Risk Management and Payout Design of Reverse Mortgages

1 Risk Management and Payout Design of Reverse Mortgages Daniel Cho, Katja Hanewald and Michael Sherris School of Risk & Actuarial ARC Centre of Excellence in Population Ageing Research (CEPAR) University of New South Wales 1st CEPAR International Conference, 2-4 July, 2013, University of New South Wales, Sydney

2 Background Population Ageing Population ageing - retirement income, health and aged care costs. Substantial assets in housing. Increase in use of reverse mortgages by retirees. Concerns about solvency of providers and product designs. Reverse Mortgages Allow retirees to convert their equity in real estate assets into lump sum or income. Provide retirees with additional funding to finance consumption, medical costs and/or nursing home costs.

3 Motivation Aim of the research Quantify and compare risk and profitability for different reverse mortgage designs (lump-sum, lifetime income, inflation-indexed lifetime income). Contribution Growing literature on pricing and risk management of RMs, e.g.: Hosty et al. (2008); Chen et al. (2010); Shao et al. (2012); Alai et al. (2013). Pricing of RMs with regular income payments: Chinloy and Megbolugbe (1994) value the cross-over option; Lee et al. (2012) value the regular payments. Our focus: lender s net financial position and required risk-based capital for three payout types of RMs.

4 Reverse Mortgage Main features The provider loans the borrower a lump sum or an income stream and obtains a mortgage charge on the borrower s house. The contract is terminated upon death or permanent move-out of the borrower, at which time the house is sold and the proceeds are used to repay the outstanding loan balance. Major provider risks: interest rate risk, delayed termination (longevity), house price depreciation. Loan balance exceeding the house value at termination: no negative equity guarantee (NNEG).

RMs with Different Payouts Illustration: Development of the loan balance over time. (Loan principal and accumulated interest and NNEG premiums) 0 1 2... T 0 1 2... T Quarters (a) Lump-sum RM. Quarters (b) Income stream RM.

6 Methodology Models for RM termination and economic variables Markov termination model Vector autoregressive (VAR) model: economic scenarios, stochastic discount factors Pricing of the NNEG guarantee Simulation of product cash flows Cash flow analysis, risk metrics and sensitivity analysis

7 Vector Autoregression - Economic Variables VAR(2) z t = µ + A 1 y t 1 + A 2 y t 2 + ɛ t, where ɛ t N(0, I) Table: State Variables of the VAR Model Variables (in order) r (1) r (40) r (1) dln(hi ) dln(ri ) dln(gdp) dln(cpi ) Definition 3-month zero-coupon bond yields Spread between 3-month and 10-year ZC yields ln(sydney house price index) ln(sydney rental index) ln(australian GDP) ln(nsw CPI)

8 Loan Termination Model Multi-State Markov Model Single, female policyholder aged 65, 75 and 85 Mortality: estimated from Australian mortality data (ages 50-105, 1950-2009) from the Human Mortality Database Factors of Termination (Ji, 2011) At-home mortality: scaled-down mortality rates Long-term care incidence: age-dependent factor applied to base mortality rates Prepayments/Refinancing: dependent on the contract duration

9 Termination Model Table: Assumptions on Reverse Mortgage Loan Termination. LTCI At-home Mortality Prepayment Refinancing Age Proportion Proportion Duration Probability Duration Probability 65-70 0.050 0.970 1 0.00% 1-2 1.00% 75 0.060 0.970 2 0.00% 3 2.00% 80 0.070 0.970 3 0.15% 4-5 2.50% 85 0.110 0.955 4 0.30% 6-8 2.00% 90 0.150 0.940 5 0.30% 9-10 1.00% 95 0.185 0.940 6+ 0.75% 11-20 0.50% 100+ 0.220 0.940 21+ 0.25%

10 Key Variables - June 1993 to June 2011 Figure: Fitted stochastic discount factors, SDF, house price growth rates, dlnhi, and three-month zero-coupon yields, r (1).

11 Base Case Results Base case Female borrower, age 75, LTV = 40%, ϕ = 92%, no mortality improvements, VAR(2) model Table: Risk and profitability measures for RMs with lump-sum (LS), fixed income stream (IS) or inflation-indexed income stream (IIS) payments Contract Payment NN π(p.a.) EPV VaR CVaR LS 240,000 239 0.011% 51,977-40,395-36,336 IS 8,133 6,404 0.409% 35,829 7,742 14,176 IIS 6,835 9,714 0.641% 30,859 17,411 23,506

12 Loan Accumulation over Time Figure: Average loan balance, L t, and house price, H t, with 90% confidence intervals for RMs with lump-sum (LS), fixed income stream (IS) or inflation-indexed income stream (IIS) payments.

Sensitivity Analysis Different borrower ages Different loan-to-value (LTV) ratios Mortality improvements Different leverage ratios ( risk-based capital) VAR(1) instead of VAR(2) model 3

14 Sensitivity Analysis: Different LTV Ratios Figure: Profitability and risk for RMs with lump-sum (LS), fixed income stream (IS) or inflation-indexed income stream (IIS) payments.

15 Sensitivity Analysis: Different Borrower Ages Figure: Profitability and risk for RMs with lump-sum (LS), fixed income stream (IS) or inflation-indexed income stream (IIS) payments.

16 Conclusions Lump-sum RMs are more profitable and less risky for the lender than income stream RMs. Income-stream RMs are more exposed to longevity risk. All three contract types are more profitable and less risky when offered to younger retirees, more profitable, but also more risky for higher LTV ratios. Maximum LTV ratios vary with the age of borrower and the payout design of RM. Current Australian industry practice for LTV ratios conservative.

17 References Alai, D. H., Chen, H., Cho, D., Hanewald, K., and Sherris, M. (2013). Developing Equity Release Markets: Risk Analysis for Reverse Mortgages and Home Reversions. UNSW Australian School of Business Research Paper No. 2013ACTL01. Chen, H., Cox, S. H., and Wang, S. S. (2010). Is the Home Equity Conversion Mortgage in the United States Sustainable? Evidence from Pricing Mortgage Insurance Premiums and Non-Recourse Provisions Using Conditional Esscher Transform. Insurance: Mathematics and Economics, 46(2), 371 384. Chinloy, P. and Megbolugbe, I. F. (1994). Reverse Mortgages: Contracting and Crossover Risk. Real Estate Economics, 22(2), 367 386. Cochrane, J. and Piazzesi, M. (2002). Bond Risk Premia. National Bureau of Economic Research. Deloitte and SEQUAL (2012). Media Release: Australia s reverse mortgage market reaches $3.3bn at 31 December 2011. Deloitte Australia and Senior Australians Equity Release (SEQUAL). Hosty, G. M., Groves, S. J., Murray, C. A., and Shah, M. (2008). Pricing and Risk Capital in the Equity Release Market. British Actuarial Journal, 14(1), 41 91. Ji, M. (2011). A Semi-Markov Multiple State Model for Reverse Mortgage Terminations. Annals of Actuarial Science, 1(1), 1 23. Lee, Y.-T., Wang, C.-W., and Huang, H.-C. (2012). On the Valuation of Reverse Mortgages with Regular Tenure Payments. Insurance: Mathematics and Economics, 51(2), 430 441. Shao, A., Sherris, M., and Hanewald, K. (2012). Equity Release Products allowing for Individual House Price Risk. Proceedings of the 11th Emerging Researchers in Ageing Conference, 2012.

18 Data Table: Sources of Data Variables Source Series 3 month Zero-coupon yield RBA a Zero-coupon Interest Rates 10 year Zero-coupon yield RBA Zero-coupon Interest Rates Nominal Sydney house price index Residex SYDHPI Nominal Sydney rental yield index Residex SYDRYI Nominal GDP ABS b 5206.0 NSW CPI ABS 6401.0 a Reserve Bank of Australia b Australian Bureau of Statistics

19 Loan-to-Value Ratios in Australia Figure: Average Loan-to-Value Ratio of Reverse Mortgages sold in Australia. Source: Deloitte and SEQUAL (2012) (%) of the House Value at t=0 30 20 10 0 Actual LVR Max LVR <65 65-69 70-74 75-79 80+

20 Stochastic Discount Factor Model Stochastic Discount Factors Derive bond yield curve based on the development of the state variables under the VAR(2) model. Derive risk-adjusted stochastic discount factors M t assuming no arbitrage (Cochrane and Piazzesi, 2002;?). Use stochastic discount factors to price the NNEG. Specification M t+1 = exp (δ 1 z t + 1 2 λ tλ t + λ t ɛ t+1 ) δ 1 z t is the short rate with δ 1 = (1, 0, 0, 0, 0, 0). 1 2 λ tλ t + λ t ɛ t+1 relates shocks in the state variables to the pricing kernel. λ t = λ 0 + λ 1 z t is a time-varying vector of market prices of risk