ORSA and Multi-Year Capital Projection
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Transcript of ORSA and Multi-Year Capital Projection
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
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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?!
21
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
22
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