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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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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



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)



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



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



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



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



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



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%)

10



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

11

Historical Backtest with E.U. economic data (2003 ~2015)

12



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

…



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.



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



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.



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%



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



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


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



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



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.



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)

24



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).

25

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


1 x 151 x 23 x 1000 = 3.47 Million Unique Paths

Dec 2028… … … …

…

Aug 2015



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.



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.

27

Modeling Dynamic Investment Strategies

28



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

29



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.



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.



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%



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



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.



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.



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.



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



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)

39



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



Solvency II – Shocks Specific to product

41



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



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



Solvency II – Risk Aggregation

The Basic SCR is aggregated SCR sub categories using correlation matrix

44



Sample SCR Breakdown Report

45



Sample SCR Breakdown Report

46

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