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

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Title: 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 Model The 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

2
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

3
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

4
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

5
Life-Health Insurer Assets (Ins. Information
Institute)
                                               
                                                  
                                                  
                
6
L-H Insurer Asset Distribution (Ins. Information
Institute)
( billions)
                                               
                                                  
                                                  
                
7
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

8
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

9
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

10
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

11
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

12
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

13
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.

14
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

15
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)

16
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

17
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

18
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

19
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

20
Interest Rate Sensitivities The 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

21
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

22
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.

23
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.

24
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.

25
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.

26
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
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