Stein Roe Funds

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					Financial Pricing Models in
Property/Liability Insurance
           The Basic Formula
• Financial Premium =
     • Present Value of Expected Loss & Expense (at risk-adjusted
       rate)
     • MINUS Present Value of Default Option
     • PLUS Cost of Capital
• Actuarial Premium =
     • PV of Expected L&E (risk-free rate) + “Risk Load”
• Financial Formula is an “Equilibrium Model”
     • Determines “fair” premium to compensate shareholders for
       investment risks and capital costs
     • Any higher premium results in value creation
 Pricing as a Two-Step Process
• Step 1: Determine the Total Required
  Premium for the Entire Book of Business
  – Depends on Aggregate Loss Distribution
  – Compensates Shareholders for Corporate-
    Wide Risks and Capital Costs
• Step 2: Allocate this Total Premium Down
  to Component
  PV of Expected Loss & Expense
• Key Input: Aggregate Loss Distribution
  – Gives you expected value of loss
• Where do you get the “risk-adjusted”
  discount rate?
  – Use a market model
     • CAPM
     • Fama-French 3-Factor Model
     • APT
  – Current Research in this area (RPP, et al.)
        PV of Default Option
• Generally valued by Option Pricing Theory
  (e.g. Margrabe’s formula)
• Potential Problems/Complications
  – Requires Complete Markets Assumption
  – Uncertain Impact of Guarantee Funds
• Generally small portion of overall premium
  – Insurers manage risks to keep it small
  – But may be important in certain allocation
    procedures (e.g. Myers/Read)
              Capital Costs
• Capital Costs = Total Capital x Frictional
  Capital Costs (as percentage)
  – Misconception Regarding Financial Pricing
    Models: “In financial models, the only risk that
    matters is systematic risk. The total variability
    of the loss distribution doesn’t impact
    premium.”
  Two Types of Frictional Costs of
             Capital
• Costs of Holding Capital
  – Double taxation
  – Agency costs
• Costs of Raising Capital
  – Underwriting spreads
  – Administrative costs
  – Asymmetric information
  Allocation to Line of Business
• Determine risk-adjusted discount rate by
  line of business
• Is the capital allocation problem solved?
  – Problems with Myers/Read
     • Homogeneity Assumption
     • Only considers costs of holding capital in allocation
     • Other practical difficulties
• RMK as an alternative
What doesn’t work: Expected Utility
          Approaches
• TV’s Definition of Expected Utility
  Approach to P/L Insurance Ratemaking:
  The application of a criterion with no
  economic meaning to an object with no
  economic meaning.
• Object = Probability distribution of NPV’s
  at risk-free rate
• Criterion = “Corporate” utility-of-wealth
  function
Probability Distribution of NPV’s
• Common approach in actuarial literature
• Two major problems
  – Ignores individual investor’s ability to diversify
  – No economic rationale for the discounting: It is very
    difficult to interpret a distribution of NPVs. Since the
    risk-free rate is not the opportunity cost of capital,
    there is no economic rationale for the discounting
    process. Because the whole edifice is arbitrary,
    managers can only be told to stare at the distribution
    until inspiration dawns. No one can tell them how to
    decide or what to do if inspiration never dawns.
    (Brealey/Myers, Chapter 11)
     “Corporate” Utility of Wealth
             Functions
• Individual utility functions can be determined, in
  theory
• But they are unique to individuals –
  interpersonal comparisons of utility functions not
  possible!
• It is not possible to know how real-world utility
  functions for different individuals should be
  aggregated. It follows that group utility
  functions, such as the utility function of a firm,
  have no meaning. (Copeland/Weston)
         Moral of the Story
• Financial theory works – use it!
• Spreadsheet example of Froot/Stein
  Corporate ROE pricing with RMK
  allocation

				
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