Edit: after doing some basic estimates, I've found that the value of doing this is very low, generally less than 100 basis points: http://i.imgur.com/9of14il.png Therefore this strategy would only make any sense as a tiebreaker between very similar investments.
All of my investments are split between US stocks, US bonds, and EU stocks, and here I will explain why. The investment ideas I will provide here apply to any effective altruist individual or organization investing funds with the intention of using them for altruist projects.
Financial advice for the common person often suggests that people divert some of their investments to international markets in order to mitigate domestic market risk. Emerging markets in particular (like China, Brazil, and South Africa), are considered to have value because the risks in those markets are not very well correlated with Western markets. Frontier markets (like Sri Lanka, Kenya and Pakistan) are similar in this regard. The least-developed countries, like Uganda and Malawi, seem likely to be similar although they are not common investment targets for several reasons. International stock indices generally have a mix across developed and emerging market stocks.
The limited covariance of international, emerging and frontier stocks with the US/EU/Japan markets means that a typical risk averse investor can benefit, reducing their risk while preserving expected returns, by taking a portfolio of US stocks and reallocating some of it to foreign markets. They may also sacrifice expected returns in this way - even if they believe that US stocks will outperform emerging market stocks, it may still be prudent for them to invest in some emerging market stocks, because it will reduce the severity of their exposure to the domestic market.
However, it is commonly accepted by now that altruists should generally be less financially risk averse than other people. This implies that we shouldn't worry too much about diversification, but only about expected value. So if an altruistic investor thinks that US markets will beat emerging markets, they should only invest in the US, and vice versa. If they perceived no significant difference it wouldn't matter much.
The basic idea
If you are investing money and plan to use it in the future to support a charitable cause, there is an additional consideration which is relevant to your choice of how to invest: the value of each dollar of your donations, conditional on your investments being successful. If you expect that altruistic projects' value will be correlated with a particular set of financial instruments, then you should prefer investing in those instruments since the potential profits will be more valuable to you whereas your potential losses are more likely to occur in the scenarios where your money doesn't have much use anyway. This means that, rather than maximizing expected financial returns, we should seek to find investments which are covariant with the value of our donations.
The basic idea, if you're not convinced, is explained in greater detail here.
If you plan to make donations to reduce poverty, then you should seek to correlate investment returns with scenarios in which aid to the developing world is more effective. Now the reason that aid to the developing world is so much more effective than aid to the US or other countries is that people there have much less income and therefore have more basic needs. So the ideal financial instrument for a poverty-focused altruist who is saving money would be something that hedges against a rise in the wealth of the least developed countries. The most obvious choice here would be to short-sell the stocks of companies based in those nations. Now investing in the least developed countries is already a very niche area of finance, so I don't know what the prospects are for shorting those stocks. There may be other financial instruments which are sufficiently inversely covariant with the economies of the least developed countries to be worth pursuing, but I can't say for sure what they are.
This also relies on the assumption that a growing economy will also help the poorest people in the country. While this is not always strictly true, it's a general trend of capitalist economies ("a rising tide lifts all boats"). If you are considering making these investments, it may be worth investigating the degree and rapidity of this phenomenon, though even if the economic effects don't play out quickly enough, a fiscally stronger government in an economically growing nation will be able to direct its domestic health and welfare provision more successfully, providing a similar effect.
Animal rights and welfare
Meat consumption is strongly correlated with incomes in developing countries, and so are "self expression" values implying a wider role for progressive ethics in public life and decision making. If you think that much of the value of animal advocacy comes in the form of preventing future meat consumption in currently rising economies, whether in emerging, frontier, or least-developed markets, then you'll want to be positively exposed to those markets: if these economies become strong, then people will obtain both the money to buy lots of meat and the socioeconomic security to expand their moral circle, making activism more highly leveraged. This means those countries should get much or even all of your money.
However if you think that the value of animal advocacy is just in shifting Western practices, then it's not really clear to me what to do. There is evidence that meat consumption eventually begins to reverse with advanced economic development, which would naively imply that you should hold short positions on U.S. markets, but if changing moral values caused by economic development make advocacy more effective in the US (or if wealth makes people more open to buying meat replacements or humane meat) then this may be the wrong position to take. So whether to be short, long or indifferent is not clear to me, but analyzing the issue may provide better answers.
An alternative approach, instead of investing on the basis of markets, is to make investments oriented around companies which specialize in meat production, animal feed, or meat replacements.
If you view EA as something that is going to be good for setting global priorities and growing much larger than it is now, it makes sense to be positively correlated with U.S., western European, and ANZAC markets.
One reason for this is that local economic success will increase the amount of donations which new EAs will be able to make, and possibly other factors such as their education and productivity. The great majority of our new members are from the West, and I believe this is likely to continue indefinitely due to language barriers, geographic distance, and cultural values. This means that the average incomes of new members will be higher in the case that Western economies are strong, so recruiting new people will be higher in value. A good objection to this idea is that the wealthier EAs are and the larger the community, the more well-funded our projects will be, so marginal funding will be less important. However, the more people there are in the movement, the more new projects we will have in disparate cause areas, so the value of marginal dollars might not significantly decline.
A second reason for correlating movement building funds with Western markets is that it is important for EA to be situated in the culture which has global dominance. It means that EAs will have access to the most powerful governments, the most influential individuals, and the most elite institutions of the world. Western countries' practices and moral values have spread to other countries through a variety of mechanisms due to our cultural, economic and military dominance of the global system (the former and latter being due at least in part to our economic dominance). If the West retreats on its position here, then EA will be less influential for the general course of global civilization. But if the West remains dominant or becomes even stronger relative to other countries, then EA will be more valuable.
A final factor is that increased wealth in the West is likely to make people more receptive to ideas of altruism -- see the world values survey linked above. This means that efforts in EA marketing will see a higher rate of return.
I think that AI safety donors should be positively correlated with U.S. AI companies.
One issue here is the second reason described under movement building. AI efforts in the U.S. are situated in the presence of research and advocacy efforts where we have some measure of influence and leverage. If competent AI is developed in China or Japan then it will be less influenced by our safety and ethics advocacy than it would be if it were developed in the U.S. It's possible that AI ethics and safety organizations may arise in those countries in the future, although we will be less able to communicate with them and evaluate the value of funding them due to language and distance barriers, and they will be unlikely to match well with EA values due to the lack of EAs over there along with cultural and moral differences. This is more true if powerful AI is developed with some level of institutional secrecy, as it is likely to be if strategic considerations are perceived by developers or governments.
The reason this matters here is that progress in general AI will lead to potentially enormous economic returns and it's likely that these returns will be most concentrated in the companies which actually develop AI.
A second argument is that the US/West is currently the world leader in AI development, and game theoretic modeling implies that having a clear world leader in AI improves the degree to which safety considerations will be adhered to. So efforts for advocacy and research in safety and ethics will make more headway if the US remains in the lead than if competing nations become competitive, as China is beginning to do.
A third argument is that even holding constant the prospect of general AI being developed fastest in the US/West, a more rapid development of AI increases the value of our research, since it reduces the window of time available for safety work and advocacy.
Does economic growth really matter?
It may seem odd to claim that the fluctuations of markets matter much for these long-run considerations about the trajectory of the global system. However, fluctuations over these timeframes aren't just a reflection of previous growth in economic output; they also signal investors' rational expectations about the value to be had in various markets.
A note of caution: efficient markets doesn't imply equal expected returns
Though you may accept the Efficient Markets Hypothesis, you shouldn't assume that any financial instrument where you have a personal comparative advantage in preferring its variance is one that you ought to choose without doing some measure of due diligence. Many investments, such as frontier market stocks and anything used for hedging, are selected for reasons which don't fit well onto risk/return curves - namely, their limited or negative variance with mainstream markets. This means that an efficient market may invest in them to a degree that makes their expected returns lower than that of other financial instruments with equal variance. So you shouldn't assume that you should automatically make a certain investment just because your altruism lines up with it; ordinary investors often have similar reasons for making those investments.
For most cause areas, there are arguments that EAs with investments which they plan to donate should allocate funds on the basis of the expected value of donations conditional on certain investments succeeding or failing. The arguments may be strong enough to compel one to invest somewhere with a lower expected financial value, or to make investments where otherwise one might have chosen to donate immediately because of haste considerations.