Weak Evidence for International in Vanguard Research - Am I Missing Something?

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InKirkWeTrust
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Weak Evidence for International in Vanguard Research - Am I Missing Something?

Post by InKirkWeTrust »

Vanguard's research paper, "Global Equities: Balancing Home Bias and Diversification," seems to provide very weak evidence for the benefits of large international allocations. Yet Vanguard's default option for its all-in-one funds is 40%. Why? Link here: https://www.vanguard.com/pdf/ISGGEB.pdf

The chart on p. 5 shows that international allocations up to 40% have only led to a 1 percent decrease in portfolio volatility for 100% stock portfolios, on average. The volatility reduction is less, only 0.5%, for a 60/40 portfolio.

On the next page it says, "a significant weakness of this analysis is that it is backward-looking and particularly dependent on the time period examined. For example, at different observation dates, the “optimal” allocation to non U.S stocks has been as low as 20% or as high as 70%. As recently as year-end 2005, the bottom of the “U” pattern in Figure 3 fell between 40% and 50%; through both year-end 2008 and year-end 2013, however, the curve clearly bottomed out between 30% and 40%. And even more recently over shorter time periods, we have seen non-U.S. stocks fail to reduce the volatility of a portfolio at any allocation."

Am I missing something here? Why is the mainstream view that international is so important, if the average benefit is a .5% reduction in volatility? Even Bill Bernstein's "If You Can" recommends 50/50 US/International stock.

Vanguard concludes with "Allocations closer to 40% may be suitable for those investors seeking to be closer to a market proportional weighting or for those who are hoping to obtain potentially greater diversification benefits and are less concerned with the potential risks and higher costs. On the other hand, allocations closer to 20% may be viewed as offering a greater balance among the benefits of diversification, the risks of currency volatility and higher U.S. to non-U.S. stock correlations, investor preferences, and costs."

That seems like a pretty tepid endorsement of high international allocations. Where is the evidence supporting big international AA? Why does Vanguard put 40% international in its Target Date and Life Strategy funds? Your thoughts?
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Re: Weak Evidence for International in Vanguard Research - Am I Missing Something?

Post by Thesaints »

Define "big". For me, "big" is any allocation substantially above cap weight, that is 50%.

Since cost of foreign investing is now just a few points above the cost of domestic investing, I see no compelling case for not having a "normal" (i.e. cap weigthed) allocation in foreign assets.
Past data only covers a few decades at best and it is only one of the possible outcomes. Human brain is notoriously blind to past volatility.

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Re: Weak Evidence for International in Vanguard Research - Am I Missing Something?

Post by lack_ey »

In investing in general it is difficult to get much improvement in volatility, return, etc. People argue over fractional return improvements all the time, so I think your expectation is maybe too high.

Much more importantly, the real motivation has to do with the interpretation of history and theory. Looking at historical data, a U.S. investor would never have really needed or benefited all that amazingly, particularly over longer periods of time, from investing elsewhere. The same is definitely not true for an investor in many other countries historically. To the degree that potentially the U.S. was relatively lucky rather than special, or that the property will not necessarily continue to hold (is the secret out now? have things changed?), there is more of an argument for looking to diversify. Statistically we are looking at pretty limited datasets anyway, not enough performance history to estimate the relationship between assets with high confidence, never less estimate means and variances and so on, even before we consider the reality that the behavior changes over time (the future draws from a different distribution from what generated the past).
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Re: Weak Evidence for International in Vanguard Research - Am I Missing Something?

Post by afan »

Theory:
Investing only in US companies means buying only a subset of public stocks, with the criterion for choosing which to own being arbitrary. Why just US stocks?

History: There have been times when owing a broader mix of stocks has resulted in lower volatility, higher returns or both as compared to US only.

For cap weighted US and international stocks the returns are by definition dominated by the performance of the large cap companies. But large cap companies, wherever they may be incorporated, depend on both US and international markets for their revenue. So the international and US stock markets are highly correlated. It seems unlikely this trend will reverse.

If high correlations persist, then it will not make a big difference whether one has a small or large allocation to international stocks. But the ability to have country specific risks come up, particularly short term, still argues in favor of substantial allocations to both US and non-US stocks.
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Re: Weak Evidence for International in Vanguard Research - Am I Missing Something?

Post by Lauren Vignec »

40% is not a large allocation to international because it is still less than the market weighting, although it is not much less. I think the US is around 53% or 54% of the global stock market.

Any time an investing strategy deviates from the market portfolio it is the strategy that needs a justification, not the market portfolio. It doesn't matter whether it's "slice and dice" with small and value or "put all your money in the S&P 500". So the Vanguard research shows, as far as I can tell, no justification for deviating from the market portfolio with regard to international stocks.
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Re: Weak Evidence for International in Vanguard Research - Am I Missing Something?

Post by nisiprius »

Nice response by lack_ey.

InKirkWeTrust, you're not missing anything. It is an indication of Vanguard's general straightforwardness that they give us an interesting and data-rich paper that isn't simply propaganda for one position.

There is a) weak, b) evidence, for c) some benefit to international stock investing, and Vanguard presents it.

In my opinion, one of the reasons that this topic generates such perennial and heated arguments is that nothing in the past data (from 1970, start of the first accepted international index, EAFE, to the present) suggests that it would ever have made much difference one way or the other whether or not you had international stocks. The intense arguments always involve special pleading and selection of time periods. Recency plays a huge role--around the end of the last decade, the dollar had weakened and international did well, so that it was a lost decade for U.S. investors but not totally lost for people with international allocations. At that time, if I commented that international hadn't made much difference, people would always say "well, you didn't include emerging markets"--which a) only had data going back to 1988, and b) just happened to have been going gangbusters at that time. Now, both international in general and EM in particular have been doing poorly.

People shouldn't have been overoptimistic about international circa 2008-9-10, and they shouldn't be overpessimistic now. Eh, it's an asset class. It's not exactly the same as U.S. It probably adds some diversification, but not a whole awful lot because the whole world is coupled. Vanguard's paper says, basically, from 20% up to global cap weight (about 50%). That's reasonable. I'm in that range, toward the low end, Vanguard in that range, toward the high end.

You'll never settle the argument between people say "since it doesn't matter, you should use the minimum" and those that say "since it doesn't matter, you should use the maximum."

Meanwhile, this drives people bananas, but John C. Bogle has said, quite consistently, over and over, that he doesn't think anyone needs international at all, and that if you decide you want it, fine, but (he says) you should limit it to 20% of your stocks.
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Re: Weak Evidence for International in Vanguard Research - Am I Missing Something?

Post by nedsaid »

I don't think you are missing anything. The efficient frontiers bounce all over the place over time. What might have been optimal over the last 15 years might not be optimal over the next 15 years. From what I have seen is that there doesn't seem to be much difference between having 20% of stocks allocated to International and having 50% of stocks in International. There seems to be a diminishing incremental benefit as you ratchet up your International allocation. This is all inexact anyways.
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Re: Weak Evidence for International in Vanguard Research - Am I Missing Something?

Post by Uncle Pennybags »

InKirkWeTrust wrote:Why is the mainstream view that international is so important,
Probably something to do with the popular ignorance of one world all holding hands singing kumbaya. This forum forced me to hold foreign stocks. I was at 20% at one time. I stopped contributing until it fell to 10% and that's where it will stay. Not only are foreign stocks more expensive to hold they also have a currency play going on. Mr. Boggle said we don't need any foreign stocks. I tend to agree.

[OT comments removed by admin LadyGeek]
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Re: Weak Evidence for International in Vanguard Research - Am I Missing Something?

Post by nedsaid »

Uncle Pennybags wrote:This forum forced me to hold foreign stocks.
Really? You might have been shamed into it but as far as I know, no one here sends anyone around with a tire iron. Or making an offer than can't be refused. Last I checked, no one forces anyone to do anything around here. Indeed, there are many here, including myself, who are not 100% Boglehead.
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Re: Weak Evidence for International in Vanguard Research - Am I Missing Something?

Post by Thesaints »

Response to [OT comments removed by admin LadyGeek]

From a more general point of view Mr. Bogle is almost 90 years old as, I believe, several posters are. I'm not implying a decline in mental faculties, but people of that age have formed much of their judgment based on experience accumulated in a financial world rather different from today's.
Sticking with one's domestic stock market in the past may have had a good reason behind it (higher costs, mainly), but has served Japanese, British, French and Italian investors quite badly. Who can tell if our turn is just around the corner.
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Re: Weak Evidence for International in Vanguard Research - Am I Missing Something?

Post by bigred77 »

There are some things in investing that I pretty much accept as inevitable:
- There will be another recession eventually and stocks will suffer big (20%, 30% 40%, 50%, maybe even more) losses.
- There will be another decade or longer will US treasuries outperform stocks
- There will be a decade or longer where US stocks really under perform International equities. Like 2%, 3%, 4%+ annual under performance.

In the first 2 examples I think I know what kind of posts we will see on bogleheads (hint: we will see a lot less "why do I need any bonds at all?" type posts).

I'm genuinely very curious to see the tone and attitude of this board when the 3rd example happens.
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Re: Weak Evidence for International in Vanguard Research - Am I Missing Something?

Post by dbr »

The actual question was not what is the argument for international diversification but rather that given the argument is so weak why is Vanguard so adamant about adopting such a large international allocation in its balanced funds? The question might come up even stronger about the international bonds and about Vanguard PAS making pretty large allocations in some recommendations (50% in a recent post).
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Re: Weak Evidence for International in Vanguard Research - Am I Missing Something?

Post by nedsaid »

bigred77 wrote:There are some things in investing that I pretty much accept as inevitable:
- There will be another recession eventually and stocks will suffer big (20%, 30% 40%, 50%, maybe even more) losses.
- There will be another decade or longer will US treasuries outperform stocks
- There will be a decade or longer where US stocks really under perform International equities. Like 2%, 3%, 4%+ annual under performance.

In the first 2 examples I think I know what kind of posts we will see on bogleheads (hint: we will see a lot less "why do I need any bonds at all?" type posts).

I'm genuinely very curious to see the tone and attitude of this board when the 3rd example happens.
Scenario three is why I keep an allocation of International Stocks in my portfolio. It is also a hedge against my beliefs in US advantages in the world markets and the world economy being wrong.
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Re: Weak Evidence for International in Vanguard Research - Am I Missing Something?

Post by Thesaints »

dbr wrote:The actual question was not what is the argument for international diversification but rather that given the argument is so weak why is Vanguard so adamant about adopting such a large international allocation in its balanced funds? The question might come up even stronger about the international bonds and about Vanguard PAS making pretty large allocations in some recommendations (50% in a recent post).
Why do you think the argument is "so weak" ?
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Re: Weak Evidence for International in Vanguard Research - Am I Missing Something?

Post by dbr »

Thesaints wrote:
dbr wrote:The actual question was not what is the argument for international diversification but rather that given the argument is so weak why is Vanguard so adamant about adopting such a large international allocation in its balanced funds? The question might come up even stronger about the international bonds and about Vanguard PAS making pretty large allocations in some recommendations (50% in a recent post).
Why do you think the argument is "so weak" ?
That is how the OP characterizes it. The question is his. The weak part of the argument in my opinion is that they do not show a rationale for why a large allocation to international is preferred over a lesser allocation and therefore for why they adopt a rather extreme choice. It is interesting that their choice has shifted from 30% to 40% in the last year or so. Also they don't argue for a true world cap index even though Vanguard actually has a world cap fund. That argument might actually be more convincing. They are also clearly demonstrating second order effects compared, for example, to the important of stock/bond allocation or even the importance of small cap value tilts, which are also arguable.
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Re: Weak Evidence for International in Vanguard Research - Am I Missing Something?

Post by MarkRoulo »

InKirkWeTrust wrote:Why does Vanguard put 40% international in its Target Date and Life Strategy funds? Your thoughts?
Short answer: I don't know.

Slightly longer and maybe more useful is to note that the most recent semi-annual report for at least *some* of their International funds they are writing about home country bias. Vanguard claims that:
  • US is about 50% of world stock market, but US investors hold about 80% US stock.
  • Canada is about 3%, but Canadian investors hold almost 60% Canadian stock.
  • UK is ~7% and ~26%
  • Australia is ~2.5% and 66%
  • Japan is ~7% and 55%
I'm going to claim that it is VERY risky for Canadians and Australians to have 60%+ of their stock investments in one fairly small country whose economies are not super diversified. Japan is structurally a bit better (though this hasn't been so great for Japanese investors the last three decades). UK investors seem more reasonable.

So ... possibly Vanguard is starting from some place like, "If it makes sense to *ONLY* invest in the US for US investors, does it also make sense for Canadians to ONLY invest in Canada? If not, why not? And is the US special, or should Chinese only invest in China, etc.? Or should *everyone* only invest in the US?"

Looking top-down I can see how Vanguard would find it easier to defend a more world-centric view rather than a US centric view for US investors and a world centric view for everyone else OR a US centric view for US investors and a Canadian centric view for Canadians, etc.
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Re: Weak Evidence for International in Vanguard Research - Am I Missing Something?

Post by InKirkWeTrust »

Qualitatively, I find the argument that international stock acts as a hedge against the long-term decline of US markets to be the most convincing. But quantitatively, I just haven't seen the data that would back up the other claims that Vanguard and others make to justify it being fully 40% of my equity allocation.

The diversification benefit is a whopping 0.5% and some years adding any international increases volatility, according to their research. If you are not concerned with diversification, but instead want to get higher returns from abroad when the dollar is weak, then would you put 40% of your bond allocation in unhedged international bonds, also?

Without data, we have to make decisions based on belief, and a just-as-convincing qualitative argument can be made for why US markets can continue to outperform international. Favorable demographics compared to Europe, Japan, and China, and debt-to-GDP ratios (while not great) still better than other developed economies, are examples.
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Re: Weak Evidence for International in Vanguard Research - Am I Missing Something?

Post by Thesaints »

MarkRoulo wrote:
InKirkWeTrust wrote:Why does Vanguard put 40% international in its Target Date and Life Strategy funds? Your thoughts?
Short answer: I don't know.

Slightly longer and maybe more useful is to note that the most recent semi-annual report for at least *some* of their International funds they are writing about home country bias. Vanguard claims that:
  • US is about 50% of world stock market, but US investors hold about 80% US stock.
  • Canada is about 3%, but Canadian investors hold almost 60% Canadian stock.
  • UK is ~7% and ~26%
  • Australia is ~2.5% and 66%
  • Japan is ~7% and 55%
I'm going to claim that it is VERY risky for Canadians and Australians to have 60%+ of their stock investments in one fairly small country whose economies are not super diversified. Japan is structurally a bit better (though this hasn't been so great for Japanese investors the last three decades). UK investors seem more reasonable.

So ... possibly Vanguard is starting from some place like, "If it makes sense to *ONLY* invest in the US for US investors, does it also make sense for Canadians to ONLY invest in Canada? If not, why not? And is the US special, or should Chinese only invest in China, etc.? Or should *everyone* only invest in the US?"

Looking top-down I can see how Vanguard would find it easier to defend a more world-centric view rather than a US centric view for US investors and a world centric view for everyone else OR a US centric view for US investors and a Canadian centric view for Canadians, etc.
I'd say the argument should rather be "if it makes sense for US investors to invest only in US equities, shouldn't make sense for Canadian investors to invest only in US equities as well ?"
This, of course, unless someone can show that investing abroad comes at substantially higher costs, or unfavorable tax treatment, which I don't think they can.
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Re: Weak Evidence for International in Vanguard Research - Am I Missing Something?

Post by MarkRoulo »

InKirkWeTrust wrote:Without data, we have to make decisions based on belief, and a just-as-convincing qualitative argument can be made for why US markets can continue to outperform international. Favorable demographics compared to Europe, Japan, and China, and debt-to-GDP ratios (while not great) still better than other developed economies, are examples.
I think to invest US only (or mostly only) you have to believe this sort of thing and ALSO believe that this hasn't been properly priced into the market. No?
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Re: Weak Evidence for International in Vanguard Research - Am I Missing Something?

Post by Wakefield1 »

I see Vanguard is advising that it will have some kind of online roundtable or forum via its website on July 20,1 PM Eastern time concerning the desirability of International investing or allocation:it appears that they are currently collecting questions from people who preregister for the web cast for the speakers to address

If as a result of advice from the expert community lots of investors steer a lot more of their new investable money into International stocks,I would expect that,at least at first,that the indexes and the stocks making them up would get at least a one time or short term (but perhaps permanent) boost in valuations and price per unit earnings,at least to a new plateau.
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Re: Weak Evidence for International in Vanguard Research - Am I Missing Something?

Post by Avo »

The diversification benefit of US total market vs S&P 500 is also minimal; but most here recommend total market. Why the dichotomy in thinking?

Similarly, it seems to me that the total world market should be the starting point. Then we can discuss reasons for tilting away from it.

Possible reasons are (1) absence of currency fluctuations (which increase volatility without providing a compensating return) for US residents, and (2) a belief that the US will outperform (or at least not underperform) because of ____________, which has not yet been priced into current US stock valuations. I have no idea what _____________ might be, but many here seem to know.
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Re: Weak Evidence for International in Vanguard Research - Am I Missing Something?

Post by dbr »

Avo wrote:The diversification benefit of US total market vs S&P 500 is also minimal; but most here recommend total market. Why the dichotomy in thinking?
In this case it would come down to there being no reason at all to not just pick TSM. I wouldn't rate that as a recommendation so much as just the obvious thing to do. Sometimes people are in a plan that has only S&P 500, and that is fine. You can also get tangled up that it is possible to find funds to combine with S&P to get TSM, and therefore, presumably, we should consider doing it, because one can.

I suppose you have read all the consternation about Buffett recommending the S&P 500 and everyone trying to figure out what he thinks is wrong with US TSM.
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Re: Weak Evidence for International in Vanguard Research - Am I Missing Something?

Post by InKirkWeTrust »

Avo wrote:The diversification benefit of US total market vs S&P 500 is also minimal; but most here recommend total market. Why the dichotomy in thinking?
I think people would prefer TSM to S&P 500 given equivalent costs and risks. Would people still advocate buying the Extended Market Index fund to get the marginal diversification benefit if it was in another currency?
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Re: Weak Evidence for International in Vanguard Research - Am I Missing Something?

Post by Avo »

Well that's a good question.

I would like to see a quantification of currency fluctuations as an expected decrease in Sharpe ratio for intl stocks vs domestic (for a US investor). Surely this has been calculated by somebody somewhere, but I haven't seen it ...
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Re: Weak Evidence for International in Vanguard Research - Am I Missing Something?

Post by patrick »

If we were comparing the whole US market with investing in just whichever sector you worked in, would you consider the evidence weak if it only showed a modest volatility reduction if you went beyond your own sector?
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Re: Weak Evidence for International in Vanguard Research - Am I Missing Something?

Post by Dirghatamas »

The way you are posing the question is backwards (IMO)

The logical starting position for investors is to start with market cap weighted stocks. That is called the world stock index. Then you tilt (if desired) in favor of or away from certain sectors (energy, technology, financial whatever) or factors (value, growth, size whatever) or country/region (home country, international, emerging whatever).

The onus is on the investor to justify to themselves WHY they want to tilt away from the market consensus. Consider that much of the invested money in stocks is not by retail investors (who tend to have huge home country bias) but by large sovereign funds/ pension funds/ endowments..who tend to flow more freely across the world. The extra cost of international investing has come down markedly over the last two decades. The currency fluctuation is a feature that can both help you or hurt you so you can't classify it as positive or negative a priori.

I don't invest US/International by any fixed %. I just invest in world stocks because I can never convince myself strongly enough that any tilt I like will beat the market long term.
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Re: Weak Evidence for International in Vanguard Research - Am I Missing Something?

Post by staythecourse »

Why do we keep having these arguments? If you want to invest it international do it. If you don't don't. The only thing wrong is if you believe in investing in market cap and you decide to exclude a HUGE part of the market cap in the rest of the world. Nothing wrong with it, but just don't rationalize it.

Good luck.
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Re: Weak Evidence for International in Vanguard Research - Am I Missing Something?

Post by TD2626 »

Dirghatamas wrote:The way you are posing the question is backwards (IMO)

The logical starting position for investors is to start with market cap weighted stocks. That is called the world stock index. Then you tilt (if desired) in favor of or away from certain sectors (energy, technology, financial whatever) or factors (value, growth, size whatever) or country/region (home country, international, emerging whatever).

The onus is on the investor to justify to themselves WHY they want to tilt away from the market consensus. Consider that much of the invested money in stocks is not by retail investors (who tend to have huge home country bias) but by large sovereign funds/ pension funds/ endowments..who tend to flow more freely across the world. The extra cost of international investing has come down markedly over the last two decades. The currency fluctuation is a feature that can both help you or hurt you so you can't classify it as positive or negative a priori.

I don't invest US/International by any fixed %. I just invest in world stocks because I can never convince myself strongly enough that any tilt I like will beat the market long term.
I agree. There are ways to try and justify a home country tilt (avoiding currency or political risk, for example). One needs to know if they are doing a home country tilt for rational easons (like avoiding currency/political risks), or is instead doing it for emotional reasons or for speculative purposes. Speculation is bad and I feel that home country tilters are essentially betting that Apple will do better than Samsung, that Ford will do better than Toyota, etc. Have you read these companies's annual reports?

I think a mild home country tilt to avoid currency risk is reasonable - but folks who are <20% international would be in trouble if US stocks performmed like Japanese ones did when their bubble burst.
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Re: Weak Evidence for International in Vanguard Research - Am I Missing Something?

Post by joe8d »

For an American, no more than 20% International.
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Re: Weak Evidence for International in Vanguard Research - Am I Missing Something?

Post by staythecourse »

joe8d wrote:For an American, no more than 20% International.
Good one. :D
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Re: Weak Evidence for International in Vanguard Research - Am I Missing Something?

Post by nisiprius »

Thesaints wrote:I'd say the argument should rather be "if it makes sense for US investors to invest only in US equities, shouldn't make sense for Canadian investors to invest only in US equities as well ?"
This, of course, unless someone can show that investing abroad comes at substantially higher costs, or unfavorable tax treatment, which I don't think they can.
Investing across borders comes with a substantial amount of currency risk. We all are aware of this when we travel, and yet somehow we forget about it when we are investing. For a U.S. citizen, sometimes visiting Canada is a bargain, sometimes it's really expensive.

A U.S. investor who invests in U.S. stocks experiences the risk of U.S. stocks, whatever it is.

A Canadian investor who invests in U.S. stocks experiences this amount of risk piled on top of the intrinsic risk of U.S. stocks:
Image
Unlike the extra cost of overseas investing, which nowadays is close to negligible, that is not a negligible amount of extra risk. Maybe it's not humongous, but it's not negligible. That's an extra 60% swing. It's not clear that a Canadian investor should want to take that much risk unless they have reason to think that risk will be rewarded. But the standard thinking is that currency exchange has zero long-term return--and it's not clear why Canadian investors deserve a reward for taking a risk that U.S. investors don't need to take.

Morningstar actually lets us visualize stock returns in different currencies. Here is Total Stock, VTSMX (blue) and iShares MSCI Canada, EWC (orange).
From the viewpoint of a Canadian investor, the U.S. stock fund is clearly more volatile than the Canadian stock fund:
Source
Image

From the point of view of a U.S. investor, it is the Canadian stock fund that is more volatile:
Image

In both cases, over this time period, yes, the U.S. stock fund outperformed the Canadian stock fund in both currencies. Nevertheless, Canadian investor should not be completely indifferent to currency risk. A 100%-U.S. portfolio should be less attractive to a Canadian investor than to a U.S. investor.

I wish that advocates of global cap-weighting, instead of simply shouting down U.S. tilters as being motivated purely by xenophobic "home bias," would instead look seriously at the question "if you take currency risk into account, how much does that shift the optimum portfolio away from cap-weighting?" Based solely on currency risk--and other widely acknowledged additional risks of international investing, listed in every prospectus, how much U.S. tilt is rational for a U.S. investor. It's some number large than zero.
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Re: Weak Evidence for International in Vanguard Research - Am I Missing Something?

Post by Thesaints »

nisiprius wrote:Investing across borders comes with a substantial amount of currency risk. We all are aware of this when we travel, and yet somehow we forget about it when we are investing.

We don't forget. My point (and Vanguard's) is that the added currency risk is small compared to all the other risk stocks are subjected to.
Look at it this way: a yearly 10% movement is a very large one in currency exchanges, while a 10% movement happens more often than not in the stock market.
I'm talking about principal currencies, of course. Periferal ones can be much more volatile.
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Re: Weak Evidence for International in Vanguard Research - Am I Missing Something?

Post by jbranx »

I always enjoy reading these threads on domestic vs. international vs. World, so I hope the issue doesn't get settled! Something in passive has to be fun.

To my SO's great annoyance, for decades in our foreign travels I have always visited every grocery/pharmacy/retail store I can squeeze in to see what US products are sold there. Almost never been to a spot where Colgate toothpaste and Gillette razors were not sold. And, of course, Coke and maybe Pepsi. In fact, the only place I've ever been where there was nothing American for sale was South Georgia island off Antarctica, which the UK administers. A little further up, the Falklands has some American products. And everybody has some US software/computer/cell phone or other hardware, including Masai settlements in Kenya and Bedouin tents in Jordan. No surprise at the 44% sales of the 500 from overseas.

And I don't see many examples of overseas companies that have higher ROE's than the US on any consistent basis. Further, except for the late eighties when Japanese management techniques were so vaunted, I haven't seen much evidence non-US companies have mastered ways to take market share any better than us. There are about as many places where the dollar is gladly accepted as there are places that won't accept it.

All that said, as I read and try to understand more the theories of MPT pioneers like Sharpe, etc., I find myself adding more to tickers like VT, VXUS, VWO and VSS. I can even be convinced that Shiller is right that we should have derivatives that allow us to short our occupation and to invest in a product that provides the equivalent of decent human capital returns to a son/daughter who decides to pursue a career in a low-paying artistic or service position. I'm not there with Sharpe yet on the Vanguard Total Everything Stock/Bond Fund. OTOH, I recall I wasn't with him in the early nineties on just dividing up an index into growth/value by book value.

As productivity and growth slows in the US and I see S. Korean washing machines, cars, and cell phones here, and Indian tractors on farms, and Brazilian short haul aircraft and on and on, I begin to think the world is changing under my feet. Same when I see how incredibly hard people in EM work to try to become middle class. I want to own a piece of their vigor a bit above that 44%. Admittedly, the US seems ideally suited to create innovators/disruptors, but we certainly aren't the only place in an incredibly integrated world where smarties can find a garage.

At the moment my approximate solution to an insoluble problem is to make a decision to own more of the World just in case.
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Re: Weak Evidence for International in Vanguard Research - Am I Missing Something?

Post by MossySF »

Here's my pet theory:

People making their own specific AA decisions can direct as much money to U.S. as possible.

But for Vanguard and the entire mutual fund industry as a whole, they absolutely must set a major allocation to international for any of their blended funds (target retirement, balanced, etc.).

Let's ignore all the past history stuff. The sample sets are too low. Pick different cycles and you get different results.

What is the case is that money inflows cause prices to go up. We already have entire world preferring U.S. stocks over their own. And what happens if we have 100% of U.S. money going to U.S. stocks also? One gigantic bubble (worse than usual) ready to burst and give bloody noses to fund-holders sending them fleeing in terror (again and maybe never to return). This will cost Vanguard money -- this will cost shareholders money. So if International isn't much more expensive and has roughly the same return, it makes sense to spread out the money inflow.
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Re: Weak Evidence for International in Vanguard Research - Am I Missing Something?

Post by rj49 »

Foreign returns are heavily skewed by the Japanese megabubble in the 1980s, where they dominated the foreign index and have never recovered. Thus VG didn't promote international until the 2000s, when it outperformed US after the bubble crash (few Bogleheads or writers promoted foreign either, since it didn't reflect well in historical returns). If you believe in buy low/sell high, then you should have been buying foreign developed and emerging markets, since GMO, Rob Arnott at research affiliates are projecting foreign developed to outperform US stocks in the coming decade, and EM to outperform even more. Right now if you compare the P/E, CAPE ratio, and other measures of valuation, foreign stocks are undervalued compared to US stocks and should theoretically outperform them eventually.

The same historical bias exists with fixed income, after many decades of a bond bull market and decreasing interest rates--research will show that balanced funds offer similar returns to a stock portfolio with much lower volatility. But it's difficult to imagine that sort of bond returns again in our lifetimes, with limited yields and returns on bonds adding to the rush to buy steadily-rising US stocks, high-dividend stocks, and other risky assets. So basically historical studies give a limited view of past returns, so you should look at valuations and projected returns and diversify accordingly.
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Re: Weak Evidence for International in Vanguard Research - Am I Missing Something?

Post by staythecourse »

Uncle Pennybags wrote:Lower risk with better returns, easy choice.
Oh dear lord. Someone actually advocating for the free lunch. Didn't think I would EVER see that on this site.

Good luck.
"The stock market [fluctuation], therefore, is noise. A giant distraction from the business of investing.” | -Jack Bogle
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Re: Weak Evidence for International in Vanguard Research - Am I Missing Something?

Post by dharrythomas »

My theory is that I'm diversifying the currency risk with international stocks. I'm kidding myself if I think I can avoid currency risk.

If all my assets are in dollars, I'm betting big on the dollar. While I can tell myself that my future spending will be in dollars, people in 1920s Germany were better off if they held assets denominated in another currency. That could never happen here. :shock: Currencies change relative value, since the world market returns are generally similar, I think of international as a hedge against a falling dollar. If we mess around and lose our status as the world's reserve currency (every country before us with the status, abused the privilege and lost it), the dollar will lose value.

If you don't want to make that bet, there are investment firms such as Tweedy-Brown that offer (and recommend) currency hedged international equity funds. So you can invest in more stocks without the currency risk.
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Re: Weak Evidence for International in Vanguard Research - Am I Missing Something?

Post by TD2626 »

nisiprius wrote:
I wish that advocates of global cap-weighting, instead of simply shouting down U.S. tilters as being motivated purely by xenophobic "home bias," would instead look seriously at the question "if you take currency risk into account, how much does that shift the optimum portfolio away from cap-weighting?" Based solely on currency risk--and other widely acknowledged additional risks of international investing, listed in every prospectus, how much U.S. tilt is rational for a U.S. investor. It's some number large than zero.
Yes, currency risk (and other risks like political risk) is a big reason why a home-country tilt can be rational - but it should be thoughtfully considered and done intentionally. Too many people start from 100% US and add international - instead, it's best in my opinion to start from a global perspective and tilt based on specific, rational considerations like currency risk.

One issue is that for most investors, they have 100% of their cash, 100% of their home equity, 100% of their emergency funds, 100% of their human capital in domestic. Maybe they have some foreign bonds, but very, very few do cap weight there. If you have no foreign bonds, shouldn't at least equities be close to (or even over) cap weight to make up for all other assets being US? Currency diversification is important as you get protection from tail risk - if the dollar declines by a lot, it will help by a lot to have holdings in foreign currency.

The dollar can fall by any amount against a basket of currencies (hyperinflation), but it is unlikely to rise by an arbitrary amount as all the other currencies in the basket would have to hyper-inflate at the same time (am I correct in this thinking?). Thus, currency diversification can provide protection from some tail risk scenarios.

I think that currency risk is a hard one. One is taking on substantial, uncompensated risk with very little reward. It does probably justify a small tilt toward domestic for many investors.
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Re: Weak Evidence for International in Vanguard Research - Am I Missing Something?

Post by patrick »

nisiprius wrote:I wish that advocates of global cap-weighting, instead of simply shouting down U.S. tilters as being motivated purely by xenophobic "home bias," would instead look seriously at the question "if you take currency risk into account, how much does that shift the optimum portfolio away from cap-weighting?" Based solely on currency risk--and other widely acknowledged additional risks of international investing, listed in every prospectus, how much U.S. tilt is rational for a U.S. investor. It's some number large than zero.
Currency exists in domestic stocks also. Most companies (based in the US or not) have customers, suppliers, employees, etc. who use a variety of currencies. The other risks in prospectuses are questionable and seem mainly to provide cover against lawsuits -- surely it is true that political events could harm non-US investments, but political events could harm US investments too, and in any case that risk ought to be factored in to the market price.

If we are going to try to quantify what impact the higher level of currency risk would shift the optimum portfolio towards the home country, we should also look at the reasons to tilt away from your home country. After all, if you live and work in the US you are already heavily exposed to the health of the US economy. An economic crisis in the US is likely to lead to a reduction in your salary, or you losing your job and having to take a lower paying one, or perhaps even losing your job and never getting another one. Even without any investment in US stocks your economic situation is already dependent on the overall US economy. Just like investing in your employer's stock is considered riskier than investing in some other stock, the same should apply on a country level.
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Re: Weak Evidence for International in Vanguard Research - Am I Missing Something?

Post by harvestbook »

People talk about currency risk as if there's zero risk in the US dollar.

From Vanguard's viewpoints, I suspect they are fine with a straight-up global market weight yet veer toward minimizing the international allocation because of the comfort level of their client base (through home bias, recency bias, familiarity, etc.) Their published position seems to be more of an explanation of why they are below market-cap weight, not a defense of why they are so (presumably) heavy on the international allocation.

I'm somewhere around 43-45 percent international myself. Even if the benefits and risks are relatively small, I like that extra bit of diversification not just for currency reward (as opposed to just the "risk" people often claim for foreign currencies, since we make our money off of risk), but for possible sequence-of-return risks in case I need to sell when one or the other market is down. I am also investing in the future, not the past. I can't live Bogle's or Buffet's life and I don't know how future events will change global investments. Since I don't know, I default to the base case. (And yes, I am slowly nudging my international up to 50 percent).

That said, I have no problem if everyone else owns only US for whatever reason. I can't fault your logic and I hope it works out for everyone. I doubt all of this tinkering around the edges makes much difference in the long run, but it passes the time.
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Re: Weak Evidence for International in Vanguard Research - Am I Missing Something?

Post by nisiprius »

harvestbook wrote:...People talk about currency risk as if there's zero risk in the US dollar....
There's zero currency risk when a U.S. investor who spends and earns dollars holds dollar-denominated assets. There are other risks but they are not currency risk. See below for explanation.
dharrythomas wrote:...My theory is that I'm diversifying the currency risk with international stocks. I'm kidding myself if I think I can avoid currency risk...
You misunderstand. The term "currency risk" doesn't mean what you think it means.

"Currency risk" does not mean "the risk that fiat money will become valueless." That's a separate issue.

The term "currency risk," also called "exchange rate risk," is a defined term with a meaning. It applies only to transnational transactions involving currency conversions, and refers to the extra uncertainty in the value you will receive if currency needs to be converted, due to uncertain variations in the exchange rate.

If you book a hotel room in Canada for a firm price of CAD $100, and don't pay in advance, you might expect it to cost you USD $77, but when the time actually comes to pay, it might cost you $85 or it might cost you $70. That uncertainty in the value of your U.S. dollars buying something denominated in Canadian dollars is what is mean by currency risk.

If there's no transnational transaction and no currency conversion, there's no currency risk. A U.S. investor holding only dollar-denominated assets experiences no currency risk. There is a risk that the U.S. economy collapses, the dollar becomes worthless, and the Treasury defaults on TIPS, but none of that is currency risk. I'm not sure what you'd call it--economic catastrophe risk, perhaps.

Please check the definition of "currency risk," aka "exchange rate risk," in any way you think is appropriate and report back on what definition you found.
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Re: Weak Evidence for International in Vanguard Research - Am I Missing Something?

Post by nisiprius »

MossySF wrote:Here's my pet theory:

People making their own specific AA decisions can direct as much money to U.S. as possible.

But for Vanguard and the entire mutual fund industry as a whole, they absolutely must set a major allocation to international for any of their blended funds (target retirement, balanced, etc.).

Let's ignore all the past history stuff. The sample sets are too low. Pick different cycles and you get different results.

What is the case is that money inflows cause prices to go up. We already have entire world preferring U.S. stocks over their own. And what happens if we have 100% of U.S. money going to U.S. stocks also? One gigantic bubble (worse than usual) ready to burst and give bloody noses to fund-holders sending them fleeing in terror (again and maybe never to return). This will cost Vanguard money -- this will cost shareholders money. So if International isn't much more expensive and has roughly the same return, it makes sense to spread out the money inflow.
Yes, I suspect something like this, too. I think some of Vanguard's behavior could be explained if Vanguard thinks that they are growing so big that they have outgrown the United States. Similarly, their failure to go in for any kind of factor tilts (e.g. small value) might be explained by a feeling that they are getting so big that if all their customers had small value tilts, there wouldn't be enough small value to go around. Another possibility is that Vanguard feels that the future for them is in becoming an international company and they are trying to build up their core competencies in investing everywhere, not just in the U.S.
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Re: Weak Evidence for International in Vanguard Research - Am I Missing Something?

Post by nedsaid »

jbranx wrote:I always enjoy reading these threads on domestic vs. international vs. World, so I hope the issue doesn't get settled! Something in passive has to be fun.

Nedsaid: My suspicion is that like blondes, tilters are more fun!! In my own portfolio, I have done a lot of things and to be honest a lot of it is the "fun" factor and the desire for an intellectual challenge. So you have heard it here first, my portfolio is "fun" tilted.


To my SO's great annoyance, for decades in our foreign travels I have always visited every grocery/pharmacy/retail store I can squeeze in to see what US products are sold there. Almost never been to a spot where Colgate toothpaste and Gillette razors were not sold. And, of course, Coke and maybe Pepsi. In fact, the only place I've ever been where there was nothing American for sale was South Georgia island off Antarctica, which the UK administers. A little further up, the Falklands has some American products. And everybody has some US software/computer/cell phone or other hardware, including Masai settlements in Kenya and Bedouin tents in Jordan. No surprise at the 44% sales of the 500 from overseas.

Nedsaid: The reach and influence of US companies overseas is rather ubiquitous. You almost can't get away from it. Pretty much the John Bogle and Warren Buffett argument.


And I don't see many examples of overseas companies that have higher ROE's than the US on any consistent basis. Further, except for the late eighties when Japanese management techniques were so vaunted, I haven't seen much evidence non-US companies have mastered ways to take market share any better than us. There are about as many places where the dollar is gladly accepted as there are places that won't accept it.

Nedsaid: American business is amazingly ruthless. As the pointy haired boss on Dilbert said, "Employees are our most valuable asset. Lay some off and the stock price goes up!" The Nedsaid version would go something like this, "When in doubt, lay them off." A nice way to say this is that we have a rather dynamic work force. This gives American business a competitive advantage.

All that said, as I read and try to understand more the theories of MPT pioneers like Sharpe, etc., I find myself adding more to tickers like VT, VXUS, VWO and VSS. I can even be convinced that Shiller is right that we should have derivatives that allow us to short our occupation and to invest in a product that provides the equivalent of decent human capital returns to a son/daughter who decides to pursue a career in a low-paying artistic or service position. I'm not there with Sharpe yet on the Vanguard Total Everything Stock/Bond Fund. OTOH, I recall I wasn't with him in the early nineties on just dividing up an index into growth/value by book value.

As productivity and growth slows in the US and I see S. Korean washing machines, cars, and cell phones here, and Indian tractors on farms, and Brazilian short haul aircraft and on and on, I begin to think the world is changing under my feet. Same when I see how incredibly hard people in EM work to try to become middle class. I want to own a piece of their vigor a bit above that 44%. Admittedly, the US seems ideally suited to create innovators/disruptors, but we certainly aren't the only place in an incredibly integrated world where smarties can find a garage.

Nedsaid: A well stated case for investing in International Stocks. It is an exercise in conceit to believe that the world revolves around the United States or that we have a monopoly on innovation.

At the moment my approximate solution to an insoluble problem is to make a decision to own more of the World just in case.
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Re: Weak Evidence for International in Vanguard Research - Am I Missing Something?

Post by dharrythomas »

nisiprius wrote:You misunderstand. The term "currency risk" doesn't mean what you think it means.

"Currency risk" does not mean "the risk that fiat money will become valueless." That's a separate issue.

The term "currency risk," also called "exchange rate risk," is a defined term with a meaning. It applies only to transnational transactions
I understand the concept (that's why I used the examples I did rather than a general crisis like the depression or the worldwide inflation of the 1970s). In an interconnected world, I cannot avoid being part of transnational transactions involving currency exchanges. Just because there is a middleman that does the actual transaction, I as an ultimate consumer bear my part of the currency risk. Food, building supplies, clothes, electronics, whether I like it or not, almost every transaction I make (and the cost of that same transaction next time), is dependent on exchange rates and the dollar is a concentrated beat.
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Re: Weak Evidence for International in Vanguard Research - Am I Missing Something?

Post by TD2626 »

nisiprius wrote:
harvestbook wrote:...People talk about currency risk as if there's zero risk in the US dollar....
There's zero currency risk when a U.S. investor who spends and earns dollars holds dollar-denominated assets. There are other risks but they are not currency risk. See below for explanation.
dharrythomas wrote:...My theory is that I'm diversifying the currency risk with international stocks. I'm kidding myself if I think I can avoid currency risk...
You misunderstand. The term "currency risk" doesn't mean what you think it means.

"Currency risk" does not mean "the risk that fiat money will become valueless." That's a separate issue.

The term "currency risk," also called "exchange rate risk," is a defined term with a meaning. It applies only to transnational transactions involving currency conversions, and refers to the extra uncertainty in the value you will receive if currency needs to be converted, due to uncertain variations in the exchange rate.

If you book a hotel room in Canada for a firm price of CAD $100, and don't pay in advance, you might expect it to cost you USD $77, but when the time actually comes to pay, it might cost you $85 or it might cost you $70. That uncertainty in the value of your U.S. dollars buying something denominated in Canadian dollars is what is mean by currency risk.

If there's no transnational transaction and no currency conversion, there's no currency risk. A U.S. investor holding only dollar-denominated assets experiences no currency risk. There is a risk that the U.S. economy collapses, the dollar becomes worthless, and the Treasury defaults on TIPS, but none of that is currency risk. I'm not sure what you'd call it--economic catastrophe risk, perhaps.

Please check the definition of "currency risk," aka "exchange rate risk," in any way you think is appropriate and report back on what definition you found.
This is a really good concept - I like the separation of "currency risk" and "economic catastrophe risk".

When you invest internationally, you take on currency risk. This is zero-return, uncompensated risk, and that's not a good thing.

But investing internationally reduces "economic catastrophe risk". This is the risk that the home country's "fiat money will become valueless" - and/or the risk that the home country's stock market experiences the kind of event that Japan had - large implosion followed by staying down by decades.

Diversification is the only free lunch - and by diversifying among different economies/countries, you diversify away much of the economic catastrophe risk. This is a fat tail risk, and as someone who places a lot of value on reducing fat tail risk, I believe that the "Japan Scenario" protection provided by international goes a long way to offsetting currency risk (which is more Gaussian and able to be understood and modeled better).

I want a solid, mathematical framework that shows numerically or analytically exactly how much international to invest in. I am not very comfortable with the "everyone should just go with a gut feeling, anything between 20% and cap weight's OK" mentality that is fairly prevalent.

Mabye someone could run some Monte Carlo simulations comparing these two assets:

1. Domestic stocks - annual return distribution has fat tails due to Japan-scenario economic catastrophe risk. Mean 9% nominal, Standard Deviation 18%, but a non-Gaussian distribution that has the fat tails. (Note that fat tails may be cancelled out by autocorrelation as discussed recently here: viewtopic.php?f=10&t=222695&newpost=3440136)

2. International stocks - annual return distribution doesn't have as fat of a tail with single-country meltdown risk largely diversified, has the same 9% nominal expected return, but the standard deviation is not 18%, it is higher, since market SD plus SD of currency risk are the square root of the sum of the squares.

Hopefully by optimizing this sort of simulation, one could find the tangency portfolio.
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Re: Weak Evidence for International in Vanguard Research - Am I Missing Something?

Post by dbr »

TD2626 wrote:
This is a really good concept - I like the separation of "currency risk" and "economic catastrophe risk".

When you invest internationally, you take on currency risk. This is zero-return, uncompensated risk, and that's not a good thing.

But investing internationally reduces "economic catastrophe risk". This is the risk that the home country's "fiat money will become valueless" - and/or the risk that the home country's stock market experiences the kind of event that Japan had - large implosion followed by staying down by decades.

Diversification is the only free lunch - and by diversifying among different economies/countries, you diversify away much of the economic catastrophe risk. This is a fat tail risk, and as someone who places a lot of value on reducing fat tail risk, I believe that the "Japan Scenario" protection provided by international goes a long way to offsetting currency risk (which is more Gaussian and able to be understood and modeled better).

I want a solid, mathematical framework that shows numerically or analytically exactly how much international to invest in. I am not very comfortable with the "everyone should just go with a gut feeling, anything between 20% and cap weight's OK" mentality that is fairly prevalent.

Mabye someone could run some Monte Carlo simulations comparing these two assets:

1. Domestic stocks - annual return distribution has fat tails due to Japan-scenario economic catastrophe risk. Mean 9% nominal, Standard Deviation 18%, but a non-Gaussian distribution that has the fat tails. (Note that fat tails may be cancelled out by autocorrelation as discussed recently here: viewtopic.php?f=10&t=222695&newpost=3440136)

2. International stocks - annual return distribution doesn't have as fat of a tail with single-country meltdown risk largely diversified, has the same 9% nominal expected return, but the standard deviation is not 18%, it is higher, since market SD plus SD of currency risk are the square root of the sum of the squares.

Hopefully by optimizing this sort of simulation, one could find the tangency portfolio.
I don't think MPT style portfolio analysis applies to figuring out the optimum asset allocation to manage a catastrophic risk. Risk in MPT refers to the variability of returns. It is a property of returns and not a separate entity.

Off hand, one might imagine that the allocation to manage catastrophic risk would be to put no more in any given asset than 100% less the chances of occurrence of catastrophe. For example, if one believes there is a 1% chance the US economy will catastrophically collapse, or equivalently, that the dollar as fiat money will become worthless, then no more than 99% of the assets should be in the US. I won't single out any country by name, but one could probably list a dozen or two where the estimate of catastrophe is 100% and one would invest nothing in those countries. This algorithm clearly fails to be well defined because there are many countries where the risk is so small that the investor could invest 99%+ in each of them. Maybe that is why the question seems to have no settled answer; people are not really afraid of most of the world's economies.
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Re: Weak Evidence for International in Vanguard Research - Am I Missing Something?

Post by dharrythomas »

TD2626 wrote:
I want a solid, mathematical framework that shows numerically or analytically exactly how much international to invest in. I am not very comfortable with the "everyone should just go with a gut feeling, anything between 20% and cap weight's OK" mentality that is fairly prevalent.

Mabye someone could run some Monte Carlo simulations comparing these two assets:

1. Domestic stocks - annual return distribution has fat tails due to Japan-scenario economic catastrophe risk. Mean 9% nominal, Standard Deviation 18%, but a non-Gaussian distribution that has the fat tails. (Note that fat tails may be cancelled out by autocorrelation as discussed recently here: viewtopic.php?f=10&t=222695&newpost=3440136)

2. International stocks - annual return distribution doesn't have as fat of a tail with single-country meltdown risk largely diversified, has the same 9% nominal expected return, but the standard deviation is not 18%, it is higher, since market SD plus SD of currency risk are the square root of the sum of the squares.

Hopefully by optimizing this sort of simulation, one could find the tangency portfolio.
Good luck, the problem is that while there is one best answer for a particular time period, it is not knowable in the future. Whatever assumptions. you put in the simulation will drive the results. People here used to spend a lot of time discussing MVOs, the problem is that the one true constant is change. In the US you are probably OK with anywhere from zero to market weight in international. But you never know the optimal answer for you except in hindsight. Decide what risk you want to take and how much, then guess.

As Kenny Rogers said "You never count your money, while you're sitting at the table there'll be time enough for counting when the dealings done."
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Re: Weak Evidence for International in Vanguard Research - Am I Missing Something?

Post by lack_ey »

To run a mathematical framework, you need to input so many unknowable parameters that it's really just spitting back out your own input assumptions. You can't get around some subjectivity and qualitative analysis somewhere along the line, in the process for determining the parameters or somewhere later.
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Re: Weak Evidence for International in Vanguard Research - Am I Missing Something?

Post by jbranx »

My impression is that most of the US megacorps engage in currency hedging, so that complicates any effort to try to sort out with great precision the currency effects. Gold and metals companies hedge, airlines hedge on fuel costs, and the currency markets win the race in value traded every day.

Question: Does anyone compute the sum total of hedging that the US megacorps do? I know at my old firm the CFO some years did and some years didn't, explaining sometimes that we had a "natural hedge" based on where we were earning the most non-dollar money overseas. Makes my head spin trying to figure out how all this adds up, but it would be nice to know the aggregate figures.

The point about economic catastrophe risk is very good. I lived and invested during the "Rust Belt," hyper-inflation, US is doomed 1970's era, and remember all the dire forecasts--and the silly WIN, whip inflation now buttons--of how we'd never pull out. (Great time to invest in stocks as 1982 approached; GE was at 6 P/E and 6% dividend as Tall Paul pulled off the recovery). The faith that we have a dynamic system that always recovers is awesome, but it's not a given.

Or maybe these economic events are almost always self-healing in a market economy. One of my most memorable events in the 1980's was to Brazil and watching a grocery store worker changing the pricing labels as frenzied shoppers tried to grab the goods before the price changed. One result of the hyper-inflation/wrecked currency was that Brazil leapfrogged the world in electronic cash management. They recovered and had a nice boom, followed now by an Olympic-scale corruption scandal. I remember a ratings agency quote from the last Argentine default that said they'd never be able to access the credit markets again! Whoopee, just did a well received 100-year. Hard to know how to get precision in these calculations, but the patterns are there for sure.
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Re: Weak Evidence for International in Vanguard Research - Am I Missing Something?

Post by Avo »

Here's a simple mathematical exercise that I found instructive.

Assume the US market and the exUS market both have the same variance. Then the optimal (minimum variance) portfolio is 50-50, no matter what the correlation R between the two markets is. (50-50 is also pretty close to current valuations, so this is not a ridiculous model.)

Now add currency variance; model this as a conversion factor of 1+C from exUS to USD, with C having expectation zero and variance V.

Then I find that the minimum-variance portfolio (for a USD-based investor) holds a fraction f_US in the US market given by

f_US = (1-R+V)/(2-2R+V).

Historically R varies between something like 0.5 and 0.9. I can't find long-term data on V for (say) the USD vs the euro, it looks something like V=0.3, but this may be an overestimate long-term.

Anyway, here is what you get from that formula:

Code: Select all

 R    V   f_US
0.9  0.3  0.80
0.5  0.3  0.62
0.9  0.1  0.67
0.5  0.1  0.55
So 20% to 45% exUS (when the market valuation is 50%). Right in line with what is usually advised!
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