Transcript Pitfalls of Capital Allocation Donald Mango, FCAS, MAAA American Re-Insurance

Pitfalls of Capital
Allocation
Donald Mango, FCAS, MAAA
American Re-Insurance
CAS 2001 Spring Meeting
“The Happy
Sholom”
Step One: A Single Name
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We allocate CAPITAL
And we have Premium-to-SURPLUS
And we talk about Return on EQUITY
We need ONE NAME
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Step One: A Single Name
SQUAPITAL
 SURQUITY
 EQUITUS
 SQUIRTAL
 SCRAPITAL
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Should We Allocate Capital?
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Yes
No
Maybe
Splunge
See Monty Python
It isn’t yes, and it isn’t no, but I’m not
being indecisive.
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Look At All the Benefits
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Risk-adjusted performance
measurements for products
Strategic insights into the efficiency of
our capital management
Determine which activities create
shareholder value and which destroy it
SOUNDS GOOD !!
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What Total Amount Should We Use?
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Statutory, Economic, GAAP Equity,
RBC, BCAR, S&P?
Static or Dynamic?
Top-Down (true allocation) or BottomUp (rolled up from “atomic” level)?
Tied to financials or purely theoretical?
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Do We Want More or Less?
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The Home Office allocates capital to our
underwriting division
 Do
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we want MORE or LESS?
Depends on what it represents
 Underwriting
capacity, Vote of Confidence
 MORE
 Return burden (Subject to a “Hurdle Rate”)
 LESS
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MORE on this later …
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What About the Bathwater?
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Everybody likes to assume a single
policy, with dedicated assets, and
capital that gets released over time in a
nice non-increasing manner, …
 Then
a single IRR falls out !!! :-)
 Forget
the actual reserves, current asset
portfolio, runoff operations, A&E, steady
state, … They just cloud the picture.
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What About the Bathwater?
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But for a steady-state, multi-line carrier
with substantial casualty reserves,
those reserves can carry the majority of
the future calendar year risk
Show of hands - who works for a
company that has had material adverse
development on prior accident years in
the last two calendar years?
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What About the Bathwater?
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What should we do with that reserve (or
asset or A&E or runoff) risk?
it  Incomplete, misleading overall
picture; throwing away the majority of the
risk
 Allocate to it  Less allocation to
prospective business; nobody wants that
hot potato burden anyway; but it’s an
ongoing maintenance nightmare
 Ignore
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What’s the “R” in “ROE”?
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Risk-adjusted profitability ( RAROC /
RORAC / ROE ) needs investment
income
Allocate actual or develop theoretical?
Use realized or “promised” yield?
Include investment income on Squirtal?
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Should It Be a Zero Sum Game?
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If Total Surquitus decreases, all our
LOB ROE’s go up, and vice versa.
 We
can adjust the hurdle rates, but that
sensitivity response doesn’t inspire
confidence
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We increase our risk assessment of
LOB1  LOB1 gets more Capital
 But
the others get less (zero sum), which
increases their ROE’s
 Has our view of their profitability changed?
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What About the Risk Measure?
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We want to know each segment’s
contributions to “Total RiskTM”
 Anybody
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define “Risk” yet?
First we select one of many fine
available measures:
 Prob
of Ruin, Std Dev, Variance, EPD,
VaR, CVaR, TVaR, Tail Conditional
Expected Value, Default Loss Rate, …
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Which one do we choose?
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What’s the Relative Contribution?
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Each segment’s contribution to “Total
RiskTM”
Many marginal methods:
a.k.a. “Last-In”
 Stand-alone a.k.a. “First-In”
 Build up the portfolio one segment at a
time a.k.a. “Need an Entry Order”
 Swap-in-and-out
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Which one to choose? Does it even
matter?
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What About Order Dependency?
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Any of the marginal methods, using any
of the probabilistic risk measures, will
face the same issue:
Each marginal method implies a certain
order of entry into the portfolio
And all the risk measures are orderdependent
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What About Order Dependency?
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Fact of life with most popular actuarial
risk measures
Many consider it an “annoyance” to be
normalized or re-balanced away…
But it is symptomatic of decomposition
of an aggregate distribution into its
component distributions
 Especially
problematic when there is a
dependency structure
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What About Order Dependency?
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Underneath lie politically loaded issues
of ALLOCATION
 Covariance
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SharingTM
How do we split the impact of a
dependency relationship between
segments?
My Brain Hurts!!
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Self-Serving Advertisement
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“An Application of Game Theory:
Property Catastrophe Risk Load”
1998 Proceedings
Available on the CAS website:
www.casact.org/pubs/proceed/proceed98/index.htm
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Frames the problem more rigorously
and provides a possible solution
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But The Benefits...



Risk-adjusted performance
measurements for products
Strategic insights into the efficiency of
our capital management
Determine which activities create
shareholder value and which destroy it
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But The Benefits...
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Risk-adjusted performance
measurements for products
An ILL-POSED PROBLEM
Anybody define “Risk” yet?
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But The Benefits...
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Strategic insights into the efficiency of
our capital management
More on this in a minute…
Determine which activities create
shareholder value and which destroy it
Russ showed you can get your arms
around that without using allocated
capital
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Now It Gets
Weird
Where Did We Get This Idea?
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“Das Kapital” = Means of Production
“Capital” in a “Spend-then-Receive”
industry
 Costs
are current, well known
 Revenues are future, unknown
 Sink Costs now  hope for Revenues later
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Capital “Allocation” means spending
available cash for Production (and
Distribution) Capacity
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“Spend-then-Receive” Industry
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No issues about whether we want
MORE or LESS capital -We want MORE
No issues about which total amount to
use -- it’s CASH ON HAND
No issues about mismatched allocation
abstracted over time -- The money
funds current production efforts
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“Receive-then-Spend” Industry
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Insurance is a “Receive-then-Spend”
industry
 Revenues
are current, well known
 Costs are future, unknown
 Take Revenues now  hope Costs aren’t
too high/soon
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Our business model requires no
CAPITAL EXPENDITURE for
production - our “production” is revenue
collection !!
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“Receive-then-Spend” Industry
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For current underwriting activities, what
we are really allocating (spending) is
FUTURE CAPITAL
Current Capital is already spoken for by
the reserves !!
Given this fundamental difference,
should we even attempt insurance
capital allocation?
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Can Capital Be Meaningfully Atomized?
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Concept comes from Ancient Greece
(Leucippus, Democritus)
 Decompose a “Whole” into its component
parts--“atoms”
 Dangerous mental framework
– Becomes the hammer looking for nails
 Every
thing (!!!) we analyze must be
decomposable into meaningful subsets,
right?
 That’s the road that leads to all the trouble
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Can Capital Be Meaningfully Atomized?
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Quantum Physics pulled down the whole
“atomic” framework
Yet 100 years later the full impact of this
revolution / evolution in thinking has not
soaked in
The Physicists are in line with the Taoists
Gary Zukav, “The Dancing Wu Li Masters”
 Fritjof Capra, “The Tao of Physics”
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Can Capital Be Meaningfully Atomized?
 Pr omisesToPay   Pr omiseToPay 
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Capital is a FLOW PHENOMENON that
only exists at the Portfolio level
We must resist the urge to decompose
 We
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don’t reserve at the policy level
Butsic, 2000 Reinsurance Call Paper,
atomizes capital and default …
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Call Ourselves “Insurings”
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Use gerunds to describe flows
 Nouns
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in motion
Many of the problems we have
considered here are results of
assessing a flow situation using
imperfect, mismatched, static
measures and practices
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Call Ourselves “Insurings”
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Capital is a living buffer that is fed by
current activities and depleted by prior
activities
 Amounts
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move in and out of it all the time
It only exists and has meaning in total
 “A
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jar of water is not a river”
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Allocating Flows?
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Do we allocate Life to the various
bodily organs?
Last-in, order dependency…
INSANITY
 First-in,
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Can we allocate Health to food, drink,
rest, warmth, vitamins, exercise, prayer,
…?
Dissection  a cut-up frog on a table
is not a living frog
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Yes, I Had an Agenda
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I came to BURY capital allocation, not
praise it
Nor rehabilitate it
Instigate, yea, even rouse the rabble
“Catalyze discussion”
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“What I tell you three
times is true.”
- Nasrudin