The Cost of Financial Frictions for Life Insurers

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1 The Cost of Financial Frictions for Life Insurers Ralph S. J. Koijen Motohiro Yogo University of Chicago and NBER Federal Reserve Bank of Minneapolis 1 1 The views expressed herein are not necessarily those of the Federal Reserve Bank of Minneapolis or the Federal Reserve System.

2 Theories of insurance markets Traditional theories: Market equilibrium determined by the demand side. Life-cycle demand (Yaari 1965). Informational frictions (Rothschild and Stiglitz 1976). Assumes efficient capital markets on the supply side.

3 Theories of insurance markets Traditional theories: Market equilibrium determined by the demand side. Life-cycle demand (Yaari 1965). Informational frictions (Rothschild and Stiglitz 1976). Assumes efficient capital markets on the supply side. Modern view: Insurance companies are financial institutions. Vulnerable to balance sheet shocks. Pricing affected by financial frictions and statutory reserve regulation.

4 Evidence on individual annuities and life insurance 1 Firesale of policies in January Term and life annuities: Average markup of 25%. Universal life insurance: Average markup of 52%. 2 Larger price reductions for Policies with looser statutory reserve requirements. Insurance companies with more adverse balance sheet shocks. 3 Firesale of policies complements conventional channels of recapitalization: Direct capital injection from the holding company. Reduction of required capital by shifting to safer assets.

5 Evidence on individual annuities and life insurance 1 Firesale of policies in January Term and life annuities: Average markup of 25%. Universal life insurance: Average markup of 52%. 2 Larger price reductions for Policies with looser statutory reserve requirements. Insurance companies with more adverse balance sheet shocks. 3 Firesale of policies complements conventional channels of recapitalization: Direct capital injection from the holding company. Reduction of required capital by shifting to safer assets. 4 Exploit exogenous variation in required reserves across policies to identify the shadow cost of financial frictions. Nearly $5 per dollar of excess reserve in January 2009.

6 Example: Allianz Life Insurance Company 20-year term annuity: Guaranteed payment of $1 for 20 years. Allianz priced it at $14.37 in July $11.84 in January $14.80 in July 2009.

7 Example: Allianz Life Insurance Company 20-year term annuity: Guaranteed payment of $1 for 20 years. Allianz priced it at $14.37 in July $11.84 in January $14.80 in July Replicating portfolio of Treasuries cost $14.56 in January Economic profit: $11.84 $14.56 = $2.72

8 Example: Allianz Life Insurance Company 20-year term annuity: Guaranteed payment of $1 for 20 years. Allianz priced it at $14.37 in July $11.84 in January $14.80 in July Replicating portfolio of Treasuries cost $14.56 in January Economic profit: $11.84 $14.56 = $2.72 Statutory reserves (liabilities) recorded at accounting value. A L $11.84 $11.47 Sale creates statutory capital: $11.84 $11.47 = $0.37

9 Example: Allianz Life Insurance Company 20-year term annuity: Guaranteed payment of $1 for 20 years. Allianz priced it at $14.37 in July $11.84 in January $14.80 in July Replicating portfolio of Treasuries cost $14.56 in January Economic profit: $11.84 $14.56 = $2.72 Statutory reserves (liabilities) recorded at accounting value. A L $11.84 $11.47 Sale creates statutory capital: $11.84 $11.47 = $0.37 Cost of statutory capital: $2.72/$0.37 = $7.35

10 Annual premiums for individual annuities and life insurance Billions of dollars Annuities Life insurance Year

11 Data on annuity and life insurance prices Annuities: January 1989 July 2011 (semiannual) Over 30,000 observations Over 100 insurance companies. Types of policies: 1 Term annuities: 5- to 30-year maturities. 2 Life annuities: Male and female, 50- to 90-years old. 3 Guaranteed annuities: Male and female, 50- to 90-years old, 10- or 20-year guarantees. Universal life insurance: January 2005 July 2011 (semiannual) Nearly 4,000 observations Over 50 insurance companies.

12 Data on annuity and life insurance prices Annuities: January 1989 July 2011 (semiannual) Over 30,000 observations Over 100 insurance companies. Types of policies: 1 Term annuities: 5- to 30-year maturities. 2 Life annuities: Male and female, 50- to 90-years old. 3 Guaranteed annuities: Male and female, 50- to 90-years old, 10- or 20-year guarantees. Universal life insurance: January 2005 July 2011 (semiannual) Nearly 4,000 observations Over 50 insurance companies. Calculate the actuarial value for each type of policy. Mortality tables from the American Society of Actuaries. Zero-coupon Treasury yield curve. Merged with A.M. Best data on balance sheets and ratings.

13 Average markup on term annuities 30 year term annuities 20 year term annuities Markup (percent) Average 95% confidence interval Jan 1989 Jan 1994 Jan 1999 Jan 2004 Jan 2009 Date Markup (percent) Jan 1989 Jan 1994 Jan 1999 Jan 2004 Jan 2009 Date 10 year term annuities 5 year term annuities Markup (percent) Jan 1989 Jan 1994 Jan 1999 Jan 2004 Jan 2009 Date Markup (percent) Jan 1989 Jan 1994 Jan 1999 Jan 2004 Jan 2009 Date

14 Average markup on life annuities Life annuities: Age 50 Life annuities: Age 60 Markup (percent) Average 95% confidence interval Jan 1989 Jan 1994 Jan 1999 Jan 2004 Jan 2009 Date Markup (percent) Jan 1989 Jan 1994 Jan 1999 Jan 2004 Jan 2009 Date Life annuities: Age 70 Life annuities: Age 80 Markup (percent) Jan 1989 Jan 1994 Jan 1999 Jan 2004 Jan 2009 Date Markup (percent) Jan 1989 Jan 1994 Jan 1999 Jan 2004 Jan 2009 Date

15 Average markup on universal life insurance Markup (percent) Universal life insurance: Age 30 Average 95% confidence interval Jan 2005 Jan 2007 Jan 2009 Jan 2011 Date Markup (percent) Universal life insurance: Age 40 Jan 2005 Jan 2007 Jan 2009 Jan 2011 Date Markup (percent) Universal life insurance: Age 50 Jan 2005 Jan 2007 Jan 2009 Jan 2011 Date Markup (percent) Universal life insurance: Age 60 Jan 2005 Jan 2007 Jan 2009 Jan 2011 Date

16 Default risk 1 Policies backed by the state guaranty fund. What if it fails? Lower bound on the recovery rate: 84%. Only 16% of life insurers assets are risky. Asset deficit of 5 10% in past cases of insolvency.

17 Default risk 1 Policies backed by the state guaranty fund. What if it fails? Lower bound on the recovery rate: 84%. Only 16% of life insurers assets are risky. Asset deficit of 5 10% in past cases of insolvency. Risk-neutral default probabilities implied by term annuities in January 2009: Must be upward sloping. 100% for maturity greater than 15 years. Inconsistent with default probabilities implied by CDS.

18 Default risk 1 Policies backed by the state guaranty fund. What if it fails? Lower bound on the recovery rate: 84%. Only 16% of life insurers assets are risky. Asset deficit of 5 10% in past cases of insolvency. Risk-neutral default probabilities implied by term annuities in January 2009: Must be upward sloping. 100% for maturity greater than 15 years. Inconsistent with default probabilities implied by CDS. 2 No discounts on life annuities during the Great Depression. Inconsistent with default story. Consistent with our explanation based on statutory reserve regulation.

19 Default probabilities implied by term annuities in January 2009 Maturity (years) Insurance company Panel A: Markup (percent) Allianz Life Insurance of North America American General Life Insurance Aviva Life and Annuity Genworth Life Insurance Lincoln Benefit Life MetLife Investors USA Insurance Panel B: Default probabilities implied by term annuities (annual percent) Allianz Life Insurance of North America American General Life Insurance Aviva Life and Annuity Genworth Life Insurance Lincoln Benefit Life MetLife Investors USA Insurance Panel C: Default probabilities implied by credit default swaps (annual percent) Allianz Life Insurance of North America American General Life Insurance Aviva Life and Annuity Genworth Life Insurance Lincoln Benefit Life MetLife Investors USA Insurance

20 Statutory reserve regulation Standard Valuation Law: Present value formula for calculating required reserves for each type of policy. Discount rate for annuities: (y t 0.03) where y t is a moving average of the Moody s composite bond yield.

21 Statutory reserve regulation Standard Valuation Law: Present value formula for calculating required reserves for each type of policy. Discount rate for annuities: (y t 0.03) where y t is a moving average of the Moody s composite bond yield. Discount rate for life insurance: (min{y t, 0.09} 0.03) (max{y t, 0.09} 0.09)

22 Discount rates for annuities and life insurance Percent Annuities Life insurance 10 year Treasury Jan 1989 Jan 1994 Jan 1999 Jan 2004 Jan 2009 Date

23 Reserve to actuarial value for annuities Term annuities Ratio of reserve to actuarial value years 10 years 20 years 30 years Jan 1989 Jan 1994 Jan 1999 Jan 2004 Jan 2009 Date

24 Structural model of insurance pricing Insurance company sells i =1,...,I different types of policies: P i,t :Price V i,t :Actuarialvalue V i,t : Reserve value Q i,t (P): Demand function with Q i,t (P) < 0 C t : Fixed cost

25 Structural model of insurance pricing Insurance company sells i =1,...,I different types of policies: Profit: P i,t :Price V i,t :Actuarialvalue V i,t : Reserve value Q i,t (P): Demand function with Q i,t (P) < 0 C t : Fixed cost Π t = I (P i,t V i,t )Q i,t C t i=1 Firm value: J t =Π t + 1 R E t[j t+1 ]

26 Assets: A t = R A,t A t 1 + Statutory reserves: I P i,t Q i,t C t i=1 I L t = R L,t L t 1 + V i,t Q i,t i=1

27 Assets: Statutory reserves: Leverage constraint: A t = R A,t A t 1 + L t = R L,t L t 1 + L t A t φ I P i,t Q i,t C t i=1 I V i,t Q i,t i=1

28 Assets: Statutory reserves: Leverage constraint: A t = R A,t A t 1 + Choose P i,t to maximize L t = R L,t L t 1 + I P i,t Q i,t C t i=1 I V i,t Q i,t i=1 L t A t φ K t = φa t L t 0 L t = J t + λ t K t

29 Optimal insurance pricing Price of policy i: P i,t = V i,t ( 1 1 ɛ i,t ) 1 } {{ } Bertrand price where ɛ i,t is the elasticity of demand. Shadow cost of financial frictions: λ t = λ t + 1 [ ] R E Jt+1 t K t ( ) 1+λ t Vi,t /V i,t 1+λ t φ } {{ } Financial frictions = Π t K t

30 Optimal insurance pricing Price of policy i: P i,t = V i,t ( 1 1 ɛ i,t ) 1 } {{ } Bertrand price where ɛ i,t is the elasticity of demand. Shadow cost of financial frictions: λ t = λ t + 1 [ ] R E Jt+1 t K t ( ) 1+λ t Vi,t /V i,t 1+λ t φ } {{ } Financial frictions = Π t K t Model predicts deeper discounts for 1 Policies with looser statutory reserve requirements (i.e., lower V i,t /V i,t ). 2 Insurance companies that are more constrained (i.e., higher λ t φ).

31 Empirical specification Policy i, firmj, andtimet: ( ) ( Pi,j,t log = log 1 1 ) ( ) 1+λ j,t Vi,t /V i,t +log + e i,j,t V i,t ɛ i,j,t 1+λ j,t L j,t /A j,t Elasticity of demand: Shadow cost: ɛ i,j,t =1+exp{ β y i,j,t } λ j,t =exp{γ z j,t } Explanatory variables: Insurance company: AMB rating, leverage ratio, asset growth, and log assets. Dummies and interactions for policy type and date.

32 Identifying assumptions 1 Identification if demand is correctly specified. Average markup must be nonnegative in the absence of financial frictions.

33 Identifying assumptions 1 Identification if demand is correctly specified. Average markup must be nonnegative in the absence of financial frictions. 2 Identification even if demand is potentially misspecified. Linear approximation to the pricing model: ( ) ( ) Pi,j,t 1 Vi,t log α j,t + L j,t + u i,j,t V i,t 1/λ j,t + L j,t /A j,t V i,t A j,t Standard Valuation Law generates relative shifts in supply that are orthogonal to demand: ( ) Vi,t Cov, u i,j,t =0 V i,t

34 Shadow cost of financial frictions Dollars per dollar of excess reserve Shadow cost 95% confidence interval Jan 2000 Jan 2003 Jan 2006 Jan 2009 Date

35 Shadow cost of financial frictions in January 2009 A.M. Asset Best Leverage growth Shadow Insurance company rating ratio (percent) cost MetLife Investors USA Insurance A Allianz Life Insurance of North America A Lincoln Benefit Life A OM Financial Life Insurance A Aviva Life and Annuity A Presidential Life Insurance B EquiTrust Life Insurance B Integrity Life Insurance A United of Omaha Life Insurance A Genworth Life Insurance A North American for Life and Health Insurance A American National Insurance A American General Life Insurance A

36 Change in Annuity Policies Issued from 2007 to 2009 Financially constrained companies that lowered prices also sold more policies. Consistent with supply curve shifting down. Quantity growth (percent) Shadow cost (Dollars per dollar of excess reserve)

37 Conventional channels of recapitalization in Financially constrained companies also 1 Received large capital injection from their holding company: Issuance of surplus notes. Reduction of stockholder dividends. 2 Reduced required risk-based capital by shifting to safer assets. Percent Inflow of capital surplus funds Shadow cost (Dollars per dollar of excess reserve) Percent Change in cash and short term investments Shadow cost (Dollars per dollar of excess reserve)

38 Fully specified model for welfare analysis Continuum of one-period consumers: 1 Has quasi-linear utility over life annuities and wealth. 2 Implies constant-elasticity demand for life annuities: Q t = X t P ɛ t where X t is a stochastic demand shock. 3 Faces a search cost to be matched with an insurance company. Continuum of insurance companies: 1 Constant returns on assets and liabilities, equal to the riskless interest rate. 2 Fixed cost creates operating leverage. 3 Heterogeneity in initial excess reserves, and therefore, financial constraints. Equilibrium price dispersion: Lucky consumers get matched with a financially constrained company and pay a lower price.

39 Optimal insurance price and firm value in the calibrated model 10 Optimal insurance price 100 Firm value Shadow cost Markup (percent) Dollars Initial excess reserves (percent of firm value) Dollars per dollar of excess reserve

40 Welfare cost of deviations from actuarially fair pricing Markup (percent) Demand and marginal cost Demand Marginal cost Surplus lost (net profits gained) Profits lost (net surplus gained) Percent of sales under zero markup Welfare cost Quantity (share of sales under zero markup) Markup (percent)

41 Welfare cost of deviations from actuarially fair pricing Markup (percent) Demand and marginal cost Demand Marginal cost Surplus lost (net profits gained) Profits lost (net surplus gained) Percent of sales under zero markup Welfare cost Quantity (share of sales under zero markup) Markup (percent) A simple modification to statutory reserve regulation (i.e., V = φv ) can eliminate firesales.

42 Broader implications 1 Household finance: Literature mostly about frictions on the demand side. Household borrowing constraints, asymmetric information, moral hazard, and near rationality. Financial and regulatory frictions on the supply side are also important for market equilibrium and social welfare.

43 Broader implications 1 Household finance: Literature mostly about frictions on the demand side. Household borrowing constraints, asymmetric information, moral hazard, and near rationality. Financial and regulatory frictions on the supply side are also important for market equilibrium and social welfare. 2 Macro models with financial frictions: Micro evidence necessary. We quantify the cost of financial frictions for life insurers. Extend our empirical approach to other types of financial institutions.

44 Average markup under the U.S. agency yield curve Markup (percent) year term annuities Average 95% confidence interval Jan 2000 Jan 2003 Jan 2006 Jan 2009 Date Markup (percent) Life annuities: Age 50 Jan 2000 Jan 2003 Jan 2006 Jan 2009 Date Universal life insurance: Age 30 Markup (percent) Jan 2000 Jan 2003 Jan 2006 Jan 2009 Date

45 Summary statistics for annuity and life insurance prices Number of Markup (percent) Sample Insurance Standard Type of policy begins Observations companies Mean Median deviation Term annuities: 5 years January years January , years July years July years July years July Life annuities: Life only January , year guaranteed July , year guaranteed July , Universal life insurance January ,

46 Estimated model of insurance pricing Explanatory variable Average marginal effect Rating: A to A 3.26 (21.58) Rating: B++ to B 8.13 (10.70) Leverage ratio (-24.43) Asset growth 0.10 (0.00) Log assets 1.88 (36.81) Interaction effects for life annuities: Rating: A to A (-19.96) Rating: B++ to B (-9.90) Leverage ratio (28.43) Asset growth (-5.27) Log assets (-28.59) Female 0.28 (4.74) Age (1.10) Age (1.61) Age (9.28) Age (12.79) Age (5.05) Age (7.65) Age (8.36) Age (6.46) Interaction effects for life insurance: Rating: A to A (-5.15) Leverage ratio (4.15) Asset growth (-5.22) Log assets (-7.57) Female 0.17 (0.00) Age (0.84) Age (0.00) Age (0.00) Age (0.00) Age (0.05) Age (6.27) R 2 (percent) Observations 29,756

47 Parameters in the calibrated model Parameter Symbol Value Riskless interest rate R 1 0.5% Ratio of reserve to actuarial value V /V 0.71 Elasticity of demand ɛ 11 Standard deviation of demand shocks σ 28% Size of the fixed cost c 1% Sensitivity of the fixed cost to demand shocks ω 4.02 Maximum leverage ratio φ 0.97

48 Reserve to actuarial value for universal life insurance Ratio of reserve to actuarial value Male aged 30 Male aged 40 Male aged 50 Male aged 60 Jan 2005 Jan 2007 Jan 2009 Jan 2011 Date

49 Asset growth and the leverage ratio for life insurers Asset growth (percent) Asset growth (percent) Leverage ratio Year Leverage ratio

50 Price change versus asset growth in January 2009 Term annuities Life annuities Price change (percent) Asset growth (percent) Price change (percent) Asset growth (percent) 10 year guaranteed annuities 20 year guaranteed annuities Price change (percent) Asset growth (percent) Price change (percent) Asset growth (percent)

51 Average markup on life annuities in Life annuities: Age 50 Life annuities: Age 60 Markup (percent) Average 95% confidence interval Markup (percent) Jan 1929 Jan 1931 Jan 1933 Jan 1935 Jan 1937 Date Jan 1929 Jan 1931 Jan 1933 Jan 1935 Jan 1937 Date Life annuities: Age 70 Life annuities: Age 80 Markup (percent) Markup (percent) Jan 1929 Jan 1931 Jan 1933 Jan 1935 Jan 1937 Date Jan 1929 Jan 1931 Jan 1933 Jan 1935 Jan 1937 Date

52 Reserve to actuarial value for life annuities in Ratio of reserve to actuarial value Male aged 50 Male aged 60 Male aged 70 Male aged 80 Jan 1929 Jan 1931 Jan 1933 Jan 1935 Jan 1937 Date

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