By Dean Buckner and Kevin Dowd, 25 February 2019
Tunaru’s half-way house between ‘real world’ and ‘market consistent’ approaches does not work and the ‘real-world’ NNEG valuation approach remains indefensible.
Last Thursday (21 February 2019) saw the release of Professor Radu Tunaru’s long-awaited report on the IFoA-ABI sponsored but independently carried out NNEG valuation (aka astrology) project. In a sense, the Tunaru report did not disappoint. It provides a novel approach to NNEG valuation and manages to meet the expectations – one might even say hopes – of its sponsors who had asked him to consider the possibility of a half-way house between the industry’s preferred ‘real world’ approach and the ‘market consistent’ approach put forward by the PRA and ourselves (CP 13/18; PS 31/18; Buckner and Dowd, 2018; Dowd, 2018). The problem is that the novelty adds little value and Tunaru’s proposed half-way house does not work.
The proposed approach is the ARMA-EGARCH approach – or to give it its mellifluous full name, the Autoregressive Moving Average Exponential Generalised Autoregressive Conditional Heteroskedastic approach (see here for the vanilla GARCH and here for the EGARCH variants). This approach has been around for a long time however and is well known to time-series econometricians and applied economists, who use it principally to model short-term volatility dynamics in asset markets. But it is not obvious why one would want to apply a model of short-term volatility dynamics to a long-term problem such as NNEG valuation. Just as ‘is’ does not imply ‘ought’, ‘can’ does not imply ‘should’. The ARMA-GARCH approach adds more complexity to a problem that is already much misunderstood and adds further confusion to a debate that is already needlessly confused.
The underlying issues are simple, however. We are talking here about the valuation of a put option or, more precisely, of a basket of put options, and put option valuation has been (fairly) well understood since the 1970s. All you need to know is that the new approach gives broadly similar results to the old bog standard Black’ 76 approach, provided much the same calibrations are fed into the models. It is the calibrations that matter and the choice between the two modelling approaches is secondary. Of the calibrations, the one that matters most is the net rental rate or q rate, which is approximately equal to the deferment rate. It is this parameter that does most of the heavy lifting whatever model one uses. A second parameter that also matters is the volatility.
To cut to the chase, put in plausible calibrations for the net rental rate and the volatility and you will get results in the same ballpark as ours. You can add refinements, but the basic story will remain the same: the ‘real world’ approach will give NNEG valuations that are a sliver of those produced by the ‘market consistent’ approach, but the ‘real world’ approach is demonstrably indefensible and that should be the end of the matter. The trouble is that there is a vocal lobby group with a vested commercial interest in the ‘real world’ approach and which promotes that approach as if it were a scientifically defensible alternative to the ‘market consistent’ approach. It is not.
On the net rental rate, Tunaru suggests a ‘best-estimate’ figure of 0.66%, which is lower than both the CP 13/18 ‘best-estimate’ (2%) and the PRA’s recommended minimum (1%). We regard the PRA ‘best estimate’ as being too low and would recommend at least 3% and plausibly more.
On the volatility, Tunaru suggests a range of values between 3.85% to 6.5%, with a baseline volatility of 3.9% (pp. 37ff). These values are considerably lower than the PRA’s plausible range of 10% to 15% and its recommended minimum value of 13%. We would suggest that even the PRA’s volatility numbers are too low, but more on that subject in our blog posting tomorrow.
Commercial sensitivity
The calibrations of these parameters are hugely commercially sensitive. Using the Tunaru values for net rental and volatility would have a significant impact on the financial position of Just Group, for example. According to the sensitivities they published in their 2017 Solvency and Financial Condition Report they would gain roughly £80m from a 0.25% decrease in the deferment rate – so they would gain over £100m in moving from the PRA minimum of 1%, to Tunaru’s proposed 0.66%. They report that a 0.5% decrease in the implied volatility would increase capital by roughly £30m. Accepting the suggested 9% decrease suggested by Tunaru (the PRA’s 13% minus his baseline of about 4%) would result in an overall increase in reported capital of £540m, i.e., 18 step reductions of 0.5% and 18 times £30m = £540m. The reported capital position of that firm would then benefit by over half a billion pounds if the Tunaru proposals were adopted. Whether these capital increases are ‘real’ or not is another matter, however.
Commercial sensitivity is a point to note, especially when the research is sponsored by firms or organisations (e.g., ABI) that have a stake in the outcome of that research, or when members of the committee that awarded the research contract work for firms that have a commercial interest in the outcome of the research. We are not of course suggesting that the researchers themselves were influenced by these considerations, but what reassurance do we have that the committee would have resisted any temptation to award the contract to a research team whom they believed would produce results that aligned better with their own views? We raised this issue with the IFoA in November and their response was that the research would receive “robust peer review” and be overseen by the three co-directors of the Actuarial Research Centre. That is a reasonable response as far as it goes, but the tension between commercial interests and (for want of a better term) the academic independence or integrity of the project is still an issue.
The stakes are further raised by the fact that the research took place under the aegis of the IFoA, which operates under a Royal charter with an obligation to promote the public interest and avoid even the appearance of conflict of interest, but which is also on record as endorsing questionable views about NNEG valuation and has yet to pronounce on the validity or otherwise of the ‘real world’ approach. This state of affairs is comparable to one in which the Institute of Mathematics and its Applications might take a neutral (at best) view on basic mathematical truths. You see, some mathematicians believe that 2+2=4, but others are of a different opinion.
The net rental rate
Focussing now on the rental rate, the ‘real world’ approach is typically associated with q rates that are well below zero. In the case of Just’s 2016 Annual Report, the firm reported using an expected HPI of 4.25%. Assuming a risk-free rate r = 1.5%, say, we then get an implied q rate equal to r – HPI = 1.5% – 4.25% = -2.75%. The absurdity of this q rate is obvious when one considers that q is an average net rental rate, which would suggest that a house worth £100k would yield an average net rental income to the landlord of minus £2.75k p.a. But can one possibly have a negative average rental rate? The ‘market consistent’ approach, on the other hand, would suggest much higher and comfortably positive net rental rates, and we mentioned earlier that these could be 3% and easily much more. They also vary considerably, e.g. by property and region.
So we have q = -2.75% or thereabouts from the ‘real world’ approach and q = 3% or more from the ‘market consistent’ approach. Tunaru then comes in with a recommended q rate of 0.66% and pretty much splits the difference. Tunaru thus provides the half-way house that he was asked to look for and everyone is delighted. We didn’t think it could be done.
We still don’t think it can be done. Tunaru starts (p. 32) with a gross rental yield of 5.1776% based on figures derived from the Office of National Statistics. There is no reason to disagree with him here, except to note, as we already have, that there are also considerable regional variations. To account for expenses such as management, maintenance and voids, he deducts 30% from the gross to obtain the net rental. We had deducted 35%, but there is little reason to disagree. He then gets a net rental yield of 70% times 5.1776% = 3.62% and this number seems reasonable to us.
Tunaru then makes a howler of a mistake: he claims (p. 32) that since less than 20% of properties are rented out, the total gross rental yield would be 5.1776% times 20% = 1.03%, giving a net rental yield of 0.66%. He cuts the net rental by 80% on the grounds that less than 20% of properties are actually rented out!
As our friend Andrew Smith wrote to us, “I can’t see any perspective from which this makes sense.”
This argument is like suggesting that even though you have freely contracted to pay your landlord £1000 a month in rent, you only really owe him £200 because only 1 in 5 people are renters.
The proportion of properties rented out is irrelevant to the determination of the net rental yield, however! Even if only 1% of properties were rented out, the net rental yield would still be calculated in the same way and the proportion of properties rented out does not enter into the calculation: we divide the gross rent by the property price to obtain the gross rental yield, then subtract some proportion of that (e.g., 30% to 35%) to obtain the net rental yield. It’s a simple as that. That we should not multiply the answer by the proportion of renters is confirmed by the fact that the Tunaru logic would also suggest that the net rental would go to zero as the proportion of rented properties gets very small. The Tunaru approach to the estimation of the net rental rate gets it wrong by a factor of five. Not a minor error.
To be fair, Tunaru concedes that his approach is controversial:
The 20% weighting is my view as the author and this is open to challenge. It has been debated with other academics and market practitioners who are not entirely convinced about the weighting being applied.” (p. 32, fn 16, our emphasis)
So we are not the only ones who are not entirely convinced. Daniel Alai, a participant in a 28 January 2019 workshop on NNEG valuation organised by CEQUFIN (Kent Business School), raises a similar objection:
I was wondering why you multiply the rental yield by the proportion of properties that are rented out. In other words, why is 5.1776% divided by 5. I just do not see how it is relevant whether other properties are being rented out or not in determining the appropriate rental yield for a certain property. The 80% that are not rented out presumably could be rented out and could provide 5.1776% yield (on average). (p. 74 of Tunaru report)
That’s right, Daniel. The economic rental – that is, the use value, the value of the ‘roof over one’s head,’ etc. – is still enjoyed by someone (or potentially enjoyable even if the property is void) regardless of whether the property is rented out or not. What matters is that the economic rental is valuable, not whether the property is actually rented out. Even if there is an owner-occupier, the property still has use value and the best estimate for the market value of that use value comes from the rents currently prevailing in the property rental market, not those rents multiplied by 20%.
In any case, the claim, indeed the whole report, completely fails to engage with the rationale given by CP 13/18 (para 3.16, p. 19), that the only difference between a contract for immediate possession and one for deferred possession, is the value of foregone rights (e.g. to rental income or use of the property) during the deferment period. You will pay less for deferred possession because you will lose the income that you could get by renting the property out or, alternatively, you will lose the use benefit that you could get by living in the property. Why would you rob yourself by pretending that you have only lost 20% of that income or use? You have lost 100% of what you have lost.
If this argument fails to persuade, consider what would happen if the percentage of rented properties fell to zero. According to the Tunaru argument, the rental would then be zero and the value of deferred possession in 10 years would be the same as that of immediate possession. But how could that be? Why would you pay the same for a property that you could not take possession of for another 10 years, when you could buy a similar property now and have the use of it for the same 10 years?
The import is that once we recognise that we should be using a net rental rate of over 3% rather than one of 0.66%, then the half-way house goes out of the window and we are using some form of ‘market consistent’ approach. This conclusion holds even if one uses a put option model based on a ARMA-EGARCH process instead of, say, Black’ 76. As we mentioned earlier, it is not the particular model that really matters – any reasonable model will do and both are reasonable – but the input calibrations that are fed into the model.
Biting on granite
Tunaru’s analysis also fails to engage with the implications of the PRA’s Principle II from PRA SS 3/17. Principle II states:
The economic value of ERM cash flows cannot be greater than either the value of an equivalent loan without an NNEG or the present value of deferred possession of the property providing collateral.
This Principle puts a model-free, volatility-free lower bound under the NNEG valuation and thereby enables us, for some given set of calibrations, to determine ranges of NNEG valuations that are impossible.
Table 1 shows some illustrative results:
Table 1
| Variable | Assumed q | Output value |
| NNEG | q = 3.62% | £22.44 |
| NNEG Principle II lower bound | q = 3.62% | £18.65 |
| NNEG | q = 0.66% | £10.50 |
Notes: Results based on the Black’ 76 put option model and the M5 version of the Cairns-Blake-Dowd mortality model (Cairns et alia, 2006, 2009). The mortality model is calibrated using Life & Longevity Markets Association data for England & Wales males spanning years 1971:2017 and ages 55:89. Source: llma.org. The borrower is assumed to have just turned 70 and to have taken out the ERM loan on their 70th birthday. The Loan-to-Value ratio is 30%, the risk-free interest rate is 1.5%, the ERM loan rate is 6% and the volatility is 13%. The house price is £100, so the initial loan is £30.
For a given set of calibrations, the first line shows the Black’ 76 NNEG valuation, which turns out to be £22.44. The second line shows the corresponding lower bound, which depends on the same calibrations except for the volatility calibration. This lower bound is £18.65. This lower bound result is telling us that, given these calibrations, it is impossible to get a NNEG valuation lower than £18.65. The third line gives us the NNEG valuation assuming Tunaru’s q = 0.66%, which is £10.50. Now we know that this £10.50 valuation is wrong, because it differs from the true valuation which is £22.44, but what this table is telling us that we didn’t know before is that this £10.50 valuation also violates Principle II.
The fact that this valuation violates Principle II is a big deal, because no validly calibrated valid model can do that. Therefore, we know that there is something wrong with NNEG valuations based on q = 0.66%, given the other calibrations and choice of model. Going deeper, what this result is telling us is that the approach used to produce the £10.50 NNEG value is unsound. Thus, Principle II is a litmus test of soundness.
The results in Table 1 were specific to an assumed age of 70 and an assumed LTV of 30%. Figure 1 shows plots of the corresponding plots for ages ranging from 55 to 90 assuming that ERM loans have just been taken out with LTVs determined by the standard “age minus 40” rule, i.e., LTV = (age-40)/100.
Figure 1: Alternative NNEG Valuations and the Principle II Lower Bound:
Volatility = 13%
Notes: As per Notes to Table 1
We see that except for the very high 80s, all the NNEG values based on q = 0.66% violate Principle II. The NNEG values based on q = 3.62% however do not.
Table 1 and Figure 1 are based on the PRA’s ‘best estimate’ volatility of 13%, but what happens if we use Tunaru’s baseline volatility of 3.9%? The answer is shown in Figure 2:
Figure 2: Alternative NNEG Valuations and the Principle II Lower Bound:
Volatility = 3.9%
Notes: As per Notes to Table 1 except for vol = 3.9%.
What we see is that the NNEGs are lower, as we would expect, because a lower volatility implies a lower NNEG. We also see that the lower bound curve is the same as it was before, because the lower bound is not dependent on the volatility.
The red (q=0.66%) NNEG curve is now way below the Principle II lower bound curve across the entire age range: it never even gets close to the lower bound.
But we also see that the blue correct (q=3.62%) NNEG curve is almost on top of the black lower bound curve. This result is interesting because it tells us that we cannot get a correct NNEG curve that is much lower than the one we have, and that curve is based on Black ’76. So from the perspective of any sponsors of the ABI-IFoA NNEG project who might prefer a lower NNEG to a higher one, then there is simply no point in using the ARMA-EGARCH model: they may as well use Black ’76. The fancier dynamics of the ARMA-EGARCH model do not add any extra value.
Conclusions
Doubtless the industry will welcome the Tunaru report: it fails to condemn their preferred ‘real world’ approach based on a nonsensical negative net rental rate and proposes a new half-way house between the ‘real world’ and ‘risk neutral’ approaches based on low calibrations of the net rental rate and volatility parameters that then produce low NNEG valuations.
This new approach is fatally flawed, however. Tunaru makes a major error in his net rental rate calibration and his volatility calibration is also way too low. As a result, his approach gives NNEG valuations that are also way too low and in some cases impossibly so. Any approach that can give impossible valuations is unreliable and should never be used, especially when we already have a decent alternative in the ‘market consistent’ approach.
We are then left with the same choice we had before, i.e., we can use an approach that is not scientifically respectable or we can use an approach that is.
Still, whilst we are disappointed that Professor Tunaru has not called out the hocus pocus approach, he had the good sense not to endorse it either.
In the meantime, the campaign continues to promote a scientific approach to NNEG valuation.