Dean Buckner and Kevin Dowd, 1 March 2019
Professor Tunaru opens his NNEG report with an oft-cited quote from George Box: “All models are wrong but some are useful.” The Box aphorism is an apt one, but Professor Box went on to state
Since all models are wrong the scientist must be alert to what is importantly wrong. It is inappropriate to be concerned about mice when there are tigers abroad. (Box, 1976, p. 792)
For us the most interesting of the terms of reference in the ABI-IFoA aka astrology project on NNEG valuation was (to quote the project’s request for tender) to “consider whether there are any “halfway house” solutions between real world and risk-neutral approaches … .”
Now we never felt that anyone would be able to find a defensible half-way house between the two approaches. After all, the risk-neutral or market consistent approach is scientific and the other is not, and in these circumstances you really shouldn’t just split the difference.
So it turned out. Tunaru did not find a half-way house between the two approaches, let alone a defensible one.
But he did find something else that was interesting: he found a new approach which produces very low NNEG valuations much like those produced by the ‘real world’ approach, but which does not rely on the latter’s absurd premise that the average net rental rate is well below zero. Tunaru thus allows firms, if they choose and the regulator allows them, to continue to get low NNEG valuations without getting all that flak about the real world approach being – not to put too fine a point on it – a load of cobblers.
So we now have three approaches, which we can roughly characterise as follows:
The first is a market consistent approach based on plausible input calibrations, which we would suggest might be, e.g., a net rental rate = 3.62% (as per Tunaru’s analysis before he spoiled it by applying his 20% multiplier, see his report p. 33), loan rate = 6% (as per our report “Equity Release: Another Equitable in the Making,” p. 13) and a vol in the range 16% to 24% for reasons we explain in our previous posting on Tunaru.
The second is the ‘real world’ approach which uses plausible calibrations of all parameters bar the net rental rate, which is taken to be << 0, an example being the net rental rate of around -2.75% which is consistent with the 4.25% HPI rate assumed in Just Group’s 2016 Annual Report. (Assuming a risk-free rate of 1.5%, then HPI = 4.25% implies a net rental rate equal to 1.5% – 4.25% = 2.75%.)
The third uses the Tunaru calibrations, which are a combination of implausibly low net rental rates, implausibly low loan rates and implausibly low vol. The natural example is his baseline scenario (p. 35) in which these are taken to be 0.66% (or 0.66% rounded up to 1%), 4.15% and 3.9%. This baseline scenario is consistent with the ‘best advice’ (or one presumes at least good advice) he was given by industry experts who working for the main firms and industry bodies in the equity release space. No worry about conflict of interest there.
In all 3 cases we use Black ’76 as our option pricing model. We recognise that Tunaru’s preferred but highly unparsimonious ARMA-EGARCH-based put valuation model is a different model from Black ‘76, but we believe that differences in valuations arising from differences between the models are secondary compared to differences in the valuations arising from different calibrations fed into these models. When choosing between models that deliver similar results, it is advisable to go with the more parsimonious one. To quote Box again (1976, p. 792):
Since all models are wrong the scientist cannot obtain a “correct” one by excessive elaboration. On the contrary following William of Occam he should seek an economical description of natural phenomena. Just as the ability to devise simple but evocative models is the signature of the great scientist so overelaboration and overparameterization [is not to be recommended].
The NNEGs from these alternative calibrations are shown in Figure 1.
Figure 1: NNEG Valuations Based on Buckner-Dowd vs. Real-World vs. Tunaru Calibrations
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 house price is £100, so the initial loan is £30. The risk-free interest rate is 1.5%. Our preferred calibrations are a net rental rate of 3.62%, a rollup rate of 6% and a vol in the range 16% to 24%. We take the ‘real world’ calibrations to be a net rental rate of -2.75%, a loan rate of 6% and a vol equal to 11%. The Tunaru calibrations are a net rental rate of 0.66%, a rollup rate of 4.15% and a vol of 3.9%.
The red line in the upper part of the Figure shows the NNEG valuations using our calibrations across the entire range of volatilities, and the red * plot shows our NNEG valuations across the range of volatilities that we consider plausible. The green line shows the NNEG valuations using the ‘real-world’ calibration and the green * point shows the NNEG valuation using the ‘real-world’ calibrations including Hosty et alia’s 11% vol (Hosty et alia, 2007). The blue line in the lower part of the Figure shows the NNEG valuations using the Tunaru calibrations but across the entire range of volatilities and the blue * point shows the NNEG valuation using the Tunaru calibrations including his baseline vol of 3.9%.
We see that there isn’t much to choose from between the NNEGs from the Tunaru and ‘real world’ calibrations, but there is an enormous difference between those and the NNEGs based on our calibrations.
It is interesting to look at the NNEG valuations we would get if we set the volatilities to the preferred values underlying the starred points in Figure 1, or in the case of our range of preferred volatility calibrations, to the middle volatility in the range. Table 1 shows the resulting NNEG valuations:
Table 1: NNEG Valuations Based on Buckner-Dowd vs. Real-World vs. Tunaru Calibrations
| Calibration | Net rental | Loan rate | Risk-free rate | Vol | NNEG |
| Buckner-Dowd | 3.62% | 6% | 1.5% | 20% | £26.59 |
| ‘Real world’ | -2.75% | 6% | 1.5% | 11% | £1.05 |
| Tunaru | 0.66% | 4.15% | 1.5% | 3.9% | £0.14 |
Notes: Calibrations not in table as per Figure 1.
The ‘real world’ and Tunaru calibrations produce NNEGs that are 0.5% and 3.9% of those produced by our calibrations.
It is also interesting to look at the NNEG valuations we would get if we standardise the volatility, e.g., at the PRA’s recommended 13% minimum volatility. These NNEG valuations are shown in Table 2:
Table 2: NNEG Valuations Based on Buckner-Dowd vs. Real-World vs. Tunaru Calibrations: Vol = 13%
| Calibration | Net rental | Loan rate | Risk-free rate | Vol | NNEG |
| Buckner-Dowd | 3.62% | 6% | 1.5% | 13% | £22.40 |
| ‘Real world’ | -2.75% | 6% | 1.5% | 13% | £1.96 |
| Tunaru | 0.66% | 4.15% | 1.5% | 13% | £3.05 |
Notes: As per Table 1.
Standardising the volatility at 13%, the ‘real world’ and Tunaru calibrations now produces NNEGs that are 9% and 14% of those produced by our calibrations.
All of which goes to show that there is more than one way not to skin a cat.