Ricardo vs. Markowitz

Economics has its founding fathers, like Adam Smith and David Ricardo. If list of greats were compiled for finance, Harry Markowitz would number among them. Markowitz helped invent Model Portfolio Theory, a mathematically elegant approach to optimizing investment portfolios that considers not only how well one expects investments to do, but also how certain one is of ones judgments, and the typical inter-relationships between “surprises” in different investments.

Markowitz’s theory of investment and Ricardo’s theory of trade are meant for very different domains, but the contrast between them is striking. Ricardo teaches that nations should determine their comparative advantage, and specialize in that, trading for what they do not produce most efficiently. Markowitz suggests that investors beware the temptation of specialization, and diversify even into apparently inferior investments to limit risk. Both are revered. What explains the difference?

Nations, after all, are investors, in the aggregate. Specializing in manufacturing or software or wine or cloth entail vastly different portfolios of fixed structures and human training. And investors, like nations, have comparative advantages. Consider a venture capitalist, or an “angel” investor. Each faces different investment opportunity sets, determined by who they know and the localities or domains in which they invest. Every investment has an opportunity cost (the expected return on other investments). Using return estimates alone, most investors would find that choosing one or a very few investments would uniquely maximize expected return, net the cost of foregone opportunities. The situation of a nation that can trade for what it does not produce is broadly similar to that of an investor, for whom a high return in a software venture yields specie that can be used to purchase food, shelter, and yachts. (The no-trade analogy would be an investor whose profits at a stocking factory would have to be taken in the form of inedible socks.)

So, should nations and investors both specialize? Or both diversify? Or should they behave differently, and if so why? From an investment perspective, the question would turn on two considerations, uncertainty and the optimal locus for diversification. Uncertainty is the easiest factor: An investor who can perfectly predict the real returns on investments should absolutely not diversify, even under Markowitz’s theory. Ricardo took the comparative advantages — that is the relative investment returns — of nations as fixed and given. Under these circumstances, Markowitz would agree that specialization is the way to go. But how good are nations, really, at knowing their comparative advantages? And even when they choose correctly, how likely is it that changes in circumstance or random surprises render judgements inaccurate? The greater the uncertainty, either of estimation or environment, the greater the case that nations should diversify.

A second question hinges on who is best placed to diversify. In the 1960s, it became fashionable among corporations to form “conglomerates”, large groups of unrelated businesses held under a single corporate umbrella. There were a bunch of rationales for this, including the ability of subsidiaries to raise capital internally, economies of scale in shared functions, and the market and political power associated with size. But one important motive for conglomeration was Markowitz’ portfolio theory. It was argued that a diversified firm faced fewer risks than a specialized one, since when one industry was fairing poorly, other business units might do well to make up the difference.

Conglomerates are no longer fashionable. Investors rejected the case for corporate diversification, because they were perfectly capable of diversifying themselves. Why should MegaCorp include unrelated businesses A, B, and C, when an investor can divide her own portfolio between stock in A, B, and C? In fact, MegaCorp’s diversification harms the investor, because the investor loses the opportunity to customize exposure to A, B, and C according to her own circumstance and expectations.

Unfortunately, most citizens can’t hedge their exposure to nations in the way that investors can diversify investments in firms. This is a strong argument in favor of diversifying at the national level, even when it cuts against maximizing comparative advantage.

There are a several ways that nations may be different than investors that buttress the case for national specialization. Investors choose their investments according to flawed analytical processes, and make mistakes. When a capitalist economy specializes under open trade, it is a vast market that decides in which fields to specialize, what factories to build, what competences to educate. Perhaps owing to “the invisible hand”, “the wisdom of crowds”, or whatever, market economies make such better choices than private investors that there effectively is no uncertainty. The market always chooses correctly, so specialization is the optimal choice. I find this argument unpersuasive, both because I think markets can be short-sighted and mistaken, and because I believe in irreducible uncertainty that no predictive institution can overcome. Another difference between nations and ordinary investments is that national investment has dynamic effects. When a nation begins to specialize in, say, electronics manufacturing, economies of scale and network effects kick in that serve to magnify any original advantage the nation had in that field, and turn the investment into a kind of self-fulfilling prophecy. This, I think, is a quite reasonable point. But the difference between investors and nations can be drawn too starkly. A venture capitalist or angel investor also works, post-investment, to advise firms, to recruit good people, and to create connections between complementary firms. But these kinds of investors still do diversify.

If one buys the case that nations are like investors, and that investors ought diversify in an uncertain world, what does that mean in practical terms? It depends. It might mean nothing. Perhaps the ordinary functioning of national markets produce sufficiently diversified national portfolios on their own, in which case all is well and good. But it does suggest the possibility of market failure. If national investment is skewed or concentrated in some fashion whose future performance (relative to other possible portfolios) is uncertain, public action to promote diversification might be reasonable.

“Industrial policy” is unfashionable, and it is of course true that political processes are flawed and corruptible. The case I’ve made opens the door for rent-seeking operators to seek government handouts in the form of “diversification subsidies”. Any policy based on this argument would have to be designed with great care. Nevertheless, that chemotherapy is poisonous does not imply that cancer does not exist.

Note: While David Ricardo long ago joined Zeus on Mount Olympus, Harry Markowitz, whose work I much admire, is a living, active scholar. The views expressed in this essay are entirely my own, and if I seem to have put words in Harry Markowitz’s (or David Ricardo’s) mouth, I do apologize.

Update History:
  • 06-May-2007, 02:41 p.m. EDT: Neurotically transposed he words “hedge” and “diversify” in a sentence. Also changed a “diversification” to “diversifying”.
  • 08-May-2007, 11:12 p.m. EDT: Changed “approach for” to “approach to”. Grrr.

14 Responses to “Ricardo vs. Markowitz”

  1. I think the biggest risk in these terms is risk of losing ones job and the best insurance is broad education.

    I think education is an area where there is a strong conflict of interest between buissness and workers. Buisness wants people to be very specialised, because it has lot of ways to insure itself while workers can only have a broad skill base as insurance.

  2. *Any change* can be painful. Catastrophic events are rare but possible. What you do at times is to take the hit and walk it off. You can’t do better than combining your expectation and your risk aversion.

    I think you’re too quick to dismiss markets as mechanism for “creating” rational expectations allocations.

    If markets are short-sighted at any one time then I’m sure that wise investors such as yourself, which are not short-sighted, will bid the price back to the proper value, making a small fortune in the process.

    As for “industrial policy”, we can go beyond public choice/incentive compatibility issues and question the task itself… Would any such industry planner have all the relevant information? Why should we assume that he could do better? The experience of the USSR, African countries and even India to a certain degree seems to cast serious doubt on such a proposal, much more than the anecdotal short-sightedness of markets.


    I can’t learn to do one job properly, you want me to do two? That’s crazy!

  3. Michael, It’s an interesting point that a specific employer has less interest in employees’ adaptability than the employee himself.

    But the sort of risks this essay was about aren’t easily hedged by individual diversification, e.g. a more diversified skills portfolio. If a national infrastructure (fixed assets, other peoples’ skills in the aggregate) is mismatched to current opportunities, those with diverse skills will suffer along with those whose skills have been deleted. In relative terms, individual hedgers may do better (e.g. jobs are scarce, but the better prepared still have them), and some may even leave for booming nations. But the world is filled with nations in which even very well-educated people, with diverse skills that would be easily marketable in other places, do very poorly because of national problems.

    Technological change may change this some. In theory, if all skills are tradable, if one develops ones own capacity with the world market in mind, one needn’t fear national error. In practice, skills from faraway places, geographically and cultural, are only purchased by firms in booming nations at a steep discount. Plus, even to the degree that one can protect ones own income, a bust at a national level is likely to harm your environment (economic, social, cultural, infrastructural, um, environmental), so that individuals still experience significant harms. We are, alas, still bound to nations.

  4. Gabriel,

    I’m hardly quick to dismiss the capacity of markets to rationally allocate over a long time-frame. This whole blog, over a period of more than a year already, is largely devoted to arguing that proposition! You may take issue — a lot of people do — but that’s the crux of the argument.

    I should note that I don’t enjoy bashing market mechanisms in favor of government interference. I am a lapsed libertarian, after all. I do support policy action to remedy pressing market failures. But I very much would prefer if we would fix and improve our very obviously (in my opinion) inadequate market institutions so that they would make long-term allocation decisions more rationally. (That’s really what this blog and its author hope to devote themselves to.)

    But before we can fix market systems and institutions, we have to recognize there is a problem. Very ideological supporters of markets often, in my opinion, undermine the long-term case for market capitalism by rigidly pretending antiquated, broken institutions are “the market” and ex cathedra, infallible. When a crisis comes, and it will if existing control structures aren’t improved, the case for markets, and freedom, could be set back for decades or worse.

    With respect to your suggestion that patient investors should be able to correct short-term allocative errors, so they should. In theory. In practice, there’s a whole “limits to arbitrage” literature discussing why it’s very difficult in practice (again, under current institutional arrangements). I’m familiar with these limits quite personally, as a short-side investor. When markets are undervalued, a far-sighted but patient investor who eschews leverage can always profit. But when markets are overvalued, patience is unsupportable, as continued irrationality even for a short period of time, or inflation over a long period of time, can wipe you out. Markets are prone to bubbles, and bubbles lead to consequential misallocations of human and physical capital.

    I dislike the notion of centralized “industrial policy”. Governments are corruptible and informationally constrained, as you say. I’d prefer we didn’t have to go there.

    But, you list the USSR, African countries, arguably India as empirical confirmation of the theoretical deficiencies of industrial policy.

    Japan, Korea, Singapore, Taiwan, and especially China argue the opposite case rather persuasively. The 1990s “Washington Consensus” has proven to be a failure, from a developmental perspective, while other models (which I dislike, aesthetically) have proven very workable. These nations adopted hybrid systems, in which significant degrees of both central planning and market allocation were allowed to interact, and, despite major errors, so far this approach has proven quite successful. (Japan’s lost decade is the exception that proves the rule. For 90% of the planet, Japan’s long recession would have seemed like a great economy.)

    I do think that hybrid systems are capable of making better allocative decisions than existing market institutions (and thus I advocate certain forms of government interference today). But I don’t like that. Aesthetically and philosophically I think it’s bad; the corruption that always accompanies such systems strikes me as particularly pernicious; and long-term these hybrids may prove quite unstable, perhaps decaying in Road to Serfdom style scenarios.

    But bad decisions made by “markets” won’t be tolerable forever. Either we have to improve market institutions to compete better in terms of allocative foresight, or watch another long oscillation in the contest between markets and central planning, authoritarianism and freedom.

  5. “I believe in irreducible uncertainty that no predictive institution can overcome.”

    Mmmm, Popper kind of proved that, didn’t he?

    “When a crisis comes, and it will if existing control structures aren’t improved, the case for markets, and freedom, could be set back for decades or worse.” — again. October 29, 1929 did that, didn’t it? But wasn’t it met with attempts at government measures, and then with attempts at reform of the market institutions?

  6. Gabriel M. writes:

    Huh… this happens to me all the time. My point was not about you and if you’re a good person or not. You shouldn’t defend yourself in these terms. That being said, my comments were overly polemical. (It’s fun.)

    More, on the fundamentals ;-), later tonight.

  7. Gabriel! I didn’t take your point to be about me at all, really, and if anyone was too polemical it was me! I whipped off those comments very late and very quickly, and I’m sorry if I overly personalized the debate, which I certainly enjoy!

  8. Harald,

    Time seems to run in circles, doesn’t it. But it really runs in helices, or spirals, because changing technology gives an arrow to time. Just as there are market failure scenarios today that would have been impossible in 1929 (e.g. a derivatives meltdown), there are possibilities for market reform and innovation that could not have been contemplated then.

    That said, post-crisis reform is usually reactionary, not innovative. It’s a long road from here to better engineered markets, and crisis-as-catalyst is a wildcard that cuts both ways.

  9. Gabriel M. writes:

    Well, first of all, the “long run” is a bundle of “short runs”, so it’s hard for me to understand your claim about the market working in the long run but not in the short run.

    If you mean that the economy converges slowly to some desired path (from one p.o.v. or another) and that political action can make that convergence faster, I guess it depends. We might need to be far more specific about how things work and also about what costs are implied by any policy.

    You talk of “pressing market failures” and bubbles and so on with surprising certainty. It’s clear that we’re looking at different literatures (and that I’m looking to less literature) yet I can’t help myself to think that you’re overselling it (phun, phun!).

    Markets are more volatile that rational expectations representative agent models will predict (and models isomorphic to them) and even with rational expectations you can get bubble-like paths but we’re dealing with a phenomenon of huge complexity for which adequate grand theories are still missing. Hence my skepticism.

    Even behavioral finance guys advise to “buy and hold”, so I think we can safely dismiss any notion that the government could out-think, out-guess, out-forecast the market in a way useful to guiding it to a faster convergence to the bliss path. But I don’t think you’re saying that…

    What you’re saying is that maybe there’s a free lunch from changing “institutions”.

    If you mean the NYSE, then by all means you could set up your own stock exchange, with better rules and if people share your assessment of how things work then they’ll join you. (From what you said I understand that everyone sees the bubble but is powerless to resist it. Hence they will move to your better market, slowly but surely?)

    If you mean that institutions such as property rights, contracts, etc. are at fault… that would be too broad. But those are pretty much sufficient for people to keep markets like those of today going.

    If you mean a sort of nationalization of investment, an all time favorite of Keynes &co. (and many real life traders, who are disillusioned with the market, I noticed), or even a “light” version of such a policy, I think that the gamble is huge and unavoidably a loosing one. (This connects with your mention of “industrial policy”.)

    You can do OK, granted that you have access to a free lunch of innovation and experimentation in other countries, if you keep corruption and nepotism at bay and if you don’t live through substantial changes in tastes or demographics. You can do this for the war-time economy of a small nation. But in the end, it all falls down.

    I must admit that I have followed only at times your year-long exposition on this, but a lean on the “investment for the people” approach is a hard sell.

    On the other hand, drawing a wedge with taxes, to supply different industries with different rates for loanable funds… that’s a market-based policy, not industrial management.

    I guess the issue is pretty much sterile…

  10. Gabriel,

    So,first, apologies again if I somehow personalize or polemicized things.

    Here are a few thoughts in response to your last comment:

    1) I don’t think the problem is just a matter of markets being slow to converge (and I don’t advocate that governments intervene to somehow speed up the process). Capital markets not only describe economic reality, they alter it. If an asset market bubble leads to substantial malinvestment in some sector (and underinvestment in others), the economy as a whole suffers real opportunity costs that can’t be recovered. I think markets are broken for the long run as well as the short run. Though they eventually converge to reality, the reality they converge to is one that they’ve damaged.

    2) If markets can err, that is, if we don’t take it as a priori true that the market-derived applications of capital are value-maximizing (by whatever definition), then it is conceivable that a government could be right when the market is wrong. That of course, depends on the quality of decision-making produced by governments, which in practice is a quite serious issue.

    3) We have few benchmarks with which to compare capital allocation by markets to capital allocations by other means. We have history and anecdote. We can talk about the USSR, or China, or the United States. We can look to corporate organization for models, where more hierarchical and more decentralized decision-making process coexist, between firms and within firms, and look at what sort of decisionmaking succeeds when. If we did this, I think we’d find success accompanies a lot of improvisational mixing, rather than a single path to virtue.

    4) I could (and mean to) go on and on about the kinds of institutional changes worth considering. But here’s a very obvious one: The definition of corporate stock. When an investor is asked to value a share of stocks, they are asked to discount an infinite horizon series of cash flows that will vary over time in difficult to predict ways, and which represents a fractional claim on the profits and residual value of an entity which can alter the size of that fraction as it wishes. Is that a sensible thing for an individual to try to value? What heuristics would a person use to come up with a valuation? Here are some possibilities:

    i) Simplify earnings or cash flow streams by extrapolating them indefinitely into the future;

    ii) Truncate streams, and consider only the relatively predictable near future;

    iii) Rely on the valuations of others, and try to use existing price as the starting point of valuation, and ask whether you have divergent information that suggests the true value should be under or over market value.

    The first two heuristics will lead directly to overincorporating short-term information. The third guarantees feedback loops, as any market mispricing becomes a starting point for future valuations.

    Now you might say, libertarianishly, that people are free to contract and define enterprises and financing arrangements however they please. But that is not, in fact, true. Firms must be defined in certain ways, and conventional definitions of equity and debt must be adhered to or innovated upon carefully and with many lawyers. What I claim is a very poor way of cutting up claims on enterprise cash flows is enshrined in law and practice, and can’t easily be undone. If I’m right, we could improve capital markets a great deal just by defining claims on venture cashflows more sensibly, in a manner that human beings with information about the real world are likely to be able to reasonably value independent of current price.

    I don’t like the idea of nationalizing much of anything, but seeing capital markets as flawed, I am open to government intervention where I perceive what I take to be very obvious errors. Persistent trade deficits applied to consumption rather than investment in future tradable output is the kind of thing I take as obviously a collective mistake. Government interventions are always dangerous. There should be a strong presumption against such action. But a presumption can be overcome. Obviously, we should insist that great care be designed into the form of the intervention, to minimize what we can not eliminate, the possibility that the intervention will just be an occasion for corrupt coercion.

    As you suggest, the line between industrial policy and market-based influence is not sharp. My intuition is that the best state interventions leave a lot of room for markets to weigh in.

    No apologies required (and I’m sorry if I made it seem like they should be) for not reading my crap religiously. I’ve not read every word of your blog either. Anyway, hopefully this has been fun for you too.

    I gotta run, no time to proofread! Hopefully I haven’t said anything too awful or stupid….

  11. Gabriel M. writes:

    My issue with [1] is that great care must be taken to treat information-related constraints as such. There’s always the risk of a “free lunch”-like approach, due to (ex post) obvious ways in which things could have gone better. Without ways in which the government can, ex ante, out-predict/out-allocate the market, then [1] and [2] are basically moot.

    If you take some of that allocative choice out of the hand of people, government, implicitly or explicitly, must allocate. What objective should it follow? Would that system be incentive compatible? — It’s a very hard road.

    Regarding [3], “policy as corporate management” is a tempting but problematic analogy. The optimal size of the firm approach is interesting because it shows, or it tries to show, how much fiscal issues are at work in creating these large companies. Fiscal issues and other legal aspects.

    Many people are perplexed how large companies manage to stay afloat, given the things they witness when working there. Arnold Kling posted something to this effect. I must admit that my limited by varied work experience makes me ask myself the same thing (about former employers, of course!).

    A fair prediction would be that if subjected to less demanding legal and fiscal pressures, companies would find it optimal to be smaller, more flexible, to rely more on markets.

    There’s a lot of planning as such going on in “free market”-like systems. The thing is that it’s subjected to competitive pressures. In the end, that’s what makes or breaks a plan. With regulation, it’s hard to say, even ex post, how good you’re doing.

    Regarding [4]… there’s complexity in ANY choice. Does this mean that I should have government assign a girlfriend to me? Who knows, she might get fat after we marry. How am I supposed to evaluate, ex ante, the value of this relationship? Risky stuff!

    I see little point in conflating investors and models of investing. People choose to include an asset in their portfolio because they expect the most gains from it, at a level of risk at which they’re comfortable. They think it serves their purposes, overall.

    Maybe for wrong reasons, but how does that look in the aggregate? For me, it looks OK. For you, it’s a mess.

    Not everyone needs to invest. And there’s some division of labor going on. With our flawed system and everything, I think you’ll agree that more people could benefit from buying-and-holding tax-smart index funds instead of using term bank deposits, for example. (Maybe).

    Re: your proposal… What you’re proposing is a new model for the firm, a new form of organization. If so, if it were legal, would you expect it to outperform traditional financing models? If yes, why not compete rather than force everyone on the new model?

    Let a thousand flowers bloom. Diversity the rules of the game. :-)

    Could you elaborate on “Persistent trade deficits applied to consumption rather than investment in future tradable output is the kind of thing I take as obviously a collective mistake.”? I’m unfamiliar with the issue you raise.

  12. Gabriel,

    So we agree more than we disagree, though it may not seem that way.

    1) Sure. That a perfect government might, ex-post, have done better than what actually occurred is not a strong case for government action. Cases for government action depend upon identifying circumstances in which market failure is likely (ex-ante, though perhaps based on ex-post experience of similar situations), and identifying actions that seem more likely to help then to hurt, given the strong possibility of government error. Note that not all government action is coercive, and the choice is not really between government action or “pure markets”. Market behavior is defined and constrained by law and policy constantly. Often government can act in ways that don’t translate into “more or less” intervention, just different. I suggest in the main post that perhaps nations ought to be concerned with diversification of aggregate investment. If that’s right, and if markets as they are (not “free markets”, just where history has placed us now), are provoking overspecialization, intervention needn’t be particularly intrusive. Obviously, governments can (and do) subsidize activities that they think the private sector underemphasizes. (And obviously, there is a lot of corruption and favoritism involved, but still, in the US we get a lot of great science out of it.) Governments tax in a wide variety of ways, all of which is coercive. If governments believe capital market behavior is provoking economic distortion, capital gains taxes can be raised, and other taxes lowered, to attempt to remedy. If capital market participants are sure their bets are good (and government skepticism is misplaced), they can ignore such mild incentives. But if their bets are marginal, even gentle medicine could go along way towards fixing the problem. Similarly, central banks could raise rates into alleged asset price bubbles. Again, if the investments are really good, temporary rate rate spikes should be largely ignored by the market (so long as long-term interest expectations don’t go too high). I don’t mean to be suggesting that governments should claim superior knowledge and start uprooting decision-making by capital markets or private parties. All I’m suggesting is sometimes capital markets may be off in ways that governments can recognize, and it’s not a bad idea for policymakers to create modest incentives for capital markets to either accept or override.

    2) The firm analogy is loose and imperfect,. I suggested it only because we have such few things to look at. It is not firm size that interests me. It is the mix of decision-making processes within firms, some hierarchical, and some decentralized, and the fact that the optimal mix depends very much on the work of the firm. I think it’s foolish as a practical matter, though ideologically tempting and perhaps morally correct, to presume that the work of national economies should have no central planning component. As I’ve said, I think empirically various sorts of hybrids work best.

    Despite that, my preference, like yours I think, is for the minimal level of centralization consistent with broadly good outcomes. But the size of that reasonable minimum depends upon the quality with which decentralized institutions are allocating national resources. I’m not really about advocating “industrial policy”, though I might under some circumstances do so. I’d like to improve market institutions so that less industrial policy is consistent with better quality outcomes. But, as I’ve said, if one regards existing market institutions as near-perfect, or any changes as too dangerous, then it’s hard to move to better ones.

    3) Lots of choices are complicated, but if they are needlessly so, we should try to improve the context in which they are made. That’s particularly true if bad choices have externalities, so the befuddlement of the chooser leads to widespread harm. That absolutely does not mean that the government should step in to improve the decision-making environment. Acknowledging that something could be better is not the same as advocating for government to make it so. Simply generating a consensus that a problem exists for which solutions could be discovered might provoke useful progress.

    4) So yes, I am arguing for novel organizational and corporate forms. And no, I’m not asking government to compel people to use them. On the contrary. If I sound statist, I’m not communicating well. With respect to forms of organization, it’s the vitrification of capital structure into narrow categories of debt and equity (and exotic hybrids crafted with great care by lawyers) that I oppose. I do want a thousand flowers to bloom. I’d like to start up a kind of investment startup that lets especially small (limited liability) businesses issue very small-scale equity securities, that would be tied to very specific cash flows, and that would be publicly tradable. Right now, that would be very illegal. I don’t want the government to compel anything. I want it to get out of the way. In writing, though, I am not yet trying to persuade the Man to let me start a microstock exchange. I’m trying to persuade you, and a broad public, that it would be a good idea if somebody tried something like this, and that it should be legal (and that someone should fund me to try it). Let a thousand flower bloom indeed! (And don’t arrest them and send them to reeducation camps afterwards, please.)

    5) The US and many European countries are running historically large trade deficits (vs GDP) at the same time as exports (in goods or services), and investment in export-related sectors are stagnating, in favor of consumption and investment in nontradable sectors. Call me old fashioned, but that strikes me as a problem. That’s the primary “market failure” for which I actually do advocate policy action be taken now, although I would advocate a very market-centered approach.

    Anyway, thanks for reading, and writing sharp ripostes. It’s lots of fun.

  13. notsneaky writes:

    Well, from a theoretical point of view, at the aggregate level, the answer seems to be to liberalize both the current account and the capital account simultanously. Then specialize production in where you have comperative advantage, get those gains, then diversify the risk by buying an international portfolio – insure against the uncertainty that comes from specialization. There’s some evidence that trade liberalization leads to capital flow liberalization and perhaps vice versa (a Harvard grad student did his dissertation on this a couple years ago, his name escapes me at the moment).

    Of course the caveat is that with an underdeveloped domestic financial system, capital account liberalization may not succesfully insure against shocks (terms of trade or others) and may in fact increase the volatility.

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