The Theory of Stock Market - Essay Example

PART A This paper summarises the major argument presented in Ray Ball (1994, p. 3-46)'s article, The Development, Accomplishments and Limitations of the Theory of Stock Market. DEVELOPMENT For the first half of the twentieth century, the phenomenon of stock price changes being independent was called the "random walk hypotheses" or the "brownian motion" from the arenas of statistics and physics respectively. Roberts (1959) set the path for the "random walk hypothesis" with the economics of competitive markets, while Fama (1965) mooted the notion of "efficiency" - "a market where there are large numbers of rational, profit-maximisers actively competing, with each trying to predict future market values of individual securities, and where important current information is almost freely available to all participants". He also drew the implication of efficiency: "In an efficient market, on the average, competition will cause the full effects of new information on intrinsic values to be reflected "instantaneously" in actual prices". Around the same time, Samuelson (1965) and Mandelbrot (1966) proved the independence of successive price changes as proposed by Roberts (1959). FFJR (1969) carried the economics further by connecting random walks not only with "efficiency", but also with the capital asset pricing model (CAPM) of Sharpe Lintner (1965). They also relaxed the stationarity assumptions of the random walk model. Fama (1970) continued the formalisation of the notion of "efficiency" in economic terms. He defined an efficient market as one "in which prices always 'fully reflect' available information". He also stated the conditions that would suffice for efficiency: "(i) there are no transactions costs in trading securities, (ii) all available information is costlessly available to all market participants, and (iii) all agree on the implications of current information for the current price and distributions of future prices of each security." Though adopting a statistical viewpoint, Fama (1970) differentiated information as "weak", "semi-strong" and "strong" forms. Later on, Rubinstein (1975), Beja (1976), Beaver (1981), and Latham (1986) adopted the framework of information economics where the definition is expressed in terms of the actions of individuals, as opposed to the actions of the market as defined by Fama (1970). Specifically, according to Beaver (1981): "A securities market is efficient with respect to a signal yt if and only if the configuration of security prices {Pjt} is the same as it would be in an otherwise identical economy (i.e. with an identical configuration of preferences and endowments) except that every individual receives yt as well as [that individual's own information]." Ray Ball (1994, p. 12-13) has a few criticisms of this school of thought. First, he argues that security prices in the "otherwise identical world" are ultimately priced using CAPM, which is implied by Fama's (1976) model. Secondly, he critiques that this model has confused properties of market with properties of information. Grossman (1976), Grossman and Stiglitz (1980) and Jordan (1983) associated "efficiency" with incentives to produce information. ACCOMPLISHMENTS First, the theory of stock market efficiency has developed prevalent respect for markets. Empirical evidence pointed to the efficiency of the stock markets, changing academic and even non-academic attitudes from suspicion to respect. Furthermore, the pioneer work on "efficiency" coincided with the surge in interest in and respect for markets in general among economists, and subsequently among politicians. The pioneer empirical work thus assumed importance and attracted interest beyond its direct impacts on stock markets. It led the global trend toward liberalising financial and other markets. The theory of stock market efficiency has also changed perceptions about how stock markets work. Before FFJR (1969)'s work, market reaction to information is viewed from a single point in chronological time to broad cross-section of events. When viewed from this perspective, it is difficult to detect the systematic features of the market. After FFJR (1969)'s work, market reaction was viewed from a period of chronological times to a single event, and rational and systematic behaviour could be seen. The main accomplishment of the theory of stock market efficiency was to open up the stock market as a legitimate arena of scholarly research, and in particular of economics. Prior to the theory, stock markets have received scant attention from economists. Two other financial theories were borne at roughly the same time as the theory of stock market efficiency, namely the Sharpe (1964) and Lintner (1965) models of asset pricing, and the theories of corporate financial policy of Modigliani and Miller (1958, 1961, 1966). The connection between these areas was close. The consistent evidence of market efficiency provided strong support for theories that shared similar assumptions about the efficiency of financial markets. Both efficiency theory and asset-pricing theory assumed rational behaviour in perfect markets; both studied exogenously-generated information; both researched on stock returns, without reference to underlying factors such as consumption and aggregate production. Researchers made frequent reference to the Sharpe-Lintner model even before it was tested and depended on the strong evidence of market efficiency. An accomplishment of the theory of stock market efficiency therefore was creating a receptive climate for Sharpe-Lintner model. Likewise, researchers were more receptive to untested irrelevance propositions of Miller and Modigliani as a result of the evidence of stock market efficiency. LIMITATIONS All financial models, such as the present value model, the Miller-Modigliani proposition on the value of firms, the Black-Scholes option pricing model, and the Arbitrage Pricing Model, are pure exchange models, ignoring the supply side. For example, the Miller-Modigliani propositions address the valuation of firms, given their investment activities and hence their operating and investment cash flows. The supply variables of investment activities and cash flows are exogenous variables. The CAPM derives the value of risky securities given the joint density function of all securities' future values. The supply variables of how the portfolio of securities and their return density functions are again exogenous variables. Serial dependence in the riskless rate and the risk premium in the CAPM model cannot be ruled out. Anomalies might be due to supply side variables rather than market inefficiencies. Also, all financial models are partial-equilibrium models. Macroeconomics variables such as money supply are exogenous variables. But anomalies might be due to such variables. Another limitation is the availability of data. Most studies were conducted on efficiency of prices of listed securities. The assumption that it is enough to study a parsimonious number of parameters from continuous density functions of future prices is yet another limitation. Also, asset-pricing models usually assume homogenous beliefs, neglecting individual diversity. Though allowing for objective return variables, homogenous beliefs make the basic constructs of efficient markets less convincing. Another limitation is that the asset pricing models do not address the costs of producing private information and hence do not allow studies on efficiency when private information is taken into account. Lastly, many features of the tax system are not incorporated into the models. Hence, anomalies might be due to correlation of the independent variables with taxes. CONCLUSION Ray Ball (1994, p. 3-46) concluded that while the research gives insights into stock price behaviour, the theory of market efficiency is imperfect and limited. "Efficiency" is a way of modeling competitive behaviour in stock markets and, like all models, it has strengths and limitations in our knowledge of what prices should be in an "efficient" market. Hence, in spite of the early strong evidence of market efficiency, the later spate of evidence of anomalies should not be surprising. COMPARISON WITH OTHER ARTICLES Comparing the article by Ball (1994, p. 3-46) with that of Engel and Morris (1991, p. 21-35) and Fortune (1991, p. 17-40), all three articles review the literature on the efficient market hypothesis. While Ball (1994, p. 3-46) and Fortune (1991, p. 17-40) provided a general overview of the literature, Engel and Morris (1991, p. 21-35) specifically looked at the efficient market hypothesis by surveying the mean reversion evidence. The authors of all three articles are biased towards the pragmatic empirical tradition school of thought, as opposed to the information economics school of thought. Ball (1976, p. 12) explicitly expressed his bias: "In comparing these approaches, I am biased by my origins toward the 'pragmatic empirical' tradition." Engel and Morris (1991, p. 21) defined an efficient market as one where "stock prices reflect the market value of future dividends" and further described an efficient market in terms of its competitive behaviour (1991, p. 22). Fortune (1991, p. 17) defined an efficient market as one where "stock prices correctly reflect available information about future fundamentals, such as dividends and interest rates". Are stock markets efficient Engel and Morris (1991, p. 32) concluded with a resounding support for stock market efficiency. They argued that "it is too early to conclude that the stock market is inefficient" (1991, p. 32). On the contrary, Fortune (1991, p. 35) is an opponent of the efficient market hypothesis. He claimed that "the efficient markets hypothesis is having a near-death experience and is very likely to succumb" (1991, p. 35). Perhaps, Ball (1994, p. 33-36) summed it up the best. After addressing the limitations of our knowledge on stock market efficiency, Ball (1994, p. 33-36) preferred not to answer this question and concluded that in spite of the limitations of the various models of stock market efficiency, they vastly improve our knowledge of the stock market and that the anomalies should serve to direct researchers' attention to areas that will further improve our understanding of competitive markets. PART B Miller and Modigliani (1958, p. 261-291) present the argument that the value of the firm and the average cost of capital are unaffected by capital structure in a world without taxes or transaction costs. The contributions of Modigliani and Miller path breaking 1958 article to the theory of corporate finance are justly celebrated. Yet, several authors (Copeland & Weston, 1988, p. 384-398; Ross, Westerfield, & Jaffe, 1996, p. 400-409) show that capital structure is relevant in a world with taxes. Below, the argument of Copeland & Weston (1988, p. 384-398) is presented. Under the assumption of corporate taxes, the cost of debt is the risk free rate. The cost of equity is NI: return to equity holders, that is, the net cash flow after interest and tax S0 + SN: change in shareholders' investment S: change in total equity of the firm We know that since B0 = 0 (1) (2) Since (NOI - rD)(1 - tc) = NI, NOI(1 - tc) - rD(1 - tc) = NI NOI (1 - tc) = NI + rD(1 - tc) (3) Substitute (3) into (2), we get (4) To find the relationship between NI and S, we equate (1) and (4) and get Then multiplying both sides by I, we have Subtracting B from both sides, we get Hence, S = NI - (1 - tc)( - kb)B Since rD = Bkb It implies that the opportunity cost of capital to shareholders increases linearly with changes in the market value ratio of debt to equity (assuming B/S = B/S). As long as the firm has no debt in its capital structure, the levered cost of equity capital, ks, is equal to the cost of equity of all equity firm, . A Graphical Presentation for the Cost of Capital Assuming that B/S = B/S, this is the same as the Modigliani-Miller definition. The figure below shows that the cost of capital and its components as a function of the ratio of debt to equity. The changes in WACC and the cost of capital, with increase in B/S, are listed in the following table for both with and without corporate tax. WACC The cost of equity capital No corporate tax No change Increase With corporate tax Decline Increase As debt increase, shareholders' position becomes riskier as their residual claim on the firm becomes more variable. Hence, they require a higher rate of return to compensate them for the extra risk they take. B/S = B/S, assuming the firm establishes a "target" debt-to-equity ratio equal to B/S and then finances all projects with identical proportion of debt and equity so that B/S = B/S. % WACC = Kb B/S % (1 - c) Kb(1 - c) B/S VL = VU + cB in a world with corporate taxes and no personal taxes. Let G denote the gain from leverage, which is the difference between the value of the levered and unlevered firms. Therefore, G = VL - VU = cB This section relaxes the assumption that there are no personal taxes and shows how the introduction of personal taxes into the original model affects firm valuation and the gain from leverage. Let ps denote the personal tax rate on income received from holding shares and pB denote the personal tax rate on income from bonds. VU is the present value of an unlevered firm, VL is the present value of a levered firm, NOI is the net operating income, c is the corporate tax rate, is the discount rate for an all equity firm, r is the interest rate, D is the principal sum of debt, rD is the interest on debt, kd is the before-tax cost of risk-free debt, and B is the market value of debt. For the unlevered firm, After-tax cash flows to shareholders = (NOI)(1 - c)(1 - ps). The value of the unlevered firm is given by discounting the cash flows at the cost of equity for an all-equity firm: For the levered firm, After-tax cash flows to shareholders = (NOI - rD)(1 - c)(1 - ps) After-tax cash flows to bondholders = rD(1 - pB) Total cash flows to suppliers of capital = (NOI - rD)(1 - c)(1 - ps) + rD(1 - pB) = (NOI)(1-c)(1-ps)-rD(1-c)(1 - ps) + rD(1 - pB) It should be noted that in the above equation, Therefore, When personal tax rates are set equal to zero, that is, ps = pB = 0, G = [1 - (1 - c)]B = cB, which is equal to the gain from leverage in a world with corporate taxes and no personal taxes. Also, when personal tax rate on share income equals the rate on bond income, that is, ps = pB = p, = [1 - (1 - c)]B = cB, which is equal to the gain from leverage in a world with corporate taxes and no personal taxes. When (1 - pB) = (1 - c)(1 - ps), = 0, there is no gain from leverage and the value of the levered firm is equal to the value of the unlevered firm. Here, the lower corporate taxes for a levered firm are exactly offset by higher personal taxes. Let r0 denote the rate paid on the debt of tax-free institutions, rD denote the demand rate of return, rS denote the supply rate of return, and denote the marginal tax rate on income from bonds. When the personal tax rate on income form common stock is zero, that is, ps = 0 or pB > ps, and if all bonds paid only r0, no one would hold them with the exception of tax-free institutions which are not affected by the tax disadvantage of holding debt when pB > ps. Individuals will only hold corporate bonds until their return is "grossed up", or, to put it another way, when the after-tax return on corporate bonds is equal to r0. Therefore, . Since the personal income tax is progressive, the interest rate which is demanded has to keep rising to attract investors in higher and higher tax brackets. Bonds must pay a rate of in equilibrium. To illustrate the above graphically, % Supply r0 Demand Dollar amount B* of all bonds Aggregate supply and demand for corporate bonds (before tax rates). To see that in equilibrium, rs = is true, recall that , since ps = 0. In equilibrium, rS = rD If then Or, 1 - c = 1 - pB, and the gain from leverage in equilibrium will equal zero. From the graph, we can see that if corporations were to offer a quantity of bonds greater than B*, , or , or 1 - c> 1 - pB, then will be negative. Some levered firms would find leverage to be a losing proposition and will reduce their supply of bonds until the volume of bonds in the economy reaches B*. , or , or 1 - c < 1 - pB, then will be positive. Some unlevered firms would find it advantageous to resort to borrowing and the volume of bonds in the economy will increase until it reaches B*. The conclusion is that there will be an equilibrium level of aggregate corporate debt, B*, and hence an equilibrium debt-equity ratio for the corporate sector as a whole. But there would be no optimal debt ratio for any individual firm since it would depend on the relative corporate and personal tax rates. It is obvious from the equation that companies following a no-leverage or low leverage strategy would find a market among investors in the high tax brackets; those opting for a high leverage strategy would find the natural clientele for their securities at the other end of the scale. But one clientele is as good as the other. And in this important sense it would still be true that the value of any firm, in equilibrium, would be independent of its capital structure, despite the deductibility of interest payments in computing corporate income taxes. References Ball, R 1994, 'The development, accomplishments and limitations of the theory of stock market', Managerial Finance, vol. 20, no. 2,3, pp. 3-46. Copeland, TE & Weston, JF 1988, Financial Theory and Corporate Policy, Addison Wesley, Massachusetts. Engel, C & Morris, C 1991, 'Challenges to stock market efficiency: evidence from mean reversion studies', Economic Review - Federal Reserve Bank of Kansas City, vol. 76, no. 5, pp. 21-35. Fortune, P 1991, 'Stock market efficiency: an autopsy', New England Economic Review, pp. 17-40. Miller, M & Modigliani, F 1958, 'The cost of capital, corporation finance and the theory of investment', American Economic Review, vol. 48, no.3, pp.261-291. Ross, SA, Jaffe, JF & Westerfield, RW 1996, Corporate Finance, Irwin, International Edition. Read More