NETWORKING Is the Home Equity Conversion Program in the United - PowerPoint PPT Presentation

NETWORKING Is the Home Equity Conversion Program in the United States Sustainable? Hua Chen, Temple University (with Samuel H. Cox and Shaun Wang)

Motivation • Mortality improvement – life expectancy at birth was 60.95 in 1933, 77.87 in 2004 • “House Rich & Cash Poor” dilemma – Aging population: 34m elderly now; 71m elderly by 2030 • Reduced monthly incomes • Rising health-care costs • Decreasing pension plan benefits. • Difficult to maintain financial independence and living standards. – 12.5 million elderly have no mortgage debt, and the median value of these unmortgaged properties is $127,959 (American Housing Survey) • Reverse Mortgage – Enable elderly homeowners to convert their home equity into cash income without selling their home

Reverse Mortgage Figure 1: Comparison between Forward Mortgage and Reverse Mortgage • Deferred repayment until – a borrower sells the property, moves out, or dies – fails to pay property tax/homeowner insurance – fails to maintain the condition of the home)

HECM Program • Borrower requirements – 62 years of age or older – Own the property outright or have a small amount of balance – Occupy the property as the principal residence – Not be delinquent on any federal debt – Participate in a consumer session given by an approved HECM counselor • Payment options – Lump sum – Line of credit – Monthly cash advance (tenure/term) • Initial principle limit (IPL) or principle limit factor (PLF) – Age of the youngest borrower – Current interest rate – Adjusted property value (maximum claim amount)

Non-Recourse Provision • Repayment under the non-recourse provision − <  , H H L = t t t  Repayment − ≥  , L H L t t t = − + − max( , 0 ) L L H t t t • The borrower is holding a debt position and an exchange option H L – exchange the property value for the loan outstanding balance t t • The non-recourse provision (NRP) is equivalent to writing the borrower a series of European exchange options with different times of maturity ω − − x 1 [ ] ∑ = − − rt NRP max[ , 0 ] p q e E L H + t x x t Q t t = 0 t

Mortgage Insurance Premiums • HECM loans are FHA insured – protect lenders from suffering losses if nonrepayment occurs – guarantee borrowers receiving monthly payments if the lender defaults • Mortgage insurance premiums (MIP) as of Oct. 4, 2010 – 2% of the property value at closing – 0.5% of the loan balance annually ω − − 1 x ( ) ∑ = + − rt MIP 0 . 02 0 . 005 H p e L 0 t x t = 1 t • Under the equivalent principle NRP = MIP

Insurance Risks in HECM • Mortality risk – HECM model: period life table • Fail to capture the dynamics of mortality rates over time • Fail to capture the mortality improvement jumps and adverse mortality jumps – Our paper • Generalized Lee-Carter model with asymmetric jump effects • Dynamic life table • Mobility risk – Health-related (move into long-term health-care facilities or nursing homes) – Non-health-related (marriage, divorce, death of the spouse, disasters, etc) – Practice: 30% of mortality rate (Jacobs, 1988; Deutsche Bank, 2007)

Insurance Risks in HECM • Interest rate risk – HECM loans are opt for adjustable interest rates – Practice: A fixed interest rate with a risk adjustment (150 bps) • House price depreciation risk – Geometric Brownian motion (Cunningham and Hendershott, 1984; Kau, Keenan and Muller, 1993) – Autocorrelations (Case and Shiller, 1989; the Institute of Actuaries, 2005b; Li, 2007) – Time series analysis!

Mortality Modeling: The Lee-Carter Model = + + ln( , ) m a b k e • . , x t x x t x t ∑ ∑ = = 1 and 0 b k The normalization conditions: x t x t = ∑ 1 T ⇒ ln( ) a m , x x t T = t 1 and A two-stage procedure for b k x t − ln( ) m a – Apply the singular value decomposition (SVD) method to , , x t x ( ) ∑ = + k exp( ) D Pop a b k – Re-estimate by iteration, s.t. t t x , t x x t x where is the actual total number of deaths at time t , D t is the population in age group x at time t . Pop , x t

Mortality Modeling: The Lee-Carter Model • Dynamic of from 1900 to 2006 k t

Mortality Modeling: The Lee-Carter Model • How to model ? k t – Lee and Carter (1992): random walk with drift = + µ + σ + (1918) k k Z Dummy + + t 1 t t 1 – Modeling mortality with jumps • Biffis (2005) • Cox, Lin and Wang (2005) • Bauer and Kramer (2007) • Chen and Cox (2009): transitory vs. permanent mortality jumps • Cox, Lin and Pedersen (2008): combine two types of jumps, complicated model • Chen, Cox and Wang (this paper): asymmetric jumps, normal distribution • Brockett, Deng and MacMinn (2010): asymmetric jumps, double exponential

Mortality Modeling: The Jump Process • A model with permanent jump effects = + µ − Λ + σ + Ι ( ) ( ) k k Z Y N + + + = + 1 1 1 { 1 } 1 t t t t N t + 1 t ~ ( , ) – Jump severity Y N m s  1, with probability p =  – Jump frequency N −  0, with probability 1 p – Random variation ~ N ( 0 , 1 ) Z Λ = = – Compensation term [ I ( )] E Y N pm = { 1 } N • A model with transitory jump effects ~ ~  = + µ + σ  k k Z + + t 1 t t 1  ~ = +  I ( ) k k Y N  + + + = + 1 1 1 { 1 } 1 t t t N t + 1 t

Mortality Modeling: The Jump Process • A model with asymmetric jump effects ~ ~  = + µ − Λ + σ + ( ) ( ) ( ) I I  k k Z Y Y N + + + < + = + 1 1 1 { 0 } 1 { 1 } 1 t t t t Y t N t + +  1 1 t t ~ = +  I ( ) I ( ) k k Y Y N  + + + > + = + 1 1 1 { 0 } 1 { 1 } 1 t t t Y t N t + + 1 1 t t Λ = = − Φ − φ I Ι • Compensation [ ( ) ( )] [1 ( )] ( ) E Y Y N pm m s ps m s < = { 0} { 1} Y N > ⇒ 0 mortality deterioration and transitory effect Y < ⇒ 0 mortality improvement and permanent effect Y Table 1: Parameter Estimates via CMLE

Model the HPI • Data: Nationwide House Price Index (HPI) from 1975 to 2009 Figure 2: HPI Log Returns (Y) Figure 3: The First Difference of HPI Log Returns (DY)

Model the HPI • ARMA(2,0) + GARCH(1,1) = φ + φ + ε ε Φ σ 2 DY DY DY | ~ ( 0 , ) , where N − − − t 1 t 1 2 t 2 t 1 t t t σ = + α σ − + β ε 2 2 2 d − 1 1 1 1 t t t Figure 4: ACF of the Standardized Innovations Figure 5: ACF of the Squared Standardized Innovations

Conditional Esscher Transform • Exponential Tilting [ ] λ = exp( ) | E Y X x = * ( ) ( ) f x f x [ ] λ X X exp( ) E Y • Esscher Transform (Esscher, 1932) [ ] λ = λ exp( ) | exp( ) E X X x x = = * ( ) ( ) ( ) f x f x f x [ ] [ ] λ λ X X X exp( ) exp( ) E X E X – Justified by maximizing the expected power utility of an economic agent • Conditional Esscher Transform (Buhlmann, Delbaen, Embrechts and Shiryaev, 1996) λ exp( ) x Φ = Φ * t ( | ) ( | ) f x f x [ ] − − λ Φ X t 1 X t 1 exp( ) | t t E X − t t t 1 – Justified within the dynamic framework of utility maximization problems

How to Transform? • ARMA(2,0) + GARCH(1,1) ε Φ σ = φ + φ + ε 2 – , where | ~ ( 0 , ) N DY DY DY − − − 1 t t t 1 1 2 2 t t t t σ = + α σ − + β ε 2 2 2 d – − 1 1 1 1 t t t • Under the physical measure P µ = φ − + φ Φ µ σ 2 DY DY – | ~ ( , ) , where DY N − − t 1 t 1 2 t 2 1 t t t t µ = µ + Φ µ σ 2 ˆ ˆ | ~ ( , ) Y Y N – , where − − 1 1 t t t t t t t • Under the risk adjusted measure Q λ λ Φ − = q q [exp( ); | ] exp( ) – Choose s.t. (Buhlmann et al., 1996) E Y r Q t t t t 1 t   1 Φ − − σ σ   2 2 | ~ , Y N r – t t 1 t t   2

Numerical Results: Assumptions • 6-month delay from home exit until the actual sale of the property • Transaction cost: 6% • Risk-free interest rate: 10 year U.S. Treasury rate (3.42%) • Interest rate charged on the loan: one year CMT rate (0.42%) plus a lender’s margin (1.5%) and an additional MIP (0.05%) • Rental yield: 2% per annum. • Initial house value: $300,000 • Assume the property is located in Philadelphia, Zip code 19104.

Numerical Results: MIP vs. NRP Table 2: Value of NRP and MIP at Different Ages • NRP decreases with the age at origination • MIP decreases, but MIPs are far more than NRPs. • The HECM program is sustainable ?!

Numerical Results: Declining Housing Market • What if the housing price dropped by 5%, 10%, 15% or 20%? Figure 6: MIP and NRP at Different Scenarios Figure 7: Ratios of the MPI to NRP 10 H 0 =300,000 H 0 =285,000 9 H 0 =270,000 8 H 0 =255,000 H 0 =240,000 Ratio of MIP to NRP 7 6 5 4 3 2 60 65 70 75 80 85 90 Ages at Closing