13 Jun 2019 On the Actuarial Treatment of Equity Release Mortgages

The actuarial treatment of equity release mortgages (ERMs) is currently a very active topic within the UK profession. Over the last year, several significant research reports have been published which, collectively, contain a broad array of sometimes-conflicting ideas and recommendations (most notably, Dowd (2018), Jeffery & Smith (2019), Tunaru (2019); Buckner & Dowd also have a 26-chapter ERM valuation manual forthcoming). Meanwhile, the PRA has been evolving its regulatory treatment of ERMs, particularly in the context of how the asset class is treated in Matching Adjustment (MA) portfolios (see the December 2018 update of SS 3/17, which is currently scheduled to come into force at the start of 2020; and the Dear CEO letter of 3rd April 2019).

There is little in this note that is fundamentally new. The purpose of the note is to contribute to the resolution of the confusion that has arisen from the contradictory technical views and arguments that have been expressed in the above papers.

An equity release mortgage is a complex asset. There is no liquid secondary market in the asset class. The No Negative Equity Guarantee (NNEG) creates optionality of a form that is not regularly traded, and which is a complicated mix of house price risk and longevity risk. A tranche of a securitisation of a portfolio of equity release mortgages is yet more complex. The complexity arising from the asset itself, its re-structuring by insurers, and the complicated regulatory treatment arising from the MA add-on to Solvency II, have all combined to create a quite complicated situation.

However, I argue below that tools and techniques that are very familiar to actuarial science can be deployed to produce some quite common-sense actuarial answers to the questions raised by the valuation, capital assessment and MA treatment of the asset class. Sensible and intuitive results can quickly follow once the essential nature of the ERM asset is recognised as a long-term loan with material credit risk.

For the avoidance of doubt, this note does not attempt to make any comment or judgement on the attractiveness of equity release mortgages as a consumer product or the role the product may play in an individual’s retirement plan.

Fair Valuation of an Equity Release Mortgage

Let’s first consider how we approach the fair valuation of an ERM. This note does not consider any IFRS-specific aspects of asset valuation. Here we simply consider what we might call valuation on an economic basis, or valuation according to generally-recognised fair value principles or even valuation generally consistent with the rules set out in rule 2.1 of the Valuation Part in the PRA Rulebook.

Everyone seems agreed that the natural way to value an equity release mortgage is to de-compose its cashflow into two parts:

• A risk-free lump sum payable at exit. The size of this cashflow is a contractually-defined fixed amount, determined by the product’s roll-up rate and the exit date. This risk-free cashflow should be valued by discounting it at the relevant risk-free rate.
• Less the cashflow arising from the NNEG. The NNEG is a put option on the residential property which represents the mortgage collateral (or, more accurately, a probability-weighted series of put options with various times to exit). All the valuation controversy relates to the valuation of the NNEG. This controversy can be distilled into three key questions: what valuation method and formula should be used to value the NNEG? What volatility assumption(s) should be used in the formula? What house price growth rate and discount rate assumptions should be used in the formula? Let’s briefly discuss each of these three questions in turn.

The NNEG Valuation Framework

The NNEG is a put option on the residential property that forms the mortgage collateral. Actuaries have extensive experience of valuing put options on both the asset and liability side of insurance balance sheets. So why is there a dispute over what an appropriate option valuation formula looks like for the NNEG?

The residential property underlying the NNEG is not an easily-traded asset. The option pricing theory that actuaries use in valuing with-profit guarantees and equity put options is based on the idea of frictionless, continuous dynamic trading of the underlying asset. Of course, such trading is not strictly possible even for equity indices or bond indices (and with-profit guarantees also include property as a part of the underlying asset mix). But the idea of continuous, dynamic trading is arguably not remotely possible in the case of UK residential property assets. Moreover, no futures or forward contracts on individual residential properties are available to act as substitutes in the dynamic hedging process.

Some have argued that this means standard option pricing theory is irrelevant to the NNEG valuation. In particular, it could mean that the NNEG valuation should depend on the size of the property return risk premium (a dependency that does not arise under standard option pricing theory). Some have even argued the NNEG should be valued by projecting the house price with its risk premia in place, and then discounting the resulting NNEG cashflow with a risk-free discount rate (see Tunaru, sections 3.2.4 and 11.2; ‘under this method securities are priced using real-world probabilities…and a risk-neutral discount rate’, p. 13). This could result in much smaller NNEG valuations.

I would argue, however, that it is a highly dubious valuation approach. If we applied this real-world-probabilities-with-risk-free-discount-rate approach to the valuation of both calls and puts, we couldn’t even generate option prices that comply with the basic put-call parity condition. This isn’t a merely academic point. The ERM can be equivalently expressed either as a risk-free cashlow less a put, or as the house value less a call. This approach would therefore produce different values for the same cashflow, depending on the arbitrary choice of how the cashflow is de-composed for the purposes of its valuation. Furthermore, the approach wouldn’t ensure ERM valuations respected the PRA’s (uncontentious) Principle II (in particular, the requirement that the ERM should always be worth less than the current value of deferred possession).

At a more technical level, we can note in passing that option pricing theory is perfectly compatible with valuing options using ‘real-world’ asset assumptions, including a property risk premium. But economic theory tells us that a non-zero risk premium requires that a corresponding (stochastic) discount function be applied to the projected option cashflows (which is sometimes called the state price deflator). For put options, when a positive property risk premium is assumed, the correct state price discount function would imply a discount rate for the real-world expected cashflow that is less than the risk-free rate. This is a perfectly intuitive and obvious result when we recognise that the put option has a negative exposure to changes in the underlying asset (which has been assumed to have a positive risk premium).

Option pricing theory does not require an assumption of risk-neutrality. It shows that we can assume any size of risk premium we want (positive, zero or negative) and, providing we use the consistent (state price) discount function, we will always get the same valuation. Risk-neutrality is a popular assumption simply because it removes some redundant maths and avoids estimating parameters that are not relevant to the valuation.

Now, we could argue that option pricing theory goes out the window when we are dealing with something as illiquid as residential property. But that wouldn’t provide a rationale for valuing the NNEG by discounting its (real-world) expected cashflow at the risk-free rate (or higher). Fundamentally, the NNEG has a negative exposure to the underlying asset. This negative exposure is not just the implication of some abstract economic theory. It is a very obvious and basic feature of a guarantee that it is worth less when the underlying asset value goes up and vice versa. If the underlying asset has a positive (‘real-world’) risk premium (and it surely does), and the NNEG has a negative exposure to the underlying asset (and it surely does), then the NNEG’s expected return (and discount rate on the real-world expected cashflows) must therefore be less than the risk-free rate. Option pricing theory says exactly this, but we don’t need option pricing theory to tell us this, the basic property is simpler than that. The NNEG has a negative expected return and its valuation principles should be consistent with that.

Tunaru’s paper implicitly seems to recognise the difficulties with the real-world-probabilities-with-risk-free-discount-rate approach that he presents: the paper ultimately only uses a risk-neutral valuation approach in accordance with standard option pricing theory (that is, house price risk premia do not feature in the formula, either in projection or discounting). The Tunaru paper advocates using a risk-neutral GARCH process rather than the geometric Brownian motion used in the Black-Scholes formula. In the context of valuation, I don’t believe this choice is likely to be of material consequence…in a risk-neutral setting, the key valuation questions relate to the parameterisation of the formula to house price volatility and the (adjusted) rental yield. Given the great divergence of opinion on these parameters (see below), the particular structural form of the risk-neutral valuation formula is a secondary consideration.

It should also be noted that option pricing theory has developed approaches to allowing for frictions such as transaction costs in the trading of the underlying assets (see Jeffery & Smith section 5.2.5 for references). Allowance for such costs invariably increases the cost of the option (for both puts and calls). The presence of real-life frictions in dynamic hedging does not provide any obvious rationale for a reduction in the option value relative to that which applies in the frictionless case. Existing theory, whilst incomplete in its treatment of illiquidity, nonetheless suggests such frictions should result in an increase in the option value.

The Volatility Assumption(s)

Like any option, the value of the NNEG is a function of the assumed volatility of the underlying asset. What is the volatility of the typical residential house that underlies a NNEG? This is a hard question that has produced a startling range of answers in recent months – from less than 4% (Tunaru) to as high as 24% (Eumaeus blog, 27th Feb 2019).

There are several factors that drive this extraordinary range of suggested values for the volatility assumption. First, the underlying asset is an individual residential property, not a diversified index. So, we might expect to build this volatility up by estimating a diversified residential property market volatility and then adding a house-specific risk component. Twice as many assumptions mean twice as much scope for divergence in opinions. Moreover, there is no observable option-implied volatility for the diversified UK residential property market, so we must use historical price volatility to inform the assumption. And the historical price data is not especially well-behaved. For example, the Nationwide UK house price index’s monthly returns exhibit a positive serial correlation of +0.36 for the period Feb. 1991 to May 2019. This is unusual behaviour for well-functioning market prices. It may be partly explained by the way the index uses mortgage valuations and expert expectations as well as actual transaction prices as inputs into its calculation.

In any case, the positive serial correlation in the historical data means that the ‘annualised’ historical volatility of holding a house for 5 years (12% according to Jeffery & Smith, p. 25) is materially higher than the 1-year volatility (8%, again J&S) as derived from the Nationwide index data (quarterly from 1952 to 2018). Tunaru’s 4% p.a. assumption is derived from the volatility of the Nationwide index monthly returns from 1991 to 2016.

Equity release mortgages are long-term instruments, and the longer-term numbers would therefore seem intuitively more relevant. So, common sense would suggest an assumption for the diversified market volatility of the order of 10%-15% is reasonable. This volatility level is also broadly consistent with how Solvency II requires insurers to stress their diversified property portfolios in their capital assessment (the 25% capital charge, if it is interpreted as a 99.5th percentile 1-year event, is consistent with a volatility of 10%).

Estimating the house-specific risk component is probably even more difficult, and is not a well-researched topic to date as far as I am aware. But it is certainly materially greater than zero (which is what the Tunaru paper implicitly assumes by not considering it at all). Jeffery & Smith suggest 11%. Assuming this house-specific component is independent of the diversified index, then a market volatility of 12% and a house-specific volatility of 11% combine to produce a total volatility of 16% for an individual house.

The PRA’s SS3/17 specifies a minimum house price volatility assumption of 13% should be used in the NNEG valuation.

In summary, a common-sense volatility assumption for individual residential property in the context of a long-term NNEG is somewhere in the mid-to-high teens. NNEGs close to maturity may be justified in using a lower volatility assumption. For especially long-term NNEGs, a higher assumption may be appropriate. It is hard to say much more than that. This is not the sort of figure that can be reliably estimated to three significant figures.

The House Price Growth Assumption

As noted above, a (perhaps tentative) consensus is present amongst all the papers referred to above: a risk-neutral projection and discounting approach should be used in the NNEG valuation. This means that everyone agrees that expectations for future house price growth should not feature in the valuation. We might be forgiven for expecting this to mean that the house price growth assumption must therefore be very uncontroversial, but, unfortunately, this is far from the case.

Whilst the risk-neutral valuation does not require an estimate of future house price growth, it does require an assumption about house rental yields, and an allowance for maintenance costs, rental voids, etc to be deducted from the yield. It is difficult to be precise about this deduction, but Tunaru’s assumption (p. 32-33) that it is around 30% of the rental yield seems quite reasonable.

So, all we have left to do is estimate the rental yield. Why is this difficult? Actually, it isn’t! Everyone would seem to agree that UK residential property rental yields are currently around 5% (Tunaru, section 4.5). For the purposes of our difficult NNEG valuation, one significant figure will do. So that would seem to be a straightforward end to the yield story.

But the Tunaru paper then proposes a very curious twist. Because only 20% of UK houses are rented out, we should, it is argued, assume the rental yield is not 5% but 1% (i.e. 20% of 5%). This is a peculiar argument. The reason the rental yield figures at all in the NNEG valuation is because deferring ownership of the property foregoes the opportunity to earn rental income on the property during the deferral period. The fact that many houses are owner-occupied is simply irrelevant to this consideration. After all, not owning the property during the deferral period also means you forego the right to occupy it (without paying rent) during the deferral period. And the owner presumably values the right to live in the property at least as highly as receiving the rent, otherwise the owner-occupier would obviously choose to rent it out instead of occupying it. The 20% argument seems to have garnered very little support since its publication (and the PRA’s Dear CEO letter of 3rd April 2019 makes clear their rejection of the argument). It is best left behind.

The rental yield net of the allowances for maintenance costs, voids and dilapidation is referred to as the deferment rate. A higher deferment rate results in a higher NNEG value (and, hence, a lower ERM value).

The PRA’s SS3/17 specifies that a minimum deferment rate of 1% should be used in the NNEG valuation.

The c. 5% rental yield currently prevalent in the UK residential property market, and a c. 30% proportional allowance for maintenance costs, dilapidation, voids, etc. suggests a common-sense deferment rate assumption of 3%-3.5% for the NNEG valuation. It is very hard to find a way of reasonably justifying a 1% deferment rate assumption.

A Simple Valuation Example

Let’s now plug some of these numbers into a very simplified ERM valuation calculation in order to get a sense for what they imply. For this purpose, we will ignore many complicating features. We will not use decrement modelling but will simply assume the ERM terminates at a known fixed point in time. So, for our current illustrative purposes, we shall ignore the effects of mortality uncertainty, long-term care decrement uncertainty and pre-payment risk. The valuation of an actual ERM would consider it as a probability-weighted portfolio of mini-ERMs or ERM-lets of various terms to maturity, where these exit probabilities are defined by a set of decrement assumptions (mortality, pre-payment, long-term care where relevant). The valuation logic presented below would then be applied to each of these mini-ERMs or ERM-lets.

We assume the borrower is age 65 today, and the mortgage will terminate in 25 years (ERMs are usually joint-life contracts, which extends their duration significantly. 25 years is therefore possibly slightly optimistic from a NNEG valuation perspective – see Jeffery & Smith, p. 59). We will also assume the starting Loan-to-Value is 30% (this is in the middle of the LTV range quoted in the Tunaru paper for L&G’s products for 65 year-olds, see p. 28); the house price volatility is 16%; the 25-year risk-free rate is 1.50%; and the deferment rate is 3.0%. Finally, we will assume the roll-up rate of the ERM product is 4.00% (industry roll-up rates quoted in the research papers tend to be a bit higher, but risk-free rates are currently 30-50bps lower than 6-12 months ago. We expect the roll-up rate would be ‘priced’ with a spread over risk-free rates. In any case, a lower roll-up rate will tend to result in lower NNEG values, all other things equal, so again we are perhaps erring slightly on the side of valuation optimism).

For ease of presentation, we will work in units of the starting house price (i.e. our numbers assume a current house price of 1) and consider the value of a product written today (rather than the valuation of a back book of products). The house price of 1 and LTV of 30% means we are lending 0.3 to the ERM borrower. Now, finally, for some numbers!

Recall that the ERM value can be expressed in two components: a certain cashflow that pays the rolled-up debt at maturity (which can be discounted at the risk-free rate as it is certain); less the NNEG.

The present value of the rolled-up risk-free component of the debt is 0.551 (= 0.300 x 1.04025/1.01525).

Under these assumptions, the NNEG is a 25-year put option with a strike of 0.800 (= 0.300 x 1.0425). Plugging the relevant parameters described above into a Black-Scholes formula produces a NNEG valuation of 0.200.

This implies an ERM value of 0.351 (= 0.551 – 0.200).

What does this number mean? We have made a loan of 0.300 and valued it at 0.351, implying a day-1 (economic) profit of 0.051 (before making any allowances for expenses and costs). This seems a fairly sensible result and suggests the roll-up rate has been set at a reasonable level (in this highly simplified example). If we assessed that the NNEG cost much less (for example, by assuming a volatility of 4% instead of 16% and a deferment rate of 1% instead of 3%), it would imply that the ERM produces a very large day-1 economic profit that might be difficult to rationalise.

How else can we get a sense for what these numbers are saying? Well, one way is to think about the ERM as a form of credit-risky loan and express this fair valuation in terms of its implied yield and credit spread. If we ignore the NNEG, the ERM would be worth 0.551 today, and this value (naturally) implies the asset earns a yield equal to the risk-free rate of 1.50% (= (0.800/0.551)1/25-1).

After allowing for the NNEG, the ERM fair value implies the ERM has a gross yield to maturity of 3.35% (= (0.800/0.351)1/25-1).

Put another way, the ERM fair valuation implies it offers a credit spread of 185 bps (= 335bps – 150bps).

How does this compare with the pricing of public credit-risky bonds? This comparison is tricky for a few reasons. Corporate bond prices and indices are readily available, but they do not include many 25-year loans. Also, ERMs are less liquid than corporate bonds, and we might argue that an illiquidity effect is present in ERM values (though our ERM valuation method has not allowed for any illiquidity effect). According to the BofAML BBB Sterling Corporate Index, BBB Sterling corporate bond spreads over gilts have traded at between 178bps and 201bps between the start of January and the end of May 2019.

So, a simple way of interpreting the above valuation result is that this ERM is valued like it is a long-dated BBB credit-risky loan. (Again, note this is an illustrative, simplified valuation example that has ignored some potentially important sources of risk.)

If we used the Tunaru paper’s assumptions of a house price volatility of 4% and a deferment rate of 1%, the valuation of our example NNEG is essentially negligible (0.002), implying the ERM is, to all intents and purposes, risk-free. This may sound like great news for all concerned, but it does beg an obvious question….if the loan is essentially risk-free, why is the ERM borrower being charged an interest rate that is 250bps greater than the risk-free rate?

Our illustrative calculations suggest that the interest rates being charged to ERM borrowers have a quite reasonable explanation….ERM borrowers are paying interest rates well in excess of the risk-free rate because the loan has material credit risk.

Solvency Capital Requirements of an Equity Release Mortgage

The above valuation discussion suggests a couple of potential approaches to assessing the solvency capital requirement of the ERM. We briefly discuss these in turn below.

Fair Value-based Approach

Perhaps the most natural approach given the above valuation discussion and the SII 1-year 99.5th percentile VaR method would be to subject the ERM valuation to 99.5th percentile stresses of the key valuation parameters. The impact of key risk factors such as house prices, rental incomes, house price volatility, the risk-free interest rate and longevity could all be assessed naturally by such an approach (we will ignore longevity risk in our example, as per above). Of course, these stresses would need to be plausibly calibrated, which inevitably brings its own set of significant challenges. Below we present some numerical analysis, only for the purpose of demonstrating the workings and implications of plausible assumptions.

The most important stress will be the house price stress. A volatility of 16% is broadly consistent with a 40% 99.5th percentile house price fall. We might argue that house price changes will have fat tails and should be subjected to a greater stress, but we won’t consider this today and will simply use 40%.

Now, an important secondary question emerges when implementing the house price stress….what do we assume happens to rental income? If we assume rental income is unchanged in the stress, then the deferment rate increases from 3.0% to 5.0%. This produces a ‘double-whammy’ effect on the NNEG valuation (house price down, deferment rate up) that results in a (stand-alone) house price risk capital requirement that is greater than the assumed 40% house price fall. Note that this would then be partly offset by the capital requirement that arises from a stand-alone (upward) shock to rental incomes, if we assume that rental incomes and house prices are positively correlated.

For our current illustrative purposes, we will make the simplifying (and optimistic) assumption that house prices and rental incomes are perfectly correlated so that the deferment rate never changes. This means we assume the deferment rate is unchanged at 3.0% in the house price stress, and we do not need a separate deferment rate stress. Plugging the 40% house price fall into the valuation formula with the 3.0% deferment rate results in the NNEG value increasing from 0.200 to 0.301. The ERM asset value would therefore fall from 0.351 to 0.250 under this stress, implying a 29% capital requirement for the ERM asset.

Next, we can consider a house price volatility stress. This is, again, a difficult stress to calibrate. But we should bear in mind that the volatility we wish to stress here is not a 1-year volatility, but an annualised 25-year volatility (which should be materially less changeable). For our current illustrative purpose, let’s assume the volatility is stressed upwards from 16% to 20%. This results in the NNEG fair value increasing to 0.236; the ERM falling in value to 0.315; and a ERM capital requirement of 10%.

The interest rate stress will probably be the least important stress for the balance sheet, as the ERM asset will typically be held to back liabilities of similar duration. However, it should be noted that the interest rate sensitivity of the NNEG put option can reduce the effective duration of the ERM very materially.

Aggregating the house price and volatility capital requirements with some allowance for diversification, we will reach a total SCR of some 30%-40% in this illustrative example.

Ratings-based Approach

Another approach to assessing the solvency capital requirement of the ERM would be to use a ratings-based approach. Given the valuation is consistent with a 25-year BBB bond, we could apply a credit stress similar to the one applied to a corporate bond of that duration and credit quality. For reference, the SII Standard Formula prescribes a credit spread capital requirement of 32.5% for a 25-year BBB bond.

So, in our highly simplified example, a couple of different approaches both suggest an SCR of 30%-40% is likely for the (non-restructured) ERM.

Finally, putting these numbers together: we have made an ERM loan of 0.300 and assessed it has a day-1 economic value of 0.351 and a solvency capital requirement of around 0.12 (= 35% (SCR) of 0.351 (asset value)).

ERMs and the SII Matching Adjustment

Many UK annuity books hold significant and growing exposure to ERMs. However, this exposure has mainly been obtained via senior tranches of structured ERM vehicles. The conventional wisdom is that this structuring work has solely been done to meet the PRA’s requirements around MA asset eligibility – specifically, around the requirements for the asset to have fixed cashflows. The dependency of ERM cashflows on longevity outcomes makes ERMs ineligible assets under MA rules (putting aside that MA-eligible liability cashflows also depend on longevity outcomes). If we securitise a portfolio of ERMs and take the senior (safest) tranche promising a fixed rate coupon for a fixed term, then the cashflows are sufficiently fixed to become MA-eligible in the eyes of the PRA.

But the valuation and capital discussion above suggests the sole focus on the MA eligibility issue might be a red herring. Let’s suppose (non-restructured) ERMs somehow had no MA eligibility issue. Would they fit naturally into MA asset portfolios? The above analysis suggests it is perhaps unlikely. Even if they were MA-eligible, the credit quality and consequent potential capital consumption of non-restructured ERMs could be MA-inefficient. There is a material risk that a 25-year BBB-quality loan could downgrade into sub-investment grade quality at some point in its lifetime. The severe lack of MA efficiency of long-dated sub-investment grade credit coupled with the difficulty and likely material cost of disposing of these very long-term illiquid assets could give an MA asset strategist serious pause for thought.

Securitising an ERM portfolio is necessary not only to meet the MA eligibility criteria, but in order to construct a higher quality investment-grade asset that fits with annuity balance sheet’s investment risk appetite and annuity firms’ MA regulatory capital incentives.

Finding the right home for the residual equity tranche of the ERM securitisation is an interesting challenge that is happily beyond the scope of this note.

Areas for Future Research?

This note has tried to demonstrate that an intuitive and common-sense analysis of the value, risk and capital requirements of equity release mortgages, and the rationale for their restructuring for their use in MA portfolios, can be developed using tools and techniques that are familiar to actuarial science.

However, the discussion has also highlighted that the parameterisation of both the valuation and capital assessment of ERMs is quite challenging and inevitably imprecise. Further research into these parameterisations would doubtless be valuable and welcome. We should, however, also be intellectually honest about the limitations in precision that are plausibly attainable in the valuation and capital assessment of this asset class.

Moreover, important and difficult questions of a more theoretical nature remain that would benefit from further research. The most important and difficult of these, I believe, relates to how asset illiquidity impacts on the ERM valuation (the Jeffery & Smith paper (Chapter 5) offers an insightful and thought-provoking discussion of this topic). An ERM is a non-exchange-traded, illiquid instrument. Should the ERM valuation method include a downward adjustment to the value which reflects that investors generally require an asset illiquidity premium to be incorporated into the yield of illiquid assets? More complex still, the residential property that provides the mortgage collateral is also an illiquid asset that may be priced to generate an illiquidity premium. If so, how does the house price illiquidity premium impact, if at all, on the NNEG fair value? These questions are genuinely challenging and arguably sit at the cutting-edge of financial economic theory.

Acknowledgments and Disclaimer

I have recently had numerous stimulating discussions with industry experts which have been very useful in developing my thinking on this topic. In particular, I would like to express my thanks to Dean Buckner, Kevin Dowd, Gareth Mee, David Roseburgh and Andrew Smith. All views and any errors are my own. This article is written in a personal professional capacity as a Fellow of the Institute and Faculty of Actuaries, and the views expressed herein are not intended to represent those of my employer.