The Equity Release seminar that Dean and I presented at the London School of Economics on Monday October 1st got a good turnout and prompted a lively, and at times, stormy, discussion.1 The most entertaining contribution to the discussion came from NUMIS equity release analyst Marcus Bernard, who has been pushing Just Group hard as a buy.
Marcus and I are on opposite sides on this issue.
Let me start by saying that Marcus has form when it comes to No-Negative Equity Guarantee (NNEG) valuation. His analysis of the PRA’s CP 13/18 is a classic:
We are unsure why the PRA want to value NNEG guarantees using an option pricing formula, when there are no embedded options within the product. This seems to fall foul of two principles of option pricing: the mortgagee cannot choose to exercise this option other than by dying (or going into care). Secondly there is no financial gain for the mortgagee or its estate in exercising this option.2 (My emphasis)
There are a number of (contradictory!) mistakes in this statement.
Mistake #1: The NNEG jolly well is an option. Look at the payoff: the NNEG holder, the mortgagor (not the mortgagee!) has the choice to pay the minimum of two amounts, either the house price or the rolled-up loan amount. This choice to pay the minimum of two values defines the NNEG as a put option.
In any case, if the NNEG is not an option then why are firms valuing the guarantee using a variant of the Black Scholes option pricing formula?
Marcus is in a minority of 1 on this issue. Everyone else says the NNEG involves an option, Marcus says it doesn’t.
Mistake #2: “mortgagee cannot choose to exercise this option other than by dying (or going into care)”. Even correcting for the mortgagee/mortgagor muddle, this statement misses the point. If the mortgagor dies before the loan is repaid, then someone else (typically, the trustee of their estate) will exercise that option if it profitable to the estate to do so. And if the mortgagor moves into a care home, then one would normally expect the mortgagor to have previously delegated power of attorney to someone capable of exercising that function, and that person would exercise the option if it was appropriate to do so.3
Mistake #3: “no financial gain for the mortgagee or its estate in exercising this option.” The correct statement is there may or may not be a financial gain to the mortgagor or their estate in exercising. As with any other option, whether it will be exercised will depend on whether there is a payoff to doing so. If the guarantee does not bite (i.e., if the option expires out of the money), there will be no payoff from exercising the option, but if the guarantee bites and the option expires in the money, there could be a considerable financial gain in exercising: the gain will be the excess of house value and compounded loan value. This is Options 101.
****
Back to the seminar, I had got ten minutes into it when Marcus interrupted. I had explained that there is a correct approach to value the NNEG that uses a net rental rate of 2% to 3% or so, and there is the incorrect approach that the firms are using, which produces an implied net rental rate of about -2.75%, in the case of one well-known firm. The point is that a negative net rental rate for housing makes no sense. A negative rental implies a negative rent and who pays that?
The correct approach uses a forward house price as the underlying variable in the Black ’76 put option equation. The forward price is obtained by compounding the spot house price at the forward rate:
(1) f = r – q.
A reasonable calibration might take r as about 1.5% and q as about 2.5% and then give a forward rate of about f = r – q = 1.5% – 2.5% = -1%.
But the firms were replacing the forward rate with an assumption (well, a guess really) about expected (future) house price inflation (EHPI), and if we input this value into equation (1) we get
(2) EHPI = r – q
and we can then back out an implied q rate equal to r – EHPI.
I mentioned that one firm was using an EHPI = 4.25% and this calibration produces the implied q rate = 1.5% – 4.25% = –2.75%.
Enter Marcus. “Where did you get that 4.25% house price inflation number from?”4 He wanted to know.
Kevin: One of the firms used it.
I was referring to Just Group.
Marcus: OK was it in the accounts?
Kevin: Yes, it was in ….
Dean: Both in the accounts and the SFCR [Solvency and Financial Condition Report] …
Marcus: It’s not in there, so the whole basis of your analysis is based on the wrong number ie you’ve got the wrong trousers Gromit.
Gromit: No No No! It is [in there], we got that number from that particular firm’s published information.
Marcus: But it’s not in there, I had a look for it and I spoke to them about it, its not there.
Kevin: I can show it to you.
Marcus: Well lets take that offline.
Kevin: … I didn’t make it up!
Marcus: Well it looks like you have [made it up], because I can’t find it and they can’t find it.
Kevin: If you can’t find it, I can’t say anything to that.
Made it up my foot!
The number appears twice in Just’s 2016 Annual Report:
When calculating the value of the no-negative equity guarantee on the lifetime mortgages, certain economic assumptions are required within the variant of the Black-Scholes formula. …
In the absence of a reliable long-term forward curve for UK residential property price inflation, the Group has made an assumption about future residential property price inflation. This has been derived by reference to the long-term expectation of the UK retail price inflation, “RPI”, (consistent with the Bank of England inflation target) plus an allowance for the expectation of house price growth above RPI (property risk premium) less a margin for a combination of risks including property dilapidation and basis risk. This results in a single rate of future house price growth of 4.25%. (2016 report, p. 163, my emphasis)
In June 2016, the Group took a view that due to external factors there may be potential disruption in the property market in the short term but these factors would not affect the long term view and hence adopted an assumption that house prices will fall by 10% (from levels as at 30 June 2016) by 30 June 2017 and would grow thereafter at a rate of 5.0% p.a. The Group has retained this assumption for the current valuation. The impact of this assumptions is broadly equivalent to using a flat 4.25% p.a. assumption. (ibid.)
Marcus must have missed this when he read these reports.
The phrase “headline HPI assumption of 4.25% pa” on p. 18 of Just’s last (September 6) interim results presentation also jumps out a bit.
But by this point, he was on a roll.
“What information have you got about the firms?”
The information they published, not that there is much of it, I said. The information provided is not the detailed breakdown one would ideally want, but enough to do some calibrations and produce order-of-magnitude valuations that give us a sense of the scale of the issue.
“Have you spoken to anyone at the firms?”
No I hadn’t, but Dean had recently spoken to them on a number of occasions. As Dean explained, the PRA “has seen” approaches that imply a negative deferment rate, and when the PRA says it has “seen” stuff, then that invariably refers to firms’ stuff. Like what else could it refer to?
That the PRA has “seen” such stuff and disapproves of it is a matter of public record. To quote CP 13/18:
… the PRA has seen approaches that calculate property forward prices assuming property growth in excess of the risk-free rate while simultaneously discounting at the risk-free rate … and considers that such approaches are equivalent to assuming a negative deferment rate and would not meet principle (iii) [of its ERM good practice principles]. (p.8)
But Marcus still wouldn’t have it: “You haven’t even tried to find the firms’ information!” he insisted.
Whatever does one say to a claim like that? How many times do we have to repeat that we were not operating on a zero-information basis?
****
“How do you know that the firms are doing the modelling incorrectly if you haven’t got any information about what they are doing?” was the next question.
I know the firms are getting it wrong because they themselves say so, but not quite in those words, I replied.
The explanation is that we are using the Black model which is the near relative of Black-Scholes that is appropriate in this context because our underlying variable has a continuous rental yield. Neither Black ’76 nor Black-Scholes includes the house price inflation rate or the expected house price inflation rate as one of its input variables.
So how do we know that companies are getting their NNEG valuations wrong? Easy. Because in every single case where I can find any information about their approach to NNEG valuation, they tell us that they use the house price inflation rate or the expected house price inflation rate as an input to their NNEG valuation model. Their approach must be wrong because they are basing their NNEG valuations on a variable that does not belong in their valuation models.
This practice has no scientific foundation and constitutes an egregious error.
But don’t take my word for it. In case you missed it, the PRA has been issuing warnings about this problem for four years now. It has issued a number of letters going back to October 2014 and resulting consultation papers, discussion papers and supervisory statements (see, e.g., DP 1/16, CP 48/16, CP 23/17, CP 24/17, SS 3/17 and CP 13/18) that had set out its concerns about ERM firms’ exposures and modelling practices. To quote CP 48/16 on the PRA’s survey results, there is
a wide variety of practice regarding valuation of the embedded guarantee, with suggestions that sometimes diverged from conventional approaches to the valuation of guarantees in incomplete markets.” […]
[But there] was consensus that property assumptions (growth and volatility) were most significant [in the valuation of the NNEG]. (CP 48/16, pp. 6, 19, my emphasis)
In short, there is a consensus among firms that expected property growth matters for NNEG valuation and that consensus itself indicates that they are all getting it wrong.
CP 48/16 also offers a correct diagnosis of the problem:
Many respondents mentioned a version of the Black-Scholes formula known as ‘Black 76’, where the underlying price is the ‘forward price’ of the property. This version uses the current price of a forward contract. Some respondents appeared to conflate this with the forecast future price of the property, but provided no justification for why house price inflation was relevant to the current price of a forward contract. (CP 48/16, p. 25, my italics)
The word “conflate” hits the nail right on the head. The reason why these correspondents provided no justification for using projections of future house price inflation to value these guarantees is because no such justification exists.
To spell it out: some firms say that they are using assumptions about future house price growth, but the PRA points out that this is obviously wrong. From which it follows (1) that some firms are using a method wholly at odds with the one endorsed by the PRA and (2) that the PRA would not be bothering to state this at all, particularly through a protracted consultation period if it had not experienced substantial pushback from firms. We can then infer (3) that firms with equity release exposure have been undervaluing their no negative equity guarantees. We can infer this because the PRA would not be publishing on the subject or seeking industry consultation if they thought that these guarantees were correctly valued. Consequently, some firms are presumably undervaluing them. Also (4) by a similar logic, if firms are dedicating substantial resources to pushing back, they must think that the valuation of guarantees is a material issue.
You want direct evidence from the firms’ themselves? Here are some samples of five firms’ statements about their NNEG valuation approaches from their recent reports:
“When calculating the value of the no-negative equity guarantee on the lifetime mortgages, certain economic assumptions are required within the variant of the Black-Scholes formula. […] In the absence of a reliable long-term forward curve for UK residential property price inflation, the [firm] has made an assumption about future residential property price inflation. … This results in a single rate of future house price growth of 4.25%.”
“[The value of the NNEG] is calculated using a variant of the Black Scholes option pricing model. The key assumptions used to derive the value of the no-negative equity guarantee include current property price, property growth and property volatility.”
“Stochastic modelling is used to capture the expected cost of [the NNEG], which will depend on the expected rate and volatility of future house price growth …
“Equity release and securitised mortgage loans … are valued using an internal model. Inputs to the model include primarily property growth rates, mortality and morbidity assumptions, ….”
“The fair value of the guarantee is determined using a stochastic model. The fair value of the loans is determined using assumptions for interest rates, future house price inflation and its volatility …”
Almost all this firm information was in my earlier report Asleep at the Wheel and should not be news to anyone who has been following the equity release story.
****
Once the Q&A came a number of people raised issues about the validity of Black ’76 and the implications for NNEG valuation. Dean and I had expected such questions, so we wheeled out some supplementary slides we had prepared and explained the second and third of the PRA’s good practice Principles
These ideas underlying these principles were originally set out in DP 1/16 and provide a model-free way of obtaining an upper bound on the value of the ERM. They are explained in the following slide:
The red line gives the value of deferred possession for any future time or horizon measured in years ahead. Principle III says that the value of deferred possession is less than the spot value and is represented by the red line sloping downwards. Principle III follows from the q net rental rate being positive. Principle II says that the value of the ERM can never exceed the minimum of the loan value – that is, the value of the loan considered as if it were risk-free and guaranteed to be repaid in full – and the deferment house price. Principle II is represented by the blue line being bounded above by the green (loan value) and red (deferment value) lines.
Now remember that the value of the ERM is equal to the value of the loan (considered as risk free and guaranteed to be repaid in full) minus the value of the NNEG. Therefore, since that loan value is known, an upper bound on the value of the ERM implies a lower bound on the value of the NNEG.
These Principles are critical because they allow us to place lower bounds on the NNEG without relying on any option pricing model.
These lower bounds cannot be breached. To try to do so is like trying to achieve a temperature lower than absolute zero or biting on granite.
I pointed out that if we had done the presentation again but used these lower bounds for the NNEG valuation instead of Black ’76 NNEG valuations then we could tell the same story, the only difference being that the NNEG valuations would be somewhat but not that much lower.
So you can throw away Black ’76 if you wish to, but the core ‘NNEG under-valuation is a problem’ story still holds.
I asked Marcus how he would respond to this argument and he responded to the effect that he wasn’t aware of the Principles. Here is the exchange:
Kevin: This goes to anyone who doesn’t like Black ’76. Suppose I told you the same story, which I could have done and I kind of alluded to at the end … that if I did the lower bound analysis instead [of Black ‘76], you’d get something very similar, You would get results that were very similar, results not quite as dire, as the ones I’m getting, but they wouldn’t be that far off.
And none of the criticisms of Black ‘76 or of the option price model or the volatility, none of that would apply … if I’d couched [the story] in those terms.
I just wondered what you’d say to that Marcus? …
Marcus: Well look, I haven’t seen that chart before.
Kevin: It’s in the Principles. I’m surprised you’ve not read the Principles.
Dean: [Pointing to the chart] That is Principle 2 the Blue line, bounded by those [other two lines] lines, P3 is the red line …. That’s in CP 13/18.
Kevin: And its in DP 1/16. Its in a number of them.
Dean: Its in practically all the ones published, I think even the original DP1/16 which is March 2016, even that has it as a question.
Marcus: Well I’ll take that offline if I may.
So he had missed all that stuff as well.5
These Principles are key features of the regulator’s approach to the sector and are central to the NNEG valuation controversy. They were not exactly hidden either: the core ideas were introduced in DP 1/16,6 developed as a set of principles in CP 48/16 (see esp. p. 17), and then developed further in SS 3/17 (p. 12) and CP 13/18.
For an equity release analyst, Marcus sure seems to have missed an awful lot about equity release. It’s not the wrong trousers; it’s all fur coat and no knickers.7
End Notes
- I thank Ron Anderson and my old friend Charles Goodhart for organising the seminar.
- M. Barnard (2018) “CP 13/18 contains flawed thinking, in our opinion.” NUMIS Securities, 8 August.
- I imagine that this passage might have prompted a smile at the PRA. To quote the PRA’s Policy Statement that accompanied SS 3/17:
One respondent … considered that it was inappropriate to view the NNEG as an option, arguing that: (a) the guarantee can be neither traded nor exercised other than at the death or entry into long-term care of the borrower; and (b) the NNEG does not apply if the borrower chooses to avoid selling the property, eg because the borrower places a value on the property [that] is greater than the market value. (My emphasis)
The borrower might well put a higher value on the property than the market does but this makes no difference: the borrower still has to repay the loan and if the NNEG bites then it is cheaper to pay the loan by exercising the NNEG than by not exercising it however the mortgagor values the property. Then consider the PRA response:
2.35 The PRA does not consider that the inability to trade the guarantee, or the conditions on when it may be exercised, changes the nature of the risks that it poses. Further, the PRA has not seen reliable evidence that borrowers would choose to waive their rights under the NNEG in order to retain ownership of a property. Absent such data, the PRA does not consider it prudent to assume that borrowers would … [waive their NNEG rights], particularly given that many ERM providers market the NNEG as an important benefit to potential customers. (My emphasis)
- My reconstruction of the discussion is based on our recollection supplemented by notes that Marcus provided afterwards. I thank him for those. There was a little more that I cannot clearly remember, although I do recall Marcus asking about my motivation for doing the research, who was paying me, it would be very public spirited if I were doing it for nothing, etc. For the record: I wasn’t paid anything for the report. I just like poking things with sticks.
- And he got the deferment rate wrong too. See also https://www.justgroupplc.co.uk/~/media/Files/J/JRMS-IR/investor-docs/financial-reports-and-presentations/2018/just-hy-18-qa-transcript-final.pdf
“Marcus Barnard: Marcus Barnard from Numis. Could you share with us any insights you’ve got about the deferment rate, because this is something I certainly hadn’t heard of more than six months ago. It seems a rather arbitrary rate that’s come out of this consultation paper, and it seems to be something that is having a material impact on your capital. You know, any help in explaining this in this forum would probably help all of us. Sorry to put you on the spot. (My emphasis)”
To help you all out, the deferment rate is the key to NNEG pricing and was not invented by CP 13/18 and I didn’t make it up either. The PRA first used the term “deferment rate” in CP 48/16 published in December 2016 so it has been around for a while in the regulatory space and before that has long been an established concept in the real estate literature. “[I]t seems to be something that is having a material impact on your capital.” Yes, you could say that.
- To quote DP 1/16:
4.9 The following two relationships hold regardless of whether or not the NNEG is construed as a series of put options, or whether it is valued any other way. First, the present value of an ERM payoff at an assumed exit date cannot exceed the present value of receiving the property at that date where a NNEG applies (because the NNEG restricts the loan repayment to the value of the property, as discussed in paragraphs 3.9 and 3.10).
Second, the value of having immediate possession of the property is higher than the present value of receiving the property at some point in the future (put differently, deferral of possession leads to a reduction in current value, arising from foregone income or inability to use an asset).
- If Marcus wishes to continue this discussion, we would be happy to post any response in full.