## Mathematical operations with the Normal distribution

Interesting post about the USS pension `deficit’ and why it is strongly dependent on the valuation method.

This post is a little off-topic, as the exercise I am about to illustrate is not one that most corpus linguists will have to engage in.

However, I think it is a good example of why a mathematical approach to statistics (instead of the usual rote-learning of tests) is extremely valuable.

### Case study: The declared ‘deficit’ in the USS pension scheme

At the time of writing nearly two hundred thousand university staff in the UK are active members of a pension scheme called USS. This scheme draws in income from these members and pays out to pensioners. Every three years the pension is valued, which is not a simple process. The valuation consists of two aspects, both uncertain:

• to value the liabilities of the pension fund, which means the obligations to current pensioners and future pensioners (current active members), and
• to estimate the future asset value of the pension fund…

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### 12 Responses to “Mathematical operations with the Normal distribution”

1. Anton Garrett Says:

It’s all tosh anyway, the problem is that the return on investments has fallen because the interest rate has fallen because of QE, and nobody has the faintest idea whether politicians will dare to enact policies that bump up the interest rate and thereby risk an escalating wave of bankruptcies of the over-borrowed. THAT is what you want information about in order to see the future of this fund, and the information is unknowable. This analysis is technically correct on its own terms of the variables it takes into account, but utterly futile.

• telescoper Says:

Behind the revaluation of the fund is a putative switch from `risky investments’ (e.g. shares) and `safe’ investments (e.g bonds). yields on the latter are low because of `Quantitative Easing’. If bond yields go up that might lead investors to ditch shares and move their money into bonds. If that does happen soon (as it may) then the USS is `de-risking’ at exactly the wrong time!

• “the return on investments has fallen because the interest rate has fallen”

Normally (I see it literally every day), if interest rates are low, stocks are high and vice versa (for the simple reason that if one is low, people invest in the other). There are exceptions, but this is a very general rule. Presumably USS invests in stocks rather than savings accounts.

“bump up the interest rate and thereby risk an escalating wave of bankruptcies of the over-borrowed”

Normally the interest rate of a loan does not change while it is being paid back. This would thus be a problem only for those who borrow money to pay off debts. In such a dire situation, a modest change of interest rates is unlikely to make much difference.

• telescoper Says:

There are many alternatives to stocks. There are government bonds and other tradeable instruments.

• True, but apart from government bonds (as opposed to bonds from a corporation, in which you essentially lend the corporation money by buying the bond and get (as long as the company is solvent) a fixed interest payment as opposed to hoping for a good dividend (though, as with stock, you can speculate that the price will rise and sell the bond), most such instruments as they are called go up when general interest rates go down and vice versa. My guess (though I don’t know) is that USS has a substantial investment in stock portfolios.

Of course, this is just a rule of thumb; there is no guarantee and all investments are speculative to a greater or lesser degree.

• Anton Garrett Says:

Pension funds are conservative and tend to invest in both bonds and stocks, to cover themselves. In many jurisdictions (including I think the UK, but I’m not sure) they are *required* to invest a minimum porsion in government bonds. The government says this is for safety purposes, but it is actually because pension funds are very large and government wants their money available to it.

• telescoper Says:

Yes, pensions are regulated – one of the things the regulator does is limit the proportion invested in stocks etc.

I think pension funds probably do keep some funds in money accounts, but that’s probably a small fraction.

• Since there are now government bonds with negative interest, the safety-purposes argument is becoming increasingly dubious.

• telescoper Says:

Not really. They might still be better than stocks if the market crashes…

• True. Of course, there is also the possibility that the country defaults (as has happened).

2. One reason stocks are so surprisingly risky is that movements are not distributed normally *at all*. Price movements have very, very long tails.