Different sovereign wealth funds (SWFs) have different mandates. The largest are presumed to have a mandate similar to that of an endowment. The idea is that the state owns a large but fixed amount of a valuable commodity, usually oil, and that this oil is the property of not just the living citizens but also of all future citizens. Therefore, some of the income from today’s sale of the commodity needs to be saved for the future. So in effect the SWF is a future generation fund.

The question becomes, how much needs to be saved to make this all fair? Well, one way to define fair is that the government expenditure per citizen across all time should remain the same, adjusting for the time value of money. Another way to state this is that the purchasing power per capita remains constant. I think that most reasonable people would consider this fair.The problem here is that there are multiple variables to estimate, such as inflation, efficiency gains, price of the commodity being sold across time, etc. This does not preclude us from making some assumptions just to look at the challenge through a new lens.

So, some simplifying assumptions: inflation and the real rate of interest remain at 0%, the current population is 100, the growth rate of the population is 0%, the income from the commodity per annum is USD 100 per annum and lasts for 10 years and there is no other income for the government other than investments and the government starts off with no investment or savings. There will be other simplifications, such as computing end of year balances rather than average balance, but directionally we should be fine.

In the case that government expenditure is 100% of income then expenditure per capita in this scenario is USD 1 per citizen for  10 years and then USD 0 per citizen thereafter. Clearly not fair. So the government needs to invest some of this income into a SWF to generate future revenue. Let us assume that the SWF can achieve a long-term return of 7.5% per annum. What should the government strategy be?

Qualitatively, at the end of 10 years there will be no commodity income, it will be 100% investment income. So the government needs a strategy that in the first 10 years splits income between investment and expenditure so that the expenditure every year in the first 10 years is the same and equals the investment income starting in year 11.

A quick computation shows that if the expenditure rate of commodity plus investment income starts at 45% in year 1 and falls to 33% in year 10, then the expenditure per capita will range slightly between USD 45 and USD 46. In year 11 onwards, the government spends 100% of the investment income to generate about expenditures of USD 46 per capita per annum. This means that to create a “fair” spending versus investment scheme, such a government would need to start its savings rate at 55% of income and increase those savings to 67% of total income.

There are a couple of major factors here that we should be aware of. The first is that population growth/decline would have a significant impact in this situations, as would inflation/deflation. Any volatility in the price of the commodity would also create challenges in managing these issues, although being more conservative in terms of price prediction makes sense as the endowment has a long maturity and any excess return can be smoothed over.

There are also non-financial factors. For example, Norway struck oil in 1969 but was already a well developed country. The Emirates, on the other hand, was a young country and that needed far greater initial investment. These initial investments feed positively bank into both the economy, for example better educated Emiratis improve the efficiency of the economy, as well as quality of life.

The bottom line is that it is a complex issue. Looking at the pure, simplified economic picture I was a little surprised at the savings rates that the arithmetic points to.