Say you had a very, very thoughtful and considerate ancestor living in Octavian's Rome, who invested the purchasing equivalent of one modern dollar for you at a constant real (inflation adjusted) rate of return. After 2000 years, you'd have the following amounts at the given rates:

Real Rate of Return	Principal in 1997	Radius of Gold Sphere (at $280/oz.)
1.0%	$440,000,000	8.1 meters
3.0%	$4.7 x 1025	3,800 kilometers
5.0%	$2.4 x 1042	1,400,000,000 kilometers
7.0%	$5.9 X 1058	4.1 x 1014 kilometers

(Thanks to my daughters for lending me their scientific calculator; my financial calculator proved inadequate to the task.)

Even at 1%, you are now wealthy beyond most of your rational desires. At 3% your accumulated wealth buys a sphere of gold larger than the moon. At 5% the gold sphere has a radius reaching to Saturn's orbit, and at 7% it is 43 light years in radius, a tidy sum indeed. (To give due credit, the above paradigm isn't mine, it's Peter Bernstein's.)

What is the point of this exercise? Well, perhaps we need to question the current universal assumption of high expected equity returns. Over the past 200 years English speaking investors have been very lucky indeed, earning real equity returns of about 6%. If were you a stock investor elsewhere in the world (say, Germany, Japan, or South America) you weren't so lucky, with long term returns not greatly exceeding inflation.

Unless you dropped out of school long before you reached puberty (or perhaps spent too much time watching MTV and Fox) the speedbumps on your road to the above theoretical wealth are pretty obvious. Little things like the sacking of Rome, dark ages, plague bacillus, and assorted European and global Armageddons.

Have we gotten any smarter in the interim? For starters, publicly traded equity is a relatively modern invention. The first recorded publicly traded stock was probably that of a water mill in southern France, at Bazacle. Built about 800 AD, its ownership was divided up into shares around 1100, with more or less continuous pricing from 1400 on, until the French government nationalized the mill a few decades ago. (But then again, what do you expect from a culture which finds subtext in Jerry Lewis movies?) So maybe it is different this time. One can only hope.

The long term economic growth of the world economy can be looked at from another perspective. Let's be wildly optimistic and assume that the productivity of the average citizen had increased by a factor of 1,000 since Roman times. This translates into an annualized per capital growth rate of 0.35% over the past 2 millennia.

What's the bottom line here? Take another look at the above table. Even at a real rate of return of 3%, the result of a 2000 year investment of one dollar is billions of times greater than the world's current wealth. In other words, over the long term a real rate of return in excess of 1% is mathematically impossible. If you're planning for 5%-7% real returns over the next 30 years to fund your retirement, you may or may not wind up being very unpleasantly surprised.

You say you're planning a 10% return to fund your retirement? Sure, go ahead. Just don't set up any trust funds for your distant descendants.

copyright (c) 1998, William J. Bernstein