ORSA and Multi-year Capital Projection

Gavin Conn, Director Moody’s Analytics Originally presented at the Life and Pensions Nordics ConferenceMay 24, 2013 | Stockholm, Sweden 

2

Own Risk and Solvency Assessment (ORSA)

» ORSA is emerging as a global regulatory standard

» Pillar II of Solvency II

» US and Canada have each proposed ORSA frameworks for 2014 implementation

» Core part of International Association of Insurance Supervisors (IAIS) Common Framework

» ORSA implementation approaches may have local differences, but in all cases they require insurance firms to make assessments of their current and future solvency capital requirements

3

Quantitative modelling requirements of ORSA

Modelling requirements of ORSA could be considered in three categories:

» Backward-looking

Analysis of annual change in Pillar 1 regulatory reserves

» Current-looking

Real-time monitoring of Pillar 1 regulatory capital requirements

Own assessment of current solvency capital requirements

» Forward-looking

Multi-timestep forward projection of solvency capital requirements (regulatory capital and / or economic capital)

4

Capital & Solvency Projection (ORSA)

5

Calculating solvency capital along the path

Multi time-step projection is orders of magnitude more calculation intensive than a capital calculation

Capital calculation Multi-timestep capital projection

6

LSMC: From One Year to Multiple Years

One year LSMC Multi-year LSMC

7

‘Local’ vs ‘Global’ fitting

1. ‘Local’ fitting

Separately calibrate different proxy functions for each time t:

Market-consistent value(t)

= ft (risk factors)

A potential drawback with this fitting method is that certain coefficients in the polynomial may vary widely over time.

2. ‘Global’ fitting

Include time as an additional variable and calibrate once:

Market-consistent value(t)

= fglobal(time, risk factors)

Equivalent to assuming that the coefficients of the ‘local’ polynomials ft are themselves polynomials.

8

Multi-Year Fitting Example

9

Product Example

» Annual return credited to policyholder is calculated as

• Credited return (t) = max (Fund return (t) – 1.5%, 2%)

• i.e. Policy Account (t) = Policy Account (t-1) * { 1+ credited return (t) }

• Policy Account (0) = Asset Portfolio Value (0)

• Product pay-out at time 10 is Policy Account (10)

» Asset fund invested in diversified portfolio of investment-grade corporate bonds

• 70% A-rated

• 30% BBB-rated

• Term of 8 years

• Re-balanced annually

» No allowance for taxes, expenses, lapses, mortality

10

Market-consistent liability valuation

» The policy pay-out is path-dependent, i.e. it is a function of the 10 annual returns, not the 10-year return

• Market-consistent simulation required to produce the time-0 valuation

» Market-consistent liability value at time 0 was calculated to be 119% of the starting fund value in end-2012 market conditions

• Calculated using market-consistent scenario set for interest rates and corporate bond returns

» How will this market-consistent liability value behave over the 10-year lifetime of the product?

11

Proxy Function Fitting

» Proxy functions produced using 5 risk factor variables

• Two risk-free yield curve factors

• Interest rate volatility factor

• Credit return factor

• Policy account value (i.e. roll-up of credited returns)

» Proxy functions produced for valuation at each time-step using the ‘global’ and ‘local’ methods described earlier

• Functions fitted to quadratic term in individual risk factors and cross-terms

• Fitted local functions had around 10 statistically significant parameters

• Global function had 32 statistically significant parameters

12

Validation Results – Year 1

1.1

1.15

1.2

1.25

1.3

1.1 1.15 1.2 1.25 1.3

Prox

y

Actual

'Local' fit

Adverse scenarios

Random scenarios

1.1

1.15

1.2

1.25

1.3

1.1 1.15 1.2 1.25 1.3Pr

oxy

Actual

'Global' fit

Adverse scenarios

Random scenarios

13

Validation Results – Year 5

1

1.1

1.2

1.3

1.4

1.5

1 1.1 1.2 1.3 1.4 1.5

Prox

y

Actual

'Local' fit

Adverse scenarios

Random scenarios

1

1.1

1.2

1.3

1.4

1.5

1 1.1 1.2 1.3 1.4 1.5Pr

oxy

Actual

'Global' fit

Adverse scenarios

Random scenarios

14

Validation Results – Year 9

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

1.9

2

2.1

1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1

Prox

y

Actual

'Local' fit

Adverse scenarios

Random scenarios

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

1.9

2

2.1

1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1Pr

oxy

Actual

'Global' fit

Adverse scenarios

Random scenarios

15

Multi-Year Proxy Function Applications:

1. Stochastic Projections2. Reverse Stress Testing3. Scenario Testing

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Multi-Year Stochastic Projections: Liability Value

1.0

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

1.9

2.0

0 1 2 3 4 5 6 7 8 9 10

Mar

ket-c

on

sist

en

t lia

bili

ty v

alu

e

Time (years)

Percentiles 95% to 99%

Percentiles 75% to 95%

Percentiles 50% to 75%

Percentiles 25% to 50%

Percentiles 5% to 25%

Percentiles 1% to 5%

Average

» Time 0 valuation produced by set of market-consistent scenarios

» Time 10 valuation is simply the product payout in the real-world scenario

» Proxy function used to estimate market-consistent values in years 1-9

17

Multi-Year Stochastic Projections: Liability Value – Asset Portfolio Value

-0.2

-0.1

0.0

0.1

0.2

0.3

0.4

0.5

0 1 2 3 4 5 6 7 8 9 10

Mar

ket-c

on

sist

en

t lia

bili

ty v

alu

e

-fu

nd v

alu

e

Time (years)

Percentiles 95% to 99%

Percentiles 75% to 95%

Percentiles 50% to 75%

Percentiles 25% to 50%

Percentiles 5% to 25%

Percentiles 1% to 5%

Average

» M-C deficit is expected to reduce over time due to risk premium in asset fund

» c30% probability of product pay-out being less than final asset portfolio value

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Multi-Year Stochastic Projections: Liability Value – Asset Portfolio Value in Year 5

-0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045

Liab

ility

val

ue -fu

nd v

alue

@ y

ear

5

Credit spread @ year 5

-0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0 0.02 0.04 0.06 0.08 0.1 0.12

Liab

ility

val

ue -

fund

val

ue @

yea

r 5

10-year Treasury rate @ year 5

High risk-free rates also bad for shareholder in this product

But not so significant as high rates also reduce liability value

Strong exposure to credit spread behaviour

19

Reverse Stress Test:Economic scenario path for worst ranking simulation

2012 2013 2014 2015 2016 20170%

1%

2%

3%

4%

5%

6%

7%

1-yr Treasury rate10-yr Treasury rate10-yr BBB corporate spread

2012 2013 2014 2015 2016 20170.5

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

1.4

1.5

Fund valuePolicy accountM-C liability value

• Rank year 5 real-world scenarios by market-consistent deficit

• This scenario has the biggest deficit at year 5

• The economic scenario is consistent with previous scatterplots

• M-C deficit at year 5 is 0.60 (99th percentile in earlier chart was 0.30)

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Scenario Testing:Apply 7 macro-economic stress tests

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

2011 2012 2013 2014 2015 2017

Polic

y va

lue -

fund

val

ueBaseline forecast

Stronger Near-Term Rebound

Slower Near-Term Growth

Double-Dip Recession

Protracted Slump

Below-Trend Long-Term Growth

Oil Price Increase, Dollar Crash Inflation

» 7 macro-economic, multi-year stress tests specified by Moody Analytics ECCA team

» Proxy function used to project liability valuations through these scenarios

» What is happening in the oil price scenario?!

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Oil Shock Scenario

2011 2012 2013 2014 2015 20160%

1%

2%

3%

4%

5%

6%

7%

1-yr Treasury rate

10-yr Treasury rate

10-yr BBB corporate spread

2011 2012 2013 2014 2015 20160

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

Fund value

Policy account

M-C liability value

• Very significant yield curve increases in the early years of the product. Asset fund value falls by 40% after two years

• Followed by very strong bond returns in later years

• This down-then-up path is very bad for the product (shareholders)

• Early poor returns clearly hurt due to 2% minimum guarantee

• Later strong returns also hurt as they are applied to the policy account value, which is much greater than the asset portfolio value

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Conclusions

» LSMC extendable to multi-timestep proxy function fitting

» In the case study we have produced proxy functions for a path-dependent, complex guaranteed product, and the proxies perform very well in out-of-sample validation testing at all time horizons

» These functions enable a wide variety of projection analytics such as stochastic projection, reverse stress testing and stress and scenario testing

» This is extremely useful for firms who need to consider the medium-term behaviour of their solvency requirements as part of ORSA