Yesterday the Institute announced that the project to research equity release mortgages will be delivered by the University of Kent, led by Professor Radu Tunaru (Senior Researcher).
This is not a bad outcome. Tunaru was long tipped to deliver this project and he has form on real estate derivatives. But he may face formidable problems. One of the objectives set out in the request for tender is ‘To consider whether there are any “halfway house” solutions between real world and risk-neutral approaches given, in relation to the latter, the absence of a deep and liquid market’.
To explain why this may be difficult, consider our well-known chart above. The green line is the present value of a non-defaultable (or perfectly collateralised) loan, computed by projecting the initial loan value by the higher-than-risk-free loan rate, then discounting back at risk free. The form of this curve is not controversial. The red line is the ‘deferment curve’, defined by the net rental or ‘deferment’ rate. The form of this curve is more controversial, given that some firms – according to the PRA – are using negative deferment rates, implying negative rentals. This is because instead of using net rental yields to determine the deferment rate, they are making assumptions about house price growth.
The blue line is the actual ERM value. It is not controversial that the other two lines are an upper bound on ERM value, and you can easily prove that the blue curve approaches this bound as Black-Scholes volatility falls to zero.
The problem is that there can be no conceivable halfway house between the ‘real world’ approach, i.e. assume that house price growth1 determines the deferment value, and the ‘risk neutral’ approach, i.e. assume that rental yields determine the deferment value. On the first approach, we have to suppose that investors would prefer deferred to immediate possession because house prices will appreciate, as though they would not benefit from the same appreciation through immediate possession. The second approach, by contrast, recognises that investors benefit from the same appreciation whether possession is deferred or immediate. What on earth would an appropriate halfway house look like? Would we say, e.g., that investors would receive half of the appreciation through immediate possession, and all of it through deferred possession? Which is nonsensical.
Of course, Tunaru has merely been asked to consider whether such a house exists. But if there are no bricks, there is no halfway house to build.