An attempt to elaborate the relationship between the bad model problem and the Efficient Market Hypothesis or the Equity Risk Premium needs to necessarily commence with a short overview of the hypothesis. The Efficient Market Hypothesis, (EMH) was first developed by Eugene Fama of the University of Chicago, in the 1960s, to explain the behaviour of prices in equity markets.
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It has now been generalised to determine price behaviour patterns in other asset markets and has become one of the central research paradigms in financial economics. The EMH postulates that security markets are very efficient in absorbing and reflecting information about traded stocks and, as such, new information about stocks affect share prices as soon as they occur. The absence of delay in stock price adjustment makes the use of technical or fundamental analyses in predicting price movements for the use of investors redundant. It does not thus matter whether investors hold a randomly selected portfolio or choose shares after studying fundamentals or technicals; as share price behaviour will remain random and unpredictable. The EMH is well known for its association with the concept of “random walk”, a term used to evocatively describe a series of price changes, where the price movements that take place have no connection with any definable trend and represent random departures from previous prices. Random walk works on the logic that future changes in price will depend upon future information and thus should have no connection with existing prices. As news, by its very nature is totally unpredictable, the behaviour of prices must therefore necessarily be beyond prediction. Also, as existing prices reflect all available information there should not be any difference in the returns achieved by an amateur investor picking up shares at random from the montage of shares available in the market, and those achieved by experts crunching numbers on their laptops. Using an oft repeated example it also indicates “that a blindfolded monkey throwing darts at a newspaper’s financial pages could select a portfolio that would do just as well as one carefully selected by the expert”
The efficient market hypothesis has three manifestations, the weak, semi strong and strong forms. The weak form postulates that prices of shares reflect all information in past and existing prices and business volumes, thus making movements random and the probability of making gainful trades just about even. The semi strong form takes a stride further to stipulate that prices have by now factored in supplementary information such as company and business data, as well as broad financial data including interest and currency fluctuations, and inflation. These two hypotheses, in effect, state that as existing share prices account for the variables used in technical and fundamental analyses, future movement is innately volatile and investment decisions of fund managers nothing more than shots in the dark. Finally the strong form hypothesis states that all information, public and private is reflected in stock prices. Subjected to extensive investigation and research, the EMH has continuously stood up to empirical testing and is still regarded by many to be the definitive theory on market behaviour. Revolutionary theories, however strong they may, be have life cycles of cerebral domination and the EMH has had to face severe challenges in the last five years. Investment consultants and stock brokers, people whose businesses and professions depend upon continued investor interest and activity, as well as a new breed of economists have been exceptionally harsh on the hypothesis stating that stock returns, to some extent and in certain circumstances are definitely predictable. A new breed of economists’ emphasized psychological and behavioral elements of stock-price determination, and came to believe that future stock prices are somewhat predictable based on past stock price patterns as well as certain “fundamental” valuation metrics.
These conclusions have also led to the claim that investors should be able to make use of the probability and earn risk adjusted higher rates of return. Current research, moreover, states that the EMH does not account for some disturbing aspects of asset market behaviour and share prices some times appear to be subject to misalignments that persist for long periods of time. The issue of bad models and its relationship with the EMH, as well as the Equity Risk Premium are part of the research and questioning directed at the Efficient Markets Hypothesis and relate to situations wherein actual stock behaviour does not correspond with the postulates of the hypothesis.
2. Bad Model Problem The Efficient Markets Hypothesis is under constant investigation and challenge by economists who assert that a number of cases exist and continue to occur, which empirically indicate that markets sometimes do not behave efficiently. Various occurrences like the US stock markets crash of 1987, the internet and dotcom valuations of the 1990s, short-term momentum movements, the so-called January effect, wherein stock prices rise without reason in the first month of every year, and other behavioural irrationalities have indicated inefficient market behaviour. Some patterns of market predictability, detailed by Burton Malkiel  are as follows.
The debate over the validity of the EMH also includes findings of evidence of individual stocks over reacting to information, successful strategies of earning abnormal returns through selling past winners and buying past losers, the ability of various ratios including stock prices to signal future stock performance, and the persistent under reaction of individual stocks to earnings announcements. 
Researchers like Malkiel and Maxym have provided cogent and logical explanations to account for these apparent anomalies in behaviour. In fact, Malkiel takes up each of these issues individually and provides reasons for the anomalies, using empirical evidence to suggest that the EMH is, by and large, extremely robust and each of the predictability patterns suggested above do not withstand empirical verification. In spite of these consistently rational explanations these anomalies are regarded as strong evidence of the existence of a certain amount of predictability in market price movement. The role of bad models in explaining the deviations of market patters from the Efficient Market Hypothesis has been recognised by most experts, including Fama, who state that the arguments against unpredictable markets should be considered and assessed critically. The tests of market efficiency, as a rule, depend upon the use of standard asset pricing models that include the Present Value Model, the Capital Asset Pricing Model and the Arbitrage Theory. However, the applicability and suitability of these asset pricing models, to the situation at hand is, most often, a subject of debate. For example, if one were to postulate upon the basis of empirical evidence that prices are consistent with fundamentals, (an example of a clear deviation from the EMH) it would be necessary to use a model that uses a valid link from economic fundamentals to asset prices. While there are a number of models in all asset markets that can be used to establish this relationship, doubts persist over their suitability for this purpose in an empirically satisfactory manner; as they may not account for factors like “supply of shares, heterogeneity of beliefs, costs of private information production, and seasonality” 
It is important to take account of this possible inadequacy while investigating evidence of deviations from the EMH because empirical assessment of market efficiency, especially those that relate to the examination of asset price returns over extensive periods are tests, not just of market efficiency but also obviously of the adopted asset pricing model. It is thus entirely probable that in cases where the postulates of the EMH appear to be rejected by empirical data, the failure may very possibly be due to inadequacies in the pricing model and not in the Efficient Market Hypothesis. This, as per Fama, constitutes the “bad model” problem, a reason that could prevent researchers from drawing legitimate inferences about the tenets of the EMH. Economists supporting the EMH often argue that deviations in behaviour of efficient markets from the postulates of the hypothesis are actually due to the bad model problem and not due to inadequacies in the hypothesis. The bad model interpretation would thus suggest that predictability regarding excess returns could represent recompense for risk, which was poorly measured in the first instance, by the chosen asset pricing model. This reasoning however loses validity if deviations of actual behaviour from EMH postulates remain for long periods of time. In such situations it thus becomes imperative to specify alternative models that incorporate empirically assessable efficiencies. “Consequently, most long-term return anomalies tend to disappear when subjected to different models and statistical testing methods, (Fama, 1997)” 
3. The “Bad Model Problem” and the puzzle of Equity Risk Premium Accepted finance theories postulate that while investments in stocks and shares available in the equity market are far more volatile in their price movements than investments made in governmental or treasury bonds, they also provide greater return on the money invested. Analysis of historical data in most countries with mature stock markets also confirms that investments in shares, while being more volatile than official bonds, do provide higher returns. As such while rational investors should find the prospects of higher yields available from investments in stocks attractive, they would also tend to be wary of the associated risk and chances of economic loss. It would thus be natural for investors to expect higher returns, or rather premiums, from share market investments than in governmental bonds. The Equity Risk Premium (ERP) arises from these sentiments and represents the incremental rate of return expected by an investor in return for investing in shares or stocks that are associated with a higher risk than in risk free investments like, for example, government bonds. “Welch (1999) notes that this equity risk premium ‘is perhaps the single most important number in financial economics’, with implications for asset allocation decisions and providing a key input into calculations of the appropriate discount rate for evaluating investments.”
The ERP can apply to a broad based selection of stocks as well as to single stocks. If, for purposes of clarification, we take the rate of return on governmental bonds to be 6 %, the risk free rate would be the same and any investor would obviously not like to invest in any security offering a rate of less than the risk free rate. Any investment in a risky security would thus necessarily have to provide a return higher than the risk free rate. Risks are normally associated with all stocks and an expectation of 9 % from a diversified selection of stocks would indicate an ERP of 3 % on part of the investor. The final measure of risk associated with stocks is the risk associated with a particular stock, generally called the “beta”. The “beta” of a company depends upon a combination of its operational risk and financial risk and increases with increases in their perception, a larger beta being associated with an increased ERP. The extra recompense investors expect to get from investment in higher risk investments has become a bit of a puzzle. Common sense, backed by logical financial theory would suggest that this extra premium should be just enough or slightly more than the cost of the extra risk, calculated in most cases with the use of the Capital Assets Pricing Model The actual position, however, is vastly different. A number of studies have found and reconfirmed that the actual equity risk premium has been significantly larger than that required to cover the cost of the extra risk. “The Ibbotson data from 1926 through 2001, (states that) common stocks have produced rates of return of approximately 10½ percent while high grade bonds have returned only about 5½ percent”
The existence of a large historical risk premium, which is at odds and quite incompatible with the actual risk involved, implies the existence of irrationality in stock market behaviour and a sign of the fact that the Efficient Markets Hypothesis does not apply to stock markets. Various reasons put forward to account for this puzzle includes a school of thought that feels that the measurement of past premiums was erratic or due to improper selection of shares. In the short run, stocks are riskier than bonds, and it used to be assumed that the equity premium was simply the market price of risk. In 1985, however, economists Rajnish Mehra and Edward Prescott showed that no plausible model of investor preferences could reconcile the observed investor premium with the efficient markets hypothesis that is the belief that financial markets smoothly diversify all relevant risk. They concluded that an efficient market would produce an equity premium of at most half a percentage point.
Such results indicate the possibility that markets are essentially not efficient if the use of the Capital Assets Pricing Model (CAPM) is presumably correct. The CAPM was conceptualised originally by William Sharpe fifty years back and has since evolved into one of the chief models for managers to control risks for taking investment decisions. It is an equilibrium model that describes the pricing of assets as well as derivatives. It is the single most used model for valuing securities and uses the Discounted Cash Flow system with risk adjusted discount rates. The CAPM stipulates that market entry throws open investors to two types of risks, systematic risks that arise from being present in the market, and unsystematic risks, which arise from investing in particular companies. As unsystematic risks can be controlled through a process of diversification, the main risk in portfolio decisions comes from systematic risks. The validity of the CAPM and its appropriateness for all cases of valuation is however an issue of debate and repeated doubts have been raised over some of its assumptions, namely that investors are rational single period planners who seek mean-variance optimal portfolios and that security markets are ideal and large, that there are no transaction costs, that all risky stocks are traded and money is available at risk free rates. While the existence of abnormally high equity risk premiums does lead to questions about the efficiency of markets, supporters of the EMH argue that the existence of high ERPs do not automatically mean that markets are inefficient. It could simply be due to a bad model problem and the inadequacy of the CAPM to account for all the aspects of risk. Fama and French (1993) suggest that the price-to-book value ratio may reflect another risk factor that is priced into the market and not captured by CAPM. Companies in some degree of financial distress, for example, are likely to sell at low prices relative to book values. Fama and French (1993) argue that a three-factor asset-pricing model (including price-to-book-value and size as measures of risk) is the appropriate benchmark against which anomalies should be measured. 
The relationship between equity Risk Premiums and the Efficient Market Hypothesis is a matter of debate and a number of economists and market experts think of this phenomenon as a strong indicator of the inefficiency of markets and the fact that the EMH is open to questioning. Supporters of the hypothesis on the other hand refute this opinion strongly and state that this, as in the case of most other EMH anomalies, could be no more than another example where the use of CAPM is inappropriate and indicative of a bad model problem. The use of alternate and more sophisticated models could well incorporate the cost of unaccounted risk factors and, by reducing the Equity Risk Premium significantly, bring it in line with the postulates of the hypothesis. In the meantime, while the debate continues to rage, it is becoming evident that the EMH is no longer the definitive word in predicting stock behaviour that it once was. Alternate theories that point to anomalies in EMH and hypothesise that markets can be predictable, to some extent, are gaining ground.
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 Burton G. Malkiel, A Random Walk Down Wall Street, 4th ed. New York: W.W. Norton, 1985, p. 16.  Burton G. Malkiel, The Efficient Market Hypothesis and Its Critics, 2003, Retrieved January 7, 2006 from www.princeton.edu/~ceps/workingpapers/91malkiel.pdf  Burton G. Malkiel, The Efficient Market Hypothesis and Its Critics, 2003  Dedov Maxym, The Efficient Market Hypothesis and the Ukrainian Stock Market, 2000, Retrieved January 7, 2007 from www.eerc.kiev.ua/research/matheses/2000/Dedov_Maxym/body.pdf  Dedov Maxym, The Efficient Market Hypothesis and the Ukrainian Stock Market, 2000  Dedov Maxym, The Efficient Market Hypothesis and the Ukrainian Stock Market, 2000  Quiggin, J, Puzzling analysis from free market camp, Australian Financial Review, 1999, Retrieved January 7, 2007 from www.uq.edu.au/economics/johnquiggin/news/Dow9905.html –  Burton G. Malkiel, The Efficient Market Hypothesis and Its Critics, 2003  Quiggin, J, Puzzling analysis from free market camp, Australian Financial Review, 1999  Burton G. Malkiel, The Efficient Market Hypothesis and Its Critics, 2003
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