Turning Japanese
In a previous posting, we discussed a type of stress test in which house prices fall immediately after an ERM contract has been entered into.
However most stress tests are passage-of-time stress tests in which we posit some hypothetical stress over time and then use our model to see how that stress would effect something we are interested in, over the passage of time.
For example, we might assume a hypothetical rate of growth of hpi and show how the ERM valuation would behave over time under the posited scenario.
This type of exercise works as follows. We start by using our ERM valuation model to obtain the current value of the ERM. Then we obtain the expected value of the ERM after one year, which would be 1 year exit probability times the expected payoff if exit occurs in year 1, plus the 1 year probability of no exit times the ERM value after one year. This latter ERM value is obtained using our ERM valuation model, but taking account of the new age after 1 year (i.e. 1 year older), the new house price after one year (which is equal to the old house price times e^hpi), and the new LTV after one year (which is equal to the old LTV times e^hpi). We carry on in like manner for the expected value of the ERM after two years and so forth.
In practice, we would often want to compare two different scenarios: a base scenario, which might be the scenario we expect, and a stress or adverse scenario. For example, we might follow a certain firm and assume hpi=4.25% for our expected or base scenario. We then posit some alternative stress scenario, e.g., hpi=-1.7%, which was the average hpi in Japan over 1990:2017. Figure 18.2 shows plots of ERM under these two scenarios:
Figure 1: Expected ERM Valuations Under 4.25% vs. Japan House Price Growth Scenarios
Notes: NNEG is the is the present value of the NNEG guarantee and ERM is the present value of the Equity Release Mortgage. Based on the baseline assumptions: male aged 70, r=1.5%, l=5.25%, q=4.2% and σ=14.8%. For the pre-stress scenario, we assume house price = £100 and LTV=40%; for the stress scenario, we assume house price = £50 and LTV=80%. Exit probabilities are based on M5-CBD model projections using England & Wales male deaths rate data spanning years 1971:2017 and ages 55:89.
We see a much lower expected ERM valuation projection under the stress scenario. The lesson here is that if we were relying on hpi=4.25% but actual hpi turns out to be -1.7%, then the large ERM increases we were expecting will not come pass, and future ERM valuations will decline to zero considerably more quickly than we had expected.
Another type of stress test is project cashflows under an assumed house price scenario. Figure 2 show the projected cashflows under the same two scenarios:
Figure 2: Expected ERM Cashflows Under 4.25% vs Japan House Price Growth Scenarios
Notes: As per Figure 1.
If the 4.25% hpi scenario were to transpire then subsequently realised cashflows would be much larger than if the Japan scenario were to transpire.
So here’s hoping that what has been happening in Japan over the last three decades could never happen here.