Interest Rate Risk and Equity Values of Life Insurance Companies: A GARCHM Model The views expressed

1
Interest Rate Risk and Equity Values of Life
Insurance Companies A GARCH-M ModelThe views
expressed here are those of the authors and do
not represent the Board of Governors of the
Federal Reserve System or the Federal Reserve
Bank of Chicago.

• Elijah Brewer III, James M. Carson, Elyas
  Elyasiani,
• Iqbal Mansur, and William L. Scott
• Research Seminar at The University of Iowa
• Iowa City, IA
• February 4, 2005

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How this Study Relates to Selected Past Research

• Interest Rates
• (Carson-Hoyt, 92) Interest rates and policy
  loans
• (Carson, 94) Interest rates and value of
  backdating
• (Carson, 96) Credited (intra-policy) interest
  rates and LI price
• (Carson-Mao-Ostaszewski-Schoucheng, 04)
  Interest rates and LI price
• (Carson-Ostaszewski, 04) Int. rates and
  actuarial value of backdating
• Insurer Solvency / Performance
• (Carson-Hoyt, 95) Solvency and (important ir
  variables .)
• (Carson-Scott, 96) Solvency and run on the
  bank risk
• (Browne-Carson-Hoyt, 99) Int. rates, other econ
  vars, and LI solvency
• (Browne-Carson-Hoyt, 01) Int. rates, other econ
  vars, and LI perform
• Current Study Interest rates and LI equity
  returns

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Overview of Insurance Company Operations

• Insurers as Financial Institutions
• Issue stochastic debt w unknown amount and timing
  of loss payments
• As borrowers, insurers essentially lever
  ownership capital
• Two Aspects of Insurer Operations
• Underwriting Obvious value to insureds /
  policyowners, not to mention broader benefits
• Investment The business of insurance esp. has
  value if it can provide funds at lower cost than
  available elsewhere

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Perils of Insurer Operations

• Generally
• Competitive Environment (state regulation)
• Fraud
• Interaction of co. operations with economic
  factors
• Unemployment, Personal income, Interest rates
• Asset-Liability Mismanagement / Interest Rate
  Risk
• Liability Side
• Reserving Errors
• Underwriting Misjudgment
• Asset Side
• Investment Losses

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Life-Health Insurer Assets(Ins. Information
Institute)
                                               
                                                  
                                                  
                
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L-H Insurer Asset Distribution(Ins. Information
Institute)
( billions)
                                               
                                                  
                                                  
                
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Interest Rate Sensitivity Important to Insurers,
Investors, and Regulators

• Asset portfolio invested largely (half of 3.7
  T) in L-T fixed-income securities
• Solvency research indicates that life insurer
  performance negatively related to increased
  interest rates
• Rising interest rates typically erode value of
  surplus?more leverage
• Greater leverage increases IR cost of capital
• Interest rate risk leads insurers to hedge, but
  IRR likely still present

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Interest Rate Sensitivity Important to Insurers,
Investors, and Regulators (2)

• Staking and Babbel (1995) examine interest rate
  sensitivity of P-C common stocks
• At lower levels of risk firms with greater
  interest rate risk (IRR) have lower MV when
  compared with firms having less IRR
• At higher levels of risk a positive
  relationship between IRR and MV
• U-shaped curve for MV

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Literature on Interest Rates and Stock Returns

• Stone (1974) was the first to try to empirically
  isolate the interest rate sensitivity of
  financial firms equity
• RETj,t, ?0 ?1 RMKTt ?2 RATEt ?t
• Above model to investigate the interest
  sensitivity of stock returns for
• Banks and SLs
• Lloyd and Shick (77), Lynge and Zumwalt (80),
  Chance and Lane (80), Flannery and James (84),
  Kane and Unal (88), and Kwan (91)
• Life Insurers
• Scott and Peterson, (86) banks and life
  insurers
• Bae (90) insurer stocks sensitive to
  unanticipated changes in interest rates

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Literature on Interest Rates and Stock Returns (2)

• Most, with the exception of Chance and Lane, find
  interest rate sensitivity in the two-index market
  model for financial firms
• But, newer studies find that the interest rate
  dependency of financial stocks is time-varying
• Akella and Chen (1990), Brewer and Lee (1990),
  Choi, Elyasiani, and Kopecky (1992), Kane and
  Unal (1988, 1990), Kwan (1991), Neuberger (1991),
  Wetmore and Brick (1994), and Yourougou (1990)
• Maher (1997) finds that the time-varying interest
  rate sensitivity renders tests over long periods
  as inconclusive

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Discussion of Limitations of Early Studies

• Stock price data
• High-frequency speculative prices
• Involves volatility clustering (large movements
  (up or down) followed by large movements)
• Assumptions of stock return linearity and
  independence are challenged (Elyasiani and
  Mansur, 98)
• Assumption of constant variance questioned
• Important to account for time-varying
  second-order moments

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More Recent Methodologies

• ARCH models
• Introduced by Engle (82)
• Basic motivation for ARCH is to recognize the
  importance of modeling time-varying second-order
  moments
• Account for volatility clustering (large
  movements (up or down) followed by large
  movements)
• Bollerslev, Chou, and Kroner (92) Review ARCH
  models
• Song (94) ARCH(q)-type methods
• EM (98) GARCH(p,q)-M more general lag
  structure than ARCH

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Benefits of GARCH-M

• (1) Addresses the potential problems with
  heteroskedasticity that would lead to inefficient
  estimators and possibly incorrect inferences
• (2) Nests a variety of functional forms in stock
  return modeling including the CAPM, ARCH-M, ARCH,
  and GARCH, and permits a formal test for the
  choice of the appropriate model and return
  volatility
• (3) Allows for a feed back effect between
  volatility and mean return.

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Contributions of the Study

• (1) Evaluate factors generating life insurer
  common stock returns using a GARCH-M model
• (2) Test if the interest rate sensitivity of life
  insurer stock returns is constant over time
• (3) Employ 1975-2000 dataset, encompassing
  various periods of interest rate volatility
• Jan1975-Oct1979, Nov1979-Aug1982, Sep1982-Dec2000

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Sample and Data

• 61 publicly traded LICs
• Specializing in life insurance (60 of
  consolidated assets of firm related to life
  insurance)
• Sample period Jan. 1975 to Dec. 2000
• Monthly return data for CRSP
• Equally-weighted monthly portfolios (initial
  look)
• SP 500 index is used to represent the market
  index
• Holding period returns are used (instead of
  interest rates)
• Long-term (approx. 20 year maturity)
• Short-term (U.S. Treasury bill)

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Basic Model

• RETt ?0 ?1 RMKTt ?2 RATEt ?log(ht) ?t
• test whether return volatility is
  significant
• ht ?0 ?1 ?t-12 ?2 ht-1
• ARCH term GARCH term

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Extended Model 1

• RETt ?0 ?1 RMKTt ?2 RATEt
• ?3 D2 RATEt ?3 D2 RATEt ?log(ht) ?t
• test whether return volatility is
  significant
• ht ?0 ?1 ?t-12 ?2 ht-1
• ARCH term GARCH term
• D2 Nov. 1979 - Sept. 1982
• D3 Sept. 1982 - Dec. 2000

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Extended Model 2

• RETt ?0 ?1 RMKTt ?2 RATEt
• ?3 D2 RATEt ?3 D2 RATEt ?log(ht) ?t
• test whether return volatility is
  significant
• ht ?0 ?1 ?t-12 ?2 ht-1 g2 D2 g3
  D3
• ARCH term GARCH term
• D2 Nov. 1979 - Sept. 1982
• D3 Sept. 1982 - Dec. 2000

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Hypotheses

• H1 There are no interest rate effects
• H2 IR sensitivity does not change across
  monetary policy regimes
•  
• H3 Return volatility is not a significant factor
  in LI stock returns
•  
• H4 Return volatility is time invariant
•  
• H5 Return volatility follows an ARCH
  (time-variant and short- memory), rather than a
  GARCH (time-variant and long-memory)
•  
• H6 Volatility is time-variant, it has a short
  memory, and no intertemporal effects exist
  between volatility and return

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Interest Rate SensitivitiesThe Basic GARCH-M
Model

• Long rate Short rate
• Market return 0.762 0.801
• (H1) Interest rate (?20) 0.123 0.129
• (H3) Log (volatility) (?0) 0.005 0.007
• ARCH term (?10) 0.118 0.111
• GARCH term (?20) 0.749 0.757

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Extended GARCH-M Models(Long rate only)

• (1) (2)
• Interest rate 0.566 0.494
• (H2) D2 Nov. 1979 - Sept. 1982 -0.404 -0.33
  8
• D3 Sept. 1982 - Dec.
  2000 -0.513 -0.437
• (i.e., sensitivity to interest rates
  decreased in both periods)
• Log (volatility) 0.002 0.005
• ARCH term (?10) 0.134 0.128
• GARCH term (?20) 0.726 0.77
• D2 Nov. 1979 - Sept. 1982 ------ -0.00004
• D3 Sept. 1982 - Dec. 2000 ------ -0.0001

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Interpreting the Results

• Are LIC common stock returns sensitivity to
  changes in interest rates? Yes.
• Is volatility time-varying? Yes.
• Function of its own lagged value
• Function of the intensity of the previous period
  innovation
• Does the interest rate sensitivity vary across
  sub-periods following Federal Reserve MP regimes?
  Yes.

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Findings (1)

• Equity values of life insurance companies are
  sensitive to the long-term, but not to the
  short-term, interest rate
• IR sensitivity is positively correlated with
  changes in holding period returns on bonds
  (negatively correlated with changes in interest
  rates).
• Coefficients in the volatility of stock returns
  equation show that volatility is time-varying and
  evolves over time as a function of its own lagged
  value, as well as the intensity of the innovation
  that occurred in the market in the previous
  period.

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Findings (2)

• IR sensitivity varies across sub-periods in
  response to the Federal Reserve Systems monetary
  policy strategy and the general volatility of
  financial markets.

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Conclusions

• Like stock returns of depository institutions,
  we find evidence that the stock returns of life
  insurance companies are correlated with movements
  in interest rates and, hence, their valuation
  model is similar in form to that of the banks.
• The sign, significance, and magnitude of the
  interest rate variable are sensitive to the
  choice of the interest rate, model specification,
  as well as the prevailing monetary policy
  strategy. This too is similar to the results for
  depository institutions.

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Continued Research

• Related to this study
• Cross-sectional analysis of LI equity returns
• Size, b/m, A-L durations
• LI interest-sensitivity vs. other types of firms
• Insurer equity return sensitivity L vs P-C
• Individual annuities and price disparity
• Variable annuities and fee structures
• Welfare economics of backdating
• Ratings of insurers vs. bond ratings of parents