Craig Turnbull (Investment Director at Aberdeen Standard Investments, author of A History of British Actuarial Thought) offers an intriguing critique of the Matching Adjustment here. ‘To the extent that the profession wishes to defend the MA as a matter of actuarial principle’, he says, alluding to the IFoA president’s recent defence of it, ‘we must provide a clear explanation of the apparent logical contradiction at the core of its treatment of credit risk capital: that the capital required to support the risk of adverse asset outcomes can be (partly) created by assuming those same assets perform well.’ (Our emphasis).
Turnbull’s explanation rests upon a somewhat complex example but the mathematics seems impeccable. The example rests on the fact that under standard rules, the capital requirement of a BBB bond supporting annuities is 18%, whereas under Matching Adjustment there are two effects that lessen the burden, namely (i) the MA discount creating 8% of capital by a wave of the actuary’s wand and (ii) MA reducing the capital requirement from 18% to 12%. The net capital benefit under MA is therefore 12% – 8% = 4%, so the MA ‘has effectively reduced the net capital requirement arising from bearing credit risk in the bond portfolio by a factor of more than 4’.
This is not a logical contradiction, rather it is elementary mathematics, so the contradiction, as Turnbull says, is merely apparent. The real question is whether the elementary mathematics of MA delivers a good measure of the long-term risk of BBB bonds?
Turnbull is doubtful. To assess long-term default risk requires some pretty complex mathematics and assumptions. How can we be assured that such calculations and assumptions provide ‘a good measure’ of such long-term risk? It appears we can’t be.
Actuaries should recognise that this [i.e. the question of what is a good measure] is a very difficult question to definitively answer: by its nature, it is extremely difficult to robustly estimate the tail probabilities associated with long-term financial market risks.
For example, one of the key assumptions about long-term default risk requires relevant long-term default data. But we don’t have such data. Either the data set is too short, in which it is neither good nor long-term. Or it is long, but truly long-term data may not be relevant to current estimates. “… what happened in the 1960s and 1970s arguably isn’t an informative guide to our question of what may happen in the 2020s”.
It is simply not possible, I would argue, to infer a reliable estimate of the 95th percentile tail of the 10-year outcome from a statistical analysis of this data. To be clear, I am not suggesting there is a better way of estimating the statistic. Rather, I am suggesting it is simply not possible to obtain reliable statistical answers to this question …
True. I have argued many times in the past that we should look at the default experience of the 1930s (or the 1880s or whenever) in assessing the true default risk of long term credit exposure. The reply was always on the lines of “the experience of the 1930s (or the 1880s or whenever) is not relevant to the experience of the 2020s and 30s”. We can only rely on recent experience, say the last 20 or 30 years. But, as Turnbull argues, a calibration data set essentially consisting of 3 non-overlapping 10-year paths taken from a non-stationary population is simply not enough to give an enlightened answer to the difficult question of whether MA delivers a ‘good measure’ of the long-term risk of BBB bonds.
Thus to “assert that the MA calculations result in an appropriately prudent amount of capital being held to support the long-term credit default risk within MA bond portfolios requires a large and unavoidable leap of extra-statistical faith”.
I can’t put it better than that.