On Risk, Rational Expectations, and Efficient Asset Markets

Board of Governors of the Federal Reserve System International Finance Discussion Papers Number 478

August 1994

ON RISK, RATIONAL EXPECTATIONS, AND EFFICIENT ASSET MARKETS

Guy V.G. Stevens and Dara Akbarian

NOTE: International Finance Discussion Papers are preliminary materials circulated to stimulate discussion and critical comment. References in publications to International Finance Discussion Papers (other than an acknowledgment that the writer has had access to unpublished material) should be cleared with the authors.

ABSTRACT

The notion of asset market efficiency -- that market prices "fully reflect" all available information -- requires the operation of mechanisms that rapidly incorporate new information into asset prices. Particularly problematic -- both theoretically and empirically -- has been the case where new information is net widely shared, so-called "strong-form" efficiency. This paper examines the relevance of a mechanism for attaining strong-form efficiency based on knowledgeable investors being willing to take large positions in order te eliminate unexploited profit opportunities We examine theoretically and empirically, the latter using daily stock market data, the impact of a number of factors on the efficacy of this mechanism: the portfolio size and degree of risk aversion of potential investors, the ability to borrow, and the hedging opportunities

provided by the stock market.

ON RISK, RATIONAL EXPECTATIONS, AND EFFICIENT ASSET MARKETS

Guy V.G. Stevens and Dara Akbarian' I. Introduction

The notion of asset market efficiency -- that market prices "fully reflect" all available information (Fama 1970) -- requires the operation of mechanisms that rapidly incorporate new informaticn into asset prices.” Most empirical evidence is consistent with the hypothesis that markets such as the U.S. stock market possess what is called "weak form" and “semi-strong form" efficiency: that both data on past returns and other publicly available information cannot improve forecasts cf returns [Fama (1970), Abel and Mishkin (1983), Uri and Jones (1990)].* However, when we get to "strong form" efficiency -- the efficient incorporation of information that initially, at least, is not public knowledge -- there is little empirical or theoretical support for rapid convergence to the rational expectations or efficient markets price. It is the contention of this paper that, in assessing the realism of mechanisms that either promote or prevent strong-form efficiency, a key and often underappreciated factor is the effect of risk.

The empirical evidence regarding strong-form efficiency is sparse and, generally, unfavorable [Niederhoffer and Osborne (1966), Fama (1970), Baesel and Stein (1979), and Givoly and Palmon (1985)]. Theoretical support is similarly weak. Almost two decades of research on learning mechanisms, usua!ly under the assumption of homogeneous information, has given only

partial support to the attainment of a rational expectations equilibrium, and that as a long-run

_ The authors are. respectively, Senior Economist and Assistant Economist, Division of International Finance, Board of Governors of the Federal Reserve System. In the paper Stevens was responsible for sections I, II and {V, and Akbarian for data collection, econometric estimation, programming simulations, and the Appendix; section iI was the responsibility of both

We are indebted to our colleagves Pau! Kupiec and Charles Thomas for helpful suggestions and constructive criticism at every stage in this study; our thanks go also to Michael Gavin, David Gordon, William Helkie. George Henry, and seminar p ‘fants at the rederal Reserve Board for heipful comments cn various drafts of the paper. “Dac views »% paper are the auihors’ and should act be interpreted as reflecting those of the Board of Governors of the Federal Reserve System or other members of its staff

* In this paper, foliowing Mishkin (7983), Shiller (1984), and Summers (1986), we will use the terms “rationality” and “efficiency” interchangeably, as weil as the terms "efficient markets price" and "rational expectations price.”

* However, as argued persuasively by Shiller (1984) and, especially. Summers (1986), the same data are also consistent w th significant deviations from rationality.

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limit. Where problems of heterogeneity of information or differences in investors’ abilities to process it are involved, the theoretical results are typically even less favorable for stock market efficiency.” Models developed by Figlewski (1978), Shiller (1984), Haltiwanger and Waldman (1985), and De Long, Shleifer, Summers, and Waldman (1990) all possess solutions where the class of less-informed or less-rational investors prevents the market from realizing the full information, rational expectations price.

Proponents of rational expectations and strong-form efficiency have long recognized that the simple paradigms originally used for support, based on costless and universally available information and a homogeneous class of rational investors, are oversimplified and unrealistic [e.g., Fama (1970), p. 387]. However, at least since Fama (1970), supporters have suggested, if nct developed rigorously, a more realistic alternative model based on the speculative activity of the c.ass of wellinformed or rational investors. A clear statement of the nature of this model or mechanism can be found in Mishkin (1983):

"Second, this [rational expectations equilibrium] condition should be a useful approximation even if not all market participants have expectations that are rational. Indeed, even if most market participants were irrational, we would still expect the market to be rational as long as some market participants stand ready to eliminate unexploited profit opportunities." (p. 11, italics and expression in brackets added).

An examination of the empirical relevance of this mechanism is the main goal of this paper.°

The Fama-Mishkin approach implies that a few or, for that matter, even one infcrmed and rational investor, by taking large positions in an under or over-valued asset, can do exactly what would be done if all investors possessed the same information. It can be argued, further, that any leakage of the new information by virtue of other market participants observing these large positions is just a bonus in terms of promoting movement to the new efficient-markets equilibrium.’

One requirement for the action of such a mechanism is that the investor has the «bility to ¥ See Bray (1983) for a comprehensive discussion of the results. Friedman (1979) and Bray (1983) develop learning models where there is convergence to the classic rational expectations equilibrium. For cases of non-

convergence or convergence to an equilibrium other than the classic one, see Cyert and DeGroot (1974), DeCanio (1979), and Fourgeaud, Gourieroux, and Pradel (1986).

See Radner (1983) for a general discussion of problems posed by heterogeneity of information for convergence to a rational expectations equilibrium. ® Because we are interested here in short run convergence to the efficient markets or rational expectations price, we ignore the long run argument that well-informed, rational investors will make higher profits and accumulate wealth faster than other investors, eventually causing the latter to make up an insignificant dart of the market [Friedman (1953, pp. 157 ff.), Cootner (1967, p. 80)]. See Figlewski (1978) and DeLong, Shleifer, Summers, and Waldman (1990) for models that contradict long run convergence based on the above wealth argument. ’ For a discussion of leakage problems, see Hirshleifer and Riley (1992); see also footnote 10, below.

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take large positions -- through sufficient initial wealth and/or the opportunity to borrow and lend. Another is that the informed investor is essentially risk neutral or not "too" risk averse, or that the market provides ample opportunity to hedge the risks inherent in large unbalanced portfolios. As will be discussed below in detail, it thus becomes an empirical question whether unexploited profit opportunities can thus be eliminated -- the answer dependent, in particular, on the degree of risk aversion, the wealth of the investor, the size of the profit opportunity, and the existence of market opportunities to hedge or diversify away the rapidly increasing risk associated with large positions in a single: asset.

Many of the same factors are also relevant for the realism of the models, noted above, where the class of less-informed or irrational investors causes the market price to diverge from the efficient or rational expectations solution. Virtually all of these models require the class of informed

or rationa. investors to be risk averse.®

Risk aversion allows this class to reach equilibrium even when "excess" expected returns persist; and the degree of risk aversion of this class along with the level of (undiversifiable) risk in the system are directly related to the discrepancy, in equilibrium, between the existing price and the rational expectations price.

The goal of this paper, then, is to investigate the theoretical and, especially, the empirical relevance of conditions that, under risk aversion, would still allow large shifts in portfolios in response to the appearance of unexploited profit opportunities. Section II is devoted to theoretical issues, in Darticular the key individual and market factors that are necessary and/or sufficient for large changes in the holdings of a single stock. In section III, we investigate empirically the shortterm variance-covariance structure of the U.S. equities market and, using these results, calculate the extent to which investors of varying risk preferences and wealth can, single-handedly, move

selected stock prices to their new rational expectations equilibria.

I]. Theoretical Considerations

We assume initially a stock market made up of a set of risk averse investors, each of whom

TKR... : 7 . " : a " One exception is the model of Haltiwanger and Waldman (1985), where “congestion effects" (costs) and "synergistic effects" substitute for risk aversion.

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maximizes an expected utility function of the mean and variance of one-period return.’ Initially, all investors share identical expectations, the market equilibrium is fully rational and, therefore, all assets will be priced according to the capital asset pricing model. Accordingly, the expected return per dollar , i, and share price, P., of any given stock i will be related to the market portfolio and the risk-free interest rate as follows:

t= VJP.= rtf. -rd(o./o~), (1)

i iif ‘*m f'im-m where: Y, is expected nominal income per share for stock i (expected dividends plus capital gains); Tp the rate of return on the risk-free asset (1 + the riskless rate of interest, Ry): ly the expected rate of return on the market portfolio; OW the covariance between the returns on the market portfolio and the ith stock, and o the variance of the return on the market portfolio. (See, e.g., Copeland (1983) chpt. 7, Elton and Gruber (1987) chpt. 11.)

In this section and subsequent sections we will examine the ability of an investor, upon obtaining new and, for the short-run, private information, to single-handedly move market prices to the rational expectations equilibrium that incorporates this information. Let us consider a very specific example, so that one can calculate easily what the final rational expectations equilibrium would be. Assume that our investor is the only person that learns that a government subsidy, amounting to S dollars per share, will be awarded to a given firm -- a subsidy that will be announced publicly in a short period of time. In the meantime -- to avoid the complications of "leakage" problems -- we will assume further that the investor will be able to purchase, up until the announcement date, as many shares of the stock as desired at today’s price.'° Since the sub-

sidy will be paid in every state of nature, the only change in the probability distribution of the

firm’s returns (per share) will be a shift in the mean by S, to Y+ S; it is easily shown that none of

7 Since the utility function we rely on the most in the empirical section is an exponential function, U(W) = AW exhibiting constant absolute risk aversion (CARA), it is necessary to assume that all risky returns follow anormal distribution. (See Ingersoll (1987), p.98.)

1° For a consideration of the many problems that arise when, either naturally or as a result of the investor’s actions, his information leaks to other speculators, see, e.g. Hirshleifer and Riley (1992). All leakage problems break the rules of the original Mishkin formulation, because leakage implies the spread of the information, however imperfectly, to part or all of the rest of the market. By postulating that the investor

can purchase as many shares as desired at the existing market price, we are weighting the example in favor of Mishkin’s conclusion: if, on the other hand, in attempting to purchase a large block of shares, the investor causes the price to rise because of monopsony considerations, he will tend to stop his purchases prematurely because of his rising marginal cost.

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the other moments of the distribution change -- its variance or covariances with other security returns. ‘Chus, because nothing on the right hand side of equation (1) changes, the expected rate of return per dollar of stock i, i , Must remain constant; as a result the final rational expectations equilibrium price of share i, Pe. , must jump to leave the ratio (Y,+ S)/P*. equal to the unchanged ri ' Solving that relation for P.*, we find that the price must jump by Sir:

Px. = P. + Sir. (2)

As we will calculate in the next section, even small changes in price, when realized in the short run, lead to enormous rates of return -- dwarfing the contribution of the firm’s dividends.

A more topical example, but similar in structure to the above, would be information of a new takeover bid at a given premium over the current market price; if the takeover price were certain, then, once again, the new information would lead to an increase in the knowledgeable investor’s expected rate of return, with no change in his assessment of the firm’s variance or covariances.

B. Individual Equilibrium

To find the investor’s optimal holdings of all risky and riskless assets before and after the receipt of the new information, we will assume, as is customary, that the investor maximizes the expected utility of his or her income, E[u(Y)]. That income, Y, can be expressed alternatively as the sum of returns on holdings of riskless bonds (B) and risky stocks (the Z:s, below, with r i the risky retu:n), or as total wealth (W) times the riskless rate of return plus the sum of "excess"

returns on stock holdings: N _ N | = y = - Y= r,B +2 tie mW + 2 ii Tr) (3)

Given that total wealth, W, is a predetermined constant at the time of decision, by putting no restrictions on the sign or size of either B or the Zs, we are implicitly assuming that the investor can borrow or lend any amount at a constant riskless rate of interest (rp)!

TT Ww

e are assuming here that the increase in the expected return as a result of the subsidy has a negligible effect on the expected return on the market portfolio, an

12 Once again, we are weighting the assumptions in favor of large portfolio shifts; investors will not be hindered or stopped in the attempts to purchase large blocks of shares by an increasing borrowing rate.

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Maximization of expected utility by the investor leads to the well-known set of first order conditions:

E[u’(Y)(r - r,)] =0, i=1,N. (4)

After making the required assumptions about the type of utility function and the probability distribution of returns, one could work directly with this set of first order conditions (e.g. Mossin (1973), pp. 50 ff.). Given, however, that all the examples studied below will depend only on the first two moments of the probability distributions of interest, we will instead use an equivalent approach which relies on the somewhat more transparent first order conditions for the. risk-return efficiency frontier.’ 3 As will be done for specific examples below, the investor’s optimal portfolio can also be determined by maximizing expected utility subject to the efficiency frontier. C. The Risk-Return Efficiency Frontier

The risk-return efficiency frontier is defined as the locus of points minimizing variance conditional on a given expected rate of return. As noted above, with the option of unlimited lending

and borrowing in the riskless asset, the investor’s expected return, E(Y), is defined as:

N

E(Y) = Y = r.W + 2 “i (r - Tf) = r.W +7’m (5)

On the right hand side, m and z are both N by 1 column vectors of excess expected returns and nominal security holdings, respectively. The variance of the overall portfolio return, V(Y), is

equal to:

N N VWY)= % ZZ. 6.. = 7Cz, (6) izlj=1' J 1 where Gj is the covariance of return between assets i and j, and C is the N by N matrix of variances and covariances [s; j ]. Minimizing V(Y) subject to a given expected return, E(Y), leads

to the first order conditions: 2Cz- Am=0, (7) where A is the Lagrange multiplier for the constraint, (5) above. Solving this system of equations

for z leads to the following expression for the vector of optimal holdings of risky assets along the

efficiency frontier:

TS See, e.g., Elton and Gruber (1987), chapter 4, or Mossin (1973), p. 55.

z= 2/20 | m. (8)

Although the level of vector z depends on the unknown A -- and, therefore, generally on the investor’s utility function and the required expected return -- equation (8) does fix the ratios of various risky assets held along the efficiency frontier in any optimal portfolio: the famous portfolio separation theorem discovered by Tobin (1958). Thus, irrespective of the investor’s wealth or utility function, the ratio of holdings of any two assets i and j, will be constant at all points along the risk-return efficiency frontier. This optimal ratio will depend only on the investor’s estimates of expected excess returns, variances, and covariances:

Z, (2, = x cee tp 1% on G1). (9)

The numerator of (9) shows that holding of any asset, Z., is proportional to the product of the elements of the ith row of the inverse of the covariance matrix, the elements cp times the vector of excess expected returns.

By substituting the optimal z from the first order conditions (8) back into the expressions for

the variance [z’Cz] and expected return [r-W + m’z], one derives the well-known efficiency frontier that turns out to be linear in the excess expected return and standard deviation. Eliminating the Lagrange multiplier, the frontier becomes:

1

=/V(Y)= (WC ! m2 Ey) - WI. (10)

°y D. Conditions for Large Shifts in Portfolio Holdings

So far these equations and relationships do not illuminate the most important question for this paper: What are the conditions under which an investor can or cannot accumulate a large position in an asset for which he has received or derived valuable new information? And what are the conditions under which he can hedge the potential rapid buildup of overall portfolio risk by appropriately changing his holdings of other assets?

The theoretical conditions for the buildup of portfolio risk are most easily illuminated by an adaptation of the approach developed by Anderson and Danthine (1981). They partition the equi-

librium conditions similar to (7) in an illuminating way and, although not strictly necessary,

-8facilitate the linking of the theoretical terms in (7) to empirical data.

Let us denote the stock for which the private information is forthcoming as asset number 1, with expected return, Tp variance, Sp and holdings Z)- There would, therefore, be N-1 other risky assets. Following Anderson and Danthine, partition the first order conditions for the risk-return

frontier (7) into the equation for the first asset and an N-1 equation block for the rernaining risky

assets: N- 1 _ 5114) + % 15% = A\2m, (11) OZ + Com, = Am 1 N-1I°N-1 N-1

The symbols in the first equation have been defined above. In the lower block, Pa is a N-1 column vector comprising all but the first element of the first column of the original C matrix; Cn] is the

N-1 square submatrix of the variance-covariance matrix C formed by eliminating the first row and column; similarly ZN-| and my | are the N-1 column vectors comprising all but the first element of

the old z and m vectors, respectively. This partition becomes particularly meaningful when we substitute actual data for the theoretical variances, covariances and expected returns in equations (11). For the expected return

on the ith asset, Ti, one typically takes the average of observed returns over some sample period. A Thus, for example, for a sample of size T, the empirical estimate, ri, of the subjective expected

T return, Ti ,equals 1/T % Te For an estimate of an element of the vector of expected excess returns, k=1 A _ _ T m,, we subtract the riskless rate of interest, yielding: m, = 1/T > Can - Tp): Similarly, an element of k=1 . . . A qT - - i the variance-covariance matrix, C, turns out to be: 6..=1/T & (1.,-1.)(1.,-1,). Let r be the column ij k=1 ik “iV jk J

vector of the T observations on the return on asset i around its mean; and let R be the T by N-1 matrix with columns r for assets 2, N. Then the empirical estimate for the matrix Cn in equation (11), above, would be R’R/T (where R’ is the transpose of R ).

We are now ready to rewrite the partitioned equation set (11), substituting the empirical es-

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timates defined above for the theoretical means, variances and covariances appearing in (11):

A

rl Oz, + rh Ray, =(AT/2)m, (12) A 1 _— Rr'Z, + R’Ray , = (AT/2)m

N-1?

where the expression ryt is the estimate of the variance of return on variable 1, 3, P times the number of observations, T; all factors T can be moved to the right hand side of (12) for convenience.

Let us now solve the bottom block of N equations for the N-1 by 1 column vector ZN]: Assuming that the various inverses exist,

A spl = spl 1 Zn.1 = XT/2 (R’R) my) 7 (R’R) R’r Z)- (13) This expression makes the holdings, Zip for each of the other N-1 assets, a function of the

A excess returns on all these other assets (my. v and the holding for asset 1, Z) Note particularly the set of coefficients multiplying Z): -(R’R) leer 1 . This is (minus) the N-1 by 1 vector of estimated least squares regression coefficients, B, when the time series of returns for asset 1, rh is regressed on the returns for all the other N-1 assets. Thus, insofar as the return on a particular asset r has a

"high" positive coefficient in the regression for r P the holding of asset j will be correspondingly

low. Let us now substitute this expression for ZN- into the first equation in system (12). We then get: A A prt Z)-r RRR) Rr! Z, = ATM, -AT2 2 RaRY | my | (14)

9 A As noted above, the first term, ri ri iS an estimate of To, rf Moreover, the coefficient of the second

-ly> 1

bd A entry for ae ri R(R’R) “R’r’, can be shown to be equal to -To, iRi. where the latter is the multiple

correlation coefficient for the regression of the first asset’s return (r ] ) on the returns for the other

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N-l assets.” We thus have a final equation for the holdings of asset 1 along the risk-return ef- T¥ Given the definition of ‘the vector of regression coefficients, 8, the expression ri *R(R? R) Ry 1; is easily

RZ

shown to be equal to rl RB. But this term can be shown to be equal to rl rir? which in turn equals T S Ry

(Footnote continues on next page)

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ficiency frontier: A 2 _ N A. 2, = (26, RPIME 1p - X BiG 1p) (15)

As derived, equation (15) shows that the optimal holding of asset 1 in any minimum variance portfolio is related crucially to the multiple correlation coefficient, Rt given the levels of the expected excess returns and other variables in the equation, as the return of asset | is more highly correlated with any linear combination of the returns of other stocks, the holding's, Zp will be higher.

Under certain circumstances, the equilibrium condition (15) can be used to determine the change in asset holdings as expected returns and other factors change. For small changes in the own expected excess return, ry r,, where A changes only marginally, the equation shows that the change in Z) is proportional to the factor MI26, {(-R4)). More important, equation (1.5) with A equal to a constant also holds for changes of any size when the investor has a CARA utility function.' °

AS Rt approaches 1, the response to a unit change in ry Ir approaches ~, a case with a result identical to that which underlies the Fama-Mishkin mechanism. In this limiting case tke result is the same as the case of risk neutrality, because a perfect hedge exists for the risk of asset 1: as the investor increases his holding of asset 1 to capture the higher return that only later will be revealed to the market, he goes short in an optimal combination of other assets, thereby leaving his overall portfolio risk unchanged. However, for anything less than an Rt of 1, the increase in the holdings

of asset 1 will be limited. Thus, the extent to which the investor can act alone to assure: the ef-

(Footnote continued from previous page) (Johnston (1972), p. 131). As explained above, the number of observations, T, can be absorbed into the right hand side of the equation.

It turns out, in fact, that this is an exact result for a CARA utility function. This can be seen from the equation for the shares in the risky portfolio, w. and the fact that for this utility function, the total value

of risky holdings is a constant. The equation for w is aC tn, where o is a parameter of the CARA utility function. Since total risky holdings equals some constant, say K, then the equation for the dollar value cf the holding of asset 1, Z,, would be Kw, -- a constant as long as the determinants of w do not change. But in equation (15), above, we write Z, as a function of A; thus, for the two expressions to be equal, A must be a

constant for a CARA utility function. See Ingersoll (1987), p. 98, for the derivation of the equation for the asset shares in a CARA utility function.

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ficiency of the market, "to stand ready to eliminate unexploited profit opportunities," is an empirical question. The answer depends on the many variables in equation (15), but primarily on the size of R?, the size of the own variance, oy P and the size of the change in the expected return of the asset in question.

For special cases, equation (15) can be simplified even further. Where 2 continues to be assumed constant and the only cause of a change in the holdings of a given asset, AZ,, is a change in

its own expected return, Ar. one can take the first difference of equation (15) as follows: > A 2 - AZ. = {A/[20;(1-R; I} Ar.. (16)

Besides confirming the dependence of the size of changes on the product of the multiple correlation coefficient and the own variance, equation (16) also shows that, assuming the constancy of i, 3 jo and R?, changes of any magnitude can be generated by suitably large changes in the expected return. Thus, it is clear once again, that how much risk aversion limits an investor’s ability to eliminate: unexploited profit opportunities is an empirical question.

A corollary to (16), again for small changes or special cases like the CARA utility function, is a particularly simple and illuminating version of the portfolio separation theorem noted above in equation (9). Where the changes in the expected own rates of return are equal -- ie., Ar; = Ar; --

the ratio of the change in holdings depends only on the ratio of the stocks’ adjusted risk factors: Z,JAZ. = 6.,(1-R>)/ 6..(1-R2

III. Experiments With New Information Using U.S. Stock Market Data

As summarized in equations (16) and (17), we have identified three empirical factors that are crucial in determining the magnitude of the response of a given investor to cases of new information of the type we are studying. These are the stock’s "hedge-adjusted" variance ( 6,.( I-R?)), the characteristics of the investor (wealth and attitude toward risk, all embodied in 2), and the ef-

fect of the new information on the investor’s assessment of the firm’s expected return (Ar.).

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The goal of this section is to investigate the empirical relevance of these factors in helping or hindering a given investor to eliminate the unexploited profit opportunities emphasized by Fama and Mishkin. We attack this question through a number of experiments or simulations, estimating the impact of new information concerning the expected return of specific stocks on the portfolio holdings of various representative investors. These simulations are based on empirical estimates of the expected return and variance-covariance structure of a large part of the U.S. stock market, and on a variety of alternative specifications of the investor’s level of wealth arid degree of risk aversion. The criterion we shall use to assess whether it is possible for a given irvestor to eliminate the profit opportunity or price differential is the size of the change in the investor’s holdings as a percentage of the outstanding equity of the firm in question. This criterion is, of course, at best a necessary condition for strong-form efficiency: if an injection of valuable private information does not lead to a significant change in the investor’s holdings, then we conclude, in this case, that the stock’s price could not move to the rational expectations price and that strong-form efficiency could not be achieved. Should this negative result occur, an analysis of the results can determine whether the combination of the investor’s risk aversion and the buildup of portfolio risk was the major cause. If, on the other hand, the new information causes the investor to demand a large percentage of the outstanding equity of the firm, then we can say that it is at least possible, despite his risk aversion, that the investor’s actions alone are capable of driving the market price to the new rational expectations equilibrium. Without specific market demand and supply equations, one cannot, of course, be more specific.

A. Choice of Sample and Time Period

In choosing a sample, we want to include a selection of stocks large enough to provide a reasonably complete picture of an investor’s actual opportunity set for hedging the risks associated with heavy purchases of one stock. It bears reiterating that, unlike the well-known result where little more than 20 different stocks are sufficient to statistically explain the variation in the market

portfolio, it may take many more stocks -- if it can be done at all -- to explain with a high R?

the variation in the return of a particular stock. Because the market portfolio is the quintessential

highly diversified portfolio, its overall variance is affected only marginally by the idiosyncratic

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risks of individual stocks. On the other hand, for a portfolio constructed to hedge the risk of a particular stock, the importance of idiosyncratic factors is crucial; only if the variance of this particular stock is largely caused by factors common to the returns of other stocks -- hence ruling out the importance of idiosyncratic factors by definition -- will it be possible to construct a good hedge portfolio.

In principle, one could use all stocks, listed or otherwise, to form a hedge portfolio for the stock of the firm for which our investor has received or derived his private information.' © Limits in the number of observations, even for daily data, makes this maximal approach impossible for now. As acompromise, we have constructed our portfolios from a large number of stocks that are also quantitatively very important: all of the consistently reported stocks -- 245 in number -- in the top decile, by value of outstanding equity, of listed securities on the New York Stock Exchange at the end of 1991; 199 of these stocks are in the S&P 500 index, accounting at the end of 1991 for 83.7% of the total value of the shares in that index. The other 46 firms in the top decile are large foreign firms, traded on the Exchange but not in the S&P 500, which equal over 45% of the total equity value of the decile. The sample and its construction is discussed at more length in the Appendix.

The data for this study are from the stock file maintained by the University of Chicago’s Center for Research in Security Prices (CRSP); data are available on a monthly or daily basis.' / For this study, the use of daily returns seems preferable; most new information is likely to become public in a short period of time, so the risks the investor faces seem more realistically to be those captured in daily variances and covariances.

The sample period chosen for this investigation runs from the beginning of 1988 through the end of 1991. A start after the crash of 1987 seemed appropriate and, at the time of the beginning

of this empirical work (summer of 1993), the end of 1991 was the latest possible termination

> We do not treat here the possibility of using derivatives for the purpose of hedging the risks of the large unbalariced portfolios that are generated in the experiments discussed below. Partly this is because of our view that most of the conclusions below would be unaffected by their incorporation into the study. It also seems to be the case that, by postulating the existence of non-redundant derivatives. we just push the analysis of the increasing risk of holding large unbalanced portfolios back one stage -- to the provider of the derivatives; presumably, the cost of the appropriate derivative would be an increasing function of the quantity issued, because of the increasing risk exposure of its issuer.

'7 See, for details, Center for Research in Security Prices (1991).

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point. Such a sample contains 1,010 observations, allowing as many as 765 degrees of freedom for any regression one might want to run.

Chart | is a histogram of the annualized average rate of return over the sample period for each included firm.' ® The mean of these annualized returns was 24.7%, fairly high by historical standards; however, it should be recalled that rates of return were quite high as the market recovered from the crash of 1987. In fact, for the same period, the annualized daily price change for the S&P 500 was 15.5% -- before adding in the effect of dividends on the rate of return.

B. Hedge Portfolios

As shown in the previous section, one of the key factors determining how private information will be translated into stock purchases is the percentage of the variance of a stock’s return that can be explained by a linear combination of the returns of other stocks (its Re). ” Chart 2 shows the distribution of these multiple correlation coefficients for the 245 stocks in our sample. For those accustomed to dealing only with the market or other well-diversified portfolios, where the overall return can be largely explained statistically by just a few factors or stocks, it sometimes comes as a shock to discover how little of a typical stock’s return, on average, can be explained by the returns of other stocks. With a mean R? for the sample of only 0.58, it is clear that a large part of the variance for the stocks of the most important firms in the economy consists of idiosyncratic risk.

C. Specific Examples of Optimal Purchases Resulting from the Receipt of Private Information

In this section, we report on a number of experiments to assess the impact of the various factors discussed above on a solitary investor’s ability, by making "large" purchases, tc singlehandedly move the market from one rational expectations equilibrium to another. As noted above, our criterion for measuring the investor’s ability to move the market will be the size of the purchases induced by the new information -- size as measured by the change in dollar holdings, but

more importantly by the change in the percentage of the firm’s outstanding equity held by the in-

'8 The annualized (ex post) rate of return was estimated by first calculating the average daily return, ri, for

a given firm i, and then raising +r, to the 252.5 power (the latter being the average number of annual trading days for the sample period).

' *" Note also the importance of the factor (1 -R ) in equations (16) and (17) -- the percent of a firm’s variance that cannot be diversified away.

Distribution of Annualized

Mean Returns for 245 Stocks

Chart 1:

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In the experiments that follow, we have attempted to vary, within reasonable limits, the relevant parameters or factors that might affect the size of the investor’s purchases in the light of his newly arrived information. These include, in particular, the investor’s net worth and degree of risk aversion, the level of the risk-free rate, and the characteristics of the stock in question -- most importantly, the degree to which its variance can be diversified away. Where parameters are not easily varied, we have tried to err in the direction of encouraging large purchases; thus, we allow infinite borrowings at the riskless rate of interest and no limitations on short selling.

Of the alternative, but equivalent, approaches noted above for calculating the investor’s optimal por:folio, we will choose the maximization of the investor’s expected utility subject to the calculated risk-return frontier. Initially, two alternative utility functions were used for comparative purposes: a quadratic and an exponential -- the latter, as discussed above, exhibiting constant absolute risk aversion (CARA). However, because of the quadratic’s property of increasing absolute ris aversion, it became immediately clear that, for our purposes, the results for the CARA utility furrction were all that was needed.” °

C.1 The Baseline Optimum. Each experiment below compares two optimal portfolios, the first calculated for a common baseline case and the second for the case where the investor adds new information for a single stock to that already incorporated in the baseline. Below and in the Appendix, alternative baselines are calculated depending on the level of the investor’s wealth, the level of the riskless rate of interest, and the vector of expected returns for the risky stocks. The one factor that remains constant in all the experiments is the variance-covariance structure, estimated as. described above for the set of 245 securities in our sample.

In Tables 1 and 2 below, results are reported for two combinations of initial wealth and risk preferences. The first represents a moderately small investor with $1 million in net wealth and

moderately conservative risk preferences; with respect to the latter, given the expected rates of

70 Typically, we would calibrate the two utility functions so that both would result in an identical portfolio for the initial or baseline case (before the investor received or discovered his private information). However, because of the quadratic function’s increasing absolute risk aversion, in every case after the receipt of information. the portfolio chosen with the quadratic had a lower total of risky stock holdings than that chosen with the CARA utility function. Because of the separation theorem, this implied that the change in the holding of the stock for which positive new information was obtained would always be smaller for the quadratic case.

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return and covariances assumed for the baseline, the investor puts 50% of his wealth in risky assets.” ' The second case is one corresponding to a very large investor, with the size and risk preferences of a large contemporary hedge fund: command of $5 billion in net resources and risk preferences such that 90% of net wealth is invested in risky assets under the baseline assumptions.” *

Alternative baselines for different riskless rates of interest are reported in the Appendix; since reasonable variations make no difference, the results reported below set the riskless rate of interest at the mean value for Treasury Bills for the 1988-91 period, 6.97% at an annual rate.

As derived in equation (10) above, the efficiency frontier is a straight line in the standard

1 2

deviation and excess expected return of the optimal portfolio; the slope of the frontier is (m’C_ m)!/ ;

—, . -1. . where, as reported above, m is the column vector of expected excess daily returns. and C ~ is the inverse of the variance-covariance matrix of daily returns. The same C matrix, calculated over the

1988-91 period, was used for all the experiments. On the other hand, two quite different alterna-

tives were calculated for the baseline m vector. The obvious candidate would be the vector of average returns observed for the sample period. One set of experiments was run using this choice, the results reported in the Appendix. The only problem with this alternative was that the optimal portfolio chosen for the baseline case was far different from the "market" portfolio; in particular almost half the stocks were held in short positions. As discussed in more detail in the Appendix, the choice of baseline did not, however, change the qualitative nature of the results reported in Tables 1 and 2.

In order to have a baseline portfolio in line with the characteristics of the market portfolio,

we adjusted the vector of expected returns, leaving the variance-covariance matrix unchanged.

The new m vector was chosen to force a baseline portfolio that approximated the market: all stocks

mt Assuming a CARA utility function as specified above, an exponent a equal to 1/1,000,000 achieves the desired result.

> Recent newspaper stories indicate that George Soros’s Quantum Fund had almost $10 billion under management in early 1994 (Reuters, March 7,1994); approximately half that much was, at that time, managed by Steinhardt and Co. (The Wall Street Journal, April 1, 1994, p.C1). A hedge fund like the Quantum or Steinhardt funds clearly invests far more than the 50 percent of its "wealth" in risky assets assumed for the first case. The proper way

to look at such a high percentage holding of risky assets is not that the investors in the fund would be

particularly risk oriented with respect to their total wealth, but that they put into the fund only that part of

their portfolios that are to be invested in the riskiest assets.

-17-

held in positive quantities, with weights equal to those in the market portfolio. The average of these adjusted expected returns was 8.9%, significantly lower than the average return of 24.7% for the sample period. The experiments reported in the main body of this paper start from this second

baseline.

The major characteristics of the baseline portfolios calculated for the new m vector and the two alternative cases of initial wealth and risk preferences are reported in the first two columns and rows of Table 1. Holdings of key stocks in the baseline, to be discussed below, are reported in the first two columns. Important characteristics of the optimal portfolios are reported in the first two rows: the dollar holdings in riskless and risky assets (columns 8 & 9); the amounts of long and short holdings of risky assets (columns 10 & 11); the overall expected value and standard deviation of the portfolio and the slope of the risk-return locus at this optimum (columns 12-14). The overall expected return and standard deviation were 7.9% and 6.9%, respectively, for the smaller baseline portfolio (W = $1 million), and 8.8% and 12.4% for the larger (W = $5 billion). By construction, no short positions are held in the baseline and the investor holds each stock in proportion to its percentage weight in the market. In the case of the smaller investor, the portfolio contains 0.001 percent of the share value of each firm; for the larger portfolio the share jumps to 1.6 percent.

C.2_ Alternative Examples of the Impact of New Information. Tables 1 and 2 summarize the results of 12 experiments: 3 alternative scenarios for the receipt of private information with respect tc each of four different firms. The firms differ according to their sizes and their low, high, or average hedging possibilities (as measured by their R? with the other 244 stocks in the sample). On the low side, both in size and R2, is Courtaulds PLC, whose return had one of the lowest coefficients of variation with the sample -- only 0.29 -- and whose size, in terms of the value of its equity at the end of 1991, at $3.7 billion, was the lowest of the four firms. Two intermediate cases in terms of R? are Boeing Corporation (0.57) and British Gas PLC (0.56) whose multiple correlation coefficients were very close to the sample mean (0.58); two such firms were chosen because of their disparate sizes, Boeing at $13.6 billion and British Gas at $186 billion. Finally, Shell

Transport and Trading Co. had one of the highest R°s in the sample at 0.82, and also one of the

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-18-

3 In the first two columns of Table 1, one can find

larger sizes with equity valued at $169 billion.’ the holdings of each of these four stocks for the two baseline portfolios. As noted above, although the dollar value of holdings in the large fund is as much as $189 million for British Gas, in percentage terms these holdings are only 1.6 percent of the outstanding equity of each company.

C.3_An Increase in an Expected Return by | Percentage Point. The first experiment, the im-

pact of new information indicating a small increase of 1% in the expected return of a given stock,

is intended primarily to examine the properties of the system as embodied in equations (15) to (17) above. Eight related cases are presented in Table 1: results for the smaller and larger wealth levels for the common 1% change in expected return applied successively to each of the four stocks. As expected, the presence of investor risk aversion limits the change in the holdings of the affected stock for each case. Although the changes in holdings shown in Table 1 are sometimes large (all expressed in millions of dollars), in no case is this change large enough to assure that the investor could single-aandedly move the firm’s stock price to its new equilibrium value. For the smaller investor, with 50% of his $1 million in wealth invested in stocks for the baseline portfolio, the larges: iinal collar holding for the four experiments is $841 thousand for the 1% increase in the expected return for Shell Transport -- far less than 1% of the total market value of Shell’s equity (columns 3 and 4 of row 9). In none of the experiments for the smaller wealth level does the investor end up holding more than .005% of the firm.

For the case where the investor controls $5 billion in wealth, investing 90% in risky assets in the baseline portfolio, the results are somewhat less clearcut. For the larger firms, British Gas and Shell, the increased expected return results in large final holdings -- over $7 billion in the case of Shell -- but these never reach as much as 5% of the firm’s equity (column 4). For the cases of Courtaulds and Boeing, the final holdings reach 9.9 % and 14%, respectively. Although not high enough to clearly imply that this single investor’s action will force the firm’s market price to its new rauional expectations equilibrium, these percentage changes are in a range where, depending on assumptions about the behavior of other investors, a significant impact on the market price ‘wud be possible.

“* This high R* is something of a fluke, caused by the presence in the sample of the related company, Royal

Dutch Petroleunt Company. However, it is presumably possible to go long in one of these securities and short in the other.

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The ratio of the dollar changes in the holdings (shown in column 5) are closely approximated by the ratio of the hedging factors, ( -R,”)o;,- a result derived for smal] changes in equation (17), above, and true for all changes for the CARA utility function, as shown in footnote 14.7* Thus, for a common change in the expected return, such as the 1% underlyirg Table 1, the change in the dollar value of holdings in Shell Transport will always be the largest -- approximately 4.56 times the change the holdings of British Gas, 5.57 times the change in the holdings of Boeing, and 14.4 times the change in the holdings of Courtaulds.

As we have discussed above, the net change in the investor’s holdings depends, in addition to the size of the perceived change in the expected return, on two other major factors: (1) the investor’s preferred trade-off between risk and expected return (usually a function of wealth and other variables, but in the case of a CARA utility function, representable by the exponent of the utility function alone); and (2), the opportunities provided by the stock market for hedging or diversifying away the potentially large increase in portfolio risk resulting from a huge position in a given stock. The differences between the final holdings in the two cases listed in Table 1, the lines labeled $1 million and $5 billion for a given stock, illustrate the impact of the first of these factors. The size of the final holdings for the two cases listed in the table differ by a factor of 9000. If we were comparing positions with a utility function exhibiting constant relative, rather than absolute risk aversion, the different wealth levels alone would lead to portfolios differing by a factor of 5000.

How much of the increase in holdings over the baseline can be attributed to the: second factor: the investor’s ability to use the various risk diversification possibilities available in the market? A look at the composition of the investor’s optimal portfolio after the adjustment to the new information shows that the stock market is used extensively in what appears to be an attempt to minimize overall portfolio risk (columns 8 through 11). In this frictionless world with no limitations on borrowing or short positions, the optimal portfolio often has significant short positions -- varying from $0.229 million to almost $17.7 billion; thus, the British Gas experiment for

the $5 billion wealth level shows aggregate short positions of $4.791 billion balanced by long

m4 Equations (16) and (17) assume, it should be remembered, that the Lagrange multiplier, 4, does not change. The hedging factors are reported in column 7 of Table 1.

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positions of $9.354 billion, leading to a figure in column 9 of $4.562 billion for the net holdings of risky assets. A further telling example is the fact that, for both Shell Transport cases, the long positions in Shell Transport stock of $0.84 million and $7.6 billion are balanced by short positions in the highly correlated Royal Dutch Petroleum stock of $0.58 million and $5.2 billion (not shown in the table).

One way to attempt a measure of the reduction in risk offered by market opportunities for diversification is to determine what would have happened if no such opportunities were available at all. In column 6 of Table 1 one finds the results for the same 1% experiments under the assumption that the investor is limited to purchasing only the stock for which the new information is obtained. Thus, no other stocks are available, either in long or short positions, to reduce the buildup of risk as the investor purchases shares in the stock for which the new information has arrived. In this counterfactual, the capital market line would have a slope defined by the characteristics of only this one stock: ( Tr - Tp/v G;.. Using this line to calculate the holdings of the stock in question for both the baseline portfolio and the new portfolio based on the change in the investor’s information, one arrives at the changes in the holdings listed in column 6 of the table. The changes in this column are from 18 to 71 percent of those in column 5. Thus, using the changes in column 6 as a rough guide, had the large investor not availed himself of the opportunities for risk reduction through diversification, he would have increased his holdings of Courtaulds to only 10 percent of the firm’s equity and his holdings of Boeing to only 4.4 percent. Particularly striking is the case of Shell: because of the extensive risk reduction opportunities available for a firm whose R? with the rest of the market is as high 0.82, the change in column 6, at $1.4 billion, is only 18% of the optimal] change of $7.4 billion in column 5.

D. More Realistic Changes in Expected Returns

The experiments reported in Table 2 explore the impact of higher and, we will argue, more realistic changes in expected returns. For the upper panel, the investor generates information that causes him to double his estimate of the firm’s expected return (without changing his assessment of the firm’s variance and covariances). For the lower panel, the expected return is changed to be

consistent with information that causes the firm’s equilibrium price to increase 10 percent.

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D.1_A Doubling of the Expected Return. Since the expected returns for the four firms

varied frcm 7.9% to 9.2% in the baseline, a doubling of a firm’s expected return added at a minimum almost 8% to the firm’s annualized excess return -- a much larger shock than in Table 1.

Column 2 of the upper panel of Table 2 makes explicit what was implicit or suggested by the same column of Table 1: when the information implying this larger change in the expected return cornes to the large, more risk-seeking investor, for firms such as Courtaulds or Boeing, the investor’s optimal holding at the old price is close to or even greater than the total value of the firm's equity. Such changes in optimal holdings are certainly large enough to affect the firm’s share price and, if the price the investor must pay is a rising function of his purchases, large enough possibly to force the market price to the new rational expectations equilibrium price prior to the general availability of the information. Thus, for the larger investor, the optimal holdings of Courtaulds, at $3.9 billion ($3932 million in the table), actually exceeds the total value of the firm’s outstanding equity. For Boeing the percentage reaches 86 percent. Shell and British Gas are intermediate cases, at 36.5 and 7.3 percent, respectively, primarily because of the extraordinarily large value of their outstanding equity. It is also the case, as in Table 1, that the smaller investor, with his lower wealth and greater degree of risk aversion, never comes close to controlling a sigr ificant share of the firm’s equity.

Thus, even though, as expected, the risk aversion of the larger investor limits the size of his holdings, this risk aversion alone does not prevent him from purchasing very large percentages of these rather large firms. As discussed above, this result is obviously also dependent on the empirical assumptions concerning the variance-covariance structure of the market and the investor’s ability to borrow and sell short without restrictions. Of these latter factors, it may well be that the most impcrtant assumption is nor the variance-covariance structure of the market, but rather the limitless aoility to borrow and to sell short; column 4 of the the table shows that when the investor is again denied the benefits of diversification, although the new equilibrium change in the portfolio is always less than the primary case, the desired changes in the holdings are still large enough to give the investor a commanding percentage of the shares of the firm.

Although market opportunities for diversification are not always necessary to allow the large

~22-

investor to purchase a commanding share of a given firm, the optimal portfolios are highly diversified. The last row of the panel shows that for Shell, the stock with the best diversification possibilities, an unconstrained optimum leads to a portfolio with long positions of $175 billion ($61.7 billion of which is for shares of Shell), borrowing of $6.7 billion, and short positions totaling $163 billion ($44 billion of which are short positions in Royal Dutch Petroleum). Such positions seem clearly impossible in today’s world, but since they are consistent with the realistic sizes of large funds and the observed variance-covariance structure of the market, their impossibility probably is a result either of institutional and legal limitations on borrowing ar.d shortselling or the fact that new information rarely comes in such a precise (certain) form.

D.2_A Subsidy Adding 10% to the Firm’s Market Price. The dramatically different results in Tables | and 2 for the $5 billion wealth holder are wholly the result of differences in expected returns. That there exists some finite change in a stock’s expected return that will indice an investor at some point to hold a large percentage of the equity of a firm, irrespective of the increasing risk of these holdings, is a direct implication of equation (16). Given the proportionality demonstrated in that equation between the change in the holdings of a given stock and the change in its expected return, the major question becomes the determination of the range of changes in expected returns that can be considered empirically reasonable. Only a little reflection suggests that, where new information implies even a modest increase or decrease in a stock’s price in the near future, the change in the expected return over the short run, in annual percentage terms, can be very large indeed -- considerably larger than the doubling of the daily return posited for the upper panel of Table 2.

Let us consider the change in the daily and annual expected returns implied by information leading to the certainty of a government subsidy or a friendly takeover -- either to occur in the near future.” As for the size of the ultimate effect on price once the subsidy or takeover is announced, a 10% change seems well within the range of possibility. The translation of the above

price change into a rate of return depends on when it is projected (or known) to occur. In our

“° The only problem with a takeover as an empirical example is that, in the real world, takeovers are rarely certain and frequently lead to protracted battles; thus, it is usually not the case that the variance-covariance structure for the firm remains unchanged. We do not address the question of changes to the market’s variancecovariance structure in this paper.

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world, based on daily returns and correlations, and the implicit assumption that portfolios can be changed quickly with the arrival of new information, a 10% change in one day’s time translates into an aanual rate of return of approximately 2,829,130,600,000 percent.” ° Knowing precisely when the takeover or subsidy would be announced is obviously crucial for the investor to be able to realize: such Gargantuan rates of return, and might be objected to as overly unrealistic;

however. much less precise knowledge still leads to the same general conclusion. Suppose, for example, that the timing of the takeover and the 10% increase in share price is less precisely known: the event known only to be occurring sometime in the next two weeks. At a minimum, assuming that the event occurs only on the last day of the period, this information leads to an increase in the annualized rate of return of 1,092 percent.” ’

The results in the bottom panel of Table 2 assume a change in the daily expected return which, when annualized, equals 1,092 percent. We consider this an underestimate of the daily rate of return that would be expected given conclusive knowledge of a takeover to be announced in the near future. The positions that are shown in the panel are thus lower bounds for the positions that would be expected to result in such an institutional setting.’ ®

The results for this experiment confirm and underline those for the previous experiment.

For the $5 billion wealth holder, the desired positions in the stocks for which the new information becomes available are more than the total value of the firm’s equity in all cases. As adumbrated in the previous case, the investor takes enormous short positions to minimize the overall risk of holding such a long position. However, the expected return has increased so much that, even with no opportunities for diversification, the investor would increase his holdings of the stock enou gh to control almost 100% of the shares in all the companies; this is shown in column 4. Thus, for the

larger investor, the risk reduction opportunities provided by the market are not essential for our

*® For this calculation we ignore dividends and assume the average number of trading days for the 1989-91

ry period: 252.5. Thus (1.1)°°->-1 = 28,291 306.000. “7 Assuming compounding over 26 two week periods, the annualized rate of return would be 1281 = 10.918, Assuming |0 trading days in a two-week pericd. the daily rate of return leading to a 10% change in two weeks would be ( 170! -} = 0.00958. (A daily return feading to a compounded 10% return over a year is 0.000376.)

°* Clearly ina strict theoretical sense. a portfolio model based on a daily horizon is only applicable to a longer-term problem as an approximation -- in this case, we would argue, as a lower bound. Intuitively, and only roughly so, one might think of a model where the investor has information of an event that will occur two weeks hence, but which requires the investor to act immediately.

-24-

conclusion.

In contrast to the implications of the results for the large wealth level, despite these much higher changes in expected return, the holdings of the smaller investor never come close to 1% of the firm’s outstanding equity. Thus, there seems little prospect that this investor’s actio.s will affect the firm’s market price prior to the general release of the information -- at which point we would expect the stock price to jump to the new rational expectations equilibrium.

This conclusion for the smaller wealth holder is robust for even much larger changes in the expected rate of return. Even in the case where the information is precise enough to specify the day of the takeover, and thus lead, as discussed above, to an expected change of 10% in the firm’s price in one day, the optimal holdings for the smaller investor would not increase to more than 4.1% of any of the four firms. It would take an expected return of more than 100% in a given day

for this investor to desire as much as 40% of any of these stocks.

IV. Conclusions

The major goal of this paper was to investigate whether a realistic degree of risk aversion would prevent a single, but well-endowed market participant in the U.S. stock market from "eliminating unexploited profit opportunities" and moving the price of a stock to its new rational expectations equilibrium. If so, one could argue that the mechanism sketched by Fama (1970) and Mishkin (1983) could not possibly lead to a rational expectations equilibrium and strong-form efficiency. This is a question that cannot be answered a priori, so a major part of the stucly involved using data on daily returns to estimate the variance-covariance matrix for a representative sample of 245 firms and to use it to examine how optimal portfolios change as a function of new information, risk preferences, and wealth.

As predicted by our equations (15) and (16), an investor obtaining valuable new information was frequently found in the simulations to accumulate large positions in the affected stock, leading to a very unbalanced portfolio -- but one of determinate size because of the buildup of portfolio risk. However, the characteristics of the investor turned out to be crucial for determining whether

the size of this unbalanced position in the affected stock would be large enough to assu:e that the

-25-

stock price would move significantly towards, or to, its new efficient markets equilibrium value.

A moderate sized investor with about $1 million in net wealth turned out to be too small, almost irrespective of his attitude toward risk, to single-handedly move the market price. On the other hand, a large investor with wealth of $5 billion and risk preferences such that 90% of his net worth was invested in risky assets (a rough approximation to a large contemporary hedge or mutual fund), sometimes would, in our world, accumulate a position in the affected stock large enough to purchase all the outstanding equity of most firms. Thus, for the case reported in the bottom panel of Table 2, with its very large, but, we argue, realistic increase in short-run expected return, risk aversion alone did not prevent the Fama-Mishkin mechanism from operating. In fact, even when we prevented the investor from hedging the risk of his unbalanced portfolio, in some cases the large investor still sought to buy up the whole of the outstanding equity of the firm in question. For this Jatter reason, the unrealism of the enormous short positions found in some of the optimal portfolios may not be important.

Our results imply, therefore, that risk aversion alone cannot categorically refute the possibility that new information need not be widely held to be incorporated efficiently into market prices. In this sense, the model we dubbed the Fama-Mishkin mechanism could serve to justify strong-fcrm efficiency. Despite the drag of risk aversion, profit opportunities were potentially exploitable because of a combination of three factors: the size of the investor (taken in conjunction with the intesity of his aversion to risk); the opportunities for hedging (some of) the risk accumulating in large unbalanced portfolios; and the ability for unlimited borrowing at the riskless rate of interest. These last two factors led to results -- the size of short positions and borrowing -that seerred far outside the bounds of realism; of the two, we argued that probably only the latter, the avaiability of unrestricted borrowing at the riskless rate, was crucial to the results. Although the caveats are many, the importance of the first factor points to a potentially positive social role for investors with the size and risk preferences of large contemporary mutual and hedge funds. Given the size of the larger firms in the U.S. and world economy, only investors such as these seem capable of taking large enough positions to eliminate directly the unexploited profit oppor-

tunities provided by new information.

-26-

Although our results indicate that the presence of risk aversion cannot necessarily refute the efficacy of the Fama-Mishkin mechanism, they cannot, of course, prove that the market will move effortlessly from one rational expectations equilibrium to another. Given the assumption of risk aversion, and the high levels of undiversifiable risk that from our calculations are necessarily associated with large unbalanced positions, the world of this paper is potentially quite consistent with the models of noise traders and irrational investors studied by Figlewski (1978), Shiller (1984), and DeLong, et. al. (1990). Viewed in this light, one might profitably distinguish between the potential efficacy of the Fama-Mishkin mechanism and its contribution to strong-form efficiency. We have shown that this mechanism may sometimes be capable of incorporating information that is not widely shared into market prices as efficiently as public information is incorporated. However, if the original equilibrium was distorted by a class of irrational or inefficient investors, then, even if the Fama-Mishkin mechanism produced the same results as the

public information case, the final equilibrium would still remain distorted.

-27-

APPENDIX

In this appendix we consider in more detail than was possible in the text the following subjects: the choice of and composition of the sample; the calculations for representative hedge portfolics; the construction of the baseline portfolio used in the text and the alternative baseline calculated using as the expected return vector, the observed average returns for the sample period 1988-91.

I. The Sample

The data for the model were obtained from the University of Chicago’s Center for Research in Security Prices (CRSP); for more details see, Center for Research in Security Prices (1991). As described in the text, above, our sample consisted of the top decile of New York Stock Exchange traded stocks -- as measured by the annual capitalization value. Stocks with an incomplete daily trading tustory over the sample period January 1, 1988 to December 30, 1991 were eliminated from the sample. A total of 245 stocks remain in the sample. The 199 firms in the sample that were alsi listed in the S&P 500 accounted for over 83% of the value of the S&P 500 index at the end of 1991; moreover, the 46 firms in our sample not listed in the S&P 500 -- mostly large foreign-based multinationals -- accounted for approximately 45% of the equity value of the decile.

The 245 members of the sample are listed in Table A1. In addition to the company name, included in the table are each stock’s CUSIP number, the annual capitalization or equity value as of December 1991, the ratio of the firm’s equity to the total for the sample, its beta (December 1991), the R-squared for the firm’s hedge regression (discussed in the text and in the next section below). II. Hedge Portfolios

Throughout the paper we emphasized the potential importance of the multiple correlation coefficient from the regression of a given stock return on all the other returns in the sample, i.e. the proportion of the variance of a given return that can be explained by the set of all other returns. For concreteness we reproduce in Table A2 the coefficients and t ratios from the hedge regressions for the four stocks that are emphasized in our study: Boeing, British Gas, Courtaulds PLC, and

Shell Transport. Given the more than 700 degrees of freedom for each regression, coefficients

-28-

with f statistics over 1.95 are significantly different from zero at the 5% level; significant coefficients are boxed in the table. III. Baseline Portfolios

As noted in the text, the net purchase of a given stock as a result of the receipt or discovery of new information was calculated by finding the change in the investor’s final holding of the affected stock from the holding in a baseline portfolio. Two methods for calculating the baseline were noted in the paper. An obvious candidate was to use only sample information for the baseline calculation, essentially assuming that the sample means, variances, and covariances could be used as reasonable proxies for an investor’s subjective expectations for future periods. A problem that developed with this approach was that the baseline portfolio calculated using only the sample information looked very different from the market portfolio. Many stocks were held in short positions, and the ratio of a given stock’s holding in the baseline portfolio to the total outstanding value of its equity was often far different from the corresponding ratio in the market portfolio.

Although we later determined that the difference in baselines had no effect on the conclusions of this study (see Table A3 below), this unusual looking baseline prompted us to modify, in the body of the paper, the procedure used for its calculation. In the paper we modified the vector of expected returns (but not the covariance matrix) to derive a new baseline portfolic that was identical to the market portfolio: each stock was held in proportion to the ratio of the total value of the equity of the firm to the total value of equity (annual capitalization) for the whole sample of

245 stocks. (See column 5 of Table A1, below, for these ratios.) This modification was achieved by using equation (8) in the text: z= A/2C_ l m. Normally, sample estimates of the covariance

matrix C, a value for 4, and the vector of expected excess returns m would be used with equation (8) to solve for z, the vector of stock holdings. To get optimal holdings that mimic tre market

portfolio, one can define z as the series of ratios equal to those for the market portfolio and then

solve (8) for the vector of expected excess returns, m, that are consistent with the chosen vector of ratios. Tobin’s separation theorem establishes that, given this latter vector of expected excess

returns, any optimal vector of risky asset holdings will be proportional to the market portfolio.

-29-

Table A3 presents the results of two experiments with the alternative baseline, using the observed sample values for excess expected returns. In the upper panel, we reproduce the experiment for the larger wealth level ($5 billion) and a 10% change in the price of a given stock within two weeks -- first run in Table 2 using the constructed or "synthetic" baseline. As can be seen by comparing these results to those in Table 2, there is no change in the conclusion: for each firm, the investor seeks to buy up all the outstanding equity of the firm.

| In the lower panel, we gauge the impact of a change in the riskless rate of interest on the results of the previous experiment; the riskless rate of interest is raised to 8% from 6.97%. The higher riskless rate of interest changes the quantitative results only a little, and the qualitative results not at all. In fact, the changes from the baseline of both panels in Table A3 are identical.

This result is predicted above by equation (16).

Stock #

ON On F&F WD =

oe ee ee ee ee afr WN + O ©O

16

CRSP CUSIP

00176510 00192010 00282410 00814010 00915810 01310410 01371610 01951210 02003910 02224910 02261510 02355110 02451E10 02470310 02532110 02553710 02581610 02635110 02660910 02687410 03017710 03095410 03189710 03190510 03522910 03948310 04882510 05301510 05430310 05527020 05534B10 05538H20 05943810 06605010 06636510 06738E20 07170710 07181310 07785310 07986010 09367110 09702310

-30- Table A1

Sample Members and Characteristics

Stock

AMR CORP DEL

ARCO CHEMICAL CO

ABBOTT LABS

AETNA LIFE & CAS CO

AIR PRODUCTS & CHEMICALS INC ALBERTSONS INC

ALCAN ALUMINUM LTD

ALLIED SIGNAL INC

ALLTEL CORP

ALUMINUM COMPANY AMER ALZA CORP AMERADA HESS CORP AMERICAN BARRICK RES CORP AMERICAN BRANDS INC AMERICAN CYANAMID CO AMERICAN ELECTRIC POWER INC AMERICAN EXPRESS CO AMERICAN GENERAL CORP AMERICAN HOME PRODS CORP AMERICAN INTERNATIONAL GROUP INC AMERICAN TELEPHONE & TELEG CO AMERITECH CORP

AMP INC

AMOCO CORP ANHEUSER BUSCH COS INC ARCHER DANIELS MIDLAND CO ATLANTIC RICHFIELD CO AUTOMATIC DATA PROCESSING INC AVON PRODUCTS INC

BAT INDUSTRIES LTD

BCEINC

BET PUBLIC LIMITED COMPANY BANC ONE CORP

BANKAMERICA CORP BANKERS TRUST NY CORP BARCLAYS PLC

BAUSCH & LOMB INC

BAXTER INTERNATIONAL INC BELL ATLANTIC CORP BELLSOUTH CORP

BLOCK H & R INC

BOEING CO

Annual Capitalization (Billions)

5.088 4.196 25.422 5.119 5.297 6.677 4.120 8.569 4.216

6.137 ..

3.515 4.259 4.386 8.210 5.195 6.113 11.891 6.159 21.048 24.541 68.116 19.178 6.095 24.191 16.189 8.652 18.223 7.470 3.975 21.785 10.085 4.390 12.296 16.149 5.687 37.181 3.202 9.021 22.187 25.360 4.211 13.616

Relative Size

0.0011 0.0009 0.0057 0.0012 0.0012 0.0015 0.0009 0.0019 0.0009

0.0014 0.0008 0.0010° 0.0010 0.0018 0.0012 0.0014 0.0027 0.0014 0.0047 0.0055 0.0153 0.0043 0.0014 0.0054 0.0036 0.0019 0.0041 0.0017 0.0009 0.0049 0.0023 0.0010 0.0028 0.0036 0.0013 0.0084 0.0007 0.0020 0.0050 0.0057 0.0009 0.0031

Beta

1.4 1.3 0.9 1.0 1.4 0.8 1.1 1.0 0.9 1.2 1.8 0.8 0.8 1.1 1.2 0.5 1.3 1.1 0.8 1.1 0.7 0.6 1.3 0.5 1.1 1.0 0.6 1.0 1.4 1.1 0.4 0.7 1.2 1.2 1.3 0.9 1.1 1.0 0.6 0.6 0.9 1.1

R-Squared

0.70 0.36 0.66 0.61

0.54 0.54 0.69 0.51

0.38 0.71

0.49 0.57 0.55 0.50 0.57 0.65 0.60 0.43 0.60 0.71

0.60 0.77 0.59 0.68 0.57 0.50 0.69 0.50 0.39 0.53 0.46 0.39 0.48 0.57 0.61

0.54 0.53 0.52 0.77 0.77 0.51

0.56

Stock | CRSP # CUSIP 43 09959910 44 11012210 45 11041930 46 11088940 47 11080140 48 .11102140 49 11216960 50 11588510 51 12189710 52 12550910 53 12611710 54 12614910 55 13442910 56 13644030 57 13985910 58 14414110 59 14912310 60 15235710 61 16381210 62 16675110 63 17119610 64 17123210 65 17303410 66 19121610 67 19416210 68 20279510 69 20588710 70 209171110 71 2096" 510 72 21666910 73 21985010 74 22268740 75 23975310 76 24419910 77 24736110 78 24801910 79 25084710 80 25384910 81 25406310 82 25468710 83 25747010 84 2578€710

-31-

Table A1

Sample Members and Characteristics

Stock

BORDEN INC

BRISTOL MYERS SQUIBB CO BRITISH AIRWAYS PLC

BRITISH PETROLEUM PLC

BRITISH GAS PLC

BRITISH TELECOMMUNICATIONS PLC BROKEN HILL PROPRIETARY CO LTD BROWNING FERRIS INDS INC BURLINGTON NORTHERN INC ClGNACORP

CN AFINANCIAL CORP

© PC INTERNATIONAL INC CAMPBELL SOUP CO

. CANADIAN PACIFIC LTD

CAPITAL CITIES ABC INC CAROLINA POWER & LIGHT CO CATERPILLAR INC DE

CENTRAL & SOUTH WEST CORP CHEMICAL WASTE MGMT INC CHEVRON CORP

CHRYSLER CORP

CHUBB CORP

CITICORP

- COCA COLA CO

COLGATE PALMOLIVE CO COMMONWEALTH EDISON CO CONAGRA INC

CONSOLIDATED EDISON CO NY INC CONSOLIDATED NATURAL GAS CO COOPER INDUSTRIES INC CORNING INC

COURTAULDS PLC

DAYTON HUDSON CORP

DEERE & CO

DELTA AIR LINES INC DE

DELUXE CORP

DETROIT EDISON CO

DIGITAL EQUIPTMENT CORP DILLARD DEPARTMENT STORES INC DISNEY WALT CO

DOMINION RESOURCES INC VA DONNELLEY R R & SONS CO

Annual Capitalization (Billions)

4.026 34.968 33.831 246.727 186.455 378.061

58.278

4.398

3.825

4.206

6.056

7.645 10.581

4.027

8.349

4.460

5.413

5.486

4.174 23.693

9.371

7.772

8.134 54.852

8.901

4.953

8.136

7.632

4.204

5.370

7.298

3.702

5.400

3.339

2.528

3.922

4.814

4.314

5.149 22.541

6.440

5.092

Relative Size 0.0009 0.0079 0.0076 0.0555 0.0420 0.0851 0.0131 0.0010 0.0009 0.0009 0.0014 0.0017 0.0024 0.0009 0.0019 0.0010 0.0012 0.0012 0.0009 0.0053

0.0021 0.0017 0.0018 0.0123 0.0020 0.0011 0.0018 0.0017 0.0009 0.0012 0.0016 0.0008 0.0012 0.0008 0.0006 0.0009 0.0011 0.0010 0.0012 0.0051 0.0014 0.0011

Beta

1.0 0.8 1.1 0.6 0.9 0.5 0.7 1.4 0.8 1.0 0.8 1.1 1.0 1.1 0.9 0.4 1.0 0.3 1.0 0.7 1.6 0.7 1.2 0.9 1.0 0.4 1.1 0.3 0.5 1.3 1.0 1.1 1.5 0.9 1.3 0.9 0.3 1.4 1:2 1.4 0.3 1.2

R-Squared

0.52 0.71

0.56 0.68 0.56 0.57 0.39 0.54 0.50 0.61

0.65 0.61

0.49 0.52 0.49 0.56 0.53 0.63 0.49 0.69 0.49 0.61

0.60 0.76 0.64 0.48 0.57 0.62 0.56 0.55 0.57 0.28 0.56 0.54 0.65 0.52 0.49 0.54 0.55 0.58 0.61

0.55

Stock #

85 86 87 88 89 90 91

92 93 94 95 96

97

98

99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126

CRSP CUSIP

26054310 26353410 26439910 26483010 27746110 29101110 29356110 29364F 10 29765910 30229010 30257110

- 31358610

34386110 34537010

_ 36232010

36473010 36476010 36960410 37033410 37044210 37044240 37055010 37056310 37246010 37329810 37576610 37732730 38255010 38388310 39056810 40621610 41135230 42307410 42786610 42823610 43357850 43707610 43812830 43850610 44216110 44485910 45067910

-32- Table A1

Sample Members and Characteristics

Stock Annual Capitalization (Billions) DOW CHEMICAL CO 15.624 DU PONT E | DE NEMOURS & CO 31.785 DUKE POWER CO 7.401 DUN & BRADSTREET CORP 10.289 EASTMAN KODAK CO 13.171 EMERSON ELECTRIC CO 12.335 ENRON CORP 5.371 ENTERGY CORP 5.780 ETHYL CORP 3.388 EXXON CORP 75.884 F P L GROUP INC 6.586: FEDERAL NATIONAL MORTGAGE ASSN 20.850 FLUOR CORP 3.404 FORD MOTOR CO DE 20.928 G-T E CORP 32.226 GANNETT INC 7.316 GAP INC 4.748 GENERAL ELECTRIC CO ~ 73:020 GENERAL MILLS INC 11.224 GENERAL MOTORS CORP 22.743 GENERAL MOTORS CORP (GME) 6.779 GENERAL PUBLIC UTILS CORP 3.061 GENERAL RE CORP 9.790 GENUINE PARTS CO 3.893 GEORGIA PACIFIC CORP 5.500 GILLETTE CO 12.498 GLAXO HOLDINGS PLC 71.493 GOODYEAR TIRE & RUBR CO 4.899 GRACE WR & CO ‘ 3.605 GREAT LAKES CHEM CORP 4.937 HALLIBURTON COMPANY 3.080 HANSON PLC 87.736 HEINZ H J CO 11.159 HERSHEY FOODS CORP 3.521 HEWLETT PACKARD CO 17.588 HITACHI LIMITED 196.165 HOME DEPOT INC 22.337 HONDA MOTOR LTD 20.183 HONEYWELL INC 4.572 HOUSTON INDUSTRIES INC 5.941 HUMANA INC 3.249 | T T CORP 8.590

Relative Size

0.0035 0.0072 0.0017 0.0023 0.0030 0.0028 0.0012 0.0013 0.0008 0.0171 0.0015 0.0047

0.0008

0.0047 0.0073 0.0016 0.0011 0.0164 0.0025 0.0051 0.0015 0.0007 0.0022 0.0009 0.0012 0.0028 0.0161 0.0011 0.0008 0.0011 0.0007 0.0198 0.0025 0.0008 0.0040 0.0442 0.0050 0.0045 0.0010 0.0013 0.0007 0.0019

1.1

Beta R-Squared 1.2 0.61 1.1 0.69 0.3 0.60 0.9 0.46 0.8 0.51 1.2 0.60 0.7 0.42 0.7 0.40 1.4 0.49 0.6 0.73 0.4 0.56 1.4 0.61 1.5 0.53 1.2 0.67 0.7 0.60 1.2 0.56 1.7 0.54 1.2 0.75

“0.9 0.63 1.0 0.65 1.1 0.45 0.5 0.41 0.7 0.57 0.9 0.53 1.4 0.57 1.3 0.55 1.2 0.62 1.1 0.40 1.3 0.50 1.3 0.46 1.2 0.67 0.9 0.65 0.9 0.58 1.0 0.55 1.5 0.57 0.4 0.79 1.4 0.58 0.6 0.64 1.1 0.49 0.4 0.59 0.7 0.46

0.63

Stock #

127 128 129 130 131

132 133 134 135 136 137 138 139 140 141

142 143 144 145 146 147 148 149 150 151

152 153 154 155 156 157 158 159 160 161

162 163 164 165 166 167 168

CRS) CUSIP

45230810 452454110 452704150 45303840 45325840 459200110 45950610 46014610 47816010 48258<.10 48783610 49436810 50155620 53245710 53271610 54042410 56979010 57174810 57459910 576879120 57777610 58013510 58505510 58574510 58933110 5901 8&10 604056110 60705¢'10 61166210 61688010 617446110 62007€110 628900110 638535140 63858510 65163710 65248770 655844.10 65653160 66581510 669380110 67076810

Sample Members and Characteristics

Stock

ILLINOIS TOOL WKS INC IMCERA GROUP INC

IMPERIAL CHEMICAL INDS PLC IMPERIAL OIL LTD

INCO LTD

INTERNATIONAL BUSINESS MACHS INTERNATIONAL FLAVORS & FRAG INTERNATIONAL PAPER CO JOHNSON & JOHNSON

K MART CORP

KELLOGG COMPANY KIMBERLY CLARK CORP KYOCERA CORP

LILLY ELI & CO

LIMITED INC

LOEWS CORP

MARION MERRELL DOW INC MARSH & MCLENNAN COS INC MASCO CORP

MATSUSHITA ELECTRIC INDL LTD MAY DEPARTMENT STORES CO MCDONALDS CORP MEDTRONIC INC

MELVILLE CORP

MERCK & CO INC

MERRILL LYNCH & CO INC MINNESOTA MINING & MFG CO MOBIL CORP

MONSANTO COMPANY MORGAN J P & CO INC MORGAN STANLEY GROUP INC MOTOROLA INC

NB D BANCORP INC

NATIONAL WESTMINSTER BK PLC NATIONSBANK CORP NEWMONT GOLD CO

NEWS CORP LTD

NORFOLK SOUTHERN CORP NORSK HYDRO AS

NORTHERN TELECOM LTD NORWEST CORP

NYNEX CORP

~33- Table A1

Annual Capitalization (Billions)

3.649 2.568 46.567 6.154 2.440 28.770 4.188 8.154 33.063 9.945 15.950 9.469 12.996 17.777 9.782 7.820 7.142 6.653 4.507 194.686 8.737 17.740 5.673 5.554 49.751 6.115 22.049 25.166 7.062 12.554 4.240 13.990 5.219 59.932 12.536 3.395 17.331 8.616 4.519 10.662 6.040 17.295

Relative Size 0.0008 0.0006 0.0105 0.0014 0.0005 0.0065 0.0009 0.0018 0.0074 0.0022 0.0036 0.0021 0.0029 0.0040 0.0022 0.0018 0.0016 0.0015 0.0010 0.0438 0.0020 0.0040 0.0013 0.0013 0.0112 0.0014 0.0050 0.0057 0.0016 0.0028 0.0010 0.0031 0.0012 0.0135 0.0028 0.0008 0.0039 0.0019 0.0010 0.0024 0.0014 0.0039

Beta

1.2 1.2 1.2 0.5 14

0.7 1.2 1.3 1.0 1.5 0.7 0.9 0.5 1.1

1.9 0.9 1.0 0.8 1.3 0.5 1.4 1.0 1.0 1.3 0.8 1.7 0.9 0.8 11

1.1

1.4 1.5 11

0.9 1.4 0.3 2.1

14

1.0 1.0 1.2 0.6

R-Squared

0.54 0.46 0.61 0.39 0.54 0.66 0.53 0.64 0.70 0.55 0.59 0.48 0.68 0.61 0.56 0.57 0.35 0.51 0.52 0.80 0.57 0.57 0.50 0.52 0.73 0.61 0.68 0.73 0.53 0.62 0.49 0.55 0.50 0.54 0.54 0.53 0.54 0.60 0.47 0.60 0.52 0.68

205 206 207 208 209 210

69511410 69921610 70816010 70905110 71344810 71708110 71753710 71815410 71833750 73850719 F2447919 74158910 74271819 Y4a457310 74740219 7S571770 PSBV1O1O

78028770 78108810

73549Bi0

Da iat ote te 3355985.

84258710

84533310 85206110 86387150 86676210 86791410

-34-

Table A1

Sample Members and Characteristics

Ori EDISON CO

PN C FINANCIAL COAF

PPG INDUSTRIES INC

PACIFIC GAS & ELEC CG

PACIFIC TELESIS GROUP PACIFICORP

PARAMOUNT COMMUNICATIONS INC PENNEY J C INC

PENNSYLVANIA POWER & LIGHT CO PEPSICO INC

PFIZER INC

PHILADELPHIA ELECTRIC Co

PHILIP MORRIS COS INC

PHILIPS NV

PHILLIPS PETROLEUM OO

PITNeY SOWES INC

PRIMERICA CORP NEW

PROCTER & GAMBLE CO

PUBLIC SERVICE ENTERPRIS GROUP QUAKER OATS CO

RAYTHEON COMPANY

REEBOK INTERNATIONAL. >

ao 2G Oi HOC RAS APT pate SUS BEMAMAID iil SAE SSR SOA PRO DAL WA ON fa loi et

SCUTHWESTERN BELL CORP SPRINT CORP

STUDENT LOAN MARKETING ASSN SUN INC

SUNTRUST BANKS INC

Annual Wwacilsization

Relative

CALS

G.0008 0.0015 5.0076 0.0032 0.0040 0.0012 0.0012 0.0021 9.0009 0.0074 0.0054 0.0013 0.0156 0.0007 C.0015 6.0014 0.0012 6.0082 6.0016 0.001 4 0.0616 0.0007 0.0067 0.0015

0.0027 0.0050 0.0013 0.0014 0.0007 0.0012

Beta

C.6

SE 2 ee ee am ee a Oo FF MYO WO W

ch Oo Ff

Oo Oo ©

G

OOD : Ooo F O GD

Fao @ mM PO OD

c? wo oD

w

S-oivared

~35-

Table A1 Sample Members and Characteristics

Stock CRISP Stock Annual Relative Beta R-Squared # CUSIP Capitalization Size (Billions)

211 87161610 SYNTEX CORP 5.191 0.0012 1.4 0.53 212 87182910 SYSCO CORP 4.942 0.0011 1.1 0.53 213 87235140 TDK CORP 3.797 0.0009 0.3 0.63 214 87933220 TELEFONICA DE ESPANAS A 27.345 0.0062 0.8 0.55 215 88037010 TENNECO INC 5.088 0.0011 0.8 0.45 216 88169410 TEXACO INC 15.458 0.0035 0.6 0.51 217 = 88284810 TEXAS UTILITIES CO 9.236 0.0021 0.4 0.50 218 = =—88320310 TEXTRON INC 3.886 0.0009 1.0 0.46 219 = 8873°510 TIME WARNER INC 10.867 0.0024 1.3 0.41 220 = 88736010 TIMES MIRROR CO 4.018 0.0009 1.3 0.57 221 89233510 TOYS RUS 11.681 0.0026 1.3 0.58 222 89348510 TRANSAMERICA CORP 3.764 0.0008 1.1 0.53 223 =6902549910 UAL CORP 3.057 0.0007 1.4 0.46 224 = 90290582 US X MARATHON GROUP INC 4.938 0.0011 1.1 0.49 225 90291110 USTINC 6.665 0.0015 1.0 0.52 226 90476760 UNILEVER PLC 54.468 0.0123 0.9 0.68 227 = 90478450 ~=UNILEVERN V 16.684 0.0038 0.8 0.80 228 90552010 UNION CAMP CORP 3.211 0.0007 1.1 0.55 229 90654810 UNION ELECTRIC CO 3.817 0.0009 0.3 0.47 230 90781810 UNION PACIFIC CORP 11.894 0.0027 1.1 0.59 231 9127€710 UNITED STATES SURGICAL CORP 3.816 0.0009 0.7 0.44 232 9128€910 UNITED STATES WEST INC 15.864 0.0036 0.7 0.69 233, = 91301710 UNITED TECHNOLOGIES CORP 5.953 0.0013 1.3 0.53 234 91528910 UNOCAL CORP 6.131 0.0014 0.9 0.58 235 91530210 UPJOHN CO 5.648 0.0013 1.2 0.46 236 92977110 WACHOVIA CORP 5.832 0.0013 0.8 0.49 237 93114210 WAL MART STORES INC 73.560 0.0166 1.2 0.72 238 93142210 WALGREEN COMPANY 5.369 0.0012 1.3 0.49 239 93448810 WARNER LAMBERT CO 9.320 0.0021 1.0 0.62 240 94974010 WELLS FARGO &CO NEW 4.142 0.0009 1.3 0.62 241 96040210 WESTINGHOUSE ELECTRIC CORP 4.604 0.0010 1.2 0.50 242 96216610 WEYERHAEUSER COMPANY 7.519 0.0017 1.5 0.56 243 98088310 WOOLWORTH CORP 4.147 0.0009 1.3 0.52 244 = =998252510 WRIGLEY WILLIAM JR CO 3.817 0.0009 1.1 0.64

245 98412110 XEROX CORP 7.521 0.0017 1.2 0.52

~36- Table A2

Hedge Regressions for 4 Key Stocks*

(0.0086) (2.25) i.0820 (0.0320) (0.945 (0.0289) (0.76) (0.0017) (0.04)

Oo ON BD

and oO

i. 6.0004 002 3 (0.0162)

5 (0.0241

9 G.041E 23 9 (5.0762)

‘ 0.0189) 4a

| (04188)

j ADa

24S wes

37 0.0248 3.68 38 (0.0285) (0.83)

British Gas (#47)

~Aarameier eatimais

©),0379} “0185

ns

1

(5.0275) £0.88) 9.0188 28 (0.0087) (0,25) (5.0439) (4.01) 9.0344) (0. 2.0078 0 0.0257 O77 (0.0254) 9.0028 9194 ©9053

2.0151

a] oO iO — Po

we) mae wn (62) ne

iatalatet!

J359

3.0152 5.49

* Numbers in parentheses are negative values.

Courtaulds PLC (#74)

0.0320 0.52 (0.0864)

0.0483 1.4 (33,0048) (92,0048) (0.1743 G,0014 0.02

O.073E 1.16

(0.0017) (0.03)

Shell T-ansport (#203)

= grameter ? tetimate Statistic

0985 0.56 (0.0094) (0.64) 0.0068 0.35 (0.0220) 0.0151 0.93 0.0116 0.57 0.0167 1.44 (0.0027) (0.16) (0.0179) (1.47) (0.0173) 69.0535)

(0.0181)

6.0013 0.06 (9.0276) (1.50) (0.0189) (0.62)

(0.0794) (1.17) (2.0016) (0.07)

lam aEalas

Stock #

39 40 41

42 43 44 45 46 47 48 49 50 51

52 53 54 55 56 57 58 59 60 61

62 63 64 65 66

67 68 69 70 71 72 73 74 75 76

~37- Table A2 Hedge Regressions for 4 Key Stocks*

Boeing British Gas Courtaulds PLC Shell Transport (#42) (#47) (#74) (#203) Parameter t Parameter t Parameter t Parameter t Estimate Statistic Estimate _ Statistic Estimate Statistic Estimate Statistic (0.0457) (0.74) (0.0712) (1.28) 0.0226 0.23 2.47 0.0769 1.12 0.0053 0.09 (0.0376) (0.34) 0.0133 0.45 0.0286 0.83 (0.0026) (0.08) (0.0240) (1.65) NA NA (0.0065) (0.20) (0.0179) (0.31) (0.0264) (1.72) (0.0569) —(1.50) 0.0045 0.13 (0.0776) —(1.27) 0.0497 0.90 (0.0209) (0.42) (0.0410) (0.46) (0.0086) (0.36) 0.0373 1.12 0.0236 0.78 0.0526 0.98 (0.0053) (0.37) 0.0309 ~—s- 0.52 0.0249 «0.26 (0.0079) (0.20) NA NA 0.0379 0.59 0.0221 1.31 [01034] 230 _] (0.0008) (0.01) (0.0005) (0.01) (0.0200) (0.59) 0.0082 0.14 (0.0157) (0.99) 0.0130 0.45 0.0333 1.28 (0.0157) — (0.34) 0.0083 0.68 0.0154 0.50 (0.0192) (0.38) (0.0090) (0.68) (0.0208) (0.46) 0.0051 0.13 0.0189 0.27 (0.0047) (0.25) (0.0659) (1.70) 0.0130 = 0.21 (0.0205) (1.24) 0.0435 0.93 0.0803 1.89 (0.0372) (0.49) 0.0062 0.31 0.0341 1.15 0.0060 0.22 (0.0099) ~— (0.21) 0.0045 0.36 (0.0110) (0.26) (0.0571) — (1.50) 0.0020 0.03 0.0296 1.66 (0.0343) (0.82) 0.0213 0.56 (0.0536) —- (0.79) (0.0254) (1.42) (0.0855) — (1.17) (0.0297) (0.45) 0.0201 0.17 0.0469 1.51 (0.0128) (0.34) (0.0364) (1.06) (0.0324) (0.53) (0.0042) (0.26) (0.0015) (0.02) 0.0452 0.71 0.1894 1.67 (0.0508) — (1.70) (0.0468) (1.73) (0.0102) (0.41) (0.0627) (1.43) (0.0178) (1.54) 0.0503 0.95 0.0015 0.03 0.0311 1.38 0.0187 0.77 (0.0303) (1.37) (0.0529) — (1.34) 0.0098 0.95 (0.0244) (0.52) (0.0050) (0.12 0.0271 0.36 0.0074 0.38 0.0143 0.51 (0.0290) (1.14) 0.0287 0.64 (0.0149) (1.25)

(0.0438) (0.83) 0.0645 1.34 (0.2115) (2.48) 0.0021 0.09

0.0715 1.61 (0.0282) (0.70) (0.0527) (0.74) 0.0438

(9.0930) (1.89) (0.0269) (0.60) (0.0418) (0.53) 0.0174 0.83 (9.0199) (0.58) 0.0309 0.99 0.0216 0.39 0.0015 0.10 9.0628 0.96 (0.0961) (1.63) (0.0451) (0.43) (0.0057) (0.21) (0.0682) (1.52) (0.0122) (0.17) (0.0173) (0.91) 9.0123 0.32 (0.0002) 0.01) (0.0231) (0.38) (0.0036) 0.22) 9.0465 1.29 (0.0325) (1.00) 0.0087 0.15 (0.0098) (0.64) (0.0069) (0.31) 0.0120 0.59 NA NA 0.0096 1.01 0.0636 1.68 0.0528 1.54 (0.0337) (0.55) 0.0156 0.97 19.0206 0.59 (0.0129) (0.41) 0.0295 0.53 (0.0029) (0.20)

* Numbers in parentheses are negative values.

Stock #

77 78 79 80 81

190 101 . 102 103

104

105 106 . 107 108 109 110 111 112 113 114

—38- Table A2 Hedge Regressions for 4 Key Stocks*

* Numbers in parentheses are negative values.

Boeing British Gas Courtaulds PLC Shell Transport (#42) #47 (#74) (#203) Parameter t Parameter t Parameter t Parameter t Estimate Statistic Estimate Statistic Estimate Statistic Estimate Statistic 0.0112 0.27 (0.0106) (0.29) (0.0750) —(1.14) (0.0295) (1.18) (0.0476) ~— (1.35) 0.0280 0.87 (0.0187) (0.33) 0.0032 0.21 0.0708 1.36 0.0035 0.07 (0.0604) —- (0.72) 0.0374 1.69 0.0199 0.65 0.0080 0.29 (0.0041) (0.08) (0.0125) (0.96) 0.0202 0.60 (0.0066) — (0.22) (0.0084) (0.16) 0.0204 1.43 0.0437 1.09 0.0175 0.48 0.0415 0.64 0.0188 1.10 , (0,0722) (0.86) (0.0840) ~— (1.10) (0.0558) — (0.41) (0.0251) (0.70) 0500 1.18 0.0254 0.66 (0.0349) (0.51) (0.0129) (0.71) “<0.0718 4.75 0.0269 0.72 (0.0341) (0.52) 0.0130 0.74 (00073), (0. 15) (0.0219) (0.49) 0.1440 1.81 (0.0054) (0.26) (0.0030) (0.05) (0.0088) (0.15) 0.0970 0.90 0.0C78 ~=—- 0.27 0.0144 0,38 (0.0649) — (1,86) (0.0065) (0.11) 0.0C15 0.09 (0.0161) (0.46) 0.0508 1.61 (0.0196) (0.35) (0.0184) (1.24) (0.0061) (0.15) 0.0444 1.17 (0.0473) (0.70) (0.0131) (0.73) (0.0850) (1.45) (0.0179) (0.52) 0.0126 0.21 0.0035 0.21 (0.0113) (0,29) (0.0123) (0.35) 0.0172 0.28 0.0018 0.11 (0.0232) (0.79) 0.0156 0.59 0.0252 0.54 (0.0206) (1.67) (0.0318) (0.52) (0.0157) (0.28) (0.0527) (0.53) (0.0194) (0.74) _ (0.0465) ~—- (0.67) (0.0429) (0.68) (0.0981) (0.87) (0.0088) (0.30) 0.0205 0.66 0.0480 1.71 (0.0057) — (0.11) (0.0046) (0.35) 0.0172 0.64 0.0446 1.82 0.0370 0.85 (0.0242) | (2.11) | 0.0569 1.34 0.0696 1.81 0.0135 0.20 0.0059 0.32 0.0571 1,24 0.0339 0.81 (0.0080) (0.11) (0.0°48) (0.76) __0,0199 0.54 0.1105 1.85 (00°78) (1.13) ~ (0.0003) ~@.0T) = (@.0102) (0.48) (0.0111) (0.28) 0.0010 0.09 9.0165 0.29 (0.0522) (1.03) (0.0008) — (0.01) (0.0153) (0.64) 0.0109 0.23 (0.0069) ~— (0.16) 0.0391 0.52 (0.0087) (0.44) (0.0366) (0.90) .—«-(0.0108) +~—= (0.28) 0.0676 1.03 (0.0158) (0.91) [00741 [ 208 | (0.0082) (0.28) 0.0521 oot [ o.osaa | 228 | (0.0762) (1.21) 0.0529 0.92 (0.1466) (1.44) nt 191) (0.71) - (09,0103) (0.22) 0.0353 0.84 (0.0376) (0.50) 0.0091 0.46 __.0.0129 0.30 0.0168 0.24 0.0:290 1.61 ~ 0.0561 1.59 0.0302 0.94 (0.0117) (0.20) (0.0259) (1.73) (0.0024) (0.07) (0.0257) (0.88) (0.0860) (1.65) 0.0018 0.13 0.0217 0.57 0.0078 0.23 0.0539 0.88 0.0048 0.30 0.0024 0.09 (0.0079) (0.33) (0.0240) — (0.56) 0.0012 0.11 0.0072 0.25 0.0060 0.23 0.0366 0.78 0.000 0.00 (0.0475) — (1.42) 0.0121 0.40 0.0693 1.28 (0.0995) (0.67)

—39- Table A2 Hedge Regressions for 4 Key Stocks*

Boeing British Gas Courtaulds PLC Shell Transport (#42) (#47) (#74) (#203) Stock Parameter t Parameter t Parameter t Parameter t # Estimate Statistic Estimate Statistic Estimate Statistic Estimate _ Statistic 115 (0.0251) (0.69) 0.0140 0.43 (0.0617) (1.05) 0.0113 0.73 116 0.0270 0.63 0.0582 1.50 (0.0813) (1.17) 117 0.0673 1.71 0.0019 0.05 0.0311 0.49 0.0066 0.40 118 (0.0228) (0.59) 0.0122 0.35 (0.0259) (0.42) 119 0.0173 0.60 0.0170 0.65 (0.0453) (0.97) 0.0159 1.30 120 (0.0160) (0.3) (0.0072) (0.16) 0.1084 1.39 (0.0238) (1.15) 121 0.0046 0.15 0.0055 0.20 (0.0571) (1.18) (0.0104) (0.81) 122 0.0494 1.31 (0.0014) (0.04) 0.0772 1.27 0.0035 0.22 123 (0.0022) (0.06) (0.0037) (0.23) 124 0.0341 0.51 (0.0610) (0.57) (0.0262) (0.92) 125 (0.0477) (1.55) 0.0021 0.07 0.0305 0.61 0.0092 0.70 126 (0.0150) (0.30) 0.0058 0.13 0.0255 0.32 (0.0001) 0.00) 127 0.0705 (0.0619) (1.98) 0.0306 0.54 0.0021 0.14 128 (0.0957) (0.0276) (0.90) (0.0319) (0.59) (0.0015) (0.10) 129 (0.0044) (0.08) 0.0900 1.91 (0.0615) (0.7) 0.0214 0.97 130 0.0166 0.32 (0.0298) (0.63) 0.1286 1.56 0.0048 0.22 131 (0.0348) (1.05) (0.0088) (0.29) (0.0647) (1.21) (0.0206) (1.47) 132 0.0051 0.09 (0.0123) (0.25) 0.0001 0.01 133 0.0368 0.87 (0.0562) (1.46) (0.0196) (0.29) (0.0298) (1.65) 134 (0.0253) (0.57) 0.0215 0.54 (0.0686) (0.96) (0.0078) (0.41) 135 (0.0516) (0.99) 0.0502 1.06 (0.0400) (0.48) 0.0157 0.71 136 0.0090 0.25 0.0422 1.31 0.0416 0.72 0.0011 0.07 137 (0.0510) (1.11) 0.0094 0.23 (0.0893) (1.21) (0.0062) (0.32) 138 (0.0011) (0.03) 0.0652 1.77 0.1003 1.53 (0.0270) (1.56) 139 0.0373 0.92 (0.0250) (0.68) 0.0030 0.18 140 0.0070 0.15 0.0314 0.77 (0.0370) (0.51) 0.0119 0.62 141 [| oo | 197 |] (0131) (60) (0.0558) (1.44) 142 (0.0073) (0.15) 0.0077 0.18 (0.0138) 0.18) 0.0133 0.65 143 0.0141 0.62 (0.0213) (1.0) 0.0226 0.61 0.0105 1.07 144 0.0280 0.64 (0.0028) (0.07) (0.0449) (0.64) (0.0235) (1.27) 145 (0.0493) (1.51) (0.0182) (0.61) (0.1023) (1.95) 0.0237 1.71 146 (0.0236) (0.43) 0.0072 0.14 (0.0054) (0.23) 147 (0.0407) (1.12) (0.0094) (0.28) 0.0420 0.71 148 [| o0oste | 206 | (0.0429) (1.19) 0.1232 1.93 (0.0130) (0.77) 149 0.0181 0.49 0.0019 0.06 (0.0185) —(1.19) 150 0.0427 1.09 (0.0311) (0.88) (0.0385) (0.61) (0.0073) (0.44) 151 0.0415 0.71 (0.0420) (0.80) 0.0521 0.55 0.0178 0.72 152 (0.0213) (0.67) 0.0331 1.14 (0.0612) (1.19) (0.0084) (0.62)

* Numbers in parentheses are negative values.

—~40- Table A2 Hedge Regressions for 4 Key Stocks*

Boeing British Gas Courtaulds PLC Shell Transport (#42) (#47) (#74) (#203) Stock Parameter t Parameter t Parameter t Parameter t # Estimate Statistic Estimate Statistic Estimate Statistic Estimate Statistic 153 0.0513 0.90 (0.0397) (0.76) (0.1667) (1.81) 0.0178 0.73 154 (0.1148 1.85. 0.0063 0.11 0.1140 1.14 0.01224 0.47 155 (2.08) (0.0032) (0.09) (0.0970) — (1.52) (0.0154) (0.91) 156 0.0272 0.77 0.0916 1.46 (0.0046) (0.28) 157 -:0,0010 0.03 (0.0537) (1,68) 0.0679 1.20 0.02221 1.48 4158 ~~ (0.0118) —- (0.40) . (0.0056) ~—- (0.21) (0.0151) (0.31) 0.0136 1.47 459 (0.0219) 0.58) =. 0.0058) 0.17 0.0948 1.55 (0.0029) (0.18) 1605500843) = (0:94) (0.0474) (0.80) (0.0199) (1.27) asv@1 9000292) (02) (0.0018) (0.07) 0.0160 0.35 0.0138 1.38 (e162 2540:0299) (104) 0.014805 (0.0009) —- (0.02) 0.0091 —-~0.75 “163+ (00261) (1.34) ~ 90,0205 1.16 0.0286 0.91 0.0098 0.09 - 164 0.0544 1.27 (0.0111) (0.29) 0.0134 0.19 (0.0034) (0.52) 165 0:0480 1.48 0.0289 0.98 0.0897 1.71 0.0044 0.32 “166 0.0602 4.53 0.0139 0.39 0.0239 0.38 0.0097 “0.04 “467 = 0;0295 0:98 (0.0223) (0.77) (0.0262) (0.51) 0.0042 0.31 468 —-2(0}0432) (0:62) 0.0551 0.88 (0.0494) (0.44) 0.0144 0.49 169 1 0:0405 1:28. (0.0130) (0.45) 0.0323 0.63 (0.0014) (0.11) “170 = 0.0382 ——s«7@ (0.0196) (0.43) (0.0712) —- (0.88) 0.0253 1.19 171 0.0124 0.40: (0.0019) (0.07) (0.0324) (0.65) (0.0037) (0.28) 172 0.0615 1.76 0.0288 0.91 0.0547 0.97 0.0102 0.69 173°. «(0.0821 0.59 (0.0619) (1.26) 0.0973 1.11 0.0370 1.61 174 0.0023 0.05 0.0158 0.18 (0.0067) (0.29) 475: -.0,0831 1.54 - (0.0234) (0.48) (0.0284) (0.33) (0.0175) (0.76) A768 00873 1.18 0.0523 1.82 (0.0888) (1.74) 0.0255 1.89 ATT 00207 054 ~, ~—(0.0078) (0.2) (0.0074) ~—(0.12) (0.0060) ~—- (0.37) o178 =e 0280 s(«i.84)=—St—~*«ii«052 0.79 0.0801 0.60 (0.0113) 0.33) “479° 0.0233 «(O55 (0.0380) (0.98) 0.0416 0.60 (0.0003) (0.01) ~ 180 0.0663 1.64 (0.0285) (0.77) 0.0163 0.25 (0.0142) (0.82) 181 2.86 0.0269 0.63 0.0471 0.62 0.0049 ~—-0,25 182 (0.0514) (1.02) 0.0424 0.52 (0.0144) (0.67) 483 (0.0351) (1.18) (0.0208) (0.77) 0.0118 0.25 (0.0056) — (0.45) 1484 0,0189 0.64 (0.0061) (0.22) (0.0454) —- 0.91) 0.0191 1.46 485 © (0.0309) = (0.91) © 0.0292 0.95 0.0782 1.43 (0.0128) (0.89) 186 0.0514 1:74 (0.0425) (1.59) 0.0044 0.09 ‘0.0c91 0.72 187 0.0067 0.13 (0.0008) (0.02) (0.0002) (0.002) | (ooaea | (2.03) | 188 0.1002 1.64 0.0720 1.30 (0.0157) (0.16) 0.0¢51 0.20 189 (0.0647) (1.61) (0.0667) —(1.83) 0.0527 0.81 (0.007) (0.04) 190 (0.0014) (0.03) (0.0228) (0.53) (0.1126) (1.49) (0.0215) (1.08)

* Numbers in parentheses are negative values.

-41- Table A2 Hedge Regressions for 4 Key Stocks*

Boeing British Gas Courtaulds PLC Shell Transport (#42) (#47) (#74) #203 stock Pararneter t Parameter t Parameter t Parameter t

# Estirnate Statistic Estimate Statistic Estimate Statistic Estimate Statistic 191 0.0114 0.58 (0.0016) (0.09) 0.0057 0.18 (0.0062) (0.73) 192 (0.0302) (0.72) 0.0001 0.00 (0.0016) (0.02) 0.0191 1.07 193 0.0152 0.61 0.0284 1.26 (0.0036) (0.09) (0.0028) (0.26) 194 0.0331 1 0.99 (0.0086) (0.30) (0.0403) (0.79) (0.0042) (0.31) 195 (0.0°723) (0.69) 0.1505 1.58 0.0749 0.44 196 0.00032 0.09 (0.0519) (1.55) (0.0098) (0.16) 0.0236 1.51 197 (0.0358) (1.38) 0.0324 1.38 0.0117 0.28 0.0005 0.05 198 0.0511 1.25 0.0268 0.41 0.0269 1.54 199 (0.0396) (0.92) 0.0054 0.14 0.0056 0.08 (0.0179) (0.98) 200 0.07761 1.86 (0.0053) (0.14) 0.0279 0.42 0.0195 1.12 201 (0.0«429) (0.64) 0.0097 0.16 0.0124 0.12 (0.0010) (0.04) 202 0.00048 0.13 (0.0007) (0.02) (0.0461) (0.78) 0.0160 1.03 203 (0.14463) (1.72) 0.1008 1.31 0.1381 1.01 NA NA 204 0.0015 0.03 (0.0109) (0.26) (0.0105) (0.14) 0.0011 0.05 205 (0.0658) (1.14) 0.0161 0.31 0.0887 0.95 (0.0178) (0.72) 206 (0.0861) (1.48) (0.0922) (1.74) (0.1149) (1.22) 0.0150 0.60 207 0.0754 | 273 | (0.0184) (0.73) (0.0588) (1.32) (0.0013) (0.11) 208 0.0017 0.05 0.0309 0.95 0.1116 1.92 0.0014 0.09 209 0.0051 0.15 (0.0010) (0.03) (0.0126) (0.22) 0.0138 0.93 210 0.0068 0.20 (0.0035) (0.12) 0.0446 0.83 (0.0090) (0.63) 211 0.0208 0.66 0.0000 0.00 0.0042 0.08 (0.0185) (1.39) 212 (0.0297) (0.84) (0.0548) (1.70) 0.0542 0.95 (0.0109) (0.72) 213 0.0259 0.71 0.0063 0.19 (0.0467) (0.79) 214 0.04164 1.04 0.0283 0.70 (0.0787) (1.10) (0.0364) (1.92) 215 (0.0009) (0.03) 0.0460 1.55 (0.0210) (0.40) (0.0091) (0.66) 216 (0.0626) (0.73) (0.0408) (1.01) (0.0005) (0.01) (0.0174) (0.92) 217 (0.1 242) | (2.00) | (0.0488) (0.87) (0.0267) (0.27) (0.0313) (1.18) 218 (0.0001) (0.01) 0.0340 1.23 0.0186 0.38 (0.0111) (0.85) 219 0.0005 0.02 0.0008 0.03 0.0492 1.21 0.0194 1.82 220 (0.01 56) (0.48) 0.0576 1.95 (0.0087) (0.16) (0.0157) (1.13) 221 0.0024 0.08 (0.0370) (1.34) 0.0091 0.19 0.0088 0.68 222 (0.0340) (0.86) 0.0514 1.44 0.0232 0.36 0.0069 0.41

223 0.0283 1.70 (0.0068) (0.33) 0.0215 0.59 0.0211 224 0.0296 0.92 (0.0102) (0.35) (0.0644) (1.24) 0.0330

205 0.0057 0.16 0.0218 0.67 (0.0697) (1.20) (0.0008) (0.05) 226 0.0098 0.17 0.0490 0.95 0.0297 1.23 207 (0.0735) (1,04) 0.0533 0.83 (0.1350) (1.19) 0.0203 0.68 228 0.0898 1.49 (0.0284) (0.78) 0.0005 0.01 0.0277 1.62

* Numbers in parentheses are negative values.

Stock #

229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245

-42-

Table A2

Hedge Regressions for 4 Key Stocks*

Boeing (#42) Parameter t Estimate Statistic 0.0169 0.27 (0.0266) (0.58) 0.0168 0.60 0.0683 1.13 0.0367 1.08 0.0269 0.96 0.0071 0.15 0.0244 0.56 0.0432 1.23 0.0564 1.32 0.0537 1.61 (0.0198) (0.60) (0.0152) (0.45) (0.0355) (1.16) (0.0686) (1.77) (0.0285) (0.74)

British Gas (#47) Parameter t Estimate Statistic 0.0151 0.27 0.0130 0.31 (0.0200) (0.78) (0.0140) (0.25) 0.0219 0.61 (0.0484) (1.57) 0.0318 1.25 0.0382 0.88 0.0359 0.91 0.0333 1.04 0.0091 0.23 0.0221 0.73 0.0087 0.29 (0.0497) (1.62) 0.0096 0.34 0.0419 1.19 0.0288 0.82

* Numbers in parentheses are negative values.

Courtaulds PLC

(#74) Parameter t Estimate Statistic (0.0873) (0.87) 0.0261 0.35 0.0200 0.44 0.0574 0.59 (0.0681) (1.24) 0.0080 0.18 (0.0279) (0.36) (0.0723) (1.04) 0.0371 0.65 0.0077 0.11 (0.0330) (0.61) (0.0421) (0.79) (0.0283) (0.52) 0.0224 0.36 (0.1068) (1.72)

Shell Transport

(#203

Parameter Estimate

0.0008 (0.0007) 0.0039 (0 0339) 0 0098 0.0031 0.0060 (0.0296) 0.0198 0.0243 0.0032 0.0273 0.0134 (C.0191) C.0093 (0.0022) (0.0065)

)

Statistic 0.03 (0.04) 0.33 (1.32) 0.59 0.22 0.51 (1.46) 1.08 1.63 0.18 1.92 0.96 (1.33) 0.71 (0.13) (0.40)

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References

Abel, Andrew B. and Frederic S. Mishkin, "An Integrated View of Tests of Rationality, Market Efficiency and the Short-run Neutrality of Monetary Policy,” Journal of Monetary Economics, January 1983, //, 3-24.

Anderson, Ronald W. and Jean-Pierre Danthine, "Cross Hedging," Journal of Political Economy, December 1981, 89, 1182-1196.

Baesel, Jerome B., and Garry D. Stein, "The Value of Information: Inferences from the Profitability of Insider Trading," Journal of Financial and Quantitative Analysis, September 1979, 7/4, 553-71.

Cootner, Paul H., ed., The Random Character of Stock Market Prices, rev. ed., Cambridge, MA: MIT Press, 1967.

Bray, Margaret, "Convergence to Rational Expectations Equilibrium," in Frydman, Roman and Edmund S. Phelps, eds., Individual Forecasting and Aggregate Outcomes, Cambridge: Cambridge University Press, 1983.

Cyert, Richard M. and Morris H. DeGroot, "Rational Expectations and Bayesian Analysis," Journal of Political Economy, May/June 1974, 82, 521-536.

Copland, Thomas E. and J. Fred Weston, Financial Theory and Corporate Policy, 2nd ed., Reading, MA: Addison-Wesley, 1983.

Center for Research in Security Prices (CRSP), CRSP Stock File Guide, Chicago: U. of Chicago, Graduate School of Business, 1991.

De Canio, Stephen J., "Rational Expectations and Learning from Experience," Quarterly Journal of Economics, February 1979, 94, 47-57.

De Long, J. Bradford, Andrei Shleifer, Lawrence H. Summers, and Robert J. Waldman, "Noise Trader Risk in Financial Markets," Journal of Political Economy, August 1990, 98, 703-738.

Elton, Edwin J. and Martin J. Gruber, Modern Portfolio Theory and Investment Analysis, 3rd ed., New York: Wiley, 1987.

Fama, Eugene F., "Efficient Capital Markets: A Review of Theory and Empirical Work," Journal of Finance, May 1970, 25, 383-417.

Figlewski, Stephen, "Market Efficiency’ in a Market with Heterogeneous Information," Journal of Political Economy, August 1978, 86, 581-597.

Fourgeaud, C., C. Gourieroux, and J. Pradel, "Learning Procedures and Convergence to Rationality," Econometrica, July 1986, 4, 845-868.

Friedman, Benjamin M., "Optimal Expectations and the Extreme Information Assumptions of Rational Expectations’ Macromodels,” Journal of Monetary Economics, January 1979, 5, 23-41.

Friedman, Milton, "The Case for Flexible Exchange Rates,” in Essays in Positive Economics, Chicago: U. of Chicago Press, 1953.

Givoly, Dan and Dan Palmon, “Insider Trading and the Exploitation of Inside Informatior.: Some Empirical Evidence," Journal of Business, January 1985, 58, 69-87.

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Haltiwanger, John and Michael Waldman, "Rational Expectations and the Limits of Rationality," American Economic Review, June 1985, 75, 326-340.

Hirshleifer, Jack and John G. Riley, The Analytics of Uncertainty and Information, Cambridge: Cambridge University Press, 1992.

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Mishkin, Frederic S., A Rational Expectations Approach to Macroeconometrics, Chicago: University of Chicago Press for the NBER, 1983.

Mossin, Jan, Theory of Financial Markets, Englewood Cliffs, N.J.: Prentice-Hall, 1973.

Niederhoffer, Victor and M. F. M. Osborne, "Market Making and Reversal on the Stock Exchange," Journal of the American Statistical Association, December 1966, 61, 897-916.

Radner, Roy, "Comment," in Frydman, Roman and Edmund S. Phelps, eds., Individual Forecasting and Aggregate Outcomes, Cambridge: Cambridge University Press, 1983.

Tobin, James, "Liquidity Preference as Behavior Towards Risk," The Review of Economic Studies, february 1958, 25, 65-86.

IFDP Number

477

476

475

474

473

472

471

470

469

468

467

466

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International Finance Discussion Papers

Titles

199

On Risk, Rational Expectations, and Efficient Asset Markets

Finance and Growth: A Synthesis and Interpretation of the Evidence

Trade Barriers and Trade Flows Across Countries and Industries

The Constancy of Illusions or the Illusion of Constancies: Income and Price Elasticities for U.S. Imports, 1890-1992

The Dollar as an Official Reserve Currency under EMU

Inflation Targeting in the 1990s: The Experiences of New Zealand, Canada, and the United Kingdom

International Capital Mobility in the 1990s

The Effect of Changes in Reserve Requirements on Investment and GNP

International Economic Implications of the End of the Soviet Union

International Dimension of European Monetary Union:

Implications For The Dollar

European Monetary Arrangements: Implications for the Dollar, Exchange Rate Variability and Credibility

Fiscal Policy Coordination and Flexibility Under European Monetary Union: Implications for Macroeconomic Stabilization

The Federal Funds Rate and the Implementation of Monetary Policy: Estimating the Federal Reserve’s Reaction Function

Author(s)

Guy V.G. Stevens Dara Akbarian

Alexander Galetovic Jong-Wha Lee Phillip Swagel

Jaime Marquez

Michael P. Leahy John Ammer Richard T. Freeman Maurice Obstfeld

Prakash Loungani Mark Rush

William L. Helkie David H. Howard Jaime Marquez

Karen H. Johnson

Hali J. Edison Linda S. Kole

Jay H. Bryson

Allan D. Brunner

Please address requests for copies to International Finance Discussion Papers, Division of International Finance, Stop 24, Board of Governors of the Federal Reserve System, Washington, D.C. 20551.

{FDP Number

465

464 463

462

461

460

459

458

457

456

455

454

453

452

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International Finance Discussion Papers

Titles

1994 Understanding the Empirical Literature on Purchasing Power Parity: The Post-Bretton Woods Era

Inflation, Inflation Risk, and Stock Returns

Are Apparent Productive Spillovers a Figment of Specification Error?

When do long-run identifying restrictions give reliable results?

1993

Fluctuating Confidence and Stock-Market Returns

Dollarization in Argentina

Union Behavior, Industry Rents, and Optimal Policies

A Comparison of Some Basic Monetary Policy Regimes:

Implications of Different Degrees of Instrument Adjustment and Wage Persistence

Cointegration, Seasonality, Encompassing, and the Demand for Money in the United Kingdom Exchange Rates, Prices, and External Adjustment

in the United States and Japan

Political and Economic Consequences of Alternative Privatization Strategies

Is There a World Real Interest Rate?

Macroeconomic Stabilization Through Monetary and Fiscal Policy Coordination Implications for Monetary Union

Long-term Banking Relationships in General Equilibrium

Author(s)

Hali J. Edison Joseph E. Gagnon William R. Melick John Ammer

Susanto Basu John S. Fernald

Jon Faust Eric M. Leeper

Alexander David

Steven B. Kamin Neil R. Ericsson

Phillip Swagel Dale W. Henderson Warwick J. McKibbin

Neil R. Ericsson David F. Hendry Hong-Anh Tran

Peter Hooper Jaime Marquez

Catherine L. Mann Stefanie Lenway Derek Utter

Joseph E. Gagnon Mark D. Unferth

Jay H. Bryson

Michael S. Gibson