In our discussions with equity release actuaries, Dean and I have often come across some recurring arguments.
An example is what we might call the ‘hedging fallacy’ – the argument that we can’t apply B76 (or BS) to value equity release NNEGs because these option price formulas are derived under the assumption that the underlying variable, in this case, forward contracts on residential property, can be hedged. This assumption is obviously empirically invalid, so the argument goes, therefore we shouldn’t use B76/BS. And the argument (often) continues, we should then throw away B76/BS and use the discounted projection approach instead. And thankfully, the discounted projection approach delivers much lower NNEG values. So there is nothing to worry about – all that undervalued NNEG stuff is overhyped.
This argument is false, but it is false in a number of interesting ways.
First, even if B76/BS were invalid in the NNEG context, it would not follow that we should use the DP approach instead. The fact, if it is a fact, that one approach is flawed does not make another approach, that is known to be flawed, whole. The DP approach is fundamentally flawed and should never be used, regardless of what one thinks of B76. The flaw is that it conflates the forward price and the future price. This is a finance 101 hoot of an error, but it still persists among practicing actuaries. Indeed, we have encountered it so often that we have taken to referring to it as The Actuarial Fallacy in their honour.
Second, the premise of the argument – that long term forward contracts on residential property are unhedgeable – is also wrong.
There are in fact two ways an ERM firm could hedge its property exposure.
One is to construct and periodically adjust an actual physical property hedge. Dean and I show how to do this in the Appendix to Chapter 20 in the first edition of our Eumaeus Guide to Equity Release Valuation. Once the hedge is in place, the firm can apply B76 to value its NNEGs safe in the knowledge that its option position has been hedged.
Alternatively, an ERM firm could hedge its property exposure with an investment bank, and then use B76 to value its NNEGs. The investment bank will likely then use B76 to value the NNEG and add in a generous premium. It’s costly but perfectly doable.
This latter point implies that the issue is not that the property exposure cannot be hedged, but that it is expensive to hedge a property exposure. Now think it through: if the hedge is expensive to hedge rather than costless to hedge, then that makes the synthetic option, the hedge, more expensive than it would otherwise be. That then makes the actual option more expensive than it would otherwise be, because the values of the two options must be equal. And since the actual option is the NNEG, then that makes the NNEG more expensive than it would otherwise be.
Now consider the results we would get using B76.
The answer is given in the Figure below.
Annualised Returns to ERM Loans to a Borrower Couple of the Same Age
Notes: Based on a set of illustrative parameter calibrations and mortality projections using the M5-CBD mortality model.
The Figure shows a plot of annualised returns to lenders from new ERM loans to borrower couples of the same age. These annualised returns are -0.8% for borrower couples aged 55, rise to about zero for borrower couples aged 76, and rise to 1.3% for those aged 90.
But B76 does not consider the cost of operating the hedge. So returns would be even lower, or losses even higher, than the figure suggests.
Thus, most ERM loans are loss-making to lenders and that presumably makes them poor investments for investors coming into the ER sector.