CS-18: Risk Metrics
Fred Tavan, FSA FCIA
Assistant Vice President, Canada Life
ERM Symposium, Washington DC
July 29, 2003
1
Introduction
•
•
•
•
•
•
Various uses of EV
Definition
Methodology
Pro’s & Con’s
Example
Application
2
Various Uses of EV
• Information to Analysts
• Identification of BU’s that add/destroy
value
• Value added by new business during year
• Risk exposures to value
3
EV Definition
EV =
+
+
-
Shareholder’s Free Surplus
Required Capital
Value of Inforce Business
Cost of Capital
4
Shareholder’s Free Surplus
• Excess of S/H’s equity over required capital
• S/H’s equity is after-tax MV of assets
supporting surplus
5
Required Capital
• Level of statutory capital that must be
maintained before any distribution to S/H’s
• Can be affected by:
– regulation
– ratings considerations, or
– marketing purposes
6
Value of In Force Business
• Discounted value of after tax distributable
profits
• Profits calculated with reference only to
assets supporting current liabilities
7
Cost of Capital
• Opportunity cost associated with holding
required capital
• Difference between assumed future
investment earnings rate on surplus and the
EV discount rate
8
EV Components
• Adjusted Net Worth
• Value of In Force Business
• Does not measure value of Future Business
9
Methodology
• 3 General Approaches
– Full Financial Projections
– Aggregate Projections
– Approximations Techniques
• Projection techniques that project future
events using either aggregate or seriatim
models
• Claims ratio techniques acceptable in some
cases
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Value of In Force
• Full financial projections involve following
steps:
–
–
–
–
–
setting assumptions about future experience
projecting future assets and liabilities’ cf’s
projecting required capital levels
determining future annual distributable profits
calculating pv of distributable profits
11
Discount Rate
• Risk-free rate
• Risk premium addition
• Should be consistent with parameters of
economic model
12
Pro’s
• Consistent with finance practice of valuing
free cash flows
• Consistent with methods used to price new
products
• Commonly used in evaluating mergers and
acquisitions
13
Pro’s (con’td)
• Provides useful platform for risk analysis
using sensitivity and stress tests and
potentially stochastic analysis
• Gaining acceptance as a public reporting
tool in Europe and Canada
• As a by-product, can provide useful
forecasts of cash flows, earnings, etc.
14
Con’s
• Modeling intensive
• Sensitive to choice of assumptions
• Complicated to explain to non-actuarial
audience
• Generally not consistent with risk neutral
valuation of financial products and capital
markets instruments.
15
Example
Embedded Value Example
t=0
1
2
3
4
5
Present Value
at t = 0
6
Premiums
Investment Income
Total Income
$1,000
$48
$1,048
$900
$46
$946
$810
$41
$851
$729
$37
$766
$656
$33
$689
$16
$16
Benefits and Reserve Changes
Expenses
Taxes
Total Outflow
$1,500
$150
($211)
$1,439
$550
$45
$123
$718
$495
$41
$110
$646
$446
$36
$99
$581
$401
$33
$89
$523
($525)
$0
$189
($336)
($391)
$228
$205
$185
$166
$351
$439 = Value of In Force
$40
$19
$59
$36
$17
$53
$32
$15
$48
$29
$14
$43
$262
$7
$269
($71) = Cost of Capital
$287
$258
$232
$209
$620
$368 =VOIF - Cost of Cap.
Book Profits
Change in Required Capital
After Tax Interest on Req. Cap.
Net Capital Flows
($444)
($444)
$44
$21
$66
Distributable Profits
($444)
($326)
Excess Assets (at market)
Corporate Debt and Pref. Stock
Adjusted Net Worth
Embedded Value
$489
$150
$339
$339
= Free Surplus +
Required Capital
$707
16
Application
• Sensitivity Tests for :
– currency
– stock market levels
– interest rate spreads
• Room for creativity in generating various
sensitivity tests and scenarios
17
Stochastic Modeling
• Possible for companies with few products
operating in a single country
• Very challenging for multi-national
companies with a wide variety of products
– models would take very long to run
– potential solution may be distributed computing
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SOA Website
• Detailed paper can be found at:
– http://www.soa.org/sections/rmtf/embedded_val
ue.pdf
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