Craig Turnbull
Equity Release Mortgages (ERMs) are different from traditional mortgages. Both mortgages provide an upfront cash lump sum. But traditional mortgages are tied to an immediate home purchase that is repaid over a set period, while equity release mortgages are tied to a share of a future home sale. In this blog post, I examine some of the challenges with valuing equity release mortgages. Specifically, I focus on the approaches used to estimate the current home value – a key input to the mortgage valuation – which typically involves applying a simple house price index return to the most recent house survey valuation or transaction price. I show this widespread approach may understate equity release mortgage risks and overstate portfolio values.
Valuations for equity release mortgages
In the UK, equity release mortgages almost always include a ‘No-Negative Equity Guarantee’ (NNEG). These guarantees ensure that the lender cannot recover more than the proceeds of the house sale at the repayment date. Option pricing techniques play a natural role in the valuation of the mortgage’s NNEG. These option pricing approaches are now widely used both in Prudential Regulation Authority supervisory tools such as the Effective Value Test (EVT) and in firms’ asset valuation methodologies.
Such approaches to mortgage valuation take an up-to-date price of the underlying house as a given. But the house’s most recent transaction price may be decades old. And, for mortgages that have been in-force for many years, a considerable time may have passed since the house was last subject to a surveyor’s valuation.
There is wide recognition that this approach to estimating the current house value has the potential to overstate mortgage portfolio values: the use of the index return ignores the idiosyncratic risk element in the evolution of the house price and this will, on average, understate a portfolio of NNEG values and hence overstate mortgage portfolio values.
An illustrative model to value ERMs
In this section, I set out a simplified model to value ERMs. This framework is used to illustrate the impact that different house price estimates can have on ERM portfolio values.
Let’s suppose the mortgage has a fixed and known maturity date which is 30 years from origination of the loan (ERMs will actually mature on death or entry into long-term care, and may have prepayment options, but none of this is key to this analysis).
The example mortgage has a starting loan to value ratio of 30%. The mortgage is written with an interest rate of 3.63% (ie the loan amount compounds at 3.63% so that, at maturity, it has increased from 0.30 to 0.874, assuming a starting house value of 1). A Black-Scholes option pricing approach is used to value the NNEG such that the starting valuation of the mortgage is consistent with what has been advanced to the borrower. These assumptions are set out in the technical appendix.
Next, suppose we write 1,000 mortgages on the above terms, on different houses. We stochastically project the value of this mortgage portfolio over time. Within the projection, we will value the mortgage portfolio in two different ways: one, by using the simulated ‘true’ house prices projected by the model up to that point in the projection; two, by using house price estimates that have been produced by applying the simulated house price index returns to the starting house prices.
We need to make one more assumption. How volatile is the house price index relative to individual house prices? This is key to our analysis. If house prices are perfectly correlated and there is no idiosyncratic house price risk, then the process of using index returns to update prices will not produce any valuation errors (as the house price volatility and the index volatility will be the same). But we don’t expect house prices to be perfectly correlated, and the diversification benefit that this delivers means index volatility will be lower than the volatility of individual house prices. In this example, we assume the index volatility is 12% (see Technical appendix).
The impact of different house price valuations on ERM portfolio values
We can now generate some results from the model. Chart 1 and Chart 2 show the probability distributions of the projected mortgage portfolio values in the two cases: first, where the actual modelled house prices are used in the NNEG valuations; and second where the house prices are updated using index returns.
Chart 1: Projected ERM portfolio values using accurate house price updates
Chart 2: Projected ERM portfolio values using indexed house price updates
A comparison of the two charts highlights that the indexed approach results in higher returns being generated by the portfolio over time, as a result of the NNEG values being systematically understated by the use of indexation. At maturity, the true house prices are ‘revealed’, and this sometimes results in unanticipated write-downs at maturity.
Chart 3 shows the projected behaviour of the ratio of the portfolio valuation that results from indexation to the portfolio value using the accurate house prices. We define this ratio as the portfolio valuation error.
Chart 3: Projected portfolio valuation errors
You can see from Chart 3 that the portfolio valuation error is always greater than 1: the use of indexation in the presence of idiosyncratic risk systematically biases the portfolio valuation upwards. After 10 years, the median portfolio valuation error is around 3%. As the period over which indexation is applied grows, the potential for very material valuation errors also grows.
Chart 4 shows how the simulated mortgage portfolio valuation errors after 29 years of indexation behave relative to the simulated 29-year index return.
Chart 4: Portfolio valuation errors and the level of index returns (29 years)
Chart 4 highlights that the mortgage portfolio valuation error after 29 years has a very strong dependency on the level of index returns that has been experienced over the same period. This is intuitive. If index returns have been very strong for 29 years, it is likely the actual NNEG losses of the portfolio will be very low, and the indexation approach will therefore not overstate the final losses – even bad idiosyncratic risk outcomes are unlikely to result in NNEG losses when index returns are so strong. And if the index returns have been very poor, such that the NNEGs tend to be deeply in the money, then the impact of the idiosyncratic risk on the mortgage lender will be symmetric, and the under-recognition of the idiosyncratic risks will not be consequential (the borrower will participate pound for pound in good and bad idiosyncratic risk outcomes, because even the positive idiosyncratic risk outcomes will still tend to result in NNEGs that are in the money). However, if the index returns have been such that the NNEGs are likely to mature close to the money, then idiosyncratic risk can really matter: the lender will tend not to get the upside of the good idiosyncratic risk outcomes (as the final NNEG cash flow cannot be negative) but will be exposed to the downside. Here, the effect of ignoring idiosyncratic risk in the updating of house prices can result in a material overstatement of the mortgage portfolio value.
In reality, insurance firms may implement various strategies to mitigate these potential over-valuation effects. For example, firms may undertake regular ‘drive-by’ house valuations for the larger mortgages in their portfolios. But Chart 4 (albeit based on the fairly pathological example of 29 years of indexation) suggests another approach to adjusting mortgage portfolio values – using a model such as this to derive valuation adjustment factors that are applied to mortgage values where indexed house prices have been used. The following, Chart 5 shows the valuation adjustment factors produced for our example mortgage.
Chart 5: Valuation adjustment factors for the 30-year 30% LTV mortgage
The scale of these adjustment factors will heavily depend on the assumed level of house price idiosyncratic risk. The greater the idiosyncratic risk, the greater will be the implied valuation adjustment. The purpose of this analysis is not to propose a specific parameterisation, but to highlight that analytical techniques can be used to shed light on the mortgage valuation errors that can arise from the use of indexed house prices.
Technical appendix: modelling assumptions
The mortgage is valued using an illiquid risk-free rate of 2.5%; a house price volatility of 15%; and a 30-year house deferment rate of 2.5%. (Please note these numbers are used for illustrative purposes only.)
These assumptions imply an initial pre-NNEG value for the mortgage of 0.413 and a NNEG value of 0.113, and hence a starting mortgage value of 0.300.
In the stochastic projections a house risk premium of 3.0% is assumed (and so expected house price inflation will be equal to the illiquid risk-free rate (2.5%) plus house risk premium (3.0%) minus deferment rate (2.5%) equals 3.0%).
The stochastic projections assume a house price index volatility of 12%. The model assumes all houses have the same level of idiosyncratic risk and a simple single-factor structure to their correlation. These assumptions, together with the house price volatility assumption of 15% above imply an idiosyncratic risk of 9%.
Craig Turnbull works in the Life Insurance Actuaries Division at the Bank of England.
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