In the case of the partnership, shared equity mortgage and sale of remainder interest, Figure 4a, the incentives to invest are reduced over the entire range of I. The slope of the h{I) schedule in Figure 4a is scaled down, in comparison with Figure la, by the factor a. When a = 1, as was the case with the reverse mortgage, the profit maximizing homeowners will invest only 2% of the initial value of the home. Losses to investors are catastrophic; j/(1 – a) is, using equation (10), 36%. If a = 0.5, then the homeowners will invest 10% in the value of the home, and the investors thus face an expected shortfall 5/(1 – a) of 18% of their investment.

The declines in home value suggested by our calibration are often quite large. Moreover, even declines of home value that are among the smaller of those predicted by our model for our examples may be an important issue for the mortgage lenders or other parties who are the ultimate bearers of the losses, to them losses multiplied by the thousands or millions of homes that they cover. Our model illustrates how a number of different factors conspire to produce widely varying amounts of homeowner investment, and, given the uncertainty about some of imposed parameter values, there is perhaps some substantial uncertainty about the likely long-run outcomes to home equity insurance forms. While our model is only a calibrated model, it is illustrative of the kinds of calculations that must be pursued very carefully before investing in any home equity conversion form.

It is important to make a final word about general inflation. In all of our calculations, we conditioned on L, the final loan balance as a fraction of initial home value, setting it to 0.8 in both the conventional and reverse mortgage case. But general inflation has different kinds of expected effects on L for the different forms of home equity conversion. In an inflationary period, with nonindexed conventional mortgages, mortgagors are forced to pay down the real mortgage rapidly, so that the mortgage balance tends to decline quickly relative to home value. Lenders accustomed to conventional mortgages may thus learn a sort of complacency about the risks to them of declining home values. With reverse mortgages, there is no such pay down of the mortgage balance when inflation is high. Investors should be cautious not to let the experience with default losses on conventional mortgages cause them to underestimate the risks of the alternatives to it that we have considered. Moreover, inflation tends to reduce the moral hazard advantage we saw in the shared appreciation mortgage form relative to the other home equity conversion forms, by pushing the homeowners into a region of the h{I) curve where all the benefits of investing accrue to investors.