Profitable Destabilizing Speculation*

© Copyright 2007 by Michael A. S. Guth. All Rights Reserved. No portion of this site, including the contents of this web page may be copied, retransmitted, reposted, duplicated, or otherwise used without the express written permission of Dr. Michael Guth.

Professor of Financial Economics and Law
send e-mail
(E-mail is quickest method of contact).
  116 Oklahoma Ave.
  Oak Ridge, TN
  Phone: (865) 483-8309

Financial Economics Homepage      ||      Attorney at Law Homepage


cite as Michael A. S. Guth, "Profitable Destabilizing Speculation," Chapter 1 in Michael A. S. Guth, SPECULATIVE BEHAVIOR AND THE OPERATION OF COMPETITIVE MARKETS UNDER UNCERTAINTY, Avebury Ashgate Publishing, Aldorshot, England (1994), ISBN 1856289850.

Permission of Avebury Ashgate Publishing to post this chapter on the website is gratefully acknowledged. Unfortunately, the figures contained in the book would not display properly on this web page. However, the book can be purchased from Amazon or from this site



Profitable Destabilizing Speculation*



Economists have sometimes conjectured that speculators profit from buying low and selling high and thus tend to stabilize market prices.  Others contend that speculators can earn profits and simultaneously destabilize markets.  The possibility of profitable destabilizing speculation (PDS) affects the operation of competitive markets under uncertainty.  For if speculators may profitably destabilize, then clearly real world markets can be unstable.  However, if destabilizing specu­lators always lose money, then in a Darwinian sense they will fail to survive.

    Our present knowledge of the relation between speculative profits and stability evolved from studies in international economics, price theory, finance, and modern uncertainty theory.  Although PDS represents a sustainable, endogenous source for fluctuations and business cycles, macroeconomic theorists (aside from the Chicago School) have largely overlooked the debate.  Yet analyzing this conjecture will provide better understandings of the microfoundations of macroeconomics under uncertainty.  Indeed many post-Keynesian proponents of active fiscal and monetary policies point out the need to counteract such endogenous, destabilizing market forces.

    This chapter reexamines the literature on PDS, integrating various aspects of works into the general theory of speculation.  While profitable destabilizing speculation has been theoretically depicted, work in this area appears confusing and contradictory.  Many of the early uncertainty theorists employed arbitrary doctrines and primitive models which inadequately portrayed a complex phenomenon like speculation.  Utilizing the benefit of hindsight and modern analytic techniques, we aim to clarify and develop more formally some of the main themes of the speculation and stability literature.

    The text proceeds as follows.  Section 1 restates the basic proposition that profit-earning speculators stabilize markets.  Since many theorists adopted different speculation and stability definitions, Section 2 attempts to describe the semantic controversy.  Next, Section 3 reviews William Baumol's counter­examples, and the comments and criticisms they elicited.  Section 4 continues sorting valid from invalid PDS counter­examples.  Section 5 discusses some representative empirical findings, and the final section contains conclusions and a summary.  The appendices derive results from Baumol's counter­examples, which provide an excellent review for differential equation modeling in economics, and a class of nonlinear excess demand counter­examples.  Readers not interested in differential equations and Hilbert spaces can skip the appendices without losing any economic concepts.



1.1.  Speculation and Stability:  The Friedman Proposition


A number of economists have argued that profit-earning speculators stabilize markets.  The argument dates back at least to the Nineteenth Century, e.g., John Stuart Mill advanced the notion in his Principles of Political Economy.1  Ross (1938) criticized Mill's notion and offered a counter argument based on stock market fluctuations.

    The argument resurfaced in the mid-1950s, when economists began debating the merits of flexible exchange rates and the stability of a flexible regime as compared with exchange rates pegged to the gold standard.  Milton Friedman's contention that profitable speculation tends to stabilize a market shook the conventional wisdom2 blaming speculators for exchange rate instabilities during the 1920s and Great Depression era.  Supporting flexible exchange regimes and a general free market philosophy, Friedman (1953) asserted


        People who argue that speculation is generally destabilizing seldom realize that this is largely equivalent to saying that speculators lose money, since speculation can be destabilizing in general only if speculators on the average sell when the currency is low in price and buy when it is high....A warning is perhaps in order that this is a simplified generalization on a complex problem.  A full analysis encounters difficulties in separating `speculative' from other transactions, defining precisely and satisfactorily `destabilizing speculation' and taking account of the effects of the mere existence of a system of flexible rates as contrasted with the effects of actual speculative transactions under such a system.  (Friedman (1953), pp. 175, 175n)


An extensive literature then grew out of the question of whether profit-earning speculators could destabilize markets and whether proposed counter­examples had shortcomings that invalidated them.



1.2.  The Semantic Controversy


Originally, theorists, such as Friedman, based their analysis on markets without speculation.  The theory asserted profit-earning speculators' entry into such a market would stabilize prices.  With the development of the modern uncertainty theory framework, we now know that attempting to model a `nonspeculative' market is fruitless.  Chapter 3 illustrates why in an incomplete market, almost everyone is forced to speculate, because claims are not available for their optimal consumption bundle.

    Modern uncertainty theory solves comparative-statics issues for speculation via the general equilibrium contingent claims model and standard economic reasoning.  The standard format provides individuals with production functions, preferences, time-distributed endowments, etc., and specifies the available market range.  Economists then pose comparative-statics questions:  e.g., what happens if preferences change?

    Unfortunately, economists have no universally accepted economic dynamics framework; therefore, no prescribed methodology exists to address issues such as stability, a dynamic concept.  Consequently, what theorists might consider unacceptable modern uncertainty comparative-statics, e.g., arbitrarily specified speculative excess demand functions, have frequently shed light on important dynamic stability concepts.  In Sections 3 and 4, counter­examples are illustrated that employ these arbitrary methodologies; the text will thus emphasize substance over technique.  By keeping an open mind, one may glean an idea or two from these earlier works that can be transposed into a modern framework.

1.2.A.  Definitions of Speculation


The first step in reviewing specific examples of PDS is to define our terminology.  The classic speculator definition focuses on the capital gains motive.  A speculator buys (sells) goods under uncertainty, with the intent to resell (repurchase) them after some anticipated favorable price change.  We must emphasize that speculators transact in an uncertain environment.  When traders profit from purchasing goods and later reselling them at an a priori known price, the traders have engaged in arbitrage not speculation.  Moreover, speculators traditionally receive no gain from consuming or using these goods, lest speculation be confused with simple expected utility maximization.  Kaldor (1939) characterized speculative sales or purchases as those motivated solely by perceived capital gains.

    Some theorists maintain Kaldor's definition excludes `speculation' involved in dynamic consumption or production plans.  For example, does a manufacturer `speculate' by postponing a required input's purchase to realize an expected capital gain?  We can clarify our speculation definition by introducing a legal per se distinction.  To meet the three criteria for speculation per se, a person must (1) purchase (sell) a good, (2) face price/profit uncertainty, and (3) transact primarily with a capital gains motive.  The manufacturer above did not sell the desired input with the intent of later repurchasing it; therefore, he did not speculate per se.  Put another way, he could not be charged with speculation per se, since one of the three essential elements (purchase) is missing.  He did `speculate' in the sense of attempting to minimize his input costs over time, but this type of behavior lies outside the definition.

    The same distinction holds for consumers who `speculate' by shopping at a particular grocery store or who consider the potential resale value in their house and automobile purchases.  We can distinguish between investors who consider a capital good's salvage value and those primarily concerned with reselling the capital good at a profit.  The latter group primarily purchases (sells) to realize a capital gain, while the former group is not speculating per se.  The more a house purchaser weighs the capital gain potential of his investment, as opposed to wanting to capture the benefits from living in a house, the more he acts like a speculator per se.

    Consider now an individual who has no intention ex ante to speculate, but finds he can realize an ex post capital gain.  The third essential element of our definition - the capital gains motive - does not influence the individual.  An ex post transactions focus potentially would include nonspeculative capital gains as well, e.g., a Pigou effect.

    Particularly in the stock market, differentiating between ex ante and ex post speculation would sometimes fail to include investors who speculated but did not realize their ex post capital gains or losses.  Most importantly, a speculation definition based on ex post activity would deemphasize the crucial expectations and motives that economists mean when they discuss speculative behavior.

    Rather than proceeding with a common speculation definition, from which theorists might distinguish other market transactions, the profitable destabilizing speculation literature at once began to quarrel over the ongoing problem of defining `nonspeculators.'  As we will now proceed to demonstrate, the old `nonspeculator' semantic controversy appears avoidable by defining speculation per se.

    Friedman [(1957) at p.269] suggested that `perhaps a nonspeculator can only safely be defined (if this is done in terms of his demand curve) as one whose purchases are directly influenced by current prices but not by past prices or price trends.'  Telser defended Friedman's notion and added that nonspeculators derive profits from other sources.


        What distinguishes speculators from other traders in the market is that their profits depend only on the price or price change of the commodity they trade.  Nonspeculators' profits are determined not only by the price of the commodity traded on the organized exchange but also by the prices of other related commodities.  If the nonspeculators are hedgers, they can make their profits almost independent of the price level itself.  (Telser (1959), p.295)


    Telser illustrated his nonspeculator definition with a textile manufacturer purchasing raw cotton and for whom cotton fabric and textile prices also determine his profit level.  To illustrate his `profit from other sources' criterion, Telser chose an importer who profits from decreases in exchange rates and shipping costs, in addition to the imported commodity's price.  Although the textile manufacturer and importer meet Telser's criterion, they would be `foolish to ignore price trends in their supply and demand decisions.'  (Baumol (1959), p.302)

    Upon reexamination, we note that if Telser's importer purchases primarily with the intent to resell at a gain, no matter where he may derive additional profits, then he has engaged in speculation per se.  Telser's `speculator' definition - an investor who solely profits from exchange rate capital gains - is a convention frequently used in the international economics literature.  However, in this chapter we will broadly apply the Friedman Proposition across markets and will not add the sole profit motive limitation to the elements of our per se definition.

    Baumol defined nonspeculators as the speculators' trading partners.


        The practical question which has lain behind the discussion is whether the entry into a market of skillful professional speculators, people who have no desire to hedge their holdings, can be stabilizing.  Now it is clear the remaining participants in the market, the nonspeculators, the people who would like to hedge, must in their own interests consider price trends.  For price changes must also affect the values of nonspeculators' holdings and obligations unless in fact they have succeeded in setting up perfect hedges, which in most markets is out of the question.  (Baumol (1959), p.302)


    Baumol's comment raises an interesting, though not widely understood, fact about hedging.  In futures market jargon, imperfectly hedged contracts sometimes force hedgers to speculate per se on the basis, the spread between the cash and futures prices.  If the hedgers leave their hedge positions in place and do not unwind them, then they will not speculate per se.

    Consider an elevator operator who buys  bushels of corn in the period  cash market.  Let  and  denote the period  cash and futures prices.  For simplicity, assume all futures contracts in period   terminate in period .  The elevator operator short hedges  bushels, where   In period , the operator sells his corn and cancels his hedge by purchasing  futures contracts.  Suppose the operator incurs a storage cost of dollars per bushel.  If  denotes his assets in period , then his assets in period  will be


We can rewrite this expression as


For any value of , an increase in the period  basis raises .  Similarly, any increase in the period  basis reduces .  Most hedgers would rationally consider basis changes in formulating their strategies.

    Only those hedgers who intend to leave their hedges in place actually refrain from speculating per se.  In fact, these hedgers are often prepared to accept a small capital loss as the cost of locking in a known price.  Clearly, Baumol's comments refer to this type of hedger.  Our analysis confirms these hedgers do not speculate per se, but they are clearly influenced by spot and futures market prices.

    To recap this section, speculation per se involves purchases (sales) under uncertainty with the intent to resell (repurchase).  This operational definition should not be confused with the layman's use of `speculate' to refer to simple guessing under uncertainty.


1.2.B.  Definitions of Stability


Defining stability and `destabilizing speculation' is even more complex that the previous effort to define speculation.  Unlike speculation, neither `stability' nor `instability' have most preferred definitions.  This chapter therefore broadly interprets the term `destabilize' to mean increasing price fluctuations' frequency, volatility (here meaning explosiveness not the standard deviation as in option pricing), or amplitude/variance.

    In the speculation and stability literature, economists supporting Friedman most frequently interpreted stability to mean dampening the amplitude of fluctuations; these authors commonly measured stability with the price's mean squared standard deviation (MSSD).  This concept corresponds to a random sample's variance without any probability connotation.  Kemp (1963) and others loosely term this measure the `variance' even though prices in their models may contain no random element.  Throughout this chapter we call this measure the MSSD, so as not to confuse the reader with the actual price variance in modern uncertainty economics.

    Measuring stability with the MSSD required theorists to determine the spread between the MSSD with and without speculation.  Alternatively, the MSSD could be compared prior to and following a new speculative group's entry.  If the MSSD increased with the new speculators, then theorists concluded the new group destabilized market prices.

    The MSSD does not capture increases in the fluctuation's frequency.3  In criticizing Friedman's model of speculative behavior, Baumol observed `while the Friedman argument takes account of the levels of the variables it neglects their time derivatives, and the time path is dependent on both.'  (Baumol (1957), p.264n)  Friedman relied on amplitude, i.e., `buy high and sell low,' to measure stability.  Yet static measures of stability, such as the amplitude, fail to capture destabilizing changes in the time derivative of prices.

    Obst (1967) suggested defining stability as dampening the deviations from any trend line rather than exclusively its mean.  In Figure 1.1, the dotted lines indicate the impact of some speculative trading on a price  over time.  These transactions would be regarded as destabilizing, even though they are actually driving prices closer to their mean.


















Figure 1.1.  Trend Line Instability


    Stability can also be defined in terms of an equilibrium's existence or volatility.  Kenen (1979) and others examined profitable speculation's impact on the existence of a market-clearing price.  A related stability definition examined speculation's impact on generically unstable equilibria, e.g., in a Giffenesque demand.

    Finally, within the international economics field, some economists evaluate exchange rate stability based upon the Marshall-Lerner condition.  In the short run, a balance of trade deficit, ceteris paribus, would tend to increase a country's exchange rate, defined as the units of domestic currency equal to one foreign currency unit.  An exchange rate increase would tend, in the short run, to reduce the trade volume's export value and increase its domestic currency import value.  However, in the long run, ceteris paribus, the increased exchange rate would encourage other countries to import more goods and services from that country, thus tending to raise its total trade volume.  The Marshall-Lerner condition is met when long run export volume increases so much that the actual balance of trade increases.

    Williamson (1972) restates the Marshall-Lerner stability condition as follows.  Let  = the trade balance at time t, defined in foreign-exchange terms; and  = the units of foreign currency equal to one domestic currency unit.  Depreciation of domestic currency implies   < 0.  For simplicity if we write the trade balance as a function of the present and preceding exchange rates, then , with   and   


        [T]he immediate effect of a revaluation is to improve the trade balance as a result of price changes preceding volume changes, but the volume change comes through in the next period and is sufficiently powerful to outweigh the price effect (i.e., ).  (Williamson (1972), p.79)


A Numerical Example.  Suppose the dollar-mark exchange rate decreases from $0.62 to $0.55 per Deutsche Mark (DM).  Having already executed American import contracts, Germany will have an inelastic short-run demand for American dollars.  If total German purchases amount to 6 billion dollars, then the short run net effect of the change in the exchange rates will increase the American goods' cost from approximately 9.677 billion DM to 10.909 billion DM.  However, Germany has a more elastic long run demand for American dollars.  The dollar's appreciation will reduce, ceteris paribus, long-run German demand for United States exports.  Thus the Marshall-Lerner stability criterion states that the total volume decrease, perhaps down to $4 billion 31 DM 7.28 billion, will more than offset the short-run price gain:  (10.909 - 9.677) + (7.28 - 9.677) < 0.


    The Marshall-Lerner stability condition can alternatively be shown to state that the sum of domestic and foreign import demand elasticities must exceed unity.  Thus stability requires that appreciation of a given currency reduce world excess demand for that currency.

    To close this section on definitions of stability, we have identified at least four separate criteria for judging destabilizing influences:  increases in price fluctuations'  1) variance or amplitude;  2) frequency;  3) volatility, explosiveness, or nonequilibriating behavior;  and 4) the  Marshall-Lerner condition for foreign exchange.  The following sections will review the PDS literature assuming each of these four stability definitions are appropriate for applications or counter­examples.



1.3.  Speculation and Stability:  The Baumol Counter­examples


We begin studying the Friedman Proposition's dynamic aspects by first reviewing William J. Baumol's (1957) counter­examples based on a cycli­cal time path for prices.  He proposed that speculators could profit from buying after the price trough and selling after the price peak.  The speculators would in fact purchase on the price upswing and sell on the downswing, thus accelerating price swings and causing other instabilities.

    Baumol constructed three counter­examples, each with the same intuitive notion.  He attempted to show that speculators can destabilize even while buying low and selling high.  Rather than explaining why speculators may behave as he suggests, Baumol only assessed the destabilizing impact of such plausible speculative behavior. 


1.3.A.  Example 1:  Baumol's Difference Equation Model


In his first counter­example, Baumol delineated a cyclical price path using a sinusoidal, second-order difference equation,


                                         1                                (1.1)

where  and  are constants, with ** < 1.  For those readers who would like a brief refresher on differential equations, Appendix A recasts this equation into a more familiar sinusoidal form,


                                     2                            (1.2)



The price path completes a cycle every time  increases by 360°.  The  cycle has wavelength  and frequency f = /360.  The price path without Baumol's speculators follows equation (1.2), where the  = .

    When Baumol's speculators enter the market - buying on the upswing and selling on the downswing - they subsequently alter the market price expression to


                                   3                         (1.3)





Comparing (1.3) with (1.1), we find that with the speculators' transactions, the  , since the fraction  for  > 0.  This relation implies that Baumol's proposed speculation will increase the frequency of price fluctuations over time.

    Second, Baumol demonstrated that, depending on initial conditions, such speculation may increase or decrease the cycle's amplitude.  We will focus on an instance where the speculators increase the amplitude.  Let  = 0 in both the market with and without speculators and assume the same corresponding initial prices.  Then the sinusoidal equation (1.2) evaluated at  = 0 reads


If the initial price rests at the mean price level (), then V = 0 and


which has amplitude 2.  For notational convenience, denote the speculative price time path as


which has amplitude 2.  Suppose the curves also coincide at the peak of the nonspeculative cycle:  when  = 90, or  = 90/.  Evaluated at this point,





                                         4                               (1.4)




since 0 < () < 1.  Expression (1.4) shows that the amplitude of the commodity's price with Baumol's speculators exceeds the amplitude without these speculators.  Intuitively, the two sine curves coincide at an initial value, , and again at the peak of the nonspeculative curve, which has a longer cycle.  Thus the speculative price curve must have already attained its peak and be moving downward:  it must have a higher peak than the curve without Baumol's speculators.


1.3.B.  Example 2:  Baumol's Differential Equation Model


Again proposing the same speculative behavior, Baumol constructed the differential equation model,


                                               5                                      (1.5)




where  and  are positive constants, and  is the second derivative of price with respect to time.  Based on (1.5) the commodity's normal excess demand is

                                          6                                 (1.6)




At the trough when the second derivative is positive, excess demand will be low; similarly, excess demand will be high at the peak.  To incorporate the `buy on the upswing, sell on the downswing' behavior, Baumol defined a speculative excess demand by

                                          7                                (1.7)




with  > 0,  > 0, and   These speculators have greatest excess demand with simultaneously low () and rising () prices.  In equilibrium,  and  must sum to zero:


and solving for


                                      8                             (1.8)

    Baumol then demonstrated a different destabilizing impact.  Whereas for appropriate values of  the solution of (1.5) has complex roots and therefore a sinusoidal time path, the roots of (1.8) also include a positive real term given by


with  constants.  Thus the price no longer fluctuates with constant amplitude but will increase at a geometric rate.  `[P]rofitable speculation has demonstrated its destabilizing ability by (taking) the system from its position of delicate constant amplitude balance into a time path of explosive fluctuation.'  (Baumol (1957), p.269)

1.3.C.  Example 3:  Baumol's `Real' Cycle Model


In an effort to construct a counter­example in which past prices or price trends did not affect nonspeculative excess demand, Baumol developed a third model where `real' factors cause a cyclical price path.  In this model a commodity's supply varies sinusoidally, perhaps due to seasonality or other market conditions, expressed by  with constants .  In keeping with Friedman's criterion, the nonspecu­la­tive excess demand depends only on the current price:   where  and  are constants.

    When speculators then buy on the upswing and sell on the downswing, they transform the price path from its cyclical pattern into an unstable, explosive one.  As derived in Appendix B, the time path of prices in the economy cum speculators has the solution


where  are constants, and E, W, and B are positive constants.  The real term creates a problem in Baumol's third model when the speculators try to realize their profits.


        In the short run, the time path may still be cyclical....(but in the long run) the time path of P will eventually approach ....In other words, speculators will continue to buy on the rising market and, at least in terms of the value of their assets, this would appear to be profitable.  However, it is clear that difficulties can arise if speculators try to cash in these profits or if they run out of funds with which to continue their purchases.  (Baumol (1957), p.270)


1.3.D.  Comments on Profit Realization and the Underlying Market


1.3.D.1.  Speculators Must Realize Their Profits.  To derive PDS counter­examples, Baumol had to prove that his speculators could in fact realize positive profits.  Lester Telser stated more succinctly the problem with Baumol's third model:  `...the latter two terms [in equation (1.9)] are sinusoidal with constant amplitude.  Thus the solution is dominated by (and, since  > 0), the price rises indefinitely.  I must emphasize again that the price necessarily rises indefinitely.'  (Telser (1959), p.301)  Similarly, if  < 0, the price falls indefinitely.  In Baumol's third model, if all the speculators attempt to realize their profits the bubble will burst.

    Telser also recapitulated Friedman's criticism that Baumol's nonspeculators actually speculated, since past prices influenced their decisions.  Current price and recent price trends are shown in the right-hand side of (1.1), thus contradicting Friedman's independence assumption.  `If nonspeculators are not affected by past prices and if speculators have to realize their profits then Baumol's counter­examples are unacceptable.'  (Telser (1959), p.301)

    Replying to Telser, Baumol conceded that all the speculators could not realize their profits in his third counter­example, or the speculative bubble would burst.  `Hence I must agree that it is unreasonable to cite this as an example of destabilizing profitable speculation.'  (Baumol (1959), p.301)  However, Baumol maintained his first two models had demonstrated PDS, even if price trends influenced the underlying demand in them.  More important, Baumol noted that no one had disproved the central idea of buying on an upswing and selling on a downswing.4

    Kemp (1963) pointed out that Baumol was only constructing a counter­example, not a general theory of speculation.  Kemp considered Telser's speculative bubble criticism irrelevant, since economists could view Baumol's counter­example as PDS for a limited time interval before the bubble collapses.  Indeed most economists would regard speculative transactions leading to bubble formation and destruction as destabilizing influences.  The Friedman Proposition should govern even those speculators who derive profits at the expense of other speculators.


1.3.D.2.  Friedman's Criteria Restated.  Milton Friedman subsequently remained unconvinced that Baumol, Kemp, and others had validly demonstrated PDS.


        Speculators can make fluctuations wider...only by selling net when prices would otherwise be low and buying net when prices would otherwise be high.  But this means that they sell at a lower price than they buy and so make losses.  Our model therefore implicitly defines stabilizing speculation as speculation yielding gains...and destabilizing speculation as speculation yielding losses.  (Friedman (1969), p.287)


Friedman also restated the criteria necessary to disprove his conjecture.


        Consider any market in operation.  Suppose that an additional set of transactions are made in the market by an additional group of people whom we shall call `speculators' or `new speculators.'  We shall then deal only with the question whether this additional set of transactions increases the fluctuations in price ... By dealing this way with a change in the amount of speculation, we can avoid the troublesome intellectual problem of defining zero speculation without any loss in generality.  We shall make one further assumption ... that the activities of speculators do not affect the quantities demanded and supplied by other participants in the market at each current price.  (Friedman, 1969, pp.286-287)


    Superficially, Friedman's assumptions lend support to Baumol's first two counter­examples.  In light of Friedman's remarks, we might interpret Baumol's speculators as `new speculators' in an existing speculative market.  However, Friedman maintained in a footnote that Baumol had yet to propose an acceptable counter­example:  `It will be clear that our assumptions rule out the main case (Baumol) considered.  Baumol also considers a special case corresponding to our assumptions.  His own conclusion is ambiguous but only because in judging the profitability of speculation he does not require it to be carried through to completion.' (Friedman (1969), p.287n)

    The price trend terms in Baumol's underlying market excess demand curve continue to be the crux of the objections.  Originally, the model was criticized for depicting `nonspeculators' as speculators.  The models fail to meet the restated criteria, because these same price trends show that the `new group of speculators' have influenced the other market participants' demand, thus violating Friedman's independence assumption.

    Friedman's independence assumption has proven to be the most controversial in the literature.  Krueger (1969), for example, found the assumption implausible and limiting the Proposition's scope.  However, some economists supported Friedman's assumptions.


        The traditional argument is predicated on the assumption that `real' (by which is meant nonspeculative underlying demand and supply) forces dominate the market and that speculative turnover is only a small part of the traded quantity, which can consequently influence only the magnitude, not the direction, of price changes.  (Lipschitz and Otani (1977), p.38)


From the Lipschitz and Otani summary, Baumol's `nonspeculative' excess demand functions, which Friedman and others consider speculative, cannot drive the cyclical price movements without violating Friedman's criteria.  Therefore, even models examining `new speculative' effects must still distinguish between the speculators and nonspeculators:  the models must assure that only real forces predominantly determine price movements.

    If we have correctly analyzed Friedman's restated criteria, then we once again face the old conundrum of differentiating between speculators and nonspeculators.  We recommend avoiding this difficulty by separating traders using the per se distinction.  Considering price trends or past prices is not equivalent to buying with the intent to resell.



1.4.  Categories of Counter­examples


1.4.A.  Pre-Modern Depictions of PDS


Numerous authors have proposed counterexamples to the Friedman Proposition; each author envisions his own market conditions that create opportunities for profitable destabilizing speculation.  The interested reader may want to contrast some of the works in this section with the modern contingent claims example in Section 1.4.B.


1.4.A.1.  Panic-Stricken Central Bank Counterexample.  Stein (1961) proposed a narrative counter­example concerning the vulnerability of a central bank's foreign currency reserves to speculative attacks.  Suppose a central bank purchases some speculative group's supply of foreign currency (presumably for balance of trade reasons).  After acquiring the foreign currency, the central bank becomes panicked over its depleted home currency reserves and devalues it.  Following the devaluation, the speculators buy back the home currency at a profit.  The speculators apparently profited at the expense of exchange rate stability.

    The difficulty with Stein's counter­example is that when the central bank devalues the home currency, it too speculates.  Stein's counter­example depicts a zero-sum game:  the private speculative gains equal the central bank's (the public's) losses.  The central bank's reaction to the speculative sales, rather than the speculators' activity, creates the opportunity for profits and destabilizes the exchange rates. 

    Stein's proposed counter­example is important in another respect.  His work illustrated how profit-earning speculators may cause government policies to be reshaped in such a way as to destabilize markets more than if the government did not intervene.  In private correspondence, Professor Friedman told me that, in retrospect, he perhaps envisioned such misguided intervention when he included the qualifier `in general' in the Friedman Proposition.  Only coordinated and concerted intervention by the G7 central banks has proven successful in fending off speculative attacks on currency reserves.


1.4.A.2.  Lagged Trader Responses Counter­example.  Williamson (1972) suggested a second counter­example based on traders' lagged responses to exchange rate changes, the so-called `J-curve' reaction.  Recall from the discussion of the Marshall-Lerner condition in Section 1.3.B that a country's currency appreciation would in the short run raise the value of that country's exports; while in the long run, decreased foreign demand for that country's goods and services would actually reduce its net trade balance.

    Suppose a country's period 0 exchange rate rests in equilibrium at .  In period 1 a group of speculators begins selling, for whatever reason, domestic currency.  The speculative transactions lower the exchange rate to  and induce a balance of payments deficit.  Importers of that country's goods and services have relatively inelastic short-run demand, since many of these orders have been fixed by legal contract.  They will attempt to purchase the same quantity of goods and services at the new high exchange rate prices.  Thus foreign trading partners must purchase these domestic goods with more units of foreign currency, which tends to depress the value of their own currencies further.

    However, in period 2, Williamson's clever speculators realize that long-term forces will eventually raise the country's exchange rate again.  When the exchange rate drops to , Williamson's speculators begin buying up the domestic currency's commercial excess supply.  The long-term forces combine with the speculators' purchases to raise the exchange rate to

    If Williamson's proposed speculative behavior recurs, the exchange rate will oscillate about its equilibrium moving from  to . Speculators earn positive profits - buying low at  and selling high at  - yet their actions destabilize the exchange rate.  Williamson's speculators exploit profits from traders who determined their volume of exports and imports for nonspeculative reasons, based on advanced legal contracts to trade or based on commitments from experience with the equilibrium rate of . 

    As Price and Wood (1974) note, this general profit-making opportunity relies on a dichotomy in forecasting ability (or intelligence) among the profit-earning speculators and the other market participants.  These other traders cannot forecast when long-term influences will affect the exchange rates as well as Williamson's speculative group.  Levin (1983) extended Williamson's model to a rational expectations framework and obtained results indicating that unanticipated real disturbances can lead to overshooting.  Furthermore, Levin found that capital immobility may lead to exchange rate fluctuations around long run equilibrium values due to exchange rate lags behind changes in the balance of trade.

    Additional work on the rational expectations theme by Canzoneri (1984) has shown that even for unpegged exchange rates, if a speculator expects `other market participants' to react to gold price fluctuations, then he too will consider the price of gold in deciding his demand and supply quantities.  When enough speculators behave this way, then gold price changes will indeed affect the prevailing exchange rates, thus fulfilling the speculators' destabilizing beliefs.

    Under the `new' macroeconomic approach, Canzoneri's policy prescription occasionally may run counter to the present interventionist philosophy of leaning against the wind.


        If the exchange rate rises above its long run equilibrium value it must be forced down; an appreciation must be engineered.  `Rational' portfolio managers will foresee this appreciation and raise their demand for money; the (real) supply of money must be increased to accommodate this new demand.  Put another way, the monetary authority must accommodate the demand for money that is consistent with the expected appreciation or depreciation that moves the exchange rate in the desired direction.  (Canzoneri, 1984, p.76)


The correct policy may sometimes call for accommodation:  a currency depreciation should be met with an increase in the money supply.

    We conclude from the work of Williamson (1972) and Price and Wood (1974) that institutional constraints in the foreign exchange markets can permit profitable destabilizing speculation.  Speculators in these works take an exchange rate out of equilibrium by selling their carry-over stock, and then later buy back when the exchange rate has fallen still farther.  Their actions cause the exchange rate to oscillate around its long run equilibrium value while the speculators earn profits.  Moreover, Canzoneri (1984) has shown that when enough speculators believe gold prices, or other extrinsic factors, influence foreign exchange rates, their behavior leads to a self-fulfilling equilibrium.


1.4.A.3.  Giffenesque Good Counter­example.  Kemp (1963) proposed a counter­example based on excess demand for a Giffen good.  The `nonspeculative' excess demand is a function of current price `and to embrace seasonal, trend, and purely random factors, time itself.'  (Kemp (1963), p.185).  Thus Kemp's nonspeculative demand has the form, N[P(t),t].5

    Figure 1.2 shows the excess demand for a  typical Giffen good.   and  are stable equilibria;  is an unstable equilibrium.  Suppose N(P) depicts a market's excess demand, and the price rests at the equilibrium value .  Speculators enter the market, begin buying up the commodity, and shift the market excess demand from N(P) to N(P)+S.  Eventually, the price would settle at   However, the speculators withdraw from the market when the price exceeds .  The excess demand reverts back to N(P), but the price continues to rise until it reaches equilibrium at




















Figure 1.2.  Kemp's (1963) Model


    At this point, Kemp's speculators now sell their inventory holdings, which they purchased at prices less than or equal to   The speculators enter the market as sellers on curve N(P)-S.  Again, it appears the price would settle at .  However, after the price drops below , the speculators withdraw from the market.  The excess demand reverts back to N(P); the price falls to .  In fact, the price has now completed a cycle.  Kemp's speculators bought the commodities at prices below or equal to  and sold them at prices above or equal to :  the speculators profited.  By shifting the N(P) curve away from its   equilibrium, Kemp's speculators also destabilized the market.

    The principal objection to Kemp's counter­example concerns the functioning of a tâtonnement process.  In general, traders can only purchase and sell the commodity at the points , and .  Kemp's speculators seem to transact outside equilibrium, before the Walrasian auctioneer arrived at a market-clearing price.


1.4.A.4.  Multiperiod Buy-Low, Sell-High Counter­example.  Consider now a fourth counter­example with changing  preferences over time.  Let   denote an element of a speculative sales vector and  the corresponding speculative transaction price.  Define the speculative profits by    The MSSD for a particular speculative transaction is  given  by  where  is the average or mean speculative transaction price.  Let  denote the MSSD without the speculative transaction.

    Suppose market excess demand for some good across three periods is given by:  N1 = P1 - 30 - 5Q1,  N2 = P2 - 40 - 5Q2,  N3 = P3 - 50 - 2Q3, where Qi denotes the equilibrium quantity transacted in period i.  Market clearing requires zero excess demand.  Therefore, the economy has equilibrium prices of P1 = 30, P2 = 40, and P3 = 50.  The mean price is 40 and the  would equal 200/3.

    If a speculator buys 1 unit of the good in period 2 and sells it in period 3, the new equilibrium prices would be P1 = 30, P2 = 45, and P3 = 48.  In this case  = (48 - 45) > 0 and  186/3 < .  Therefore, the speculation is both profitable and stabilizing.

    If the speculator instead sells 1 unit in period 2 and repurchases it in period 3, the equilibrium price vector will be (30, 35, 52).  In this case , but  = (35 - 52) < 0.  Thus the destabilizing speculation has also been unprofitable, just as the Friedman Proposition would predict.  Note that the excess demand curves in this illustration exhibit different slope intercepts (if plotted on price-quantity axes) and different slopes, reflecting changes in demand elasticities.

    Now consider the following modification.  The excess demand for the good across the three periods is  N1 = P1 - 30 - 5Q1, N2 = P2 - 40 - 8Q2,  N3 = P3 - 50 - 1Q3.  Only the slopes in time periods 2 and 3 have changed.  Therefore, P1 = 30, P2 = 40, and P3 = 50 are still the market clearing prices, 40 is still the mean, and  = 200/3.  If a speculator buys 1 unit in period 2 and sells it in period 3, the new equilibrium prices would be  P1 = 30, P2 = 48, and P3 = 49.  In this case  = (49 - 48) > 0,  but  229/3 > .  Thus we have shown a counter­example in which speculation is profitable yet destabilizing.


1.4.A.5.  Class of Nonlinear Excess Demand Counter­examples.  For some twenty years, a theorem circulated in the speculation and stability literature that models containing linear excess demand curves were sufficient to validate the Friedman Proposition.  In contrast, nonlinear excess demand curve models were thought to generate PDS counter­examples.  This proposed theoretical limitation began when Kemp suggested if `the nonspeculative (excess) demand is linear in price and contains a component dependent on time only, profitable speculation cannot fail to be stabilizing....'  (Kemp (1963), p.189)  Note that our multiperiod counter­example in the preceding section immediately contradicts this assertion.

    Farrel (1966) followed Kemp's lead and emphasized Friedman's independence assumption.


        In the absence of transactions costs linearity (in price) of the nonspeculative excess demand function is a sufficient condition for the validity of the basic proposition...In markets where the independence assumption holds and where transaction costs are large enough to cover actual departures from linearity of the nonspeculative excess demand function, the basic proposition holds.  (Farrel (1966), p.192)


Since these assumptions - independence from past speculative activity and price linearity - severely restricted his model, Farrel concluded that his analysis had limited value.  `But ... this paper will not have been wasted if it has persuaded economists that our basic proposition is too strong to hold with any great generality and that they should therefore seek to establish weaker propositions concerning the properties of speculative markets.'  (Farrel (1966), p.192)

    Schimmler (1967) simplified and unified Kemp's and Farrel's proofs using a Hilbert space.  Lien (1984) found an error in these proofs that permitted us to generate the counter­example in Section 1.4.A.4.  Lien showed that the linear excess demand curve theorem is valid only when the slopes of the excess demand curves do not change.

    Schimmler (1967) went on to develop an entire class of counter­examples based on nonlinear excess demands.  Unfortunately, his class of models lack intuitive appeal, such as `buy on the upswing, sell on the downswing.'  Given the nonlinear excess demand curves in Baumol's and Kemp's counter­examples, it is not too difficult to imagine problems that these curves might create for the Friedman Proposition.  The derivation would also distract the reader for several pages just to establish the Hilbert space framework.  Therefore, we have placed the derivation of this class of counter­examples and the proof of the linear excess demand curve theorem in Appendix C.


1.4.B.  Modern Uncertainty Theory Counter­example


    Salant (1974) proposed a counter­example incorporating speculative carry-overs in economies with stochastic endowments.  Only the speculator has carry-over facilities.  Consider a consumer's planning problem in a two good, two period economy.  The individual has known current endowments of the two goods () and random future endowments  depending on whether it rains, , or shines, .  If the consumer had carry-over facilities, he might store part of his current endowment,  and , for consumption in the next period.  The consumer's present and future consumption would then be   

    Suppose the consumer expects rain with probability  and has a separable utility function which permits us to write his expected utility as



where  and  are concave, increasing functions, and  is a constant.  The first order condition that emerges from maximizing expected utility with respect to  is:


This expression describes the optimal quantity of good  to carry-over and the second expression shows the consumer's indifference to good   carry-overs.  Therefore, treat good  as a numeraire and set its price equal to one.  The consumer would then desire to equate his marginal utilities from present and future consumption.

    However, suppose the consumer cannot carry-over either good.  Instead of treating consumption as a dynamic programming problem, the consumer simply maximizes utility separately in each period.  In period 1 the consumer maximizes utility subject to an income constraint:


where  is the associated Lagrange multiplier and Y is his income.  The emerging optimality condition equates the marginal rate of substitution with the price ratio,

    In period 2 the individual again maximizes utility subject to an income constraint:


with corresponding optimality condition   If the speculator transports  of good X into the next period and sells it, then in period 1 the price of X will be   Similarly, in period 2 the good X price conditional on each state, rain or shine, will be    and    with probabilities   and , respectively.  The speculator expects to receive profits   given by


    How does speculative carry-over affect the random period 2 price?  If  the consumer's inverse demand curve, , is concave.  Any speculative carry-over will always increase the price variance.6  With concave and therefore increasingly steep demand, speculative carry-over, , widens the spread between good X's conditional prices for  each state  of the world.  See Figure 1.3.  Thus for any set of prices for which   > 0, speculative carry-over can increase some good's price variance.





















Figure 1.3.  Concave Market Demand Curve



1.5.  Brief Empirical Overview on Destabilizing Speculation


1.5.A.  Econometric Tests


One of the first theoretical PDS counter­examples contained the warning:  `The effects of profitable speculation on stability is in part an empirical question and ... attempts to settle it by a priori arguments must somewhere resort to fallacy.'  (Baumol (1959), p.302)  Although one might have expected the empirical tests of Friedman's Proposition to employ data on stock market speculation, the empirical work in this area has primarily used exchange rate data.  The empirical tests have yielded inconclusive results.  Frequently the research confirms that a speculative group earned profits and simultaneously stabilized prices.  However, these findings fail to disprove any of the counter­examples or theoretical limitations to the Friedman Proposition.  Representative works on both sides of the Proposition include Arndt (1968) and Kenen (1975).

    Arndt's study indicated that speculators in his sample from the Canadian foreign exchange probably follow the logic in Friedman's Proposition.  Arndt concludes, ``In a stable environment ... our theory predicts - and the data tentatively support this conclusion - that speculators' expectations will be a slowly changing variable with considerable inertia, and that speculative sales and purchases will have a dampening effect on movements in the exchange rate.''  (Arndt, 1968, p.69)

    On a more ambiguous note, Kenen (1975), in examining speculation under different exchange regimes, found no uniform data to support the conclusion that profit-earning speculators generally stabilize prices.  `Although long lags and high elasticities appear to amplify instability, we cannot conclude from (its profitability) that speculation is indeed stabilizing.'  (Kenen, 1975, p.134)

    The empirical work as a whole - as might be expected from the theoretical difficulty in isolating when a speculative group has transacted - has not provided conclusive evidence one way or the other for the validity of the Friedman Proposition.  Overall, one senses a reluctance among the econometricians who examined this relationship to categorize professional (and presumably profitable) speculation as a stabilizing influence.


1.5.B.  General Comments on Foreign Exchange Rate Stability


In the opening paragraphs of this chapter we pointed out that speculation must be profitable over time, or the losses from speculative activity would be a self-correcting problem:  the destabilizing speculators would fail to survive in a Darwinian sense.  It is of some interest then to examine how speculation has generally been perceived to influence the stability of foreign exchange markets.  Exchange rate forecasters were initially optimistic that free market speculation would attenuate exchange rate fluctuations.

    In the early 1970s when countries first adopted flexible exchange regimes, the initial swings in exchange rate values were thought to be ``what one might expect during a learning period, when speculators' views regarding long-run equilibrium values are weakly held and substantial stimulus is therefore required to make them act on them.''  (Whitman, 1975, p.138)

    After many years experience with flexible regimes, the prevalent view shifted to some disillusionment that the exchange rate mechanism may have inherent instabilities spawned by professional speculation.


        The focus of attention then shifted to market imperfections, including insufficiency of stabilizing speculation, as the cause of the volatility that characterized real world exchange rates.  But, with the passage of time, an explanation of these imperfections as temporary phenomena characteristic of a transition period became less and less credible.  (Whitman, 1984, p.300)


    Economists have thus recognized that professional (profit-earning) speculation does not necessarily stabilize foreign exchange markets, and at least some have attributed enhanced volatility to this same speculation.



1.6.  Conclusions and Future Research


We have reexamined the proposition that speculators buy low and sell high, and thus tend to stabilize market prices.  Although this proposition dates back to the Nineteenth Century, the proposition was given new life in the 1950s when Milton Friedman endorsed it to support the adoption of flexible exchange rates.  However, Friedman carefully restated the proposition in terms of `new speculators' and the reaction of `other market participants.'  This restatement seemed more closely tailored to real world conditions.

    Baumol challenged Friedman's assertion by proposing counter­examples that depict an early portrayal of `overshooting.'  The gist of Baumol's counter­example is that (some fraction of) speculators wait until after the trough and peak of a cycle, so that they wind up buying on the upswing and selling on the downswing of the cycle.

    Comments on the technical features of Baumol's model raised questions about the restrictions under which the Friedman Proposition would be valid.  These criteria include minimal, if any, effect on other market participants by the speculative group under consideration.  Baumol's work illustrates one group of speculators profiting at the expense of another speculative group, not unlike everyday transactions in capital and foreign exchange markets.

    The international exchange markets have particular institutions that may yield theoretical possibilities for profitable destabilizing speculation:  intervention by monetary authorities, `J-curve' time-delayed reactions, and overshooting.  The empirical literature has found evidence of both stabilizing and destabilizing speculation without providing conclusive evidence of speculation which is simultaneously destabilizing and profitable.  Indeed some of the initial optimism for flexible exchange regimes voiced by economic theorists and forecasters in the 1960s and early 1970s gave way to disillusionment in the wake of foreign exchange instabilities under flexible rates.

    The 30% crash in the Dow Jones Industrial Average over October 16 -19, 1987, has shown that endogenous influences can cause greater instabilities in the market than even external factors.  Panic buying and selling can lead to further panic, or trigger computer-driven program trading.  If such speculative behavior were on the whole unprofitable, then it would not be expected to recur.  Those speculators who panic and lose capital would be part of a self-correcting problem.  Yet new constraints imposed to limit program trading, such as the New York Stock Exchange's "uptick rule," show concern for this ongoing form of destabilizing speculation.  So we are left with a proposition that has engendered valid theoretical counterexamples and some anecdotal evidence to the contrary on inherent foreign exchange instability and program trading.



Appendix A:  Outline of Baumol's Difference Equation Model


In his first counter­example, Baumol proposed that some `nonspeculative' group creates a cyclical path for a commodity's price over

time.  To represent the time path, Baumol constructed a sinusoidal second-order difference equation,


                                         9                               (A.1)




where  and  are constants, with ** < 1.  Applying the quadratic formula permits us to recast this equation in a more familiar sinusoidal form.  In the homogeneous equation,


let  = 1,  = -2, and  = 1.  Substituting these values into the formula for the solution of a quadratic equation yields


and note .  Let  be some angle such that  then


The general solution for  from this equation is







Let  , and R denote the mean price level.  To derive the value of  in terms of   and  from equation (A.1), set , a constant, for all .  Substituting this value into (A.1) yields

 and solving for  leads to  . Therefore  in equation (A.1) can be expressed as


This result clearly illustrates equation (A.1)'s sinusoidal characteristics.  We can verify that  is the mean price level by evaluating (A.2) at its peak, , and at its trough,   .  These two prices sum to 2, and the mean price is therefore .

    Baumol then constructs a `nonspeculative' or underlying excess demand from (A.1):


                                   10                         (A.3)




where  is a constant, and  is a positive constant.  Current price and recent price trends, as evinced by the lagged prices in (A.3), influence Baumol's nonspeculative excess demand.

    Baumol next specified a speculative excess demand function given by


where C is a positive constant.  If  is the price immediately following a trough, then these speculators have positive excess demand.  Similarly, the speculators wish to sell immediately after a peak.

    In equilibrium the speculative and nonspeculative excess demand functions must sum to zero:    Summing equations (A.3) and (A.4), expressed in period t, yields


And the solution for 207 is


                               11                     (A.5)





    Since equations (A.5) and (A.1) have the same form, (A.5) is also sinusoidal.  Furthermore, the price expression in (A.1) must also solve (A.4), the speculative excess demand function.  With this basic construction, Baumol then illustrated that maximum speculative pur-chases  immediately  follow  the  trough,  while  maximum  sales immediately  follow the peak.  Consider (A.1) evaluated at period :    Substituting this value of  into equation (A.4) produces


Since  is a constant with ** < 1, we may rewrite the equation as  where  is a constant, and  is a positive constant.

    This latter equation incorporates speculative sales after a peak and purchases immediately following the trough `since it states essentially that speculative excess demands fluctuate inversely with prices one period earlier (note the time subscripts of  and ).'  (Baumol (1957), p.266).  Baumol's speculators profit from this activity, since the prices at which they sell exceed those at which they purchase.



Appendix B:  Derivation of Baumol's `Real' Model's Solution


In equilibrium supply equals demand (), so that , and , where   The equilibrium cum speculation is the same as before, but nonspeculative excess demand is represented by the difference between demand and supply:  , where  is expressed in equation (1.8) from the second counter­example.  Substituting for D and  in the latter equation yields,


and solving for ,


which can be rewritten as


where  are constants.  This solution for  and the corresponding value for  can again be substituted into equation (1.10) to obtain the following third-order differential equation:


                                   12                         (B.1)




    Based on this result Baumol asserts that the preceding equation has at least one real root, which must be positive since the terms in equation (B.1) alternate in sign.  `It follows that the time path of prices is changed by speculation from a cyclical pattern of constant amplitude into an unstable, explosive movement.'  (Baumol (1957), pp. 269-270)

    We will first derive the homogeneous solution for equation (B.1):

Let , and substituting in the latter equation yields,

  Next, by dividing through by  and simplifying the equation becomes

                                       = 0

                                       = 0

                                            = 0

                                        = 0,

with solutions  and .  Therefore, the third-order differential equation has a solution


                                 15                       (B.2)

where  and  are constants.



Appendix C:  Schimmler's Hilbert Space Model.


Let  denote a speculative excess demand vector and   the `nonspeculative' or existing excess demand.  Equilibrium price vectors with and without this speculation are denoted by  and , respectively.  Requiring the speculators to realize their profits implies that the speculative transactions must sum to zero, or more formally,  where  is a vector of unity elements.7  By convention, speculative profits,  have a negative sign to indicate that net sales are negative while purchases are positive.

    The MSSD for price vector P is denoted    where   To measure stability, define

 When  is positive, the speculative activity has stabilized prices.  Friedman proposed that  implies

    Farrel (1966) made the nonspeculative excess demand independent of the speculative activity by assuming that the price spread, , is a function of  alone:  .  Schimmler (1967) extended Farrel's results to temporal independence:


This seemingly innocuous assumption turns out to be pivotal to the analysis that follows.  It turns out that only linear excess demand schedules follow condition (C.1).8

    Schimmler denoted centralized vectors with an asterisk, e.g.,  where  is the mean element of .  Thus   .  Consider now the inner product of    and  :




                                            = 0.

Since  Schimmler maintained


where  is some real valued function.  When  > 0, speculative purchases increase the spread between  and .  As Schimmler noted, equation (C.2) `shows the difference between  and  is a linear function of  with temporally independent slope and temporally independent constant term.'  (Schimmler (1967), p.113).

    Schimmler's work also defined an entire class of counter­examples based on excess demand curves that are nonlinear in price.  We begin by defining the product of T and c:






                                  =                                            (C.3)

                                  =                                       (C.4)

    If  does not follow the linear relationship in (C.2), then there exist two vectors  and , such that  > 0 and c < 0.  Let    denote a vector linearly independent from .  In the plane spanned by  and , the two half-planes




have a nonempty intersection.  A vector  can be selected from   so that


    From the definition of H(S) in (C.1), it follows that


Let  then     can then be defined by


Recall from (C.3) that



from the definition of the half-plane A in (C.5).  The speculative profits are




This latter expression is positive since  and thus the properties of the half-plane B in (C.6) hold as well.  Thus the speculation has been profitable and destabilizing, or more succinctly  while .



1. Mill (reprinted 1921, at pp. 707-708) stated,  `When a speculation in a commodity proves profitable to the speculators as a body... their purchases make the price begin to rise sooner than it otherwise would do, thus spreading the privation of the consumers over a longer period, but mitigating it at the time of its greatest height...[I]t often happens that speculative purchases are made in the expectation of some increase of demand, or deficiency in supply, which after all does not occur, or not to the extent which the speculators expected.  In that case the speculation, instead of moderating fluctuations, has caused a fluctuation of price which otherwise would not have happened, or aggravated one which would.  But in that case the speculation is a losing one...[A]nd though (speculative transactions) are sometimes injurious to the public, by heightening the fluctuations which their more usual office is to alleviate, yet whenever this happens the speculators are the greatest losers.'


2. See, e.g., Dulles (1929).


3. Kemp illustrates this point more rigorously as follows.  If the price follows a regular sine path,    the cycle has period    and frequency . The price has MSSD equal to    and note    Thus a change in the amplitude  has no impact on the MSSD.


4. The literature has more frequently noted Baumol's concession than his defense of this general theme of buying on the upswing and selling on the downswing.  Compare Logue (1975), Glahe (1966), Krueger (1969), Farrel (1966), Johnson (1976), and Telser (1981); with Kemp (1963), Baumol (1965, pp.17-31), and Eichengreen (1982).


5. Speculation, as differentiated from arbitrage, only occurs under uncertainty.  Modern uncertainty theorists would explicitly define the variable adding randomness to a model, e.g., the state of the world, not merely append uncertainty to the passage of time.


6. The only instance where carry-over would not increase the price variance is if Xr = Xs.


7. Schimmler's model incorporates time-dependent variables expressed as vectors in the -dimensional Euclidean space, .  Alternatively, his model could be formulated with functions of time, such as Kemp (1963), using measurable and Lebesgue square-integrable functions in the Hilbert Space .  The scalar or inner product  of the vectors  and   would thus be defined by  in the  and by  in the .


8. This point is due to Lien (1984).



Arndt, Sven W., (1968), `International Short Term Capital Movements:  A Distributed Lag Model of Speculation in the Foreign Exchange,' Econometrica, Vol. 36, pp. 59-69.


Baumol, William J., (1957), `Speculation, Profitability, and Stability,' Review of Economics and Statistics, Vol. 39, pp. 263-71.


-----, (1959), `Reply,' Review of Economics and Statistics, Vol. 41, pp. 301-302.


-----, (1965), The Stock Market and Economic Efficiency, New York:  Fordham University Press.


Canzoneri, Matthew B., (1984), `Rational Destabilizing Speculation and Foreign Intervention Policy,' Journal of Macroeconomics, Vol. 36, pp. 59-89.


Dulles, Eleanor Lansing, (1929), The French Franc 1914-1928, New York:  MacMillan Company.


Eichengreen, Barry J., (1982), `Did Speculation Destabilize the French Franc in the 1920s?,' Explorations in Economic History, Vol. 19, pp. 71-100.


Farrel, M. J., (1966), `Profitable Speculation,' Econometrica, Vol. 33, pp. 183-93.


Friedman, Milton, (1953), `The Case for Flexible Exchange Rates,' in Essays on Positive Economics, Chicago:  University of Chicago Press.


-----, (1969), `In Defense of Destabilizing Speculation,' reprinted in The Optimum Quantity of Money and Other Essays, Chicago:  Aldine Publishing Company.


-----, (1971), `The Need for Futures Markets in Currencies,' in The Futures Market in Foreign Currencies, Chicago:  Chicago Mercantile Exchange.


Glahe, Fred R., (1966), `Professional and Nonprofessional Speculation, Profitability, and Stability,' Southern Economics Journal, Vol. 33, pp. 43-48.


Hart, Oliver D., (1984), `Price Destabilizing Speculation,' Working Paper 84/92, International Center for Economics and Related Disciplines, London School of Economics and Political Science.


Jesse, Richard R., Jr., and Radcliffe, Robert C., (1981), `On Speculation and Price Stability Under Uncertainty,' Review of Economics and Statistics, Vol. 63:1, pp. 129-32.


Johnson, Harry, (1976), `Destabilizing Speculation: A General Equilibrium Approach,'  Journal of Political Economy, Vol. 84, pp. 101-108.


Kaldor, Nicholas, (1963), `Speculation and Economic Stability,' Review of Economic Studies, Vol. 40, pp. 1-27.


Kemp, Murray C., (1963), `Speculation, Profitability, and Price Stability,' Review of Economics and Statistics, Vol. 45, pp. 185-189.


Kenen, Peter B., (1975), `Floats, Glides, and Indicators,' Journal of International Economics, Vol. 5, pp. 107-51.


Kohlhagen, Steven W., (1979), `The Identification of Destabilizing Foreign Exchange Speculation,' Journal of International Economics, Vol. 9, pp. 321-40.


Krueger, Anne O., (1969), `Balance of Payments Theory,' Journal of Economic Literature, Vol. 7, pp. 1-26.


Levin, Jay H., (1983), `The J-Curve, Rational Expectations, and the Stability of the Flexible Exchange Rate System,' Journal of International Economics, Vol. 15, pp. 239-251.


Lien, Donald, (1984), `A Note on the Nonspeculative Excess Demand Theorem,' Social Science working paper series, California Institute of Technology.


Lipschitz, Leslie and Otani, Ichiro, (1977), `A Simple Model of the Private Gold Market, 1968-1974:  An Exploratory Econometric Exercise,' International Monetary Fund, Vol. 24, pp. 36-63.


Logue, Dennis E., (1975), `Market-making and the Assessment of Market     Efficiency,' Journal of Finance, Vol. 30, pp. 115-23.


Mill, John Stuart, (1921, reprinted) Principles of Political Economy, Book IV, Chap. 2, Sec. 5, London:  Longmans, Green, and Co.


Obst, Norman P., (1967), `A Connection Between Speculation and Stability in the Foreign Exchange Market,' Southern Economic Journal, Vol. 34, pp. 146-49.


Price, Lionel D. D., and Wood, Geoffrey E., (1974), `Another Case of Profitable Destabilizing Speculation - A Note,' Journal of International Economics, Vol. 4, pp. 217-20.


Ross, James A., Jr., (1938), Speculation, Stock Prices, and Industrial Fluctuations, New York: Harcourt, Brace, and Jovanovich.


Schimmler, Jorg, (1967), `Speculation, Profitability, and Price Stability -A Formal Approach,' Review of Economics and Statistics, Vol. 49, pp. 110-114.


Stein, Jerome L., (1961), `Destabilizing Speculative Activity Can Be Profitable,' Review of Economics and Statistics, Vol. 43, pp. 301-02.


Salant, Stephen, (1974), `Profitable Destabilizing Speculation,' unpublished manuscript, Board of Governors of the Federal Reserve, Washington, D.C.


Telser, Lester G., (1959), `A Theory of Speculation Relating Profitability and Stability,' Review of Economics and Statistics, Vol. 41, pp. 295-301.


-----, (1981), `Why There Are Organized Futures Markets,' Journal of Law and Economics, Vol. 24, pp. 1-22.


Whitman, Marina v.N., (1975), `The Payments Adjustment Process and the Exchange Rate Regime:  What Have We Learned,' American Economic Review, Vol. 65, pp. 133-46.


-----, (1984), `Assessing Greater Variability of Exchange Rates:  A Private Sector Perspective,' American Economic Review, Vol. 74:2, pp. 298-304.


Williamson, John, (1977), `Another Case of Profitable Destabilizing Speculation,' Journal of International Economics, Vol. 2, pp. 77-84. 



I am grateful to Michael Guth for his useful summary of the discussion, and for providing me the opportunity to add a few words.  More than thirty years have elapsed since I left the controversy over the possibility that profitable speculation can be destabilizing.  The length of that interval certainly suggests obsolescence and reduces my qualifications for reentry into the fray.  Nevertheless, I remain convinced that speculation need not always be stabilizing to be profitable, and that the counterexamples I have supplied are perfectly legitimate.

    Two comments may perhaps help the reader to see why I am not moved by my critics.  The first deals primarily with the behavior of nonspeculators.  Let me suggest that the critics struggled to escape their trap through resort to semantics, but that, of course, will never do.  They argued that my `nonspeculators' were really speculators, because they were (subconsciously?) taking more than one period's prices into account.  This is surely an odd requirement for someone to qualify as a nonspeculator.  Is there any mentally competent adult buyer or seller of anything who has never compared past and present prices?  Yet, let me show that even with such a tortured use of the word it is easy to reinterpret my models to contain only two groups, one unambiguously composed of speculators and the other of persons absolutely free of that taint.

    For this purpose, assume that the second group is made up entirely of persons who simply put cash into the market when they happen to receive it, and withdraw it whenever they happen to need it for exogenously-determined transactions purposes.  They put it into the market to avoid the expected interest or dividend opportunity costs that would be incurred by keeping the money idle in the form of cash between the date of its receipt and the day it will be spent.  These totally passive investors-disinvestors are surely not `speculators' by any definition remotely related to standard use of language, and their purchases and sales of securities are determined fully from outside the model, with absolutely no consideration of any security prices, past, future or even present.  Now suppose that the exogenous forces happen to lead to investments and withdrawals whose time path would entail cyclical security-price behavior in the absence of speculator activity.  There you have my models, and my conclusions surely follow, exactly as before.

    Second, let me turn to a question that has been raised about the postulated behavior of my speculators.  Why do I assume that speculators sell just after the downturn and buy just after the upturn?  How can this assumption constitute a plausible element in my counterexamples?  Two reasons.  First, in an uncertain world, if prices have been rising monotonically, how else can a speculator (who, like the rest of us, cannot really foresee the future) be guided systematically to select dates at which he has some confidence that the expansion phase of the price cycle is coming to an end?  How else can that person hope to judge when the market has hit bottom?  Surely, it is not unreasonable to wait until prices actually show some manifestation of the beginnings of a downturn or the start of an upturn.

    There is another reason why this is not an implausible story.  For I have spoken to some speculators, and they have told me that this is how they actually behave.  That is not to claim that all speculators do so, or even that a substantial proportion do so always, but only that the assumption seems to me far more plausible than the one implying that speculators regularly manage to sell exactly at the top and buy just at the bottom.  In any case, since as Kemp noted, my goal is just to provide counterexamples, it is hardly necessary for me to offer a universally-accurate depiction of speculator behavior.


W. J. Baumol

C.V. Starr Center for Applied Economics

New York University   





This chapter shows that controversy still remains about whether speculation under the floating exchange rate system is stabilizing or destabilizing.  My own work on the subject (Journal of International Economics, November 1983) dealt with the implications of the J-curve for the stability of floating exchange rates.  The J-curve is the empirical phenomenon in which a depreciation of the home currency initially causes a trade deficit to widen because of the immediate upward pressure on import prices with no initial impact on trade volumes.  The latter respond only with a lag to the exchange rate movement.  Consequently, over time import volume declines and export volume expands, and the trade deficit eventually begins to move in a desirable direction.  Ultimately, the depreciation will cause the trade deficit to shrink, but the dynamic response of the trade deficit resembles the letter J tilted sideways.

    The implication of the J-curve for floating exchange rates should now be obvious.  A depreciation of the home currency initially causes the trade deficit to expand, and one might then expect the currency to depreciate even further in response.  In turn, the J-curve reaction would produce an even larger trade deficit and therefore a downward spiral of the currency.  In this scenario, the floating exchange rate system becomes completely unstable.  In my work on this subject, I introduced speculators with perfect foresight into the system but allowed them to be risk averse.  Three conclusions emerged from the analysis.  First, speculators would stabilize the floating exchange rate system, provided capital mobility is sufficiently high (i.e., speculators are not too risk averse); second, unless the degree of capital mobility exceeds an even higher critical level, exchange rates will oscillate around their long-run equilibrium values; and third, a real unanticipated disturbance will cause the exchange rate to overshoot its long-run equilibrium level.

    The first conclusion is the most important one for this discussion, because it suggests that the J-curve will not be a source of instability for floating exchange rates provided speculation is sufficiently sensitive to prospective exchange rate movements.  In the limiting case, if speculators were risk neutral, the exchange rate would be completely stabilized by speculation.  No cycles would occur.  Real disturbances would cause the exchange rate to move immediately to its new long run equilibrium level.

    These conclusions are very sanguine for the stability of floating exchange rates in the presence of speculation.  They suggest that the more speculation the better and that the imposition of capital controls is likely to be a disruptive element to a well functioning floating exchange rate system.  Moreover, although this chapter shows that a number of counter­examples have been developed in the literature suggesting that destabilizing speculation can be profitable, many of them rest on collusive behavior on the part of speculators or other unrealistic assumptions.  This suggests to me that the Friedman proposition that speculation will be stabilizing in the long run is a very plausible one, although the argument that professionals could feed off of a revolving group of amateurs and that the group as a whole could be destabilizing is also a plausible one to me.  Nor do these arguments tell us much about the possibility of speculative bubbles.  These questions can be resolved only by considering empirical tests on speculation.

    My own view is that we know very little about the stabilizing or destabilizing nature of speculation from the current body of empirical work.  There is some evidence [Froot and Frankel (1989) and Takagi (1991)] that speculators in the major currencies may be very close to being risk neutral but that their expectations may not be rational.  To the extent that speculators make systematic errors in their forecasts of future exchange rates, this could have a destabilizing effect on exchange rates.  The counter-argument is that if speculators form their expectations adaptively or regressively or with distributed lags, as some evidence suggests [Frankel and Froot (1987)], these types of mechanisms are stabilizing.  Moreover, some evidence suggests that speculators with short-term horizons may be destabilizing and those with long-term horizons may be stabilizing [Frankel and Froot (1990)].  Finally, there is little empirical evidence on the existence of speculative bubbles.  These conclusions, however, are tentative and require further empirical confirmation.


Jay H. Levin

Department of Economics

Wayne State University




Frankel, Jeffrey A., and Kenneth A. Froot, (1987), `Using Survey Data to Test Standard Propositions Regarding Exchange Rate Expectations,' American Economic Review, March 1987.


Frankel, Jeffrey A., and Kenneth A. Froot, (1990), `Chartists, Fundamentalists, and Trading in the Foreign Exchange Market,' American Economic Review, May 1990.


Froot, Kenneth A., and Jeffrey A. Frankel, `Forward Discount Bias:  Is It an Exchange Risk Premium?,' Quarterly Journal of Economics, February 1989.


Takagi, Shinji, (1991), `Exchange Rate Expectations:  A Survey of Survey Studies,' International Monetary Fund Staff Papers, March 1981.



Learn more about Jay H. Levin by clicking on the link to his name in this sentence.






*A condensed version of this chapter was originally published in the Rivista Internazionale di Scienze Economiche e Commerciali, Vol. 35:6, June 1988, pp. 523-538.  Permission of the Rivista Internazionale to reprint this article is gratefully acknowledged.

© Copyright 2007 by Michael A. S. Guth. All Rights Reserved. No portion of this site, including the contents of this web page may be copied, retransmitted, reposted, duplicated, or otherwise used without the express written permission of Dr. Michael Guth.