To fully comprehend why the New Zealand Superannuation Fund (NZS) has changed the way it invests you will have to read 'Modelling of asset returns and the economy for the 2010 Reference Portfolio Review' by Aaron Drew.

Not that it will add to the comprehension for most of us, littered as it is with phrases like "dynamic stochastic system of equations that has a well-defined equilibrium to which variables will converge following a shock" and recurring cases of kurtosis.

It only gets worse when the hieroglyphics of statistics begin, containing symbols so obscure I cannot cut and paste them from the document.

But this is the intellectual grunt work used to justify the billion-dollar investment decisions made by the NZS. And who are we to argue with it?

As this recent Financial Times article shows the NZS isn't the only Sovereign Wealth Fund (SWF) "rethinking their approach to portfolio management and to risk".

"... and the consequences will be far-reaching," the FT story says.

In the case of the NZS Drew's reworking of asset class risk and return assumptions has led to real changes in its portfolio.

Out of the equations the NZS this year finished construction of its so-called 'Reference Portfolio', which resulted in the $16 billion fund engaging in substantial trades over the last few months.

According to an NZS spokesperson, the changes included:

An additional exposure to the global equities markets of near $2.2 billion (predominantly through derivatives);

Commodities exposure of about $700m removed from the fund;

More than 700 corporate bonds sold (realising about $1 billion); and,

Sale of some $500 million of listed property exposure.

Elsewhere in its analysis the NZS argues for the resumption of Crown funding "sooner rather than later".

"Relative to the base case [where government contributions resume in 2020], the expected Excess Dollars [compared to investing in Treasury Bills] is around $20.5 billion or 5 per cent of GDP higher in the case where funding resumes in 2010," the NZS report says.

"In contrast, should funding never resume the Excess Dollars is around $10 billion lower than the base case."

Well they would say that but the NZS supports its claim with more of those crazy equations.

Better the complicated maths, I suppose, than ad hoc, politically-motivated decisions to buy dairy farms, Auckland train stations or the dud loan books of screwed-up finance companies.

Theoretically, the NZS is free of political influence and it is a signatory to the Santiago Principles for SWFs that includes a promise: "To invest on the basis of economic and financial risk and return-related considerations."

I haven't quite figured out how this squares with Bill English's directive for the fund to buy NZ-made - I must consult my logarithmic tables.