r = d + g - f - t
So this sets out the key variables and we can then look at how PIEs and ETFs/ITs cope with each factor. Obviously d and g are going to be the same for both PIEs and ETFs.
Assuming we are going to get a broad exposure to the world stockmarket, d today is about 2.5 per cent and g has been reasonably stable over the long term at 1.0 per cent above inflation or a per cent or two below nominal GDP growth i.e. about 4.0 per cent.
So 2.5 per cent + 4.0 per cent = 6.5 per cent.
This figure is consistent with what a meeting of experts in the US earlier this year concluded that the world stockmarket would achieve longer term given current prices.
So far we have got that the return on international shares is going to be 6.5 per cent over the long term, less fees and tax.
Things get different between PIEs and ETFs when you consider fees and tax.
Tax is a big determinant of returns on international shares because, thanks to the good work of Michael Cullen and Peter Dunn, we have perhaps the stupidest tax system in the world as regards international shares. In a touch of irony this tax has been called the "fair dividend tax" and it was instituted to stop naughty rich people avoiding paying their fair share of tax.
Apparently in Mr Cullen's and Mr Dunn's fantasy world rich people put all their money into international shares like Apple and Google which pay next to no dividends so they pay no tax. Bad bad bad, so we have had inflicted upon all NZers, rich and poor, the unfair dividend tax.
This tax simply assumes that no matter what your after-fee dividend yield from international stocks you will be taxed as if the dividend yield is 5.0 per cent.
So if your dividend income after fees is zero you will pay tax of say, 33 per cent of 5.0 per cent i.e. 1.65 per cent. What could be fairer?
Further irony is provided by the fact that the seriously rich have long since taken their money out of NZ and have it in tax havens like Monaco and the Bahamas etc. where no tax at all is payable.
Apparently there is trillions of dollars in these tax havens and that is where concerted action from governments around the world is needed. Goodness knows what the fair dividend tax costs NZ'ers in terms of accounting fees and other related charges.
But back to the story - where things get very different for ETFs and direct investment in international shares versus PIEs is that the former category can, when calculating the fair dividend tax, reduce the tax payable by any capital losses in that year.
So if the stockmarket has a bad year and falls by 5.0 per cent you probably don't have to pay any tax on your dividends if you own an ETF, closed-end fund or direct investment in overseas shares.
PIEs don't get this important tax advantage, despite all the people selling PIEs telling us that PIEs are the way to go if you want to avoid tax. The significance of this difference has been particularly acute of late because as we all know world stockmarkets have defied the financial advisers' spreadsheets and gone down most of the time.
To guess the impact on tax in the future we looked at the past and specifically how many down years the US stockmarket has had since 1926.
Approximately one year in four the stockmarket fell - so to very roughly incorporate this into the tax calculation we will assume that the tax payable by ETFs will be 25 per cent less than the 1.65 per cent payable by PIE funds.
The international PIE funds sold by the bigger NZ providers have average management expense ratios of around 2.2 per cent pa. In contrast if you look at the biggest ETFs available in the US offering exposure to the world stockmarket the management expense ratios are about 0.25 per cent, i.e. about one tenth of the average fee charged locally.
One of the reasons local international share PIEs have such high fees is that sometimes the NZ fund managers enlist the help of an international fund manager to actually do the work.
So you can end up paying double fees - one of the PIE funds marketed locally has a management expense ratio of 3.2 per cent, i.e. fees account for half of the prospective 6.5 per cent return and once Mr Cullen and Mr Dunn have worked their magic there is not a great deal left for Mum and Dad.
My staff had an awful time trying to get meaningful cost data from local fund managers - quite a few continue with the charade of publishing after tax costs. Hmmmm.
We need to put all this info together to see how international share PIEs and low cost direct investment funds compare. See this table.
What this shows is that the economics of investing in international shares through local PIE funds is not compelling, to put it mildly. The after tax after fee cash flow from your average international PIE fund is likely to be negative - not a great help in paying for the groceries.
Disclosure: Brent Sheather is a financial adviser and once was a member of the stock exchange. He is not a tax expert and readers are reminded of the old saying that stockbrokers, and by implication financial advisers, are frequently people who found accounting difficult at university. Accordingly readers should seek expert tax advice on their affairs.