smartinwate wrote:There are some efficient frontier graphs on the wiki showing allocations of domestic to international that seem to indicate the optimum mix for risk-adjusted return is 70/30 domestic/international. Return as shown on these graphs seems to peak at 60/40, with 50/50 having the same return but more risk.

There are two big problems with using MPT as a guide to U.S./international allocation.

The first is: even if it is real, what is the

size of the effect? How big is it in the first place... and, instead of arguing exactly where the optimum spot is, how much

difference is there between the supposed optimum and anything else?

You will notice that virtually everyone who shows an efficient frontier chart of U.S. and international, including the wiki, uses a "suppressed zero" chart that magnifies differences rather than showing how big they are in absolute terms. The reason why nobody ever plots them with axes going to zero is that if you do, the efficient frontier is a little squiggle, up and to the right, on a big blank space, and you can't see the differences clearly--and they don't look impressive. The Bogleheads' Wiki chart, for example, really

should look something about like this:

Now, obviously, if you believed that these small differences in past averages were real, robust, and that you were

guaranteed to get something close to them in your own portfolio going forward, then you could do the compounding math and "prove" that the difference in return between 9.28% at the optimum and 9.08% for 100%-U.S. was hugely important and thirty years from now would be enough to buy you a nice Rolex. But--unlike the effect of expense ratios--there's no such certainty.

Second, John C. Bogle makes this point himself, but let me make it myself a little differently. My 2007 copy of Burton Malkiel's

A Random Walk Down Wall Street illustrates diversification and modern portfolio theory, and

the example he chose to illustrate happens to be U.S. and developed foreign country stocks, i.e. the EAFE index, January 1970-June 2006. The picture is on p. 193.

For whatever reason, he chose to highlight, not the tangent portfolio, but the minimum-risk portfolio, which at that time was 76% U.S., 24% international. In the latest edition, p. 203, he has an updated chart based on data through December 2013 and the minimum risk is obtained with only 16% international. That big a change already suggests endpoint dependence, but let me put my own spin on it.

We have 46 years of international stock data in the EAFE index--nothing broader goes back anywhere near that far--and Malkiel's 2007 book showed the results of looking at the first 35 years of it.

Hey, 35 years, that's a lot, and even today you can say that's a good big part of all available data.

Instead of looking at the first 35 years, 1970-2005 inclusive, let's look at the

last 35 years of data that I happen to have in my homebrew software: 1980-2014 inclusive. Got that?

I'm still looking at most of the data, and the two date ranges

include two-and-a-half decades of overlap. Each period is a good long 35 years,

and they mostly overlap.

But even so,

just look at the difference!At the end of 2006, you've have said, based on that chart, that "the last 35 years of data show that the best allocation is 33% international." But at the end of 2014, looking at the same amount of data the same way, you'd have said "the last 35 years of data show that the best allocation is 100% U.S., zero international."

What I mean to say is: for determining the best mix of U.S. and international, using MPT on past data is a bad joke. In the context of U.S. versus international stock, MPT isn't much more than an obfuscated, pseudo-scientific way of telling you which asset class did better during the endpoints chosen--and, as with return itself, the results are highly endpoint-dependent.

What happened? It's pretty clear. The much-vaunted MPT low-correlation thing only works if the two asset classes have comparable return in the same place--meaning they are both fairly close to the yellow line. This is actually the case in the first chart. And, it only works if the two assets have low correlation, which shows up in the chart as

the amount of bend. Under the right conditions, as in the first chart, the low correlation will make the curve bend up, which will push the tangent line (yellow) up above the just-use-the-best-asset line (red). How much it pushes it up depends on the correlation--the more correlation, the less bend and the less push.

The big effect here is 2008-2009, when both U.S. and foreign stocks tanked and foreign stocks tanked a little more, and 2009-present, when foreign stocks in general had lower return than U.S. stocks. The low return brings the green dot down. The not-so-low correlation prevents the line from bending much. In theory, a sufficiently low correlation (a negative correlation would be needed) could make the curve bulge enough to the right that the yellow line would be lifted above the red line.

Annual income twenty pounds, annual expenditure nineteen nineteen and six, result happiness; Annual income twenty pounds, annual expenditure twenty pounds ought and six, result misery.