Equity Release to supplement pension: Risk analyses of reverse mortgages

Transcription

1 Master s Thesis Executive Master Actuarial Science Equity Release to supplement pension: Risk analyses of reverse mortgages C.C. Werner-Huibers 14 th November 2013

2 1 Contents 2 Introduction Equity release products The equity release market abroad The Dutch Mortgage market Behavioural aspects or other barriers of equity release products Behavioural and psychological obstacles Regulatory issues Research Questions Equity Release Product Design A Lump-Sum Reverse Mortgage Cash Flow Pattern Income Stream Reverse Mortgage Cash Flow Pattern Pricing Framework: Simulation models for reverse mortgage risks Modelling the Probability of Termination Deriving arbitrage free scenarios for reverse mortgage products State variables of the VAR Model Mortgage rates VAR(1) model Stochastic discount factors Simulation results The Base Case Scenario Reverse mortgage products; Base case results Loan balance and house price Transforming the constant term of the VAR(1)model Transform to an average growth rate of Sensitivity to the mortgage margin Sensitivity to the Loan Value Ratio Sensitivity to mortality, costs and average delay of sales Transform to the long-term historical average growth rate Backtest using historic data starting in

3 5.4.1 Main risk drivers Current barriers for development of Dutch equity release market Conclusion Suggestions for further research Appendix A: List of variables Bibliography

4 2 Introduction Increased life expectancy and healthcare costs, a shrinking working population and a financial crises puts pressure on our pensions system and poses the question how to finance adequate pension incomes in the (near) future. With pensions and accrual rates decreasing and risks increasingly shifted toward households, there will be a need for households to make individual life cycle saving. There is a school of thoughts that advocates to look at life income in a broader sense 1. A strong retirement income system requires attention to other components of wealth, like housing, health and human capital 2. In this thesis I will focus on the component house as a possible funding source for retirement. Dutch elderly hold a large proportion of their savings in the form of home equity, which can be used to provide post-retirement income and health care costs. The majority of the Dutch population are homeowners and the widest gap between house value and mortgage loan is found among older house owners. In 2012 the average housing value of over-60s exceeds 300 thousand euros 3. So for the majority of elderly people their homes represent a key source of personal wealth. This locked equity could become an important component of financing retirement needs of an ageing population. Figure 1: mortgage loans and house values 2012 The process of converting home equity into cash while the homeowner is still alive is called home equity conversion (Phillips and Gwin 1992). Home equity conversion could facilitate consumption smoothing over the life cycle. Because release home equity might also be used to pay for health care expenditure, home equity conversion could also be of interest for public policy experts who are looking for ways to reduce healthcare costs. In order to help people releasing house equity it will be 1 In 2010 at the Pensioen Expeditie 2010, a congress of the Achmea Academy ( Prof. Gerry Dietvorst presented his vision on pension thinking: from three to five pillars or layers. 2 Innovation in retirement planning, pension research council CBS; Web magazine, 06 June

5 essential that the financial industry develops useful sustainable products. In this respect several initiatives have suggested 4 the need for new equity release or reverse mortgage products for the Dutch market. With the future limited possibilities to acquire sufficient pension income and the current financial situation, households need to take more financial decisions, and releasing home equity may be a useful instrument for optimal financial planning. 2.1 Equity release products Selling the home, and renting a smaller one is the most direct form of home equity conversion. This form requires moving to another home, which is usually unacceptable for older people. The willingness to move decreases with age). Another option is a combination of an immediate life annuity and a regular interest only mortgage. Stringent underwriting criteria of current interest only mortgages and the considerable difference between mortgages rates and the interest rates used for valuing annuities makes this form either impossible or the resulting additional income too small to be of interest. While home equity conversion can be achieved by many forms of loan, lease or sale (second mortgages, overdraft credit, leases, or sale and- move arrangements) there are products that are exclusively designed for the purpose of equity release. Equity release products can take two forms. A sale model, also known as home reversions, which involves an immediate sale of the property but provide for the right to remain in occupation. Or a loan model, also known as reverse mortgages. Reverse mortgage payments can be dispensed in several options, an up-front lump sum payment; an annuity of monthly payments as long as the borrower stays in the house (the tenure plan or lifetime mortgage); an annuity of monthly cash payment for a fixed period (the term plan); a line of credit; or a combination of the above (Ma and Deng, 2006). In a home reversion scheme, the provider purchases the ownerships right over the customer s property (or a share of the property) and the property is leased back to the consumer for life. The homeowners receive a discounted payment in exchange for a fixed proportion of their home. The discount represents the value of the lease for life agreement. The provider of this contracts faces property risk and in respect to the lease for life agreement faces rental yield appreciation and termination risk. In a home reversion scheme the customer is always better off prolonging the duration of the contract (Alai et al 2013). A reverse mortgage operates as the reverse of a regular mortgage or a forward sale of the house. For the borrower it s a capitalised interest loan or roll-up mortgage. The mortgage loan is paid out as regular income or as a lump sum and during the lifetime there is no obligation to pay interest. At the time the borrower sells the property, moves out or dies the loan gets repaid with accumulated interest through the sale of the property. So reverse mortgages involve accumulation of debt while home reversions are debt free. Reverse mortgages are issued to couples or single borrowers and carry fixed or variable interest rates. Reverse mortgage contracts are usually non-recourse. Which means that in order to protect borrowers from negative equity, reverse mortgages provide a no negative equity guarantee (NNEG). A NNEG limits the loan repayment to the sale proceeds of the property (net liquidation value of the property). Contracts often allow for refinancing or early repayment. 4 Taskforce Verzilveren 5

6 Reverse mortgage products will pose other service challenges to the provider. The provider is not required to process payments, but instead needs to determine a property s occupancy status and condition, and ensuring adequate insurance (Zhai 2000). The risks involved As there is no obligation to make interest payment, the lender does not face credit risks during the lifespan of the loan. Instead lenders of reverse mortgages are exposed to cross-over risk. The Crossover point is a time in the future when the loan balance will be equal to the net liquidation value (Zhai, 2000). Due to the No Negative Equity Guarantee, the lender incurs a loss if the value of the property does drop below the loan balance. This risk is called the cross-over risk. Cross-over risk Figure 2: Cross-over point Cross-over risk is induced by three risk factors : Property depreciation risk, Interest rate risk and the risk of delayed termination. For example, a delayed termination caused by longevity increases the probability that the loan balance will exceed (`crosses over' ) the property value due to a longer loan duration. So an increase of the lifespan of the loan resulted from longevity or reduced mobility rates will impose a higher cross-over risk. Since the loan balance beyond the Crossover point is capped by the property value, a high interest rate aggravates the Crossover risk. The Crossover point will also be reached sooner than expected If property value does not appreciate as much as was expected. 6

7 Other risks Figure 3: main drivers of cross-over risk Other risk inherent to reverse mortgage a lender might face are early redemption, adverse selection and moral hazard risk. If the reverse mortgages loans gives the borrower an option to repay the loan at any point of time, the lender is faced with the risk of early redemption, as the borrower will pay back the loan when it is most beneficial to him (high property values) which might not be in the interests of the lender. Adverse selection arises if consumers expecting an unusually long life or low mobility enter into reverse mortgages at a rate disproportionate to their share of the population (Davidoff and Welke 2004). Extended staying beyond the optimal length for an otherwise identical non-mortgager might also by related to the additional funds released through the mortgage which can make life in the home more attractive. A change of behaviour after entering is one form of moral hazard. Another one is the risk that a borrower when facing default has no incentive to maintain property values, which could let to improper or negligent maintenance and not taking home insurance. Moral hazard could either negatively affect the property value or delay termination of the contract. Moral hazard problems extend well beyond the maintenance phase. It is predictable that in cases in which the crossover point is passed before the homeowner dies, the sale will wind up being handled by relatives who have no stake in the sale price. Research from Davidoff and Welke (2004) showed that selection in the US reverse mortgage market to that date had been advantageous rather than adverse. They concluded that although reverse mortgages enabled longer stays at home, the kind of people who did cash out their housing equity by a reverse mortgage, relatively soon disposed the entire asset by moving out. So in their opinion high reserves or risk capital did not justify the minor 7

8 moral hazard effects 5. The Taskforce Verzilveren also concluded in their paper that, based on a small sample of 200 home-owners, on average people with reverse mortgages moved out much earlier than expected. 2.2 The equity release market abroad While in the Netherlands the products for equity release are very limited these products are available in numerous countries including Australia, Canada, the US, the UK, India, Japan and Singapore. While the financial crisis has initially slowed down market growth, several markets including Australia and the UK have recovered after the financial crises and show strong growth rates (Deloitte and SEQUAL, 2012; Key Retirement Solutions, 2013). Most markets are dominated by reverse mortgages with lump-sum payments instead of income stream reverse mortgages. In most countries there are industry or self-regulating bodies which oversee the issuance of No- Negative Equity Guarantees or other regulation to protect consumers. The US has the National Reverse Mortgage Lenders Association (NRMLA) where Australia knows the Senior Australians Equity Release Association (SEQUAL). These associations commit their members to appropriate product design, high standards of practice and responsible borrowing and often serve as an educational source. In the UK many providers signed up to SHIP ('Safe Home Income Plans') a voluntary code of conduct which provides several guarantees. SHIP was formed in an attempt to improve the equity release market and its previous poor reputation. Ship has been rebranded as Equity Release Council (ERC) in There are several reverse mortgage products in the United States but the predominant reverse mortgage is the Home Equity Conversion Mortgage (HECM). HECM are standardised governmentbacked reverse mortgages, via the Federal Housing Administration. To encourage the development of the equity release market, the US government insures mortgages with a No-Negative Equity Guarantee. The FHA provides for the No-Negative Equity Guarantee, financed by the borrowers. The HECM is considered the safest reverse mortgage and accounts for 95% of the market share (Ma and Deng, 2006). The Australian market has shown a considerable growth over the last years and has nearly tripled in terms of the total loan book size over the last decade and is expected to continue growing (Ai et al, 2013). The reverse mortgage is predominant, home reversion schemes also exist in Australia but are relatively new. In Australia, SEQUAL members have to issue the no negative equity guarantee to ensure the borrower can never owe more than the value of his house. The most popular product in Australia are variable rate loans, who are on average 1% above the standard variable home loan (Ai et al, 2013) In the UK equity release products have been available for 10 to 30 years and is basically made up of two types of equity release plan. The most popular plan is a lifetime reverse mortgage. The other type is a reversion plan - where the homeowners sells all or part of the property to the equity release provider in return for the right to remain there rent free. Both lifetime mortgages and home 5 They did suggest that it would be interesting to observe whether the favorable selection and relatively minor moral hazard effects observed to that date would continue in any period during which interest rates would far exceed price appreciation. 8

9 reversion plans fall under the remit of the Financial Services Authority (FSA). The guarantees of the SHIP include a no negative equity guarantee. A government-insured reverse mortgage program has been launched by the Korean government in July In Korean reverse mortgage, the used types of cash advances are tenure payment and tenure payment with line of credit. The Korean Housing Finance Corporation, the guarantor of the Korean reverse mortgage program, reported the number of reverse mortgage borrowers was rising rapidly (Ma and Deng, 2006). 2.3 The Dutch Mortgage market The ability to release equity in any form are highly dependent on the difference between the mortgage rates and the rates used for discounting pension liabilities (Task force Verzilveren 2013). Mortgage rates in the Netherlands are relatively higher compared to other European countries 6, while the discount rates who are based on government bonds are low. Explanations mentioned for the high mortgage rates are besides market imperfections, inter alia the Dutch funding gap and the high loan to value ratios. Reports of the DNB show a large gap between the savings deposits in banks and outstanding residential mortgages in the Netherlands 7. About two-thirds of the consolidated balance sheet of the Dutch banking system is funded in the financial markets. Due to this funding-gap, Dutch banks rely heavily on the capital market as a source of funding, mainly with short maturities. Short-term market funding increases banks vulnerability. To reduce vulnerability it is essential to either recapitalise banks or reduce the size of mortgage loans portfolios. Figure 4: Funding Gap ;Source: Special Report Rabobank Quick Scan Hypotheekrente; NMA, november DNBulletin: Mortgage lending makes banks dependent on market funding; june 6 th

10 New regulation is trying to reduce the funding gap by limiting interest-only mortgages. Strengthening the capital position of banks in line with Basel III is another instrument, but will as a result limit the supply of mortgages for Dutch households. Various parties are making efforts to attract other institutional investors like Dutch pension funds and insurers to invest in Dutch residential mortgages and thereby use the significant pension-savings to solve the funding gap. Forthcoming Capital requirements (Basel III) and the limited funding sources will have to be taken into account in product designs of mortgage related products. 2.4 Behavioural aspects or other barriers of equity release products In the Netherlands and many other European countries the market for equity release products is non-existent or very thin. There has been considerable debate in the literature on the economic potential of the reverse mortgage market in other countries. Yet even the most pessimistic assessment suggests that the reverse mortgage market is much smaller than could be expected. This could be due to suboptimal supply and/or demand. A number of behavioural aspects or other aspect on the demand side may have prevented the reverse mortgage market from developing. Shan (2011) mentioned behavioural and psychological obstacles to be of importance and affect if equity release products are seen as a possible option Behavioural and psychological obstacles First of all, elderly homeowners with strong bequest motives may not find reverse mortgages attractive because reverse mortgages reduce the amount of wealth they can leave to their heirs. According to Chaplin a strong motive for bequest could lead to avoidance of the reverse mortgage market (Chaplin 2000). Recent research by Andersson and Sandström (2013) in Sweden showed that potential reverse mortgage borrowers did not consider leaving their house as a bequest as their main priority. Instead they were positive to spend money instead of only focusing on saving to their heirs. Another behavioural aspect is the consumer uncertainty about future preferences or needs. For an elderly household planning to move in the near future, a reverse mortgage would seem to be a very bad idea. Uncertainty about future increasing medical expenses in time might also cause that many elderly homeowners like to hold on to their housing equity in case they might need it in the future. Reverse mortgages are complex financial products and can be particularly challenging for elderly homeowners. Lang (2008) concludes that the great obstacle to the acceptance of reverse mortgage products in Germany is a lack of understanding among the public. It is suggested that people that have a higher educational background will find it easier to understand the concept of a complex financial product such as reverse mortgage (Chou et al., 2006). In the research of Anderson and Sandström (2013) concern was expressed of the possibility to be tricked into a bad deal if entering a reverse mortgage by some potential borrowers in the focus group. This aspect and the issue regarding the costs associated with taking the loan are something mentioned in the focus group to be perceived drawbacks of equity release products Another aspect in complex psychology of reverse mortgages is the aspect that many elderly households are reluctant to take on debt. They value owning their homes free and clear so much that they are averse to the idea of borrowing against them. Having spent so much of their lives trying to pay off their initial mortgage. The study of Anderson Sandström (2013) also showed that some potential reverse mortgage borrowers in the focus group would feel ashamed or embarrassed if they needed to take the loan. She concluded that these feelings of shame and embarrassment might be 10

11 important factors that have to be taken into consideration, in order for reverse mortgage to reach its full potential on the market Regulatory issues An important regulatory issue is whether or not countries introducing home equity release products also provide for a no negative equity guarantee and how this regulation is explained to the potential borrowers. For example Reed (2009) documents concern among Australian borrowers regarding the possibility of being forced out of their homes in case of negative equity. In addition to concerns about negative equity certain features of the equity release programs and its interaction with some welfare programs could be undesirable. For example, the additional income received from a reverse mortgage may disqualify one from public assistance or would increase excess and contributions. Ong (2003) mentioned the unfavourable tax regimes in the UK as one of the reasons behind the scarce development of reverse mortgage market, in case a reverse mortgage annuity were to be taxed hence reducing social security entitlements. The Australian industry body SEQUAL 8 identified the treatment of lump sum loans in government eligibility tests for the Age Pension as a barrier for growth of the market in Australia. Mitchell & Piggot (2003) focus on the potential for reverse mortgages. It could potentially, next to boost consumption among the elderly, mitigate the demand for long term care facilities. In this case, it would be in the best interest of the government and they should play a substantial role in improving the efficiency of capital markets and providing or facilitate a No Negative Equity Guarantee, in order to support the development of a market for reverse mortgages. 8 Senior Australian Equity Release Association of Providers 11

12 2.5 Research Questions The equity release market faces a huge potential of accumulated assets by the older populations but in order to develop has to deal with limitations and barriers of cultural environment, the current economic situations and volatility of the property market. The ability to release equity are highly dependent on the difference between the mortgage rates and the rates used for discounting pension liabilities. In order to successfully develop the potential, products should possess mechanisms for mitigating or addressing the specific risks involved and minimize the difference between mortgage and discount rates. Thereby also taking into account the effect of mortgage margins, economic and cultural barriers and the social demand for simplicity which might affect the attractiveness and availability of the products in the future. In order to find out the potentiality of home equity release products as a mean to supplement retirement income for elderly homeowners, the aim of this paper is to develop a model of economic variables to capture the interaction between macroeconomic variables which determine house prices based on Dutch data for use in quantifying the major risks of a reverse mortgage or equity release products. The following research questions are defined. 1. What are the specific risk factors related to reverse mortgage products and how could they be priced? 2. What are the main drivers of the cross-over risk? 3. What barriers for development of the equity release market can be defined and what could be done in order to develop the market for home equity conversion? The answers to the research questions will be organized as follows. In chapter 3 different products designs will be outlined, including the related risks and cash flow pattern. We set out the pricing formula for the No Negative Equity Guarantee embedded in the reverse mortgage products. We work out a pricing framework in chapter 4. In order to do so we define a termination model and use a VAR model to model the dynamics of interest rates and house prices. Stochastic discount factors are derived from the VAR model. Cash flow structures are analysed for reverse mortgage products. Numerical examples are used to compare these products in net payoff for the borrower and risk (NNEG) for the provider. To define the main contributors to cross-over risk we will report and analyse the results in chapter 5. We evaluate these results along with other characteristics of the product and answer research question 3. Chapter 6 will conclude and end with suggestion for further research. 12

13 3 Equity Release Product Design Developing an equity release product involves creating a product that is an intersection of insurance, banking and investment. In every equity release product the essential question is who will get the possible gains and who will bear the losses (Taskforce Verzilveren 2013). To a large degree, the independence and existence of the risks depend upon the design of the product. It is possible to design products that minimize the risks by means of conservatism, diversification, hedging, assetliability matching or sharing the risks with homeowners. Conservatism would be to limit the monthly loan-payment to the home-owner to a sufficiently low amount that would nearly eliminate all the risks faced by the providers. The disadvantage of this approach would be the product s lack of marketability. Providers should accept some risks, but should charge an appropriate price for taking that risk. In contrast to regular mortgages reverse mortgages will rarely bare a loss is early years but are becoming risky in later durations. Releasing home equity by regular mortgage products is difficult due to stringent underwriting criteria of current interest only mortgages. The considerable difference between mortgages rates and the interest rates used for valuing annuities makes this form either impossible or the resulting additional income too small to be of interest. For regular mortgages a maximum loan to value ratio is desired. To provide for a significant cash income a reverse mortgage must probably use the home s full value and even expect appreciation as well. We analyse specific reverse mortgage designs. The first one is a lump-sum reverse mortgage (or rollup mortgage) with an up-front premium for the NNEG. The net lump-sum payment could be used for an annuity for life purchased at an insurer. The second product would be an income stream reverse mortgage. The reverse mortgages contracts are non-recourse, so the no negative equity guarantee (NNEG) limits the loan repayment to the sale price of the property. Products can be designed to charge for the risks using some combination of up-front or an annual premium. An front-end charge could be expressed in terms of percentage point of the home s initial value. An annual premium could be assessed as a number of basic point of the current outstanding loan balance, so in fact the loan balance will be charged by a higher loan interest rate. In this case the annual fee will grow larger during the lifespan of the loan, and could as a result lead to undesired spreading of the fee among borrowers. A fixed annual fee could provide more equal spreading. Fixed and growing annual fee s both will create prepayment risk, which will be absent in an up-front charged fee. 9 In the following,the different product designs will be described in more detail. We review the basic features and describe the risks involved in these products. All products will be based on floating interest rates and the products will all be kept to maturity. Where the termination point is the maximum attainable age of the last homeowner. 9 The current used insurance premium in the US is an upfront charge of 2% of the loan value plus a monthly premium of 0.5% of the outstanding loan. Although this charges are been criticized for being too high (Chaplin 2002) 13

14 3.1 A Lump-Sum Reverse Mortgage The first reverse mortgage product to be considered will be lump sum reverse mortgage which is the most common type of reverse mortgage. In a lump sum reverse mortgage or roll-up mortgage the borrower receives a loan in the form of a lump sum. The loan is rolled up with interest until the last borrower dies, moves into long-term care or sells the house. To convert home equity into retirement income the Lump-sum could be used for an annuity for life (two life s) at an insurer. There will be a no negative equity guarantee (NNEG) so the mortgage provider will be faced with cross-over risk. The NNEG will be fined by an upfront mortgage insurance premium, financed as part of the reverse mortgage. The insurance premium will be deducted from the initial cross lump-sum payment. Close to default the provider could be faced with moral hazard risk, but we will not address this specific risk in these thesis. Figure 7: Loan balance and property value for a lump-sum reverse mortgage Initial loan L 0 = H 0 * α (3.1) The maximum initial loan amount is determined by the loan value or borrowing ratio that is set as a proportion of the value of the property. The borrowing ratio is denoted by α. We denote the property value at time t as H The accumulated Loan balance at time t will be denoted as L t and will increase every quarter by a quarterly risk-free rate (ri), which will be based on the 3 months Euribor rate, and a quarterly lending margin π. Loan balance i (3.2) Where is the average delay in time from the point of home exit until the actual sale of the property. the delay in sales of the property after the loan termination point and T is the termination point. 14

15 At termination, the repayment amount is min. The borrower s net equity is capped by the property value due to the NNEG. Net Equity (Ct) = Ht - min. (3.3) Max. The transaction costs of selling the house, δ are defined as a percentage of the house value. The present value of providers loss is then : Loss Tx= Max - * (3.4) Where is the risk-adjusted stochastic discount factor. The value of the No Negative Equity Guarantee can be defined by: NNEG = [ ] (3.5) We assume end-of-the year terminations and so the termination probability t is the probability that a reverse mortgage is in force by time t and will be terminated by t+1. Where is the loan termination point, i.e. the maximum attainable age of the last homeowner. The net payment after deduction of the upfront premium then becomes: NP 0 = L 0 NNEG (3.6) Cash Flow Pattern The cash flows at time zero for the borrower are the lump sum payment from the lender. This lump sum payment is used for initial premium for an annuity at an insurer. During the lifetime of the loan there will be no interest payments. The borrower could use the lump-sum payment to receive periodic income by purchasing an annuity. 15

16 Figure 8: Cash Flows mortgage borrower Figure 9: Cash Flows mortgage lender The lender provides for the lump sum payments and will not receive any interest payments. At termination the lender will receive the payoff of the loan, which is capped by the sale proceeds of the property. Figure 10: Cash Flows insurer of annuity The insurer receives a front-end premium for the joint survivor annuity and provides for periodic payments until the last survivor has died. 16

17 3.2 Income Stream Reverse Mortgage The second product design will be an income stream reverse provided by the mortgage lender. This income stream reverse mortgage has a different pay-out design. It pays out fixed amount to the borrower until terminations. The loan balance starts at zero and will increase quarterly with the accrued variable interest rate and the new payment to the borrower. There will be a No-Negative Equity Guarantee so the mortgage provider will be faced with cross over risk. Like the lump-sum reverse mortgage the lender could be faced with moral hazard risk close to default. The NNEG will be charged by a an fixed annual premium. Figure 11: Loan balance and property value of an income stream reverse mortgage. To compare the reverse mortgage products we define the periodically payment (income stream) such that the present value of all payments equals the lump-sum amount of the Lump sum reverse mortgage. Joint-Survivor annuity at T = 0 (3.7) is the in-force probability, the probability at time t that home-owners, age x:y at loan origination will still be in their homes at the end of year t. Yn,t are zero coupon yields for maturity n at time zero. For the annuity index at t=0 we used the ufr yield curve of June 2013 as published by the DNB. The initial fixed yearly payment is: Ux:y,0 = (α * H0 ) / (3.8) 17

18 The outstanding loan balance at time t is then given by: - - = ( ) (3.9) The expected present value of the lender Loss and the NNEG are derived similar to the lump-sum reverse mortgage. Loss Tx= Max * (3.10) NNEG = [t qx y oss Tx ] (3.11) The NNEG will be charged a fixed annual premium payment. We use the same annuity index for the premium payment as used to define the fixed annuity payment. x y,t t x y (3.12) The net yearly payment NYP = Ux:y,0- x y,t (3.13) 18

19 3.2.1 Cash Flow Pattern In an income stream reverse mortgage the lender pays regular payment to the borrower until the contract is terminated. The lender doesn t receive interest payments. The loan will be redeemed at termination capped to the remaining proceeds after sale of the property. Figure 12: Cash flows mortgage borrower. Figure 13: Cash flows mortgage lender. 19

20 4 Pricing Framework: Simulation models for reverse mortgage risks 4.1 Modelling the Probability of Termination The probability of termination for a borrowers couple will be derived from a Markov termination model as used by Alai et al (2013) and based on Ji (2011). A reverse mortgage may terminate for various reasons including death, entrance to a long-term care (LTC), Move out for non-health reasons and refinancing. Voluntary prepayments or refinancing occurs when the market interest rate is lower than the fixed interest rate at which the loan is accumulated. Because we will not consider fixed rates we will not include prepayment or refinancing as a possible cause of termination. Due to lacking information on termination rates we will also not include prepayment for non-health reasons and long term care as causes of termination. So we will only consider death (illustrated by the blue states in figure 17). We estimate these probabilities based on mortality data (AG ). Figure 17: A multiple state model for joint-life reverse mortgages ( Ji 2011) The probability of transition from state 0 to state I at time T is denoted by tp 0i x:y and is the probability that a reverse mortgage is in force by time t and will be terminated by t+1. This one year termination probability is of interest because the model simulations will be conducted in annual time steps. We calculate by summing the probability of transition from state 0,1 and 2 to state 5. tp 15 x:y + tp 25 x:y + tp 05 x:y (4.1) = tp y * (1- t P x ) * t q y + t P x * (1- t P y ) * t g x + t P y * t P x * t q y* t g x 20

21 The probability that someone is not in state 5; so one of the spouses is still alive and living in the home and the mortgage will be in-force is denoted by tpx;y and calculated as tp x:y = t P x + t P y - t P xy (4.2) 4.2 Deriving arbitrage free scenarios for reverse mortgage products The key inputs for a pricing framework of reverse mortgage products are mortality or longevity, stochastic interest rates, discount factors and house price growth rate. In order to numerically analyse the impacts of longevity, interest rate and housing pricing risk on the value of additional retirement income (annuity for life) for the different equity release products, we will first have to determine the parameters for the dynamics of interest rate, housing price and mortality rate. From the providers perspective, providing an NNEG is equivalent to writing the borrower a put option on the mortgaged property or house value. Some literature examining the risks in reverse mortgage focus on analysing the house price dynamics alone or model the dynamics of house prices and interest rates independently. In their models house price dynamics usually are assumed to follow a geometric Brownian motion. There are significant differences between the NNEG and a standard European Put option. At first the time to maturity is random and secondly the house price return is as opposed to typical equity returns highly correlated. Empirical studies also demonstrate that property returns and interest rates are correlated. The classical Black-Scholes option pricing formula assumes returns follow a geometric Browning motion. The GBM assumption cannot accommodate facts like heteroskedasticity and serial correlations of observed house prices and interest rates. So the classical Black-Scholes option pricing formula is therefore inappropriate for pricing the NNEG. Macroeconomic variables are likely to affect the dynamics of both house prices and interest rates. Therefore to model housing price dynamics various studies apply time-series analysis. A VAR model not only includes the correlation of the variables through time (autocorrelation), but also the correlation between variables ((cross) correlation). So a VAR-type modelling framework makes it possible to capture the correlations between variables in multivariate time series and is flexible and straightforward to use in simulations. Recent studies (Sherris and Sun, 2010; Alai et al, 2013; Shao et al, 2012 and Cho et al, 2013) all use VAR models to capture the dynamic relationships between economic variables like the house price index, rental yields, interest rates, and inflation or GDP. In accordance with this recent literature we will adopt the same approach, and use a VAR model to project economic scenarios and to derive discount factors in this thesis. For the dynamics housing price we will include, in line with other research, the variables interest or mortgage rates, inflation and GDP. When asset prices do not have the same value for all scenarios at all points in time there are arbitrage opportunities. In order to prevent arbitrage opportunities in our scenarios we should value all the assets in the economic scenarios in such a way that there is no arbitrage. For this valuation a term structure of interest rates is needed that is necessary for discounting. In order to derive an, arbitrage free, affine term structure model of interest we extend the VAR model with the pricing kernel. We use the no-arbitrage assumption to develop the term structure model and relate the pricing kernel with the state variables. 21

22 In line with (Ang et Piazzesi, 2004; Cochrane and Piazzesi, 2005 and 2008) we conduct a two-step estimation procedure. In the first step the VAR parameters are estimated. In the second step we will estimate the risk premium parameters conditional on the VAR parameters State variables of the VAR Model Macroeconomic variables are likely to affect the dynamics of both house prices and interest rates. Brooks and Tsolacos (1999) study indicated that interest and inflation are significant in explaining house price returns. Abelson et al (2005) estimated a model using several economic variables. They found that long run house price were determined significantly by disposable income, interest rates, equity prices, consumer price indexes and the supply of housing. Ang and Piazzesi (2003) describe the joint dynamics of bond yields and macroeconomic variables in a VAR model. They include GDP as a factor in predicting housing prices and the yield curve. We will also include GDP in our VAR model. In line with Recent studies ( Sherris and Sun (2010), Alai et al (2013), Shao et al (2012) and Cho et al (2013)) we will use two factors from the yield curve. The three months Euribor rate and the ten year spread. 10 So five variables will be included in the VAR model: Dutch GDP Index rates, Dutch House price index rates, Consumer price index, the 3 months Euribor rate, and the spread of 10 years zero coupon rates over the 3-months Euribor rate. The raw data, sources used for the modelled variables are described in table 1. The variables House price, Consumer prices and GDP are indices. We will transform these index variables into compounding quarterly growth rates. Table 1: variable definition frequency and source Variable Definition Source Frequency R(1) Three months Euribor DNB Daily R(40) Ten year zero coupon DNB Daily yield (nld) HPI House price index CBS Quarterly GDP Gross Domestic product CBS Quarterly disposable income CPI Consumer price-index CBS Quarterly The ten year zero coupon yield (NLD) is available for the period kw to kw Because some data are only available on a quarterly basis, other variables are filtered to quarterly frequency. The ten-year term spread is calculated as the difference between ten-year and three-month zerocoupon yields r(40) R(1). Growth rates of the house price index and of the GDP are determined by differencing the log series (ln(gdp)t+1 LN (GDP) t) and are denoted as `HPI and GDP' and CPI 10 According to Ang and Piazzesi (2006) two variables could be able to condense the information contained in many yields, due to the high correlation between yields with different maturities. 22

23 The plots of the raw data( R1) and R(40)_r(1) and the transformed raw data are given below Figure 18: Plots of raw data: HPI,GDP,CPI,R(40)-R(1),R(1) 23

24 4.2.2 Mortgage rates As can been seen in Figure 19 mortgage rates are highly correlated with the three-months Euribor rate. Based on historical time series of those two rates a correlation of 83% is found 11. The correlation was even stronger before To avoid the issue of collinearity we will not include the mortgage rate in the VAR-model, but we will use mortgage rates who are computed as the three months Euribor rate plus a fixed margin 1,84% 12. As can been seen there is a dramatic rise in the margin after This rise has been criticized by the Vereniging Eigen Huis and been investigated by the Dutch central bank 13 and the Dutch Authority on competition (NMa) 14. Because the margin is declining in the last months and seems to move back to its mean, we based or average on the total period. To analyse the effect of the margin on the pricing and risks we will perform a sensitivity analyses by using several margins. Figure 19: Floating mortgage rates and the s months euribor 11 Eigen Huis Rentebarometer (EHR) versie Margin is based on average difference between mortgage rate and the 3 months Euribor rate for the period of March 2004 to June Financieringsproblemen in de Hypotheek markt, DNB occasional studies Sectorstudie Hypotheekmarkt, Mei

25 4.2.3 VAR(1) model A vector auto regression (VAR) is a model where values of variables are explained by lags of the variable as well as lags of other variables. The vector auto regression (VAR) model is one of the most successful, flexible, and easy to use models for the analysis of multivariate time series. It is a natural extension of the univariate autoregressive model to dynamic multivariate time series. The VAR model has proven to be especially useful for describing the dynamic behaviour of economic and financial time series and for forecasting. The general specification of a VAR(p) process for an (n * 1) vector Z t is: Z t c Φ 1 Z t-1 + Φ 2 Z t Φp Z t-p +ε t (4.3) Where P is the number of lags. Z t denotes the ( n X 1 ) vector of the economic variables. C,, and are vectors and matrices and ε t is a vector of multivariate normally distributed error terms with ε t ~ N(0, Σ). When deciding on the number of lags included, one is faced with a trade-of: Choosing a short lag length p might restrict potential dynamics and yield auto correlated residuals. But choosing a higher order of lags could lead to over parameterize the problem. There are several information criteria to define the optimal lag length (p) in stable and unstable vector autoregressive (VAR) models, namely Akaike, Schwarz Bayesian (SBC), and Hannan Quinn (HQC). We used the AICBIC formula of software package MATLAB to determine the information criteria of different lags. The Lags and criteria are shown in Table 2. Table 2: Lag selection Criterion e +3 Lag Order Akaike Information Criterion (AIC) * Schwarz-Bayesian Criterion (BIC) * AIC suggest an optimal lag order of 3, whereas BIC indicate an optimal order of 1. Hacker and Hatemi (2008) showed in their investigation that SBC has relatively better performance in lag-choice accuracy in many situations. Lütkepohl (2005) preferred SIC and HQC over AIC as they are consistent even if the data series are non-stationary. So we will choose to fit a Lag order of one based on the BIC. 25

26 The estimated model for the vector of the variable Zt, is: Z t c Φ 1 Z t-1 + 1/2 ε t (4.4) contains the VAR coefficients and 1/2 is the Cholesky decomposition of the covariance matrix Σ, εt is a vector of independently distributed standard normal variables. Where Z t = en c= ( ) ( ) = ( ) ( ) R 2 are in the range of 0,377 to 0,945 for the variables. Stationarity and stability An important assumption is order to estimate a VAR model, is that the historical data is stationary. Stationarity is a crucial assumption for being able to describe the stochastic behaviour of some variable by a single model and to be able to estimate the parameters of such a model on one sample of data. Stationarity of a process requires that the mean, the variance and auto variances are infinite and independent of time. Otherwise each point in time would require another model. Stationarity will require that the 5 x 5 matrix is invertible. So our VAR(1) process is stationary if the eigenvalues of the matrix B have a modulus smaller than one. With the MATLAB function vgxqual we determine if the multivariate time series process is stable and invertible. This function also determines the largest-magnitude eigenvalue for the AR portion of the multivariate time series process. According to the MATLAB test our time series process is stable and invertible and the largest magnitude eigenvalue for the AR is which is smaller than 1. 26

27 Simulated state variables Based on the VAR(1) model simulation paths of the variables are generated. Figure 20 show the historical paths (actuals in blue) of the economic variables and simulated mean values with 95% confidence intervals (dashed red) of the Var(1) model. figure 20: historical and simulated s and confidence intervals of state variables 27

28 As can been seen in the figures of the variable R1 is that due to the low value of the sample period and the starting values negative interest rate scenarios will be possible outcomes in the simulation process. Although negative interest rates might not seem very realistic ( for example as a base for mortgage rates) we will use the simulated values in or model and simulation process. By changing or truncate variables we could obtain an undesirable probability distribution function and it would affect moments, standard deviation and correlations. For the loan balance we set the negative interest rate at zero. The consumer prices are also showing deflation possibilities in our simulation. This neglects any monetary policy of the European Central Bank To tackle this issue, Hoevenaars (2008) transforms the constant term of the VAR (c) for the scenario generation as described in Hoevenaars, Molenaar, Steenkamp (2003) to an average in line with current objectives of the European Central Bank. An even more important observation is the development of the baseline mean of the average property appreciation rate. It moves to a long-term average below zero. To test the impact of the assumptions regarding this long-term average we will adopt the strategy used by Hoevenaars to adjust the C term in our VAR model for the long-term average of the house prices Stochastic discount factors We will adopt the pricing approach used in the studies (Cho et al., 2013; Alai et al., 2013; Shao et al.,2012; Hoevenaars., 2008; Slagmolen, 2010) to develop a pricing kernel that can be used to price nominal assets. The risk-adjusted stochastic discount factors are used to discount the cashflows arising from the No negative Equity Guarantee. In order to derive the stochastic discount factors, the market prices of risk (λt) need to be estimated. To develop the affine term structure model we use the no-arbitrage assumption, and we follow Cochrane and Piazzesie (2008) and Hoevenaars (2008) in relating the price kernel to the state variables of the VAR model. To derive the stochastic discount factors using a VAR(1) model we assume that zero coupon bonds prices are linear functions of the state variables. We specify that the log nominal discount factor is a linear function of the state variables of the VAR model by, m t+1 = exp(-δ 0 - δ 1 Z t - ½ λ t λ t -λ t ε t+1 ) (4.5) λ t = λ 0 + Λt Z t (4.6) Where ε t+1 ~ N(0, ) and E ( 1/2 * 1/2 T ) and the vector λ t is a linear function of state variable. Λt is a (n X 1) vector with time varying market prices of risk which are affine in the state variables. The stochastic discount factor (mt+1) varies with the random variables in the VAR. The first component -δ 0 -δ 1 Zt is the short rate r(1) which is also included in the VAR(1) model. The other component - ½ λ t λ t -λ t ε t+1 relates shocks in the state variables to the pricing kernel. A positive market price of risk λ t leads in (4.5) to low values for the stochastic discount factor in scenarios where the values of the innovations are high. The price of an n-period nominal bond at time t can be solved recursively by the following formula P t (n) = Ln E[M t+1 * P t (n-1) ] (4.7) with the termination condition Pt 0 =1. So for a one period bond we have 28

29 P t (1) = ln E[M t+1 * 1] = -δ 0 - δ 1 Z t (4.8) As the short rate we use, the 1 quarter or 3 months Euribor rate (R1). To achieve consistency between the VAR(1) model and this short rate we let δ 0 = 0 and δ 1 = (0, 0,0,1,0), so that the first period yield can be written as Yt (1) = -δ 0 - δ 1 Z t = r1 (4.9) To derive stochastic discount factors using our VAR(1) mode, we assume that zero-coupon bond prices are exponential linear functions of the 1 quarter lagged state variables. Log prices are linear ( affine ) functions of the state variables P t n = exp ( A n + B T n Z t ) (4.10) The absence of arbitrage is imposed by computing the coefficients A n and B n recursively from the following equations: A 1 = 0; B 1 = 0 (4.11) B n+1 = ( - 1/2 λ 1 ) T * B n - δ 1 (4.12) A n+1 = -δ 0 + A n + B n (μ - 1/2 λ 0 ) + ½*B n T B n (4.13) Where e1 is a column vector with the 1th item equal to 1 and all others entities equal to 0. See for the deviations in detail Shao et all (2012), or the Appendix to Cochrane and Piazzesi (2005). Bond yields are then affine functions of the state vector: Y t (n) = -An/n - Bn T /n Zt (4.14) This equation describes the whole term structure of nominal interest rates. So the relation between the yield and state variables Zt, i.e. the coefficients An and Bn depend on the risk-neutral versions λt and the and the covariance matrix. The VAR(1) parameters (μ,, and ) have been estimated in the previous paragraph. We use the model to decompose the yield curve into expected interest rate and risk premium components. we estimate the risk premium parameters conditional on the VAR(1) parameters. Just as Hoevenaars (2008) and Slagmolen (2010) we estimate λ 0, and λ 1 instead of λ 0, and λ 1. This market price of risk is obtained by minimising the sum of the squared differences of estimated yield rates from the observed (historical ) zero coupon rates. Besides the three months we calibrate the model on the 1 and 5 years and 10 year zero coupon rate. - for N =1,4,20 and 40 (4.15) 29

30 Where are the fitted yields of the term structure model and are the historical zero coupon yields. Next we use the Matlab function fminunc to search for the values of 1/2 λ0, and 1/2 λ1 that minimizes function The calibrated values of 1/2 λ 0 and 1/2 λ 1 are given in Table 3. Table 3 Market prices of risk λ 0, and λ 1 1/2 λ0 (5x1) 1/2 λ1 (5X5) HPI GDP CPI R R40_R Term structure model fits Here are the figures shown of the historical fit of the term structure model of equation for1 year (R4), 5 year (R20) and 10 year (R40) zero coupon interest rates. Solid lines represent the actual series. Dashed lines denote the fitted series. Due to the higher rates for five year and ten year zero coupon this rates had a higher weight on the difference in the minimization. Figure 21: Historical fit of one year zero coupon 30

31 Figure 22: Historical fit of five year zero coupon Figure 23: Historical fit of ten year zero coupon 31

32 Equation(4.14) describes the whole term structure of nominal interest rates. We derived the yield curve of based on the model. Figure 24 shows the fitted yield curve. The figures shows a good fit till the 10 year, which is the last interest rate that used in the sample. Figure 24: Fitted yield curve 5 Simulation results In the previous chapter we described a termination and a VAR model for economic variables. We use these models to simulate the input variables for the pricing formula of chapter 3. To assess how risks differs amongst the two product, quarterly cash flows of reverse mortgage loans are computed based on 10,000 paths of the economic variables simulated from the VAR(1) model over a 50-year period along with the projected probabilities of loan termination from the Markov model. We then calculate the present value of net payoffs of the provider in order to price the NNEG. Sensitivity analysis is conducted to investigate the impacts of the loan value or borrowing ratio, mortality improvement, increasing sale costs, increasing delay is sale of property after termination and mortgage margins. 5.1 The Base Case Scenario In the base case scenario, we assume a couple (male aged 67 and female 64), with an initial house value of 265, We project the Property value and loan balance based on 10,000 simulated paths of the economic variables based on the VAR(1) model for 50 years. We obtain the present value of payoffs to the borrower for different products. Total net monthly income of elderly pairs without children (one elderly spouse over 65) is on average 3, The LTV ration is set to 40% 15 Based on net average value of home equity of elderly > 70; Task Force Verzilveren 16 CBS: Statistiek Gemiddeld inkomen; particuliere huishoudens naar diverse kenmerken

33 resulting in an initial loan of 106,000. Sale transaction costs are set at 2% and the average rime to sale after termination is set at two quarters. The margin used for the reverse mortgage products is set at 1.84%. In the sensitivity analysis, we will consider other loan value ratio s, transaction costs and delayed sales periods. We also allow for mortality improvement and look at the impact of the mortgage margin. 5.2 Reverse mortgage products; Base case results Loan balance and house price In order to quantify the no negative equity guarantee the first step of the cash flow analysis is to simulate the development of the house value and the loan balance. Figure 25 and 26 compare the development of the loan balance with the development of the house index for a lump-sum reverse mortgage and an income stream reverse mortgage. The cross over point is reached when the loan balance crosses the value of the property and negative equity arises. The figure shows a declining house value over time. This is caused by the fact that the house price growth (-0,01) of our sample is far beyond the long term growth ( ; ). The crossover point for a lump-sum reverse mortgage will on average be reached within 13 years. Income stream reverse mortgages start with lower loan balances but cumulate faster over time. Due to the fast decline of the house value the income stream mortgage will reach the cross-over point later in time. This in contrast to the findings of the study of Cho et al (2013) which concluded that income stream mortgage are subject to an earlier crossover point and a higher risk of negative equity in periods of increasing house values. 33

34 Figure 25: Loan balance and property value Figure 26: Loan balance and property value According to this simulation the volatility of the house price growth is the major contributor to negative equity events. In this house growth scenario both reverse mortgage will result in very high expected value of the NNEG. Table 4 shows the expected present value of the NNEG. Even with decreased borrowing ratio of 1,5% the NNEG exceeds the lump-sum or annual payment. Although an income stream mortgage reaches the cross-over point later the faster accumulation does result in a higher NNEG. Table 4: Base case NNEG 17 LVR 30% NNEG Margin 1,5% NNEG Margin 1% Lump-sum mortgage Income stream mortgage NNEG values (even at low loan value ratio s or lower margins) as presented in table 4 will not make it possible to release equity. Except for the lump-sum mortgage with a margin of 1%, the upfront or annual premiums are larger than the attainable payments. 17 Formule 3.5 for lump-sum mortgages and 3.11 for income stream reverse mortgages 34

35 5.3 Transforming the constant term of the VAR(1)model We already mentioned that our average house appreciation or growth rate was beyond the long term average. Figure 27 shows the historical house growth and interest rates. Where the grey area is our sample period. Figure 27: Historic Aibor/Euribor and House index and sample period Since the historical growth rate of (0,012) is well above the growth rate of our sample(-0,01) we will transform the constant term of the VAR (μ ) for the scenario generation as described by Hoevenaars (2008). We will transform the constant term of our VAR(1) model to an average of zero for the scenario generation (μ =(I-B) μ ) 18. We also transform λ0. To analyse the impact of the assumption of the average growth rate we will consider the adjustment to zero as well as to the historic long-term average of 0,012. To test the impact of the long-term average growth rate as a contributor to crossover risk we will only adjust the C term for this average. Adjustments to the interest rate distribution, sample period, or long term consumer inflation rates are out of the scope of this thesis and suggestions for further research. 18 Zie ook The Oxford Handbook of Quantitative Asset Management, page

36 5.3.1 Transform to an average growth rate of 0 If we transform the C term the mean will be mover upwards and the actuals will for some part fall below this average. figure 28: historical and simulated s and confidence intervals of state variables Figure 28 shows the historical paths (actuals in blue) of the variables and simulated mean values with 95% confidence intervals (dashed red) of this transformed Var(1) model. The average of the house growth rate is adjusted to zero. 36

37 Figure 29 show the development of the average loan balance and the house prices for the two products based on the simulated variables of the transformed VAR(1) model. figure 29: Loan balance and property value figure 30: Loan balance and property value In this simulation the house price on average moves around the initial value. Again the cross-over point is reached earlier by the lump-sum mortgage, but about 6 year later. The income stream reached the cross-over point on average in 25 year but is accumulating faster. 37

38 The value of the guarantee is the highest for the lump-sum mortgage. The upfront premium for the lump-sum mortgage will be 9% of the initial property value or 22,7% of the initial loan. The fixed annual fee will be 0,9538% of the initial house value. Table 5: Base case Product LVR Payment Margin NNEG Net payment Lump-sum 40% 106, % ,904 (NP) Income stream 40% 5,035 1,84% 21,269 4,024 (NYP) Sensitivity to the mortgage margin Higher lending margins are accumulating when the average duration is longer. Table 6 provides results of the NNEG of the product with different margins. The upfront fee decreases to 18,45% and 13% of the loan or 7,4% and 5,2% of the house value. And an fixed annual fee of 0,33% and 0,27% of the initial House value. Table 6: Sensitivity to mortgage margin Product LVR Payment Margin NNEG 19 Net payment 20 Lump-sum 40% 106, % ,904 (NP) Lump-sum 40% 106,000 1,5% 19,559 86,441 (NP) Lump-sum 40% 106, % 13,838 92,162 (NP) Income stream 40% 5,035 1,84% 21,269 4,024 (NYP) Income stream 40% 5, % 18,782 4,143 (NYP) Income stream 40% 5,035 1,0% 15,516 4,298 (NYP) Higher lending margins are accumulating when the average duration is longer. The lower margin nearly half s the present value of the NNEG. The expected value of the NNEG for an income stream mortgage with a lending margin of 1% will exceed the value of the NNEG of the lump-sum mortgage Sensitivity to the Loan Value Ratio In the base case we have assumed a LVR of 40%. Which is in between the low ratio offered in the Australian market (15%-35%) and the higher LVR found in the US market (55%-80%). To define the impact of the LVR on the expected NNEG, we compare the results of the base case with a lower Table 7: Sensitivity Loan Value Ratio Product LVR Payment Margin NNEG Net payment Lump-sum 40% 106, % ,904 (NP) Lump-sum 35% 92,750 1,84% 18,276 74,474 (NP) Lump-sum 45% 119, % 30,091 89,159 (NP) Income stream 40% 5,035 1,84% 21,269 4,024 (NYP) Income stream 35% 4, % 16,232 3,634 (NYP) Income stream 45% 5,664 1,84% 26,472 4,406 (NYP) The average net payment as well as the de risk increases with the LVR. The expected value of the NNEG increases with plus 25% for the lump-sum mortgage while the NNEG for the income stream 19 Formule (3.5) for lump-sum mortgages and (3.11) for income stream reverse mortgages 20 Formule (3.6) for lump-sum mortgages and (3.13) for income stream reverse mortgages 38

39 mortgage only increases plus 3% while the net payment for the borrower increase with plus 15% versus plus 9% for the lump-sum payment. The value of the expected NNEG increases with the LVR since a larger LVR reduces the gap between the house value and the loan balance, resulting in a higher cross-over risk. The impact of the higher LVR is bigger for the Lump-sum reverse mortgage Sensitivity to mortality, costs and average delay of sales We also tested the sensitivity to a mortality improvement, increasing costs and delay of sale Table 8: Sensitivity to mortality, costs and average delay of sales Product Sensitivity LVR Payment Margin NNEG Net payment Lump-sum -25% 40% 106,000 1,84% 23,832 82,168 (NP) mortality Lump-sum Costs 5% 45% 106, % 24,810 81,190( NP) Lump-sum Delay 4 45% 106, % 25,012 80,988 (NP) quarters Income stream -25% 40% 5, % 22,553 3,963(NYP) mortality Income stream Costs 5% 40% 5,035 1,84% 21,879 3,995(NYP) Income stream Delay 4 quarters 40% 5,035 1,84% 22,068 3,986(NYP) The mortality shock has a positive effect on the lump-sum mortgage while it increases the risk for the income stream mortgage. Possible because the negative equity events are placed further in time and the impact of house price appreciation and discounting are exceeding the delayed termination. The increase in cost of sale have more impact than an extension of the sale period. 39

40 5.3.5 Transform to the long-term historical average growth rate The previous results of adjustment of the average of the house growth outlined the impact of the average house price growth on the negative equity events. To show the impact of this average we also transform the constant term to the historic average of 0,012. The simulated mean and confidence levels of the variables are listed below. In this simulation the actual observations, the sample of the last decade, are considered as an extreme situation and are assumed to be placed in lower quantiles below the long-term average. figure 31: historical and simulated mean and confidence intervals of state variables 40

41 Figure 31 shows the historical paths (actuals in blue) of the variables and simulated mean values with 95% confidence intervals (dashed red) of this transformed VAR(1) model. The average of the house growth rate is adjusted to the historical average of 0,012. Figure 32 and 33 show that although the loan value on average does not face negative equity even if it does not terminate within 50 years, it is able that a negative event occurs in the case of a real estate turndown, in this simulation represented by the lower 5%-quantile of the house value distribution. figure 32: Loan balance and property value figure 33: Loan balance and property value 41

42 Table 9: Base case Product LVR Payment Margin NNEG Net payment Lump-sum 40% 106, % ,271 (NP) Income stream 40% 5,035 1,84% 992 4,987 (NYP) In this case the products are almost riskless. The upfront premiums are 0,6% of the initial loan and an fixed premium of a year. In a market of growing house values a lump-sum mortgage is less risky in line with the findings of Cho et al (2013). Table 10: Sensitivity to mortality, costs and average delay of sales Product Sensitivity LTV Payment Margin NNEG Net payment Lump-sum Base case 40% 106, % ,271 (NP) Lump-sum Margin 40% 106, % ,646 (NP) Lump-sum Margin 40% 106, % ,878 (NP) Lump-sum LVR 35% 92, % ,468 (NP) Lump-sum LVR 45% 119, % ,844 (NP) Lump-sum -25% 40% 106,000 1,84% ,324(NP) mortality Lump-sum Costs 5% 45% 106, % ,140(NP) Lump-sum Delay 4 quarters 45% 106, % ,176 (NP) Income stream Base case 40% 5,035 1,84% 992 4,987 (NYP) Income stream Margin 40% 5,035 1,5% (NYP) Income stream Margin 40% 5,035 1,0% (NYP) Income stream LVR 35% 4,405 1,0% 418 4,385 (NYP) Income stream LVR 45% 5,664 1,0% ,584 (NYP) Income stream -25% 40% 5, % ,981 (NYP) mortality Income stream Costs 5% 40% 5,035 1,84% ,981 (NYP) Income stream Delay 4 quarters 40% 5,035 1,84% ,982 (NYP) Table 10 shows that the impact on the riskiness of higher loan value ratios and mortality is rather limited in a world of growing house prices. Previous analyses show that the assumption of the average growth rate of the house prices is probably one of the major contributors to possible negative equity events. In the next section we will look at the possible negative events that would have occurred if products would have been issued in

43 5.4 Backtest using historic data starting in 1977 The model is estimated using quarterly data from the last quarter of 2003 until the second quarter of The advantage of this short period is that a recurrence of a high inflation period such as in the 1970 s does not affect the model. The disadvantage is that business cycle effects cannot be taken into account and low starting values and average are causing unrealistic growth and interest rates. We will determine the development of the average loan balance and house value for lump-sum and income stream reverse mortgage using existing historical interest rates and house indexes. The period after 2013 will be forecasted based on the average rates of the VAR model. Due to the real estate turn down and the high inflation and interest rates of the late 70 early 80 the lump-sum reverse mortgage crosses the house value the first time within 13 year for the first time. The loan balance of an income stream mortgage crosses the house value much later. Figure 34 development average loan balance and house price starting at Table 11: Base case Product LVR Payment Margin NNEG Net payment Lump-sum 40% 106, % 15,511 90,489 (NP) Income stream 40% 5,035 1,84% 489 5,011 (NYP) Figure 34 and table 11 show that the income stream mortgage is comparable to the simulation of the growing house prices. The lump-sum mortgage faces negative equity events within the first decade due to the high inflation and real estate turndown of the late seventies. 43

44 Based on our analyses we cannot conclude a lump-sum reverse mortgage is on average less risky. Lump-mortgage are more flexible as they can also be used for expenditures on care or home modifications. Lump-sum payments could also be used for term pay-out designs, for example 10 year, or lines of credit. Disadvantage will be that the liquidity will be taxed as equity in the third box. Table 12: Sensitivity to mortality, costs and average delay of sales Product Sensitivity LTV Payment Margin NNEG Net payment Lump-sum Margin 40% 106, % 9,591 96,409 Lump-sum Margin 40% 106, % 3, ,062 Lump-sum LVR 35% 92, % 8,715 84,035 Lump-sum LVR 45% 119, % 25,456 93,794 Lump-sum -25% 40% 106,000 1,84% 23,792 82,208 mortality Lump-sum Costs 5% 45% 106, % 18,425 87,575 Lump-sum Delay 4 45% 106, % 16,665 89,335 quarters Sensitivity to mortality, costs and average delay of sales Income stream Margin 40% 5,035 1,5% Income stream Margin 40% 5,035 1,0% Income stream LVR 35% 4,405 1,0% - 4,405 Income stream LVR 45% 5,664 1,0% 1, Income stream -25% 40% 5, % 1,058 4,984 mortality Income stream Costs 5% 40% 5,035 1,84% 678 5,002 Income stream Delay 4 quarters 40% 5,035 1,84% 577 5, Main risk drivers There is a lot of debate about the value of the lending margins in the Netherlands compared to the neighboring countries. Sensitivity analyses indicate that lending margins do have a significant impact on the value of the NNEG as do loan value ratio s. Cross-over risk is also increasing if the life span of the loan is extended. We tested this by a mortality shock of -25%. The extension of the duration as a result of the mortality shock has more impact on the NNEG than a higher loan value ratio (45%). But all the result also indicate that margins, mortality as well as loan ratio values are not the critical factors in the applicability of reverse mortgage products. The main risk driver of cross-over risk is the long-term appreciation rate of residential property. The assumption about the future development of this growth rate could be the crucial factor in the development of reverse mortgage products. 44

45 5.5 Current barriers for development of Dutch equity release market In order to develop equity release markets some barriers have to be overcome. What policy could be likely to speed up the development of the reverse mortgage market, and stimulate more rapid innovation in the field of equity release? On the supply side, lack of funding capital might be the major concern. The current property market crises with the on-going devaluation in the value of residential home property combined with the problems related to the funding gap will make banking institutions very reluctant to develop and market a complex risky new product. On the demand side psychological factors, financial illiteracy and bequest motives might withhold potential borrowers. Another obvious impediment to market development could be a high level of transactions costs. If upfront charges and notary fees are significant they could make products too costly for consumers and providers. There might also be some regulatory issues to consider. Mortgages could negatively influence the acceptance or amount of social benefits or special or long- term care facilities and contributions. If low-income households entitled to some social benefits or contribution will lose those entitlements, this affects the net benefits they obtain by the use of equity release. In addition to that the fiscal treatment should also be considered. Under the current fiscal regime released equity will be placed in BOX III and taxed accordingly. In the US the federal government had a leading role in the development of the market for reverse mortgages by issuing transparent standard products that were trusted by reluctant borrowers. To encourage the development of the market, the US government insures all reverse mortgages that comply with the programme rules of the HECM (Home Equity Conversion Mortgage). The most important rule is the No Negative Equity Guarantee to the borrowers. This insurance is issued by HUD s federal Housing Administration (FHA). In addition to providing an appropriate framework of regulation and education the governments could consider policies to support the development of the equity release market like the US government by providing for standardized products and the no negative equity guarantee. In order the reverse mortgage market to develop lenders and regulators need to understand the risks embedded in these products. In order to price adequately providers must have the capability to access the risks. While regulators must be confident that the appropriate capital is held against the risks. Because the most important issue to address will be to bring trust with transparent products and adequate risk management. 45

46 6 Conclusion Dutch elderly hold a large proportion of their savings in the form of home equity. This locked equity could become an important component of financing retirement needs of an ageing population. Home equity can also be used to pay for health care expenditure and could reduce the costs of intramural long-term care. So home equity conversion could also be of interest for public policy experts who are looking for ways to reduce healthcare costs. Releasing home equity by regular mortgage products is difficult due to stringent underwriting criteria of current interest only mortgages. Although the possibilities to release equity with regular interest only mortgages and annuities might improve with lower mortgage margins and floating annuities, the uncertainty and the floating income will not make this products very attractive for borrowers. In order to allow the potential of equity release to supplement pension income to be truly sustainable, providers should come up with specific equity release products and mechanisms for mitigating the risks involved. The actuarial literature in the Netherlands on equity release products is limited. In this paper, we analysed cash flows and risks to price the no negative equity guarantee of equity release products. We applied a multi-period stochastic framework for simulating and evaluating the cash flows of different reverse mortgage products. The probability of terminations is based on a multi-state Markov model. To project economic variables and to derive a stochastic discount factor for pricing a VAR model is used. We concluded the average growth rate of our sample is below the historic average. Transforming the constant term of or VAR model show that the simulation results regarding the financial risks for reverse mortgages are sensitive to the sample period and its averages. Major effects were found testing the assumption of the average house price appreciation rate. Results show that the price and potentiality of reverse mortgages are very much depending on the appreciation rate of property values. Simulations with positive appreciation rates are less risky for lump-sum mortgages while in depreciation income stream mortgage are less risky. So unlike the research of Cho et al, (2013) our research did not show lump-sum reverse mortgage to be more profitable and less risky for the lender. Because lump-sum reverse mortgages start with higher loan values, simulations containing house depreciations show they reach the cross-over point earlier and are therefore subject to higher cross-over risk. This finding is confirmed when we test the historical values including the high inflation and real estate turndown of the late seventies. Lump-sum mortgages might be favourable attractive because they are less complex and more flexible. Fiscal treatment could make them less attractive. We also analysed the impact of other assumptions on the numerical results, like the Loan value ratio mortality improvement and lending margins. There is a lot of debate about the value of the lending margins in the Netherlands compared to the neighboring countries. Sensitivity analyses indicate that lending margins do have a significant impact on the value of the NNEG as do loan value ratio s. NNEQ will increase with higher Loan to value ratio, but so is the net payment to the borrower. So from a borrower s perspective high loan to value ratios are preferable. 46

47 Cross-over risk is also increasing if the life span of the loan is extended. We tested this by a mortality shock of -25%. Sensitivity to mortality rate improvement show on average an increase in the value of the NNEG. Increased cost of sale or an extension of the period in which property is sold after termination have relatively minor impact on the price of the NNEG. The results show that margins, mortality as well as loan ratio values are not the critical factors in the applicability of reverse mortgage products. The main risk driver of cross-over risk is the long-term appreciation rate of residential property. The assumption about the future development of this growth rate is a crucial factor in the development of reverse mortgage products. The sensitivity to sample period, assumptions regarding long-term averages and model choices highlights the need for further research. Including an extension of the terminations causes. Although the related risks and pricing models are complicated and must be further developed equity release does have potential as a mean to supplementing retirement income. In order to develop the market for equity release some behavioural and psychological barriers have to be overcome. The government could support the development by providing an appropriate framework of regulation and for example like the US government issue standardized products. A very important term for the market to take of will be to protect customers by providing for a No-Negative-Equity- Guarantee. Although a lot of work needs to be done home equity could become an important and significant pillar in our pension system in the future and a very interesting field and research area for the actuarial profession. 47

48 7 Suggestions for further research A critical topic that needs some attention is the time span of the historical data, in our research we had only 10 years of historical data available on which the model was estimated and with this model we generated scenarios for the next 50 years. Ideally our historical data would have contained a longer time period. Slagmolen (2010) found that different time periods of historical data have a great influence on the parameter estimates and corresponding scenarios. He also stated that one should also be cautious with low starting values of the interest rates, since these can lead to negative scenarios. Our model also showed to be very sensitive for the average of the house index in our sample period. Extending the sample period and analysing different sample periods over time would be very useful to give more insight in the risks involved. We also mentioned the consumer prices in the simulation of our VAR model showed deflation possibilities. To tackle this issue, we could also adopt the approach of Hoevenaars (2008) for the consumer index and transforms the constant term of the VAR (c) for the scenario generation as described in Hoevenaars, Molenaar, Steenkamp (2003) to an average in line with current objectives of the European Central Bank or we could use the long term average of 2% as a fixed variable in or simulations. Next to our limited sample period we modelled the dynamics of the economic variables with VAR with one lag based on the Schwarz-Bayesian Criterion (BIC). The Akaike Information Criterion (AIC) indicated a VAR(3) model as an alternative. In order to analyse model and parameter risk it could be useful to test sensitivity to the VAR assumptions. Our termination model only addresses mortality as cause of termination. The Markov termination model as described by Alai et al (2013) and based on Ji (2011 describes various reasons for mortgage termination, like entrance to a long-term care (LTC), move out for non-health reasons or refinancing. Including other termination probabilities in the termination model will affect the average termination point of reverse mortgages and as a result will influence the cross-over risk and price of the no negative equity guarantee. From the provider perspective it would be interesting to further analyse the risk-based capital level for solvency or Basel requirements of different products. It will also be interesting to observe whether adverse selection and moral hazard do occur in period during which the interest rates exceeded the price appreciation. 48

49 Appendix A: List of variables Symbol L 0 L t+β Β Ht α δ r i π Ct Loss Tx Description Initial Loan value oan value at t average delay in time from the point of home exit until the actual sale of the property House value at time t Loan Value Ratio transaction costs of selling the house Short rate at time i quarterly lending margin The providers/lenders net equity at time t The present value of providers loss m t the risk-adjusted stochastic discount factor ω The loan termination point, i.e. the maximum attainable age of the last homeowner. NP 0 Net lump-sum payment after deduction of NNEG charged as an upfront premium NNEG Value of no negative equity guarantee t the probability that a reverse mortgage is in force by time t and will be terminated by t+1 ä x:y, 0 Joint-Survivor annuity at T = 0 (n) Y t zero coupon yield rate for maturity n at time t the in-force probability, the probability at time t that one of the home-owners, age x:y at loan origination will still be in their homes at the end of year t. Ux:y,0 fixed yearly payment (income stream mortgage) t annual insurance premium t x y Fä x;y,t Floating joint-survivor annuity at time t AI t Net additional income NYP Net yearly payment (income stream mortgage) γ Margin based on Danish system (LVR 80%) AI t Net additional income Z t the ( n X 1 ) vector of the economic state variables of the VAR model P the number of lags ε t vector of multivariate normally distributed error terms VAR coefficients 1/2 Σ C Cholesky decomposition of the covariance matrix Σ the covariance matrix The constant term of the VAR model 49

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