Sponsored by and Solvency II Risk Management Forecasting Presenter(s): Peter M. Phillips
Sponsored by
and
Solvency II Risk Management Forecasting
Presenter(s):
Peter M. Phillips
Aon Benfield Securities
Proprietary & Confidential
Solvency II Risk Management ForecastingPeter M PhillipsEquity Based Insurance Guarantees 2015Nov 17, 2015 8:30 – 9:15 a.m.
Prepared by PathWise Solutions Group
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Aon Benfield Securities
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Solvency II—Overview
– Solvency II is the new regulatory framework for the European Insurance Industry
– Solvency II consists of three pillars:
• Pillar I: quantitative requirements
♦ Technical provisions
♦ Solvency Capital Requirement (SCR)
• Pillar II: qualitative requirements
♦ Defines the risk management and governance framework that is used to identify and manage risk--ORSA
• Pillar III: reporting and disclosures
– Focus on market consistent valuation for both Assets and Liabilities
– Required capital is equal to the loss of a 1-in-200yrs event (VaR99.5%) over 12-month time horizon
– In this context dynamic investment or hedging strategies may help Insurance companies reduce their capital requirements and achieve better overall risk adjusted returns
3
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Solvency II—Balance Sheet
4
Market Value of Assets
(MVA)
Best Estimate of
Liabilities
(BEL)
Risk Margin
Solvency Capital
Requirement (SCR)
Excess Capital
When Own Funds falls below the Solvency
Capital Requirement (SCR), the insurance
company is considered insolvent
Solvency II Ratio is equal to the ratio of
Available Capital to the Solvency Capital
Requirement (SCR)
Aon Benfield Securities
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European Insurers’ Challenges—Poor Returns and Climbing Liabilities
5
− Realized General Account returns have been low while Liabilities have
increased as rates have fallen
Source: ESRB, June 2015
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European Insurers’ Challenges—Duration Gaps and Investment Spreads
6
− European life insurance companies have large net duration exposures
with high guaranteed rates for inforce business
Source: ESRB, June 2015
Aon Benfield Securities
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Solvency II—Issues and Challenges
– Liabilities are to be calculated based on “best estimate” assumptions without provisions for adverse deviations
– Many of these Liabilities are uncertain and have very long durations
– Assets are to be valued on a marked-to-market basis
– Any changes in value of Assets will be directly reflected in Own Funds and Excess Capital Levels
– Stochastic-on-Stochastic simulations are required to correctly project future Assets and Liabilities in a market consistent manner
• This means dramatic increases in computation length and complexity
♦ Need for increased capital forecasting and visibility on drivers of the change in forecasted capital levels
♦ Incorporation of dynamic investing and/or hedging strategies make the simulations even that much more difficult
7
Aon Benfield Securities
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Solvency II – Case Study
– A European annuity product with guaranteed rate
– Backtest SCR levels using historical economic data from 2003 to 2015
– Project and forecast SCR 12-months into future using a stochastic-on-stochastic economic scenario generator
– Project SCR and run off a policy until maturity along one sample real world path
≈ 3.47 Million paths
≈ 299 Million paths
≈ 3.47 Million paths
Aon Benfield Securities
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Product Features
– Product: Lifelong Annuity with Guaranteed Survivors’ Pension
– Maturity: Age 60
– Guarantee Period: 20 years
– Payout Scheme:
• If the life dies before age 60, annuity payment starts at year of death for 20 years
• If the life dies after age 60 but before age 80, annuity payment continues for (20-x) years, x being the number of years that the annuity payments have been paid. (i.e. pays until age 80 as if the policyholder did not died)
• If the life dies after age 80, since 20 years of annuity benefit have been paid, the policy terminates at age 80,
– No surrender value
– Policyholder can stop the premium payment and consider the policy as “paid-up”, with reduced annuity and death benefit levels
– Premium is fixed over the lifetime of the policy
– At each time step, 3 states of a policyholder have to be modeled: an active, died, and paid-up state
9
Aon Benfield Securities
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Assets and Guarantee Return
– A portfolio of government bonds, corporate bonds, equities
– Assume an initial and constant allocation of Asset classes:
• 66.6% corporate bond fund
• 16.7% government bond fund
• 16.7% equity fund
– At each month end, the Asset portfolio automatically rebalances between these Asset classes to the initial fixed target allocation
– The guarantee rate for the policy premium is assumed to be 3.25%.
– The actual growth rate of the policy premium is max(Rt, 3.25%)
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Aon Benfield Securities
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Sample Policyholder
Policy issued: 1988-01-31
Date of birth: 1968-01-15
Valuation Date: 2003-01-31
Issued at age: 20
Valuation age: 35
Gender: Male
Guaranteed rate: 3.25%
Monthly benefit paid out: $3000
Calculated monthly premium: $300
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Historical Backtest with E.U. economic data (2003 ~2015)
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Aon Benfield Securities
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Historical Backtest Stochastic-on-Historical Simulation
13
Historical path
The j-th month for
SCR calculation
Historical economic
scenario
Projection based on the
realized information set
from j-th month historical
economic scenario using
1000 scenarios
# paths # time steps # Exp. Calc.
1 x 12.5 X12 x 23 X 1000 = 3.47 Million Unique Paths
Monthly projection based on a realized information set from Jan 2003 to July 2015.
At each month, 1000 scenarios are simulated based on the historical information.
For each path and step pair, 22 shocked and 1 base calculation are performed.
Each inner loop path projects the policy until maturity (Age 60).
Ran on 4 GPUs, and took 37 seconds to finish.
Ran on 4 GPUs, 37 seconds ~ 23500 paths per GPU per second
12.5 yrs1 2 3… … … …
…
Monthly time steps
…
Aon Benfield Securities
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Excess Capital and SCR movement
14
Financial
Crisis
Excess Capital is defined as Market value of Asset less market value of Liabilities less SCR:
XS Capital = MVA – MVL – SCR.
At each point on this graph,
SCR levels and Excess
Capital (XS Capital) levels
changes as time passes
and capital market
conditions change.
European
Debt Crisis
Note: during the 2 crises,
the excess capital for the
company falls below zero,
which would have rendered
this company insolvent.
Aon Benfield Securities
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Own Funds vs. SCR Plot
15
When Own Funds are less
than SCR, the Market Value
of Assets (MVA) is not
enough to cover the
Liabilities plus solvency
capital.
For example regulatory
intervention would have
happened at the point
circled in red.
Own Funds is defined as the difference between market value of Asset and market value of
Liabilities. Own Funds = MVA – MVL
Aon Benfield Securities
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Spread
16
During the financial crisis,
the spread between the
30yr and 10yr bond yield
became negative. The
insurance company holds
essentially a 10yr bond as
an Asset, while the Liability
duration was close to 30yrs.
When this spread contracts,
or becomes more negative,
Asset levels fall and
Liabilities increase.
The insurance company in
this case is long the basis.
It benefits if the basis
increases or goes up and
suffers if it falls.
Aon Benfield Securities
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Account Value Performance w/o Product Cashflow
17
The equity return was
very volatile over the past
12 years, while the bond
price index increase was
more steady.
σEquity = 16.6%
σTotal = 4.63%
σBond = 4.54%
Aon Benfield Securities
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Solvency Margin Ratio
The solvency margin ratio
is defined to be the ratio
of Own Funds to SCR.
𝑆𝑀𝑅 =𝑂𝑤𝑛 𝐹𝑢𝑛𝑑𝑠
𝑆𝐶𝑅
When SMR is less than
1.0, it means the Own
Funds are not enough to
cover the Solvency
Capital Requirement
(SCR) and extra capital is
needed.
18
SOS Forecasting with E.U. economic projection(2015~2016)
19
Aon Benfield Securities
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Future SCR Forecasting with Stochastic-on-Stochastic Simulations
Monthly projection based on projected paths from Aug 2015 to Aug 2016.
1000 Real world scenarios are use to project the future economic environments.
At each month in the next 13 months, 1000 inner loop paths are simulated for the SCR calculations.
Each inner loop path projects the policy until maturity (Age 60) with 22 shocked assumptions.
Ran on 16 GPUs, and took 2 min 14 sec ~ which is about 140,000 paths per GPU per second.
20
# paths # time steps # Exp. Calc.
1 000 x 13 x 23 x 1000 = 299 Million Unique Paths
Inner Loop Paths (1000)
0 1 2 3 ….
Real World Paths (1000)
Time Steps (13)
Shocks (22)
12
Aon Benfield Securities
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Future SCR Projection (Stochastic on Stochastic)
21
Simulated the Asset and Liability for 12 months into the future under a set of real world scenarios.
For each month, simulate Asset and Liability under the same set of scenarios until the end of the policy.
1000 outer loop scenarios were used and 1000 inner loop scenarios for each month in the future.
Status of the policy as of start of the simulation:
– Market Value of Asset: $ 579k
– Market Value of Liability: - $ 442k
– Solvency Capital Requirement: - $ 57k
– Excess capital: + $ 139k
Aon Benfield Securities
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SOS Projected SCR Distribution (EU 2015~2016)
22
SCR levels tend to be
low and asymmetric
over the next
12months.
The expected SCR
level is stable over the
next 12 months.
But very high levels of
SCR can also occur
towards the end of the
12 months.
Aon Benfield Securities
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SOS Projected Excess Capital Distribution (E.U. 2015~2016)
23
The excess capital
levels are somewhat
healthy over the next 12
months.
However, there are
some tail events with
excess capital levels
significantly under 0
One Path Policy Run Off (2015 ~ 2028)
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Aon Benfield Securities
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One Sample Path Stochastic-on-Stochastic Simulation
Monthly projection based on a projected path from Aug 2015 to maturity (Dec 2028).
At each month, 1000 scenarios are simulated based on the given simulated information from the previous SOS forecast.
For each path and step pair, 22 shocked and 1 base calculation are performed.
Each inner loop path projects the policy until maturity (Age 60).
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1 sample path
The j-th month for SCR calculation
Projected economic scenario
Projection based on the projected real world information set at j-thmonth using 1000 scenarios
# paths # time steps # Exp. Calc.
1 x 151 x 23 x 1000 = 3.47 Million Unique Paths
Dec 2028… … … …
…
Aug 2015
Aon Benfield Securities
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Excess Capital and SCR movement - 1 Path (75th percentile XS Capital)
26
Under this unfavourable
scenario, the excess capital
dips below 0 for sustained
periods, which means the
insurance company has
become insolvent
Excess Capital is defined as Market value of Asset less market value of Liabilities less SCR:
XS Capital = MVA – MVL – SCR.
Aon Benfield Securities
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Key Solvency II Considerations
– Solvency II requires the modeling of Assets and Liabilities together under a complex framework.
– Total SCR is driven by the SCR market risk for products with guarantees which in this case are exposed to duration and spread risks.
– Market risk is driven by the returns and volatility of the Market Value of Assets (MVA) too.
– MVA can be very volatile.
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Modeling Dynamic Investment Strategies
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Aon Benfield Securities
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Dynamic Investment Strategies
– Dynamic investment portfolio strategies may have a role to play in improving risk adjusted MVA returns and SCR levels thereby helping companies with their Solvency II capital requirements
– In this setting asset allocation changes at each time step and is tailored to the risk tolerance of the company and the product designs of the company and can incorporate other things too:
• Realized Vol targets, returns, correlations
• Optimized movement amongst a portfolio of Assets not just cash and equities
• Data Selection—time step, sample statistic, risk of product
• Optimization—multi objective functions, inequality constraints, etc
– Such investment strategies can be designed to reduce the effective cost of financial guarantees embedded in life insurance products, and lower capital levels
– But it can quickly become fishing expedition and data dredging exercise so the use of out of sample testing, statistical significance testing and resampling methods is highly recommended
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Aon Benfield Securities
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Investment Strategies: Own Funds Plot and SCR Plot
30
A very different pattern of Own Funds and SCR Capital emerges during the back test. It is clear
dynamic asset allocation can have an impact on SCR and Own Funds levels over the back test
period.
Aon Benfield Securities
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Investment Strategies: Own Funds and SCR Plots
31
Under two allocation strategies, the dynamic allocation produces a much higher level of Own
Funds and lower amount of SCR, especially during the economic crises.
Aon Benfield Securities
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Dynamic Allocation vs. Fixed Allocation
32
0
50
100
150
200
250
300
2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015
Portfolio Index Level
Fixed Allocation Dynamic Allocation
In this situation the
portfolio with dynamic
optimized asset
allocation strategy
outperforms the portfolio
with a constant or fixed
target weights allocation.
Of course past
performance is no
guarantee of future
performance and in-
sample results can be
very different than out-
of-sample results! Monthly Log Returns and STD
Mean STD Min Max
Fixed Allocation 0.42% 1.34% -4.57% 4.46%
Dynamic Allocation 0.62% 1.81% -3.90% 4.66%
Aon Benfield Securities
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SCR Comparison
33
Dynamic Allocation
Fixed allocation
In this case the market risks of the Solvency II calculation were significantly reduced when
using dynamic asset allocation strategy
Aon Benfield Securities
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Solvency II SCR Comparison Plot
34
The differences between the fixed allocation and dynamic allocation for SCR interest risk and SCR
spread risk are significant in this case. The dynamic allocation strategy reduces the absolute level of
both risk components, in part due to initial conditions and in part due to lower projected absolute
market risk levels.
Aon Benfield Securities
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SOS Forecasting SCR with Dynamic Asset Allocation
35
Under the dynamic
allocation, the future
SCR levels are
significantly lower than
under the fixed allocation
(slide 22).
Furthermore, SCR
decreases over time
under this strategy
whereas SCR stays
constant under the fixed
strategy.
Aon Benfield Securities
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SOS Forecasting Excess Capital with Dynamic Asset Allocation
36
Under the dynamic
allocation, future
excess capital levels
are significantly higher
than under the fixed
allocation (slide 23).
Furthermore, the
chances of excess
capital falling below 0
over the next 12
months are also lower
under this strategy.
Aon Benfield Securities
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Conclusion
– With Solvency II around the corner:
• Capital requirements for some life insurance companies may increase significantly.
• Asset portfolio risk and returns for equity-based/linked products have a key role to play in determining future capital requirements.
• Managing capital becomes even more important in a low return and low interest rate environment.
• Forecasting capital and understanding the reasons why forecasted capital changes means running more computationally intensive nested stochastic simulations.
– Dynamic Asset allocation strategies may help:
• Insurance Companies
♦ Reduce modeled capital requirements
♦ Lower the cost of existing financial guarantees embedded in life insurance products
♦ Help develop new products to help drive retirement market needs
• Policyholders
♦ Achieve better risk-adjusted returns and richer benefit designs
37
Appendix
38
Aon Benfield Securities
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Historical Data
For the historical analysis, the Asset portfolio was constructed using the following weights:
– Europe
• 66.6% Corporate Bond: Barclays Euro Aggregate Corporate Total Return Index (LECPTREU Index)
• 16.7% Government Bond divided equally between the following three indices:
♦ Bloomberg/EFFAS Euro Government 1-5 years total return index (EU15TR Index)
♦ Bloomberg/EFFAS Euro Government 5-10 years total return index (EU50TR Index)
♦ Bloomberg/EFFAS Euro Government 10+ years total return index(EUG5TR Index)
• 16.7% Equity: Euro Stoxx 50 Net Return Index (SX5T Index)
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Aon Benfield Securities
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Solvency II – Standard Formula Methodology
Project out 12 months into the future for capital valuation
For each capital revaluation point, project each inforce policy to maturity
Shocks are applied to the valuation assumptions at each capital valuation date.
– SCR Life Component shocks
• Mortality: 15% increase in mortality rates
• Longevity: 20% decrease in mortality rates
• Expense: 10% increase in future expense and 1% per annum inflation
• Lapse: Max of the three sub shocks
♦ Lapse down: 50% decrease in lapse rate
♦ Lapse up: 50% increase in lapse rate
♦ Mass lapse: immediate 30% lapse of inforce
• Catastrophe: 1.5 per thousand increase in 1st year mortality since capital valuation date
– SCR Market Component shocks
• Interest rate shocks: prescribed shocks along 30 year term structure
• Equity shocks: 30% immediate shock
• Spread Shock: depends on the duration and rating of the bond, immediate shock applied to the bond value
40
Aon Benfield Securities
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Solvency II – Shocks Specific to product
41
Aon Benfield Securities
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Solvency II – Life Component
Capital for mortality risk
Capital for longevity risk
Capital for lapse risk
Capital for catastrophe risk
Capital for expense risk
𝑆𝐶𝑅𝐿𝑖𝑓𝑒 =
𝑠ℎ𝑜𝑐𝑘𝑠 𝑖,𝑗
𝐶𝑜𝑟𝑟𝑖𝑗 ∗ 𝐶𝑎𝑝𝑖 ∗ 𝐶𝑎𝑝𝑗
𝐶𝑜𝑟𝑟𝑒𝑙𝑎𝑡𝑖𝑜𝑛 𝑀𝑎𝑡𝑟𝑖𝑥 =
42
Aon Benfield Securities
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Solvency II – Market Component
Capital for interest rate risk (Mkt up)
Capital for equity risk (Mkt up)
Capital for spread risk (Mkt up)
𝐶𝑜𝑟𝑟𝑒𝑙𝑎𝑡𝑖𝑜𝑛 𝑀𝑎𝑡𝑟𝑖𝑐𝑒𝑠:
Capital for interest rate risk (Mkt down)
Capital for equity risk (Mkt down)
Capital for spread risk (Mkt down)
43
Aon Benfield Securities
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Solvency II – Risk Aggregation
The Basic SCR is aggregated SCR sub categories using correlation matrix
44
Aon Benfield Securities
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Sample SCR Breakdown Report
45
Aon Benfield Securities
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Sample SCR Breakdown Report
46