PII: 1057-0810(92)90004-V FINANCIAL SERVICES REVIEW, 2(2): 87-96 Copyright 0 1993 by JAI Press Inc. ISSN: 1057-0810 All rights of reproduction in any form reserved. The Individual Investor in the Market: Forming a Belief Regarding Market Efficiency Robert M. Peevey Gene C. Uselton John R. Moroney Do the actions of investors drive the market toward efficiency or do investors utilize fads and other information unrelated to the true value of the security to drive the market away from eficiency? Investors have been forced to examine a multitude of challenges to the eficient markets hypothesis in recent years. One of the most formidable of the challenges is the “excessive market price volatility” argument. We examine this argument, as presented in the “variance bounds” literature, and conclude that, although markets may be ineficient, the “variance bounds” literature has not proved the case conclusively. I. INTRODUCTION For investors who want to “beat the market,” there is a shortage neither of data nor of advice. Readily available are such primary data as annual reports, lOKs, and 1OQs. Secondary data sources include the financial press (e.g., The Wall Street Journal and Investors Daily); investor’s services such as The Value Line Investment Survey, Standard & Poor’s, and Moody’s; and computer data bases that can be obtained on floppy disks. For advice investors can turn to Wull Street Week or any number of newsletters published by advisors who claim to know what stock to buy and/or when to buy it. Can investors reasonably expect to “beat the market” by superior application of this information? Many, if not most, financial economists in academia believe that individuals should simply purchase a diversified portfolio of securities (or, perhaps, a well-managed, diversified mutual fund). They insist that efforts to “beat the market” Robert M. Peevey l Department of Finance, University of Houston, Houston, TX, 77204-6282; Gene C. Uselton l Department of Finance, Texas A&M University, College Station, TX, 77843-4218; John R. Moroney l Department of Economics, Texas A&M University, College Station, TX, 77843-4218. 88 FINANCIAL SERVICES REVIEW, 2(2) 1993 are destined to failure. Their argument proceeds from the “Efficient Markets Hypothesis” (EMH). According to the EMH, the prices of securities, at any given moment, reflect all of the information available to investors. Suppose that information about a common stock were available which would justify paying a higher (or lower) price than the market price. What would happen? Investors, eager to profit from the pricing error, would immediately purchase (sell) the mispriced security, thus driving its price up (down) to the price justified by the information available. Numerous attempts over the past 25 years to test the EMH have led to refinements. The EMH now comes in three different forms: the weak form, the semi-strong form, and the strong form. It is important for investors to distinguish between these three forms. The weak form of the EMH holds that the current price of any security is independent of the security’s price history. That is, knowing all of the prices at which a security has traded for every trade in the security’s history cannot help investors to predict any future price. If the weak form of the EMH is correct, then technical analysis can be of no value to investors. The semi-strong form of the EMH incorporates the assumptions of the weak form but adds more. It holds that all public information (including the series of prices at which a security has sold) is impounded in the market price. If so, reading annual reports, lOKs, lOQs, etc., is a nonproductive activity; security analysis can be of no value to investors. The strong form goes one step further; it holds that all informdon (including insider information) is impounded in the prices of securities. Under the strong form investors cannot obtain excessive profits even if they know about a buy-out before it is announced. A belief regarding the efficient markets hypothesis dictates investment prac- tices. Accepting the concept implies that investors should (1) form diversified portfolios of securities meeting their risk and income objectives and (2) trade securities only when objectives change, when excess funds are available, or when funds are needed. Investors who reject the EMH might reasonably attempt to (1) identify and purchase underpriced securities, (2) identify and sell overpriced issues, and (3) trade securities to benefit from market timing. It has long been held that security prices change only in response to new information. New information occurs randomly since any trend or prior knowledge would make the information predictable; therefore, it would not be new information. Price changes therefore must be random. However, early tests implying a random walk in stock price changes (Fama, 1965) have been modified by evidence of potential long-term price reversion (Fama & French, 1988) and short-term correla- tions (Lo & Ma&inlay, 1988). Investors and security analysts gathering and using information in an attempt to “beat the market” would appear to drive markets toward efficiency. However, market efficiency anomalies, such as the P/E Ratio effect, January effect, etc., focus The Individual Investor in the Market 89 on specific “pockets” of potential inefficiency and provide evidence that markets may not be driven all the way to efficiency. In general, empirical tests are inconclu- sive and, in some degree, contradictory.’ A basic premise in asset valuation is that an asset is worth the present value of its future cash flows. We refer to this as the true value of the asset. If the market price of a security is not consistent with its true value, investors must be responding to something other than pertinent information concerning the asset. Fads (Shiller, 1989), overreaction (DeBondt & Thaler, 1985), or speculative bubbles (West, 1988) may explain security prices. If so, markets cannot be efficient. A test which proves that market prices are not consistent with the present value of their future cash flows would prove that the EMH is false and end the market efficiency question once and for all. The “variance bounds” test is promoted as such a test. Some scholars (e.g., Shiller, 1989) performing the test find that the volatility of market prices is too great for the value of a security to equal its true value and conclude that markets are inefficient. Do investors utilize “irrelevant” information to drive markets away from efficiency? We offer no answer to this question and draw no conclusion about the efficiency of financial markets. However, an examination of the foundation of the variance bounds test will prove useful to investors who are concerned about the issue. This paper focuses on the theory which asserts that the volatility of market prices is too great to be consistent with the efficient markets hypothesis. We briefly review the theory and examine its theoretical underpinnings. Our objective is to expose weaknesses in the excessive volatility argument and to show that the variance bounds tests are not valid when risk is considered. We conclude that the individual should look with skepticism upon the excessive volatility argument when forming a belief concerning market efficiency. In Section II we explain the traditional variance bounds theory. Section III examines the theory and uncovers three flaws in the original argument. Our summary and conclusions are presented in Section IV. II. VARIANCE BOUNDS THEORY LeRoy (1989) explains that very low market prices in the mid-1970s stimulated researchers to reexamine the theory of asset pricing.* They argue that asset prices should have low volatility relative to the volatility of dividends; and, further, that these volatility implications apply directly to market efficiency theory. LeRoy and Porter (1981), Shiller (1979, 1981a, 1981b, 1989), and Singleton (1980) lay the foundation for what is now known as variance bounds testing. Their finding, that the variance of market prices exceeds that of a proxy for fundamental value,3 introduces a new challenge to market efficiency. 90 FINANCIAL SERVICES REVIEW, 2(2) 1993 The Formal Argument Shiller (1979, 1981a, 1981b), LeRoy and Porter (1981), and Singleton (1980) introduce the rationale that the fundamental value of a security is equal to the security’s market price plus a random error. This implies that the fundamental value of security i at time t, ~,, may be linearly decomposed into an expected component (i.e., market price), J+,, and an unexpected component, xi,. Pt = Pit + Xit (1) Equation (1) implies that the fundamental value is predicted by market price and disturbances. It necessarily follows that o;=cr;+0,+2cr,, (2) The market price must be uncorrelated with the random component as a condition of market efficiency. Hence the variance of the time-series of fundamental values must be equal to the sum of the variances of the price series and the series of random errors: 0; = 0; + 0, (3) Since variances are non-negative, the variance of the fundamental value series sets an upper bound on the variance of the price series. 0; 2 0; (4) Inequality (4) is the cornerstone of first generation variance bounds tests. LeRoy and Porter (1981) and Shiller (1979, 1981a, and 1981b) find that the variance of market prices exceeds that of the fundamental value series, thus leading them to question the validity of the efficient markets hypothesis.4 Many subsequent tests have been performed and, although many of the problems of the first-generation variance bounds tests have been overcome, primarily by improved econometric methods, the underlying theory has not been changed. It is this theoretical foundation that is examined here. III. THREE FLAWS IN THE TRADITIONAL VARIANCE BOUND ARGUMENT The First Flaw First, the variance bounds specification in (4) is less restrictive than it seems. Zero correlation between Pit and Xi, clearly implies the relationship expressed in (3). Equation (4) follows from (3), but the converse is not necessarily true. Equation (4) does not guarantee zero correlation between pir and xi,. In fact, the relation expressed The Individual Investor in the Market 91 in (4) implies a range of correlation between pit and Xit, Consider (2) and note that the variance bounds specified in (4) imply that o2 >21 CT2 P and, therefore, that (5) (6) where ppr is the correlation coefficient between pit and xi,. From (6) it follows that (4) actually identifies a range of values of correlation between pit and xit (7) that is, the variance of market price exceeds the variance of fundamental value if and only if (8) states the actual rejection region for market efficiency under the traditional variance bounds test5 The Second Flaw The second flaw is that traditional variance bounds testing is strongly influ- enced by the empirical relationship between 7C, andp,. Scott (1985, (2), (4), and (5)) and Easton (1985, (7)) generalize (1) as 7C, = U + bpi, + Uil (9) in performing regression-based variance bounds tests. Utilizing (9), the ratio of variances is, where R2 is the coefficient of determination from the regression of (9). Applying the traditional variance bounds criteria for market efficiency from (5) implies that 92 FINANCIAL SERVICES REVIEW, 2(2) 1993 R21b2 (11) This has the unsettling implication that the proportion of fundamental value ex- plained by market price must be smaller than some specific limit, otherwise we reject market efficiency. For example, if b2 = 0.5 markets are tested to be efficient if market price explains 10% of the variation in fundamental value and are tested to be inefficient if market price explains 90% of the variation in fundamental value. This is contrary to the intuitive concept that market price and fundamental value should be closely linked in an efficient market. Equation (11) presents no problem if b 2 1; however, Scott (1985, Table 1, p. 602) finds that b is significantly less than one; indeed, he finds b not significantly different from zero. Easton (1985) finds that b varies with the level of the discount rate used in calculating the proxy for fundamental value. The estimate of b is less than unity for the lower range of discount rates. Scott’s and Easton’s results cast serious doubt upon the validity of the linear assumption in ( 1).6 The Third Flaw The third flaw in the traditional variance bounds argument is that (1) is an inequality for any state other than risk neutrality. To examine this claim, we reconstruct the relationship. The relationship between the market price of a security and its fundamental value begins with the decomposition of the actual cash distributions, ACFi,, into their components: the expected dividends, EC%, and unexpected dividends, UCFi, ACFi, = ECFi, + UCFi, (12) The fundamental value, 7cil, can then be expressed as (13) where CPI is the Consumer Price Index at the time of the distribution (t+j) and the beginning of the time period (t) and rr is the real rate of return which is assumed to be the constant (e.g., 3%) part of the time varying realized return. Equation (13) presents the price that a rational investor would pay for a security with (1) full knowledge of all future cash (or equivalent) distributions, (2) perfect information concerning future inflation as accounted for by the CPI, and (3) a desire to achieve a realized real rate of return of rr. Note that the certain cash flow is discounted using a rate having no risk premium. Since it involves an infinite stream of distributions, we use the term “fundamental value.” We combine the inflation and real return factors into a time varying realized return, rt+j, which includes no risk premium. The Individual Investor in the Market 93 (14) Equations (12), (13), and (14) can be combined if and only if the assumption of risk neutrality is imposed. Assuming a risk neutral world we have - ACF,, c m ECF,t+j m UCF,t+j .= j=l (1 + rt+j)' c -+c j=l (1 + rt+jY j=l (1 + rt+jY (15) The left hand side (LHS) variable, ACF, is a certain cash flow and must be discounted with no risk premium. The right hand side (RHS) variables, ECF and UCF, are uncertain cash flows and can be discounted with no risk premium only under the risk neutrality assumption. However, the risk neutrality assumption is not attractive. The first term on the RHS is the discounted expected dividend stream, the market price. It is contrary to basic concepts of stock valuation to assume that there is no risk premium associated with this term. The relationship is a decompo- sition and both sides must be discounted by the same factor to maintain equality (Shleifer & Summers, 1990). If we discount the RHS by a factor containing a risk premium, the LHS, the certain cash flow, must also be discounted using a risk premium. This practice is used in variance bounds theory and the pseudo value is called the “ex post rational” price. But, this is not theoretically correct and there is no assurance that an equality is established by applying some arbitrary risk premium to the LHS. For clarity let us examine the conditions under which (15) reduces to (1). Investors price risky equities by discounting expected, but uncertain, cash distribu- tions by a discount factor, ki. Thus, the current market price is pit = c ECFiJ+j j=l ( 1 + k,t+J’ (16) The discount rate, kit, includes a risk premium and varies from firm to firm and over time as implied by the subscripts. Under the assumption of risk neutrality, ki,,+j = r,+j and Xit = - UCFi,t+j c j=l (1 + rr+j)j ’ (17) Then (15) reduces to (l), which implies that the fundamental value is a linear combination of the expected information effects, pit, and the unexpected effects, 94 F’INANCIAL SERVICES REVIEW, 2(2) 1993 xif in a risk neutral world. But, there is no reason to believe that the same relationship holds in a risk averse world. A theoretically correct relationship under risk aversion can be established utilizing assumptions normally accepted in security valuation. Without loss of generality, we treat both actual and expected dividend growth rates, (gJ and (g&, respectively, as constants over the period t = l,...,~. Thus, ECF,, = Dit( 1 + gEi)j (18) and ACFi,t+j = Di,( 1 + g,& Similarly, ki,t+j and rt+j are treated as their effective geometric average values over time and designated henceforth as ki and r,., respectively. The sum of the infinite series created by substituting (18) into (16) converges (see Gordon (1962)) to: pir = DA1 + gd ki _ gEi where (ki - g&is strictly positive for any finite market price. In a similar manner, substituting (19) into (13) (or the equivalent LHS of (15)) yields the theoretical true (or fundamental) price n, = DiXl + gAi) It rf- hi (21) where (rr- gAi) is strictly positive for any finite fundamental price.’ Solving for Di,, in (20) and substituting into (21) yields the relationship % = Pir (I+ gAJ(ki - gd (1 + gsJ(rf - gAi) 1 (22) The ratio in brackets is a certainty equivalent factor between the fundamental value (the discounted value of a stream of certain real cash distributions) and the market price (the discounted value of a stream of expected but uncertain cash distribu- tions). In a risk averse world the relationship is nonlinear as shown by (22). It is obvious that this relationship does not produce the variance boundary that is produced by (1). We argue that (1) is an inequality in a risk averse world; thus, the variances that are derived from the relationship cannot be interpreted as valid bounds. The Individual Investor in the Market 95 IV. STJMMARY AND CONCLUSIONS This study shows that the theory underlying the excessive price volatility challenge to market efficiency is flawed. We have not shown that markets are efficient; but we have given investors reason to doubt the argument for market inefficiency based on the evidence for excessive price volatility. Our conclusion is consistent with a statement by Fama (1990), “As always, then, the answer to the basic market- rationality question must be left to the reader.” NOTES 1. Fama (1991) provides an excellent review. 2. The Dow Jones Industrial Average reached a modem period low in 1974. 3. Researchers applying ex ante discount rates to realized prices and dividends refer to this proxy for the security’s fundamental value as the ‘&ex post rational price.” See Kleidon (1986a) for a discussion of this term. 4. Critics (Flavin (1983), Kleidon (1986a,b), and Marsh and Merton (1986)) quickly find problems with the early analyses. New tests intended to correct these problems are developed by Mankiw, Romer, and Shapiro (1985), Scott (1985), Campbell and Shiller (1988a,b), and LeRoy and Parke (1990). These second-generation tests are criticized by Shea (1989). Articles by LeRoy (1989). West (1988), and Gilles and LeRoy (1990) present excellent reviews of the variance bounds literature. 5. LeRoy and Porter (1981, p. 561) apparently recognize that their variance bound specification implies some range of correlation between p and x, but they do not elaborate. Their orthogonality test implicitly assumes a correlation of zero. Froot (1987), in an unpublished paper, spells out the correlation range more clearly. Frankel and Stock (1987), comparing tests of efficiency of foreign exchange markets, make a similar point. Our results are derived independently and presented in a different form. 6. We abstain from lengthy review of second generation tests because (a) that task is accomplished admirably by Gilles and LeRoy (1990) and (b) those tests are not pertinent to our examination of the model. 7. Economic rationality is lost if market price or fundamental price is allowed to assume an infinite value. REFERENCES Campbell, John Y. and Shiller, Robert J. 1988a. ‘The Dividend-Price Ratio and Expectations of Future Dividends and Discount Factors,” Review of Financial Studies, 1: 195-228. -. 1988b. “Stock Prices, Earnings, and Expected Dividends,“Journalof Finance, 43(3): 661-76. DeBondt, Werner F.M., and Richard H. Thaler. 1985. “Does the Stock Market Overreact,” Journal of Finance, 40(3): 793-805. Easton, Peter D. 1985. “Accounting Earnings and Security Valuation: Empirical Evidence of the Fundamental Links,” Journal of Accounting Research, 23 Supplt.: 54-77. Fama, E.F. 1970. “Efficient Capital Markets: A Review of Theory and Empirical Work,” Journal of Finance, 25(2): 383-416. 96 FINANCIAL SERVICES REVIEW, 2(2) 1993 -. 1990. “Stock Returns, Expected Returns, and Real Activity,” Journal of Finance, 45(4): 1089-l 108. -. 1991. “Efficient Capital Markets: II,” Journal of Finance, 46(5): 1575-1617. and K.R. French. 1983. “Permanent and Temporary Components of Stock Prices,” Journal if Political Economy, 9 l(6): 929-56, Frankel, Jeffrey A. and James A. Stock. 1987. “Regression vs. Volatility Tests of the Efficiency of Foreign Exchange Markets,” Journul of International Money and Finance, 6: 49-56. Froot, Kenneth A. 1987. Tests of Excess Forecast Volatility in the Foreign Exchange and Stock Markets. National Bureau of Economic Research working paper #2362. Gordon, Marion J. 1962. The Investment, Financing and Valuation of the Corporation, Homewood, Illinois: Irwin. Gilles, Christian and Stephen F. LeRoy. 1991. “Econometric Aspects of the Variance-Bound Tests,” Review of Financial Studies, 4(4): 753-92. Kleidon, Allan W. 1986a. “Variance Bounds Tests and Stock Price Valuation Models,” Journal of Political Economy, 94(5): 953-1001. -. 1986b. “Bias in Small Sample Tests of Stock Price Rationality,” Journal of Business, 59(2): 237-61. LeRoy, Stephen F. 1989. “Eflicient Capital Markets and Martingales,” Journal of Economic Litera- ture, 27(4): 1583-1621. and Richard D. Porter. 1981. ‘The Present-Value Relation: Tests Based on Implied Variance Bounds,” Econometrica, 49(3): 555-74. Lo, Andrew W. and A. Craig Ma&inlay. 1988. “Stock Market Prices do not Follow Random Walks: Evidence from a Simple Specification Test,” Review of Financial Studies, l( 1): 41-66. Mankiw, N.G., D. Romer, and M. Shapiro. 1985. “An Unbiased Reexamination of Stock Price Volatility,” Journal of Finance 40(3): 677-687. Marsh, Terry A. and Robert C. Merton. 1986. “Dividend Variability and Variance Bounds Tests for the Rationality of Stock Market Prices,” American Economic Review, 76(3): 483-98. Scott, Louis 0. 1985. ‘The Present Value Model of Stock Prices: Regression Tests and Monte Carlo Results,” Review of Economics and Statistics, 67: 599-605. Shea, Gary S. 1989. “Ex-Post Rational Price Approximations and the Empirical Reliability of the Present-Value Relation,” Journal of Applied Economettics, 4: 139-59. Shiller, Robert J. 1979. “The Volatility of Long-Term Interest Rates and Expectations Models of the Term Structure,” Journal of Political Economy, 87(6): 1190-1219. -. 1981 a. ‘The Use of Volatility Measures in Assessing Market Efficiency,” Journal of Finance, 36(2): 291-304. -. 1981b. “Do Stock Prices Move Too Much to be Justified by Subsequent Changes in Dividends?" American Economics Review, 71(3): 421-36. -. 1989. Market Volatility, Cambridge, Massachusetts: MIT Press. Shleifer, Andrei and Lawrence H. Summers. 1990. ‘The Noise Trader Approach to Finance,” Journal of Economic Perspectives, 4(2): 19-33. Singleton, Kenneth J. 1980. “Expectations Models of the Term Structure and Implied Variance Bounds,” Journal of Political Economy, 88(6): 1159-76. West, Kenneth D. 1988. “Bubbles, Fads and Stock Price Volatility Tests: A Partial Evaluation,” Journal of Finance, 43(3): 639-60.