MORAL HAZARD IN HOME EQUITY CONVERSION: Graphical Representations 3

The same diagram Figure 2 applies to the situation of homeowners who have taken out home equity insurance on their home, to create a floor of value on the home. Doing this is the same as buying a put option on the home with a strike price equal to 80% of home value at the initial date, and borrowing 80% of the value of the home. That a portfolio of a home, a put option and a debt is the same as a call option on the home is due to the put-call parity relation in finance.

Figure 3 shows the case of a shared appreciation mortgage in which 75% of the mortgage value above the initial home value is paid to the mortgage lender, but all of the losses for the homeowner if the value of the home on resale is less than the initial value. This g(V) curve is a broken straight line with a slope of one to the left of V0 = 1, and a slope of ,25 to the right of V0.

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Figure 4 shows the case of a limited partnership in which the ‘homeowners’ (the residents of the home) actually own only 25% of the home and the other partner 75%. Now, the g(V) curve is just a straight line with slope of 0.25. This figure also shows the case of a shared equity mortgage and a sale of remainder interest where the homeowners retain only a 25% interest in the home.
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In viewing the variety of patterns of risk management shown in Figures 1 through 4, one wonders what accounts for the simultaneous existence in the market of all these different forms. Is there some good reason why some homeowners would want one of these forms and other homeowners want another? This question is analogous to the question, in finance, why different people want different portfolios of options and other derivatives. The answer is probably sufficiently complex that there is no simple answer. The answer has probably to do with differing opinions about future price movements, differing information sets, differing asset positions and income flows, differing worries and concerns, differing ways of framing the issues. Our concern here, however, is not with reasons for these different contracts, but with the moral hazard associated with them. Fortunately, as we shall see now, the moral hazards created by all these different home equity conversion contracts have a certain family resemblance.