cyclical
effects on the equity market during the first few months
of a crisis, it does not prevent pro-cyclical effects if the
crisis has a longer time span.
The shift from equities to bonds will affect the
economy. As insurance companies (used to) hold a
notable share of Dutch stocks3, the portfolio shift to
bonds may depress the stock market prices. This shall
consequently diminish people’s wealth, which decreases
consumption; moreover it decreases the investments of
companies, since they will be less inclined to issue new
shares and invest the revenues in capital4. There exists
a variety of literature that endorses this relationship5.
Please note in this context that insurance companies are
highly appreciated shareholders as their long horizon
makes them stable partners. Since Dutch insurers invest
in Dutch companies, losing them as a shareholder is a
clear loss.
CEIOPS’s Model
The Dutch central bank (DNB) does not deny that
Solvency II gives the incentive to invest in short-term
bonds. When asked6 whether this incentive would not
be detrimental for the economy, DNB responded: “that
might be, but we need solid insurance companies”. The
assumption behind this statement is that a larger amount
of short term bonds makes an insurance company
more solid. We are, however, not convinced that this
assumption holds in the long run.
The analysis of risk chosen by CEIOPS determines
the cost for holding equity. It is therefore important to
assess this model. There are some complications in the
measurement of risk. Besides the fact that all quantitative
analyses rely on the implicit assumption that information
from the past resembles information about the future,
the form of the model on which the test are based will
influence the outcome. It is therefore crucial to have good
arguments that justify the specification of the model.
This specification, again, is an unavoidable assumption
in every quantitative model. For that very reason it is
important to substantiate the specification of the model
not only with economic theory, but also with common
sense. The lack of the latter in econometric models is
more often considered the reason for the financial crisis.
Within CEIOPS there were three proposals for the
equity charge for global equities, each proposal based
on the usual Value at Risk (VaR) of different analyses.
The choice for the basis7 level of capital requirement
of 45% was grounded on the first proposal, supported
by the majority of member states. The analysis for this
proposal used the frequency distribution of the MSCI
World Developed Markets Price Equity Index annual
returns from 1973 to 2009. In this analysis CEIOPS has
chosen to “take a rolling one-year window in order to
make use of the greatest possible quantity of relevant
data.” Although the possibility of distortion resulting
from autocorrelation is mentioned, the model does not
correct for it. This is quite strange, as it is known that
if data contains autocorrelation and the model does not
adjust for it, inference on the outcomes is unreliable.
Another invalid assumption underlying this model is that
the variance of equity is constant over time. Also note
that the time interval is 1 year, so that it is assumed that
the risk of equity is equal to the 1 year risk, irrespective
of the investment horizon.
1. The symmetric adjustment mechanism tries to reduce pro-cyclical effects during an equity crash, by reducing the capital
requirements during such a crash.
2. If the index is higher than the weighted average level, the equity charge will be higher than the standard capital charge.
Moreover If the index is higher than the weighted average level, the equity charge will be higher than the standard capital.
3. Their total portfolio is worth about 300 billion Euros
4. Tobin’s q
5. See for example: Poterba, J. (2000), and Davis, M., and M.G. Palumbo. (2001).
6. In “het Financieele dagblad Monday 10 December 2012”
7. Basis in the sense that there is no adjustment from the symmetric adjustment mechanism
AENORM vol. 19 (75) May 2012
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Actuarial Sciences
Optimal Asset Allocation
Consider a stylized example: suppose that each year
a certain asset either has a return of 20 percent with a
probability of 95 percent or a return of -50 percent with
a probability of 5 percent. If an insurance company has
liabilities for the next year, the capital requirement must
certainly be 50 percent. But if the insurance company
has a liability to meet 30 years from now, the capital
requirement of 50 percent is not adequate. Using the
binomial distribution one can calculate the probability
that more than 5 crashes occur in 30 years. This
probability is less than 0.58 percent and even if 5 of these
crashes occur the annualized return is 3.7 percent (i.e. the
monetary value of assets has grown with 200 percent in
30 years).
Of course the return of an asset is not distributed as
mentioned, but this example does show some important
characteristics in the measure of risk that are left out
in the analysis of Solvency II. Jeremy Siegel (2006)
argues that in the long run stocks bear less risk than
bonds, while they have a higher return. Bonds are risky
in real terms, because they give a negative return if the
inflation turns out to be higher than the interest rate of
the bond. Currently, Dutch Government Bonds already
have negative real yields, i.e. capital invested in bonds
will erode if the inflation keeps at the current low level
of 1.7%.
Siegel uses historical data from the US to display
(see figure 5) the best and worse after-inflation returns
for stocks, bonds and bills from 1802 to 2006 over
holding periods ranging from 1 to 30 years. Stock returns
are measured by dividends plus capital gains or losses
available on a broad capitalization-weighted index of
U.S small and large stocks.
Diebold (2012) argues that time-varying volatility
can play a crucial role in portfolio management: “The
amount of shares in an optimal portfolio depends on
variances and covariances of the assets in the portfolio.
In particular, if an investor wants to minimize portfolio
return volatility subject to achieving target return ‘µp’,
she must minimize w’∑w subject to w’µ = µp, where ‘w’
is the vector of portfolio shares, µ is the conditional mean
vector of returns and ‘∑’ is the conditional covariance
matrix of returns. If ∑ is time-varying, then so too are
optimal portfolio shares”. So if the volatility changes
due to an adjustment in measuring the volatility with
respect to time, the optimal allocation changes as well.9
Figure 2: Although the annualized standard error is high for
short time periods such as a year, if the holding period is 25
years the standard deviation is cut by half.
Campbell and Viceira (2002) find that the volatility of
equity decreases as the horizon increases (see figure 1).
Hence the risk for equity measured in annualized standard
deviations is decreasing in the holding period. On basis
of these conclusions we think it is more appropriate to
use an alternative conduct in the measurement of capital
requirements. One in which the basis capital requirement
is decreasing in the average liability duration of the
insurance company.
Conclusion
Figure 1: This figure shows the best and worse afterinflation returns for stocks and bonds from 1802 to 2006.
Solvency II intends to protect policyholders. However,
mark-to-market accounting and the application
of the Solvency II capital requirements may have
counterproductive effects by stimulating life insurers
to opt for less volatile investments, irrespective of their
liability structure or duration. This may lead to an excess
demand for fixed income instruments, as currently
observed in recent Dutch Government Bond issues. In
real terms, yields are negative and expose the investor
to inflation risk. As a consequence, life insurers will
make less strong guarantees and hence opt for defined
8. 0.33 percent
9. This part of the paper of Diebold, however, was written to argue that if the volatility changes from time to time, you should
adjust the portfolio dynamically.
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AENORM vol. 19 (75) May 2012
Actuarial Sciences
contribution plans rather than defined benefit. In fact,
investment risk is shifted to the policy holders.
The combination of mark-to-market accounting and
measuring portfolio risk as short term volatility is, in
our humble opinion, not appropriate. Literature shows
that at a longer horizon equity prices are less volatile
and that the equity returns exceed those of other asset
classes. Hence, we argue that Solvency II should take the
investment horizon into account as well. This horizon is
largely based on the duration of liabilities.
References
Campbell, J. and VICEIRA, M., 2002, Appendix to
‘Strategic Asset Allocation: Portfolio Choice for
Long-Term Investors’. Oxford University Press, USA.
Davis, M., and M.G. Palumbo, 2001, A Primer on
the Economics and Time Series Econometrics of
Wealth Effects, Federal Reserve Board Finance and
Economics Discussion Series No. 09.
Diebold, F.X. 2012, 100+ Years of Financial Risk
Measurement and Management.
Jon Danielsson, Roger Laeven, Enrico Perotti, Mario
Wüthrich, Rym Ayadi, Antoon Pelsser, 2012,
Countercyclical regulation in Solvency II: Merits and
flaws: http://www.voxeu.org/ar-ticle/countercyclicalregulation-solvency-ii-merits-and-flaws.
Poterba J., 2000, Stock Market Wealth and Consumption,
Journal of Economic Perspectives, 14(2), pp. 99-119.
Siegel, J., 2006, Stocks in the long run Mc Graw Hill.
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