Allocating Economic Capital
to Drive Business Decisions
An Application of Don Mango’s
Shared Asset Approach
April 11, 2014
Originally Don Mango’s Portion
 Why is he not here?
• He made a scheduling blunder  double-booked with a family commitment
• Recognizing this is shorter than our usual session, and that his portion covers
material in a published article, he felt his part should be edited down
• He wants you to see Tim and Terri!
 Original paper – 2005 ASTIN Bulletin (reprinted in the 2006 CAS Forum):
“Insurance Capital as a Shared Asset”
www.casact.org/library/astin/vol35no2/471.pdf
 One example of presentation:
www.casact.org/education/reinsure/2005/handouts/mango.ppt
 It is the foundational text for the Cost of Capital portion of the Institute of
Actuaries (UK) syllabus
2
Shared Asset in Two Slides (#1)
 Shared Assets
• Common pool resources that are shared
• Some are used consumptively and some non-consumptively
 Consumptive (e.g., Reservoir, fisheries)
• Instantaneous with no return and no re-use
• Think DESTRUCTION
 Non-consumptive (e.g., golf course, hotel)
• Time-based with return and subsequent re-use (with minimal maintenance)
• Think RENTAL
3
Shared Asset in Two Slides (#2)
 In good times, an insurance portfolio only RENTS the capital
• “Reserves hold”
• If we knew secretly this was a riskless portfolio, this would still represent the “keep
the lights on” minimum capital
 However, when things go badly, the portfolio CONSUMES the capital
• “Reserve strengthening” or “catastrophe”
• Our capital model gives us the supporting information
• We need to define for ourselves just how “at-risk” this portion of the capital is, which
lines are the culprits, and who should pay how much
 This exercise we are calling “Defining our Risk Preferences”
4
Explicit Risk Preferences
5
Every Approach Has an IMPLICIT Risk Preference
Risk Aversion
VaR
VaR
CARE!!
Don’t Care
Size of Loss
Don’t Care
VaR Threshold
6
Every Approach Has an IMPLICIT Risk Preference
Risk Aversion
TVaR
Additional Care per $ of
additional loss is constant
Don’t Care
Size of Loss
CARE
VaR Threshold
7
Every Approach Has an IMPLICIT Risk Preference
“Zones of Impact” of Capital
Risk Aversion
Ratings
Downgrades
Ratings
Watch
Lost
Earnings
Don’t Care
Size of Loss
CARE
EVEN
MORE
CARE
MORE
CARE
Heights of the different boxes
represent the firm’s RISK
PREFERENCE FUNCTION
8
Articulating Risk Preferences
1. Being audited by the IRS
2. Catching a foul ball at
baseball game
3. Being on a plane with a
drunken pilot
Expected
1-in-100
1-in-200
1-in-500
Using the Shared Asset Framework to allocate
capital within a company
10
Allocating capital is an iterative process
Risk Model
Data
Risk
Appetite
Feedback
Loop
Results
Smart
People
Doing Math
11
Risk model data
 Illustrative Company
•
•
•
$10B Premium
4 States
2 lines (non-volatile & volatile)
Premium Distribution
Total Co Earnings Profile
100%
100%
90%
90%
70%
70%
60%
50%
40%
LA
10%
60%
50%
40%
30%
30%
20%
Line 2
80%
MN
Percentile
80%
Line 1
20%
FL
10%
MA
0%
0.5
0%
0.0
(0.5)
(1.0)
(1.5)
(2.0)
(2.5)
(3.0)
(3.5)
(4.0)
(4.5)
(5.0)
(5.5)
(6.0)
Underwriting Income ($B)
Risk Metrics
Risk Type
Premium
C/R
Expected Profit
Prob. of Profit
Std Dev Profit
1/100
1/250
1/1,000
Line 1
Non-volatile
$7B
96.0
$0.3B
94%
$0.2B
($0.2B)
($0.2B)
($0.3B)
Line 2
Volatile
$3B
94.0
$0.2B
83%
$0.6B
($1.4B)
($2.6B)
($6.2B)
$10B
95.0
$0.5B
93%
$0.6B
($1.1B)
($2.3B)
($6.2B)
Total Co
12
Risk appetite informs target capital
 Risk appetite + Shared Asset Framework = target capital
 Everyone’s appetite is different, let’s examine two choices
• Conservative: withstand 2x 1/250 years without losing “secure” rating
• Aggressive: withstand 2x 1/100 years without losing “secure” rating
Target Capital
Line 1 Line 2
Total Co
$6.3B
Line 1 Line 2
Total Co
$4.1B
$6B
$2.5B
$4.7B
$3.0B
$3.0B
$1.4B
$1.4B
$2.2B
$3.3B
$2.2B
$1.1B
$3.3B
$2.2B
$2.2B
$0
$1.1B
Conservative
Appetite
Aggressive
Appetite
13
Allocating to state
 Guiding Principles:
• Fundamental before technical
• Keep it simple
 Rental charge applied to states via uniform P/S ratio
 Consumption charge will vary, but how?
• Could use same approach as assigning to line segments (fixed point)
• Or, could vary according to contribution to marginal portfolio risk (continuous)
$6B
Line 2 Target Capital
Total Co Earnings Profile
$4.1B
$3.0B
$0
$1.4B
Contribution to Marginal Risk
$1.1B
$1.1B
Uniform 2.7 P/S
Conservative
Appetite
Aggressive
Appetite
Line 2
100%
90%
80%
70%
60%
50%
40%
30%
20%
10%
0%
0.5 0.0 (0.5) (1.0) (1.5) (2.0) (2.5) (3.0) (3.5) (4.0) (4.5) (5.0) (5.5) (6.0)
Percentile
$2.5B
Line 1
Underwriting Income ($B)
14
Contribution to marginal risk
 Definition of marginal risk?
•
•
Total loss
Worse then expected (excess of mean)
Total Co Earnings Profile
Line 1
Line 2
100%
60%
40%
20%
0%
0.5 0.0 (0.5)(1.0)(1.5)(2.0)(2.5)(3.0)(3.5)(4.0)(4.5)(5.0)(5.5)(6.0)
Underwriting Income ($B)
Line 2 Loss x/s Mean
100%
90%
80%
70%
60%
50%
40%
30%
20%
10%
0%
0.0
MA
FL
LA
MN
Percentile
Percentile
80%
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
Modeled Loss x/s Mean ($B)
5.0
5.5
6.0
6.5
15
Allocation mechanics
 Some outcomes are worse than others, differentiate consumption charge
accordingly
 Simple Risk Preference
Line 2 Loss x/s Mean
MA
FL
LA
MN
Allocation
“Impairment”
Conservative
10yr “Earnable” Payback
“Impairment”
Percentile
100%
90%
80%
70%
60%
50%
40%
30%
20%
10%
0%
0.0
Conservative Allocation
$0.5
$0.4
$0.3
$0.2
$0.1
$0.0
Earnable
0%
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
Modeled Loss x/s Mean ($B)
4.5
5.0
5.5
6.0
6.5
Avg Loss X/S Mean
($B)
Aggressive
Avg Loss X/S Mean
($B)
• Losses that you earn your way out of (“earnable”) vs. those you don’t (“impairment”)
• Simple math is window average loss (co-x TVaR)
Impairment
100%
Aggressive Allocation
$3.0
$2.0
$1.0
$0.0
Earnable
10%
Impairment
90%
16
Results
 Capital allocation translated into target combined ratio
 These results are an important feedback loop
$0.5
$0.4
$0.3
$0.2
$0.1
$0.0
Conservative
100
Aggressive
97
98
94
95
Earnable
0%
Avg Loss X/S Mean
($B)
Line 2 Target Combined Ratio
Conservative Allocation
Impairment
100%
Aggressive Allocation
$3.0
Combined Ratio
Avg Loss X/S Mean
($B)
• Risk preferences are hard to articulate
• If you can’t accept these results, revisit your risk appetite
90
86
83
$1.0
65
$0.0
60
Earnable
10%
Impairment
76
$4.0B
Target
Capital
81
75
73
70
$2.0
93
87
85
80
$2.6B
Target
Capital
MA
NJ
FL
LA
MN
Total
90%
17
Driving business decisions with economic capital
18
Risk market in action
 Target combined ratios are the “price” in our risk market
 Prices send signals
 How would you respond to these signals?
Line 2 Target Combined Ratio
Conservative
100
97
Line 2 Returns
Aggressive
98
94
18%
18%
85
80
86
83
76
81
75
73
70
Actual
C/R
93
87
Return on Target Capital
Combined Ratio
95
90
Conservative Allocation
Aggressive Allocation
Target Return (10%)
20%
16%
14%
12%
12%
10%
10%
10%
10%
8%
8%
6%
7%
4%
5%
4%
65
2%
60
0%
3%
MA
FL
LA
MN
Total
MA
88
98
95
93
94
?
FL
Shrink
LA
MN
Total
?
Grow
?
19
The final frontier
 Managing as a portfolio requires ability to make trades
Profit
Growth
Return
Volatility
Total Co Efficient Frontier
20%
18%
MN
16%
LA
Return on Target Capital
•
•
•
•
14%
Total Co
12%
MA
10%
8%
FL
6%
4%
2%
0%
0%
5%
10%
15%
20%
Std Dev of Return on Target Capital
25%
30%
35%
20
Optimizing

Diversification has multiple benefits in optimizing portfolio
• Can make new risks look good
• Can make existing risks look better

Risk appetite and current portfolio define possibilities

Example: Remove FL
Total
CoCo
Efficient
Frontier
(Pro
Forma)
Total
Efficient
Frontier
(Base)
20%
Return on Target Capital
18%
MN
16%
LA
14%
Total Co
12%
MA
10%
8%
X
6%
0%
5%
10%
15%
20%
25%
FL
30%
35%
Std Dev of Return on Target Capital
Target Combined Ratio (Pro Forma)
Target Combined Ratio (Base)
MA
FL
LA
MN
Total
MA
FL
LA
MN
Total
Line 1
100
100
100
100
100
100
-
100
100
100
Line 2
87
73
97
98
94
88
-
98
100
97
Optimizing…Round 2
 Example: Increase LA by 50%
Total
Efficient
Frontier
(Base)
Total
CoCo
Efficient
Frontier
(Pro
Forma)
20%
Return on Target Capital
18%
MN
16%
LA
14%
Total Co
12%
MA
10%
FL
8%
6%
0%
5%
10%
15%
20%
25%
30%
35%
Std Dev of Return on Target Capital
Target Combined Ratio (Pro Forma)
Target Combined Ratio (Base)
MA
FL
LA
MN
Total
MA
FL
LA
MN
Total
Line 1
100
100
100
100
100
100
100
100
100
100
Line 2
87
73
97
98
94
88
75
95
98
94
Q&A
23