Developing Equity Release Markets: Risk Analysis for Reverse Mortgage and Home Reversion

Transcription

1 Developing Equiy Release Markes: Risk Analysis for Reverse Morgage and Home Reversion Daniel Alai, Hua Chen, Daniel Cho, Kaja Hanewald, Michael Sherris Developing he Equiy Release Markes 8 h Inernaional Longeviy Risk and Capial Markes Soluion 1

2 Inroducion Home equiy release producs Allow reirees o conver a previously illiquid asse ino cash paymens which can be used for home improvemens, regular income, deb repaymen, aged care and medical reamens ec. Reverse morgage Boehm and Ehrhard (1994), Chinloy and Megbolugbe (1994), Szymanoski (1994), Rodda e al. (24), Ma and Deng (26), Wang e al. (27), Chen e al. (21), Sherris and Sun (21) Home reversion Lile research has been done on he risk analysis of oher equiy release producs, such as home reversion conracs. Developing he Equiy Release Markes 8 h Inernaional Longeviy Risk and Capial Markes Soluion 2

3 Inroducion US Reverse morgage producs dominae. HECM accouns for 95% of he marke (Ma and Deng, 26). UK Reverse morgages, home reversion and oher equiy release producs have been available for beween 1 and 3 years Reverse morgage: 75%; home aversion: 25% (ASIC 25). Developing he Equiy Release Markes 8 h Inernaional Longeviy Risk and Capial Markes Soluion 3

4 RM and HR Reverse Morgage The provider lends he cusomer cash and obains a morgage charge over he cusomer's propery (or a share of he propery). The conrac is erminaed upon he deah or permanen moveou of he cusomer, a which ime he propery is sold and he proceeds are used o repay he ousanding loan. Typically, a no negaive equiy guaranee (NNEG) is included in he conac. Home Reversion The provider purchases he ownership righ over he cusomer's propery (or a share of he propery). The home is sold a discoun, and he conrac includes a lease for life agreemen. Developing he Equiy Release Markes 8 h Inernaional Longeviy Risk and Capial Markes Soluion 4

5 Major Risks in RM and HR Risks of RM Terminaion Risk Longeviy risk, mobiliy risk, refinancing risk Loan Ineres Rae risk House Price Depreciaion Risk Risks of HR Terminaion Risk Longeviy risk, mobiliy risk, refinancing risk Renal yield appreciaion risk House Price Depreciaion Risk Developing he Equiy Release Markes 8 h Inernaional Longeviy Risk and Capial Markes Soluion 5

6 Markov Terminaion Model Assume a single, female policyholder. Conrac erminaion is deermined by wo proporionaliy consans on female populaion moraliy. c where θ is he a-home moraliy proporionaliy consan ρ is non-moraliy driven proporionaliy consan Assume a Gomperz srucure for he populaion force of moraliy ep Developing he Equiy Release Markes 8 h Inernaional Longeviy Risk and Capial Markes Soluion 6

7 Parameer Calibraion λ and γ Use daa from he Human Moraliy Daabase: ages 5-15 and calendar years from Ausralian females. Fi boh an ordinary linear regression (LR) on he log-ransformed moraliy raes as well as a Poisson regression (PR) on deah couns wih an appropriae eposure offse. The resuls are very similar; we use PR resuls ˆ( LR) θ and ρ.217; ˆ( PR) Values are aken from Ji e al. (212) Age ρ f θ f (.171; ˆ LR) (.993; ˆ PR).117 Developing he Equiy Release Markes 8 h Inernaional Longeviy Risk and Capial Markes Soluion 7

8 Terminaion Probabiliies Developing he Equiy Release Markes 8 h Inernaional Longeviy Risk and Capial Markes Soluion 8

9 VAR Economic Model Raw daa: quarerly daa from June 1993 o June 211 zero-coupon ineres raes (3-monh and 1-year) sandard variable morgage rae (MR) Sydney house price inde (HI) Sydney renal inde (RI). Sydney GDP he morgage rae and he 3-monh zero coupon raes are highly correlaed MR(Annual).3 ZC(Annual) Developing he Equiy Release Markes 8 h Inernaional Longeviy Risk and Capial Markes Soluion 9

10 VAR (1) z c 1 Bz 1 where is a lower riangular mari, Z 1 ~ N(, I) includes he following variables: 3-monh zero coupon rae (morgage rae can be epressed as he 3-monh zero coupon rae plus a fied margin) Term srucure spread = 1-year ZC rae 3-monh ZC rae dln(hi) dln(ri) dln(gdp) Developing he Equiy Release Markes 8 h Inernaional Longeviy Risk and Capial Markes Soluion 1

11 Sochasic Discoun Facors We define he sochasic discoun facor as (Cochrane and Piazzesi 25) 1 m 1 ep 1z z is he shor rae in he VAR model where and 1 1,,,, 1 1 relaes shocks in he sae variables o he pricing kernel 2 where 1 z is a ime-varying vecor of marke price of risk The price of an asse a ime : P E m X 1 1 Recursively, P E s m s X Developing he Equiy Release Markes 8 h Inernaional Longeviy Risk and Capial Markes Soluion 11

12 Sochasic Discoun Facors SDF % 1.% SDR vs The Shor Rae SDF 8.% 6.% 4.% 2.% SDR ERP dlnzc25i.% (Years) Developing he Equiy Release Markes 8 h Inernaional Longeviy Risk and Capial Markes Soluion 12

13 Esimaion Procedure VAR parameers ( c, B, and Σ) are esimaed by maimum likelihood Risk parameers (λ and Λ 1 ) can be esimaed by minimizing he sum of he squared differences beween he fied yields of he erm srucure model and hisorical zero coupon yields. { where yˆ ( n) An n B n n and A n and B n can be solved recursively A B min n n, 1 T N ( n) ( n) yˆ y } 1 n1 A n1 B n1 z B 1 Bn c B n1b n1 Developing he Equiy Release Markes 8 h Inernaional Longeviy Risk and Capial Markes Soluion 13

14 8 h Inernaional Longeviy Risk and Capial Markes Soluion Non-Negaive Equiy Guaranee in RM 14 Developing he Equiy Release Markes For a fied erminaion ime For random erminaion ime Cash flow analysis, ma H L NN 1, ma s s H L q p m E NN 1, min c r e L H L e q p RM

15 8 h Inernaional Longeviy Risk and Capial Markes Soluion Lease for Life in HR 15 Developing he Equiy Release Markes For a fied erminaion ime T For random erminaion ime Cash flow analysis T s s g H m E LL 1 s s g H p m E LL 1 c r e LL H H e q p HR

16 NN and LL Age H LTV/Acq Reverse Morgage Home Reversion NN Premium EPV(RM) LL EPV(HR) 65 48, 64% 19, % 86,352 5,15 2, , 64% 22, % 97,146 5,642 23, 65 6, 64% 24, % 17,94 6,269 25, , 7% 18, % 61,996 7,837 25, , 7% 2, % 69,746 8,817 28,6 75 6, 7% 22, % 77,495 9,797 31, , 76% 16, % 4,568 11,24 23, , 76% 18, % 45,639 12,42 26, , 76% 2, % 5,71 13,78 29,827 Developing he Equiy Release Markes 8 h Inernaional Longeviy Risk and Capial Markes Soluion 16

17 LTV Developing he Equiy Release Markes 8 h Inernaional Longeviy Risk and Capial Markes Soluion 17

18 Payoff Comparison $AUD(,) 6 Payoff Comparison: HR&RM HR_P HR_P_hq HR_P_lq RM_P RM_P_hq RM_P_lq Developing he Equiy Release Markes 8 h Inernaional Longeviy Risk and Capial Markes Soluion 18

19 % 2% 5% 7% 9% 12% 14% 16% 19% 21% 23% 25% 28% 3% 32% 35% 37% 39% 42% 44% 46% 48% 51% 53% 55% 58% 6% 62% 65% 67% 69% 71% 74% 76% 78% 81% 83% 85% 88% 9% 92% 94% 97% 99% Quanile Funcion $AUD(,) Quanile Funcion: RM vs HR RMA65H48L64 4 HRA65H48L Developing he Equiy Release Markes 8 h Inernaional Longeviy Risk and Capial Markes Soluion 19

20 Risk Measures Reverse Morgage VaR 95% VaR 99% VaR 99.5% CVaR 95% CVaR 99% CVaR 99.5% A65H48L A65H54L A65H6L A75H48L A75H54L A75H6L A85H48L A85H54L A85H6L Home Reversion VaR 95% VaR 99% VaR 99.5% CVaR 95% CVaR 99% CVaR 99.5% A65H48L A65H54L A65H6L A75H48L A75H54L A75H6L A85H48L A85H54L A85H6L Developing he Equiy Release Markes 8 h Inernaional Longeviy Risk and Capial Markes Soluion 2

21 Conclusions Comparison beween RM and HR RM: accumulaion of deb over he life of he conrac HR: deb-free. RM: senior homeowners bear various risks, including longeviy risk, ineres rae risk and propery value risk HR: hese risks are remied o he provider wih he ransfer of he ile. RM: providers wan house price o rise, while homeowners do no care HR: The ineress of invesors and consumers are aligned: boh wan he value of he home o rise Consumers may prefer home reversion produc, bu providers bear higher risk and need more sringen capial requiremen. Developing he Equiy Release Markes 8 h Inernaional Longeviy Risk and Capial Markes Soluion 21