Kevin Dowd 20 August 2018
Earlier this week the Association of British Insurers and the Institute and Faculty of Actuaries issued a tender call for research on the valuation of the No-Negative Equity Guarantees (NNEGs) in Equity Release Mortgages (ERMs). Their timing is perfect, coming as it does a week after my report on NNEG valuation, Asleep at the Wheel: The Prudential Regulation Authority and the Equity Release Sector, and a few weeks after the PRA’s most recent Consultation Paper on the subject, CP 13/18, “Solvency II: Equity Release Mortgages.” One thing is for sure: the current manual used by practising actuaries for the valuation of NNEGs is not so much out of date as flat out wrong.
I refer to the ‘real world’ approach as set out in the 2007 article “Pricing and Risk Capital in the Equity Release Market” by Hosty, Groves, Murray and Shah. This approach leads to major under-valuations of firms’ NNEGs that mean that (some) firms are carrying large hidden losses on their balance sheets.
To their credit, the PRA have been warning about this problem for years.
Now there are two approaches to NNEG valuation. Oversimplifying slightly, the first is the ‘market consistent’ approach based on some academically respectable option pricing model such as Black ‘76. This is the model I used in my report and also the model expected by the PRA (CP 13/18, p. 20).
The key to correct option valuation is the underlying variable, the forward house price. For a horizon t, the forward house price is given by
(1) Forward house price = Current house price x exp((r–q) x t)
where exp refers to the exponential function, r is the risk-free rate and q is the net rental rate, which might be something in the range between 2% and 3%. In a low interest-rate environment, we might expect r to be less than q and in that case the forward house price will be less than the current price.
The alternative approach – the approach preferred by ERM firms – is the so-called ‘real world’ approach promoted by Hosty et alia. This approach boils down to using an option model – Black 76 or whatever – but with the expected future house price as the underlying variable instead of the forward house price. The expected future house price is given by
(2) Expected future house price = Current house price x exp(EHPI x t)
where EHPI is the expected house price inflation rate.
I cannot stress strongly enough that this approach has no validity and, unlike the case with the market consistent approach, there is no underlying theory to justify it.
Firms like it because it produces low NNEG valuations but that is hardly a justification for using it. The issue is not whether a model produces low NNEG valuations but whether it produces justifiable NNEG valuations.
That this approach is indefensible can also be seen from a recent example in which a firm used (2) with an expected house price inflation rate of 4.25%. If we set r equal to 1.5%, say, then this is equivalent to using (1) but with q = 1.5% – 4.25% or q = minus 2.75%. But a negative rental rate implies that rents are negative and negative rents make no sense.
These approaches produce quite different NNEG valuations. In my report, I gave a base case example (based on a 70-year old male, a loan-to-value ratio of 40% and various other illustrative calibrations) in which the market-consistent approach based on a q rate of 2% produced a NNEG that was equal to 52% of the amount loaned, whereas the incorrect ‘real world’ approach based on a q rate of minus 2.75% produced a NNEG that was only 3% of the amount loaned. That is some difference.
Two bullet points in the tender document made me wonder, however:
To consider the relative merits of ‘real world’ and arbitrage free (risk neutral) methods [KD, i.e., market-consistent methods] and how the assumptions should be set on both bases.
I would suggest that there are no merits to the ‘real world’ approach, period. It belongs in the bin.
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.
Mm … a half-way house between an approach that makes sense and one that does not. This is a bit like trying to rectify an astrological model by throwing a bit more astronomy into the astrolabe. Good luck on that.
One can already see the battle lines forming. There are Dean and I and the PRA on the one side saying that the ‘real world’ approach is nonsense. Then there are the defenders of the ‘real world’ approach, who will doubtless argue that Black-Scholes type models are invalidated by the absence of a deep and liquid market, market incompleteness and so forth.
There is a whole shoal of red herrings here, but I will come back to those in a later posting. Suffice for the moment to note that the ‘holes in Black Scholes’ are well known and options experts know how to deal with them.
In the meantime, well done to the ABI and the IFoA for promoting research into this important topic. A lot is riding on it.