The question of how to value a pension scheme as large and complex as USS has recently seen a number of converging arguments by a wide range of independent academic commentators following the publication of the September 2018 Joint Expert Panel report.

Notable among these has been Sam Marsh’s devastating critique of USS’ flawed approach to Test 1, ably summarised by Mike Otsuka. It is worth reading both of their accounts to make short shrift of an astonishing mathematical error which essentially renders Test 1 to be circular, and as Mike puts it, generates far too many false positives.

In response, USS trustees have told the FT that “they say they have to work within the risk appetite of the employers”.

The point of this brief contribution is to summarise just how confused UUK’s ‘risk appetite’ appears to be.

- Aside: I have to think they
*must*be confused, because if they had understood this point, the UUK would surely have rushed straight back to the September Technical Provisions after their revaluation in November 2017 had obtained an even worse projected deficit than September 2017. (Alternatively, we might think they had another agenda…)

The Joint Expert Panel criticised UUK for engaging in misleading consultation exercises with their members over this ‘risk appetite’:

*With respect to assessing employer covenant, the Panel acknowledges it is not a simple task to consult with 350 different institutions or to ascertain their risk appetite – a consultation will inevitably generate a wide range of views and possible outcomes. However, the framing and context of the questions asked of employers have, in our view, produced misleading results. These results have been distilled into a single number which feeds into Test 1, and which in turn affects contribution requirements, future Scheme benefits, the investment strategy and the estimated deficit. These are outcomes which, on exploration, appear to be inconsistent with many employers’ wishes.*

*Employers have been asked questions in consultations and questionnaires that have not fully explored the consequences or trade-offs of the issues under investigation. It is debatable whether employers have been able to give fully informed answers to important questions. In addition, time-frames for consultations have sometimes been very short, with the result that it has not always been possible for employers to consider and debate thoroughly the issues under consultation, particularly in the many universities with complex governance structures. (pp 9-10).*

### The trade-off between two different pension risks

Back in March I wrote a short post for my statistics blog corp.ling.stats explaining how, armed with some simple mathematics, you can examine the two official USS valuations (September and November 2017) and draw some important conclusions.

Crucial among these is the following:-

**‘de-risking’ increases the risk of default.**

This statement is provably true (see below) but it appears counter-intuitive.

How can reducing employer risk exposure make the chance of a default more, rather than less likely? **The answer is that two very different concepts are being conflated:**

**the risk of pension fund default**, i.e.*p*(*v*< 0), where*v*is the valuation figure at a projected point in time;**the risk of pension assets invested in stocks and shares changing in value due to stock market fluctuation**, i.e. a larger standard deviation*s*(*v*).

### Aeroplane crashes and turbulence

The first of these risks is equivalent to **an aeroplane crashing**, and would require a call on the assets of USS members (employers) and potentially the Pension Protection Fund if the worst happened. **This is the risk that employers and the regulator needs to be concerned about. It is this risk that is supposed to be covered by the Employers’ Covenant.**

The second of these risks is **turbulence**. It is an increased uncertainty of the projection forward in time due to greater exposure to short-term volatility of stocks and shares. USS Ltd has had a (confidential) long-term investment strategy for portfolio balancing and smoothing that allows it to minimise these risks. It may make for more conservative growth in certain periods, but it also spreads the risk across asset classes and time. Nonetheless, it cannot reduce this risk to zero.

### How reducing ‘turbulence’ by ‘de-risking’ increases the risk of default

Back in 2014, UUK argued to reduce their reliance on the Employers’ Covenant, and to plan for ‘de-risking’ – over time, divest oneself of assets currently 70% invested in stocks and shares and move them to low-yield, low-risk government bonds and gilts (henceforth ‘gilts’ for brevity). ‘Test 1’ was intended as a mathematical justification for this de-risking exercise.

What I pointed out back in March was that **using USS’s own valuations**, and the City’s own long-term projections for gilts, the following take place with mathematical inevitability once you decide to ‘de-risk’ the portfolio:

- ‘de-risking’ reduces the standard deviation
*s*(*v*) but it also reduces the probable performance of the asset portfolio over time, and hence it reduces the best estimate of the valuation once outgoings are accounted for,*v*; - assets placed in gilts fail to outperform CPI, therefore the greater the proportion of asset portfolio invested in gilts, and the longer that exposure, the weaker the portfolio performance will be, so
*v*tends to decline; - the small benefits of a slightly reduced standard deviation (greater certainty) do not offset this overall performance decline, consequently
**the lower bound of a confidence interval incorporating prudence**,*v*⁻ (the quoted ‘valuation’), falls with gilt exposure; - any CPI-revalued pension scheme (which is what USS CARE or to a lesser extent Final Salary represents) will be more likely to default by the iron law of compound interest.

I published my working, unlike USS.

Note: My argument is based on the observation that all valuations are not single points (even if single figures are quoted) but a *distribution of possible outcomes*, and distinguishes the best estimate (mean) from the estimate incorporating ‘prudence’, i.e. the lower bound of a confidence interval.

It is important to note that ‘de-risking’ here means permanently shifting assets from stocks and shares to gilts. The damage is not due to temporarily moving assets to gilts but the long-term effect of exposing assets to below-CPI levels of return.

- Example: Anyone who has sold a house in a rising market is aware that if they do not buy another house quite quickly, what they can afford will shrink. Inflation eats assets if they are placed in below-inflation accounts.

Consequently, contrary to the label, ‘de-risking’ increases the chance of default.

Minimising turbulence by reducing a plane’s altitude increases the chance of the plane crashing.

Even without the evidence that Sam Marsh has been able to extract from USS, it was possible to prove that at the limit, as de-risking is pushed into the future, the chance of default goes to zero.

What this graph shows is that (using USS’ own valuations and some simple assumptions) if you delay de-risking to 25 years’ time, later, or never, then the valuation allowing for prudence will not be in default.

Sam Marsh and Mike Otsuka have shown that USS applied Test 1 to the wrong data. The trigger is based on false premises.

My point is that if, in attempting to respond to this critique, USS and UUK are returning to reflex comments about ‘risk appetite’, they had better be clear that **minimising an appetite for investment risk inevitably comes with an increase in the risk of pension fund default**.

Which risks are you concerned about, colleagues?

### See also

- USS JEP report
- Sam Marsh’s blog post on Test 1
- Mike Otsuka’s further explanation
- Mathematical operations with the Normal distribution (SW)