EFFICIENT MARKETS HYPOTHESIS
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1 EFFICIENT MARKETS HYPOTHESIS when economists speak of capital markets as being efficient, they usually consider asset prices and returns as being determined as the outcome of supply and demand in a competitive market, peopled by rational traders. These rational traders rapidly assimilate any information that is relevant to the determination of asset prices or returns (e.g. future dividend prospects) and prices adjust accordingly. Hence, individuals do not have different comparative advantages in the acquisition of information. It follows that, in such a world, there should be no opportunities for making a return on a stock that is in excess of a fair payment for the riskiness of that stock. In short, abnormal profits from trading should be zero. 1
2 Thus, agents process information efficiently and immediately incorporate this information into stock prices. If current and past information is immediately incorporated into current prices, then only new information or news should cause changes in prices. Since news is by definition unforecastable, then price changes (or returns) should be unforecastable: no information at time t or earlier should help improve the forecast of returns (or equivalently to reduce the forecast error made by the individual). This independence of forecast errors from previous information is known as the orthogonality property. Under the EMH, the stock price P t already incorporates all relevant information, and, the only reason for prices to change between time t and time t +1 is the arrival of news or unanticipated events. 2
3 Forecast errors, that is, ε t+1 = P t +1 E t P t+1 should therefore be zero on average and should be uncorrelated with any information Ω t that was available at the time the forecast was made. The latter is often referred to as the rational expectations RE element of the EMH and may be represented as: P t +1 = E t P t +1 + ε t+1 (1a) E t (P t +1 E t P t+1 ) = E t ε t+1 = 0 (1b) An implication of E t ε t +1 = 0 is that the forecast of P t +1 is unbiased (i.e. on average, actual price equals the expected price). Note that ε t+1 could also be (loosely) described as the unexpected profit (or loss) on holding the stock between t and t +1. Under the EMH, unexpected profits must be zero on average and this is represented by (1b). 3
4 The statement that the forecast error must be independent of any information Ω t available at time t (or earlier) is known as the orthogonality property. The forecast error ε t = P t E t 1P t is known at time t and hence forms part of Ω t. Serial correlation in ε t implies that information at time t helps to forecast P t +1 Note that the EMH/RE assumption places no restrictions on the form of the second and higher moments of the distribution of ε t. For example, the variance of ε t+1 (denoted σ 2 t+1) may be related to its past value, σ 2 t without violating RE. (This is an ARCH process.) To test the EMH on the return on stocks R t, we need a model of how investors determine expected (or required) returns. This model should be based on rational behaviour (somehow defined). For the moment, assume a very simple model where 4
5 (i) stocks pay no dividends, so that the expected return is the expected capital gain due to price changes (ii) investors are willing to hold stocks as long as expected (required) returns are constant, Hence, R t +1 = k +ε t+1 (6) where ε t+1 is white noise and independent of Ω t. The required rate of return k on the risky asset generally consists of a risk-free rate r and a risk premium rp (i.e. k = r + rp) Since for a non-dividend paying stock, R t +1 = (P t +1 P t )/P t ln(p t +1/P t ), equation (6) implies: ln P t +1 = k + ln P t + ε t+1 (7) Equation (7) is a random walk in the logarithm of P with drift term k. 5
6 Note that (the logarithm of) stock prices will only follow a random walk under the EMH if the risk-free rate r and the risk premium rp are constant and dividends are zero. For daily changes in stock prices over a period of relative tranquillity (e.g. excluding crash periods like October 1987 and ), it may appear a reasonable assumption that the risk premium is a constant. However, when daily changes in stock prices are examined, it is usually found that the error term is serially correlated and that the return varies on different days of the week. In particular, prices tend to fall between Friday and Monday. This is known as the weekend effect. It has also been found for some stocks, that daily price changes in the month of January are different from those in other months. This is a violation of the EMH under the assumption of a constant risk premium since returns are, in part, predictable. 6
7 Rejection of the efficient markets hypothesis could be either because we have the wrong equilibrium pricing model or because agents genuinely do not use information efficiently. Under the EMH, investors make a return on each security that covers the riskiness of that security and any transactions costs. The latter is often referred to as the fair game property. 3.2 Implications of the EMH As far as a risk-averse investor is concerned the EMH means that she should adopt a buy and hold policy. Under the EMH, investment analysts cannot pick winners by using publicly available information and therefore active investment managers are wasteful. 7
8 The individual investor should simply buy a passive index fund (e.g. mutual fund or unit trust), which tracks a particular market index such as the S&P500 and has low transactions costs (e.g. less than 1% pa). Practitioners such as investment managers do not take kindly to the assertion that their skills are largely redundant, given a competitive efficient market. Paradoxically, active managers do help ensure that information is rapidly assimilated in prices, even though they may not earn excess returns (corrected for risk). Takeovers, Conglomerates and Financial Institutions The stock market is supposed to provide the correct signals for the allocation of real resources (i.e. fixed investment). Only a small proportion of corporate investment is financed from new issues, nevertheless, the average rate of return of a quoted company on the stock market may provide a reasonable measure of the cost of equity funds corrected for risk. 8
9 The latter can be used in discounting future expected profits from a physical investment project (i.e. in investment appraisal) for an all-equity firm. However, if the share price does not reflect fundamentals but is influenced by whim or fads of irrational investors then this link is broken. If the market is inefficient and prices are subject to longer-term irrational swings, then stock price volatility may be greater than that predicted from the efficient markets hypothesis. Here, a case for financial institutions to have enough resources (reserves) to overcome these situations. This is one argument for general capital adequacy rules applied to the market risk of financial institutions (e.g. under the Basle market risk directives). If there are also systemic risks (i.e. a form of externality), then, in principle, government action is required to ensure that the level of capital reflects the marginal social costs of the systemic risk rather than the marginal private costs (for any individual financial institution). 9
10 Systemic risk would also support Central Bank intervention in organising a rescue package for financial institutions, which might otherwise precipitate other bank failures (e.g. Long-Term Capital Management, LTCM, for which the Federal Reserve Board organised a rescue by a consortium of US banks in 1998). What are the implications of market efficiency in stock and bond markets for issues in corporate finance? If the market is efficient, then there is no point in delaying a physical investment project in the hope that financing conditions will improve (i.e. that the share price will be higher): under the EMH the current price is the correct price and reflects expected future earnings from the project. Also, under the EMH the firm s cost of capital cannot be lowered by altering the mix of debt and equity finance. The Modigliani Miller theorem (in the absence of taxes and bankruptcy) suggests that in an efficient market, the cost of capital is independent of capital structure (i.e. debt equity ratio). 10
11 The issue of capital-mix can also be applied to the maturity (term) structure of debt, i.e. the proportion of long-debt to shortdated debt will also not alter the cost of capital to the firm. For example, under the expectations hypothesis, low long-term rates of interest and high current short rates, simply reflect expectations of lower future short rates. So there is no advantage ex ante, to financing an investment project by issuing long bonds rather than rolling over a series of short bonds. Of course, if the market is not efficient, the Corporate Treasurer has scope to alter the stock market valuation of the firm by his chosen dividend policy or by share repurchase schemes and so on. 11
12 3.3 Expectations, Martingales and Fair Game Mathematical Expectations There are three properties that conditional mathematical expectations hold: unbiasedness, orthogonality and iterated expectations. Consider the conditional expectation based on the information set Ω : E X Ω X f X Ω dx 10 where f X Ω is the conditional density function. A conditional expectation may be viewed as an optimal forecast of the random variable X, based on all relevant information Ω. The conditional forecast error is defined as ε such that X E X Ω ε 13 12
13 It also holds: E ε Ω 0; We can reinterpret (13) as stating that the conditional expectation is an unbiased forecast of the out-turn value. Another property of conditional mathematical expectations is that the forecast error is uncorrelated with all information at time t or earlier: E ε Ω Ω 0 14 This is known as the orthogonality property of conditional expectations. E E X Ω Ω E X Ω This is the rule of iterated expectations. Rational expectations ( Muth-RE, Muth 1961) assume that individual agents subjective expectations equal the conditional mathematical expectations, based on the true probability distribution of outcomes.. Rationality also imply that agent use all of information at their disposal including past errors and theoretical notions. 13
14 For example, rational agents can find the equilibrium price of a particular market by solving a demand and supply model with shocks: P P ε f x,x ε 17 where x and x are factors that influence supply and demand. The equilibrium price is determined on the basis on all the available information contained inω : x and x. Martingale and Fair Game Properties Suppose we have a stochastic variable X t, which has the property: E X Ω X 18 then X t is said to be a martingale. Given (18) the best forecast of all future values of X t +j (j 1) is the current value X t. 14
15 No other information in Ω helps to improve the forecast once the agent knows X t. A stochastic process y t is a fair game if: E y Ω 0 19 Thus, a fair game has the property that the expected return is zero, given Ω. It follows trivially that if X t is a martingale y t +1 = X t+1 X t is a fair game. A fair game is therefore sometimes referred to as a martingale difference. One definition of the EMH is that it embodies the fair game property for unexpected stock returns y t +1 = R t +1 E t R t+1, where E t R t+1 is the equilibrium expected return given by some economic model. If we assume equilibrium-required returns by investors are constant (= k), then the fair game property implies: E R k Ω
16 Under this assumption, a test of whether returns violate the fair game property is to consider a linear regression: R α β Ω ε 21 then if β 0 (or ε t +1 is serially correlated), the fair game property is violated. Assume all investors have a common and constant time preference rate, have homogeneous expectations and are risk-neutral. Investors then prefer to hold whichever asset has the highest expected return, regardless of risk. All returns would therefore be equalised, and the required (real) rate of return equals the real interest rate, which in turn equals the constant rate of time preference. 16
17 Formal Definition of the EMH Suppose that at any point in time all relevant (current and past) information for predicting returns is denoted Ω, while market participants p have an information set Ω (assumed to be available without cost). In an efficient market, agents are assumed to know all relevant information (i.e. Ω Ω ) and they know the complete (true) probability density function of the possible outcomes for returns f R Ω f R Ω 24 Hence, under the EMH, investors know the true economic model that generates future returns and use all relevant information to form their best forecast of the expected return. This is the rational expectations element of the EMH. The expected or equilibrium return will include an element to compensate for any (systemic) risk in the market and to enable investors to earn normal profits. 17
18 For empirical testing, we need a definition of what constitutes relevant information, and three broad types have been distinguished. Weak Form: The information set consists only of information contained in past prices (returns). Semi-Strong Form: The information set incorporates all publicly available information (which also includes past prices and returns). Strong Form: Prices reflect all information that can possibly be known, including inside information. In empirical work, tests of the EMH are usually considered to be of the semistrong form. Note that, excess returns may be predictable but whether one can make abnormal profits depends on correctly adjusting returns, for risk and transactions costs. 18
19 3.4 Testing the EMH Some of the test procedures used in assessing the EMH. It is useful to break these down into the following types: (i) Tests of whether excess (abnormal) returns are independent of information Ω available at time t or earlier. To test this proposition consider: R, E R, γ Ω w 26 where E R, = equilibrium expected returns. If information Ω adds any additional explanatory power then R, E R, is forecastable. This is a test of informational efficiency and it requires an explicit representation of the equilibrium asset-pricing model used by agents. (ii) Tests of whether actual trading rules can earn abnormal profits after taking account of transaction costs and the (systematic) risk of the active strategy. 19
20 Abnormal profits are usually measured relative to a benchmark passive strategy (e.g. holding the S&P500). (iii) Tests of whether market prices always equal fundamental value. Interpretation of Tests of Market Efficiency The EMH assumes information is available at zero cost. The assumption that the acquisition and processing of information as well as the time involved in acting on such information is costless is a very strong one. If prices always reflect all available relevant information, which is also costless to acquire, then why would anyone invest resources in acquiring information? Anyone who did so, would clearly earn a lower return than those who costlessly observed current prices, which under the EMH contain all relevant information. 20
21 As Grossman and Stiglitz (1980) point out, if information is costly, prices cannot perfectly reflect the information available. Stiglitz (1983) also makes the point that speculative markets cannot be completely efficient at all points in time. The profits derived from speculation are the result of being faster in the acquisition and correct interpretation of existing and new information. Thus, one might expect the market to move towards efficiency as the well informed make profits relative to the less well informed. However, this process may take some time. Also, irrational or noise traders might be present and then the rational traders have to take account of the behaviour of the noise traders. It is, therefore, possible that prices might deviate from fundamental value for substantial periods. Recently, much research has taken place on learning by agents, on the nature of sequential trading and the behaviour of noise traders. 21
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