# MORAL HAZARD IN HOME EQUITY CONVERSION: Graphical Representations

For the purpose of understanding the incentives for moral hazard created by the various home equity conversion forms, we will summarize the incentives created for the homeowners by each of the various forms of home equity conversion described above in terms of their implied functional form relating the homeowners’ expected terminal portfolio value to the value of the home when it is finally sold. The date at which the home is sold depends of course on random factors: marriage, divorce, job changes, death, etc. For illustrative purposes, we disregard the uncertainty about date of sale, and assume that it is known, let us say, eight years in the future. Let us call g( V) the homeowners’ portfolio value as a function of the sales value V of the home on this date. In each example the portfolio is assumed to consist of the homeowners’ equity in the home (home value minus debt) plus any transfers created by the home equity conversion program. We assume that the homeowners are concerned about heirs, and so it is immaterial whether the sale is caused by death of an owner or for other reasons.

Figures 1 through 4 show hypothetical forms for the g(V) function for each of four situations: 1) conventional mortgage, 2) reverse mortgage and conventional mortgage with home equity insurance, 3) shared appreciation mortgage, and 4) limited partnership, shared equity mortgage, or sale of remainder interest In all four figures the horizontal axis shows the value of the home when it is finally sold divided by the value when the home is purchased, and so the point 1.00 on the horizontal axis represents a situation in which the final value of the home equals the initial value of the home. In all four diagrams the homeowners have just purchased a home by borrowing an amount so that the loan to value ratio, that is the loan balance on the date when the house will be sold divided by the value of the house today, is L > 0. The initial loan to value ratio would be higher than L if the homeowners are not making regular interest payments on the loan, as for example, with reverse mortgages, since the loan balance would grow as interest accumulates. The initial loan to value ratio might be essentially the same as L if mortgage payments are being made about equal to interest, as might be the case with conventional or shared equity mortgages for the first eight years of a longer-term mortgage. On all four figures, we take L = 0.8.