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11
Casualty Loss Reserve Seminar September 14, 1999
Presented by: Susan E. Witcraft
Milliman & Robertson, Inc.
DYNAMIC FINANCIAL ANALYSISWhat Does It Look Like?
22
WHAT IS DFA?
Management tool
Regulatory tool
33
USES FOR DFA
Estimate probability of attaining certain results
Identify risks to company
Capital allocation
Evaluation of alternate strategies
44
OVERVIEW OF PROCESS
Input
Scenarios
Output
SelectStrategy
FinancialCalculator
55
OVERVIEW OF PROCESS
Input
Scenarios
Output
SelectStrategy
FinancialCalculator
66
INPUT
PREMIUM
Amount
Earning pattern
Collection pattern
77
INPUT
LOSSES AND LAE Loss ratio on small claims
Frequency of large claims
Severity of large claims
Catastrophes
Reserve adjustments
Payment patterns
88
INPUT
EXPENSES
Fixed
Variable
99
INPUT MODELS
Premium volume
Losses and LAE
Reserve development
Payment patterns
Expenses
Assets
1010
LOSS RATIO MODEL
where i is the year
l/r is the undiscounted loss ratio
int is the short-term yield
inf is the inflation rate
a, b, c, and d are constants
e is a random error term
l/ri = a(l/ri-1 ) + b(inti-1 - int) + c (infi - inf) + d + ei
1111
EXPENSE MODEL
Fixed expensesi = Fixed expensesi-1 x (1 + infi) + ei
where i is the years
inf is the inflation rate
e is a random error term
1212
OVERVIEW OF PROCESS
Input
Scenarios
Output
SelectStrategy
FinancialCalculator
1313
STRATEGIES
Investment
Reinsurance
Business mix
Pricing
1414
STRATEGIES
Asset Type CurrentMore
CorporatesStocks &
CorporatesMore Non-Taxables
DurationMatch
Government Bonds 40% 10% 0% 5% 40%
Non-taxable Bonds 25% 25% 14% 60% 25%
Corporate Bonds 20% 50% 50% 20% 20%
Common Stocks 4% 4% 25% 4% 4%
Cash 11% 11% 11% 11% 11%
Bond Maturity 10 yrs. 10 yrs. 10 yrs. 10 yrs. 5 yrs.
Distribution of New Investments Among Types
1515
PORTFOLIO OPTIMIZER
Entire business (both assets and liabilities) viewed as a single portfolio
Considers risk from the perspective of the entire organization
1616
PORTFOLIO OPTIMIZER
Calculates line of business and asset mix that maximizes expected return for any
given level of standard deviation
- OR -
Calculates mix that provides lowest risk for a given level of return
1717
PORTFOLIO OPTIMIZER
Inputs Reserve to premium ratios for each line of business Expected underwriting and asset returns and standard
deviations Correlation matrix between underwriting returns, asset
returns, and between underwriting and asset returns
Constraints Constraints on line of business mix and percentages of
asset portfolio invested in various asset classes Reserve to surplus ratio (alternatively, premium to
surplus ratio)
1818
OPTIMAL ASSET MIX
Asset Type 7% 8% 9% 10% 11%
Government Bonds 44% 39% 33% 26% 20%
Non-taxable Bonds 0% 1% 8% 15% 21%
Corporate Bonds 48% 48% 42% 36% 30%
Common Stocks 6% 12% 17% 23% 29%
Cash 2% 0% 0% 0% 0%
Standard Deviation 21% 22% 24% 26% 29%
TARGET RETURNSTARGET RETURNS
1919
OVERVIEW OF PROCESS
Input
Scenarios
Output
SelectStrategy
FinancialCalculator
2020
SCENARIOS
Economy
Underwriting cycle
Catastrophes
Large claims
Failure of reinsurer
Mass torts
2121
ECONOMIC SCENARIOS
GDP growth Inflation Interest rates
Short-term Long-term
Stock returns Bond default rates
Produce simulated projections of:
2222
ECONOMIC VARIABLES
-4%
-2%
0%
2%
4%
6%
8%
10%
1998 1999 2000 2001 2002 2003 2004 2005 2006
-40%
-20%
0%
20%
40%
60%
80%
100%
Short Term Yields Inflation Dividend Yields Stock Appreciation
Note: Stock Appreciation is plotted against the axis on the right of the graph.
2323
ECONOMIC SCENARIOS
Output used as inputs for income and balance sheet variables
Each scenario provides consistent set of assumptions for projection of future financial results
2424
OVERVIEW OF PROCESS
Input
Scenarios
Output
SelectStrategy
FinancialCalculator
2525
FINANCIAL CALCULATOR-UNDERWRITING
Project net premium, losses and expenses
Income statement basis
Cash basis
Tax basis
2626
FINANCIAL CALCULATOR-ASSET MODEL
Calculate investment income Add cash from operations, asset
maturities and asset sales Produce total funds available for investment each
projection period
Invest total funds available for investment Strategy specified by user
State end-of-year balance sheet Carried forward to next projection period
2727
OVERVIEW OF PROCESS
Input
Scenarios
Output
SelectStrategy
FinancialCalculator
2828
CHANGE IN SURPLUS
-150%
-100%
-50%
0%
50%
100%
150%
200%
250%
1998 1999 2000 2001 2002 2003 2004 2005 2006
2929
FINDINGS
Strategy
Average AnnualSurplus Growth
to 2006
Probability ThatSurplus Growth Is
Less than 10%
Current 7.7% 69.9%
More Corporates 7.8% 69.1%
Stocks & Corporates 10.0% 73.3%
More Non-Taxables 7.5% 70.1%
Duration Match 7.1% 72.9%
3030
RISK/REWARD ILLUSTRATION
A
B
CD E
Risk
Rew
ard X
+ +
+
+
+
++
+
+
++
+
++
++
+
+
+
+
+
+
++ + +
++
+
+
+
+
+
+
+
+
++
+
+
++ ++ +
+
+
+
+
+ ++
++
+ +
3131
RISK/REWARD SUMMARY
4%
6%
8%
10%
12%
68% 69% 70% 71% 72% 73% 74%Ave
rag
e A
nn
ual
Su
rplu
s I
ncr
ease
Probability Net Income/Surplus < 10%
21 4 5
3
1. Current 2. More Corporates 3. Stocks & Corporates 4. More Non-Taxables 5. Duration Match
3232
RISK/REWARD SUMMARY
4%
6%
8%
10%
12%
20% 22% 24% 26% 28% 30%
Ave
rag
e A
nn
ual
Su
rplu
s I
ncr
ease
Standard Deviation of Surplus Increase
5
42
1
3
1. Current 2. More Corporates 3. Stocks & Corporates 4. More Non-Taxables 5. Duration Match
3333
Casualty Loss Reserve Seminar September 14, 1999
Presented by: Susan E. Witcraft
Milliman & Robertson, Inc.
DYNAMIC FINANCIAL ANALYSISWhat Does It Look Like?