Monitoring Changes in Capital and Hedge Effectiveness

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Monitoring Changes in Capital and Hedge
Effectiveness Under Fair Value Accounting
Principles
March 31, 2009
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Life insurance companies are risk enterprises.
Risk is the essence of their business. Beyond the
general economic and business risks faced by all
business, life insurance companies assume the
risks underlying their insurance
products--specifically, mortality, investment,
expense, and withdrawal.
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• In 1971, Richard G. Horn published a paper in the
  Transactions entitled Life Insurance Earnings
  and the Release from Risk Policy Reserve System.
  
• This landmark paper established a methodology for
  analyzing the earnings of a life insurance
  company.
• This methodology became to be known as a sources
  of earnings analysis.

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• The natural reserve is the present value of
  future benefits and expenses less the present
  value of future net premiums.
• Future benefits would include death benefits,
  withdrawal benefits and endowment benefits.
• Expenses would include commissions, acquisition
  expenses and maintenance expenses.

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The company's hazard, however, lies in
deviations from the expected values of these
risks rather than the expected values themselves.
The company must provide for the costs of both
the expected values of the risks inherent in
their products and the deviations from the
expected values. The risks of adverse variability
in realistically assumed rates of mortality,
interest, withdrawal, and expense constitute the
hazard of the life insurance endeavor.
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• Explicit recognition would be made for all the
  major assumptions (expenses, interest, mortality
  and lapses).
• These assumptions would be expected values (i.e.,
  best estimates) plus provisions for adverse
  deviation.

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• The provisions for adverse deviation would be
  released over the life of the block of policies
  as experience emerged.
• Accordingly, this reserving methodology became
  known as the release from risk policy reserve
  method.
• To measure both the amount and timing of these
  releases, a sources of earnings analysis would be
  preformed.

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  Net income Premium income Investment
income - Expenses - Benefit
payments - Increase in reserves
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  Net income Premium load Expense
margin Investment margin Mortality
margin Withdrawal or persistency margin
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• With the exception of term life insurance, most
  life insurance and annuity products underwritten
  today have significant equity risk.
• Furthermore, fair value accounting principles are
  replacing historical-based accounting principles.
  
• Finally, many insurance companies have hedging
  programs in place to manage the embedded equity
  risk in the type of products that they have
  underwritten.

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• Under fair value accounting principles, the
  capital account becomes the primary focus of
  attention.
• Accordingly, an analysis of the change in
  capital is needed to replace a traditional
  sources of earnings analysis.
• In addition, most life insurance companies have
  hedging programs to manage the embedded equity
  risks in the types of products they have
  underwritten. Thus, an important focus of this
  analysis is to monitor the effectiveness of these
  hedging programs.

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• Consider a company with 10,000 of cash and no
  liabilities sold a put option on the SP 500 with
  a strike price of 1,500 and an expiration date
  in thirty days.
• Assume that on the date that this option was
  written
• The current spot price of the SP 500 was 1,500.
• The implied volatility of the SP 500 was an
  annualized rate of 20.
• The risk-free interest rate was an annual rate of
  5 compounded continuously.
• The dividend yield of the SP 500 was an annual
  rate of 2 compounded continuously.
• Using these assumptions and the Black-Scholes
  Option Pricing Formula, the premium for this put
  option is 3,239.63.

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• Now assume one day after the option was written
• The current spot price of the SP 500 decreased
  to 1,485.
• The implied volatility of the SP 500 increased
  to an annualized rate of 21.
• The risk-free interest rate increased to an
  annual rate of 5.1 compounded continuously.
• The dividend yield of the SP 500 increased to an
  annual rate of 2.1 compounded continuously.
• Using these assumptions and noting that the
  option is one day closer to the expiration date,
  the value of the put option increased to
  4,113.81.

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Change in Capital Interest on Cash Time
Decay Change in Stock Price Change in
Volatility Change in Risk-Free
Rate Change in Dividend Rate
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Change in Capital Insurance Gain or
Loss Change in value of embedded
option Gain or loss on hedge
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The End