Those who tuned in to my presentation here may have noticed a teensy hesitation at slide 12 where I discussed the sixth stress test on an example ERM.
Well, hopefully no one noticed. I was struck, while presenting, how the two year increase in expected longevity increased the value of the loan, while at the same time increasing the cost of the no negative equity guarantee (NNEG).
Why is this? And why, generally, might ERMs with NNEG not be a good asset to back annuities with, despite all the hype?
Both the increase in the value of the loan and the cost of the NNEG are explained by the shift in the ‘hump’ in the mortality curve. If people live longer, then the hump shifts to the right, and the weighting of exit probabilities shifts to longer maturities. Since the present value of the loan increases exponentially with maturity, this shift increases the total value of the loan.
However, the deferment curve slopes downwards for reasons we have discussed many times – the longer you have to wait to receive an income producing asset, the less its value to you. Hence the same shift in weighting to towards the longer maturities decreases the value of the deferment, and by the same token, increases the cost of the NNEG.
Hence a shift to greater longevity leaves the value of the ERM roughly the same as before: increase in loan value matches increase in cost of guarantee. This is precisely why ERMs might not be a good asset to back annuities, given that an annuity – a liability – increases in cost as longevity increases. The net effect of the longevity shift will therefore be negative.
Of course the same problem exists if you are matching with gilts, however the mismatch risk is one of longevity only, and could be reduced or removed by a swap. No such possibility exists with an ERM, because the longevity shift will lead to a greater exposure to the property market. Consider, for example, an increase in longevity combined with a fall in the housing market. This is difficult to hedge, moreover the effect of the combined stress is unlikely to be a simple addition of stress #4 (30% fall in property value) and stress #6 (increase in expected longevity), becase the increase in longevity will increase the sensitivity to a fall in property. There will be what options traders call a ‘diagonal’ effect.
Sounds like a topic for a later post!
|
|
L |
NNEG |
ERM |
| Base | £65.3 | £19.2 | £46.1 |
|
Stress |
Change in L |
Change in NNEG |
Change in ERM |
| Stress test #1 | £13.6 | £10.8 | £3.0 |
| Stress test #2 | £0 | £6.2 | -£6.2 |
| Stress test #3 | £0 | £1.3 | -£1.3 |
| Stress test #4 | £0 | £7.4 | -£7.4 |
| Stress test #5 | £0 | £10.9 | -£10.9 |
| Stress test #6 | £5.4 | £5.2 | £0.2 |
ST #1: The risk-free rate falls to 0.5%
ST #2: Net rental rate rises from 2.5% to 4%
ST #3: Volatility rises from 13% to 15%
ST #4: House prices fall by 30%
ST #5: House prices fall by 40%
ST #6: Expected longevity increases by 2 years