The random walk hypothesis--论文代写范文精选

股票市场价格的另一方面，一直被认为是一个背离性的长期记忆。时间序列的长期记忆表现出异常高程度的持久性,尽管两者之间的时间跨度增加。下面的paper代写范文进行了讲述。

Abstract
The importance of the EMH stems primarily from its sharp empirical implications many of which have been tested over the years. Much of the EMH literature before LeRoy (1973) and Lucas (1978) revolved around the random walk hypothesis (RWH) and the martingale model, two statistical descriptions of unforecastable price changes that were initially taken to be implications of the EMH. One of the first tests of the RWH was developed by Cowles and Jones (1937), who compared the frequency of sequences and reversals in historical stock returns, where the former are pairs of consecutive returns with the same sign, and the latter are pairs of consecutive returns with opposite signs. Cootner (1962; 1964), Fama (1963; 1965a), Fama and Blume (1966), and Osborne (1959) perform related tests of the RWH and, 4 with the exception of Cowles and Jones (who subsequently acknowledged an error in their analysis – Cowles, 1960), all of these articles indicate support for the RWH using historical stock price data. 

More recently, Lo and MacKinlay (1988) exploit the fact that return variances scale linearly under the RWH – the variance of a two-week return is twice the variance of a oneweek return if the RWH holds – and construct a variance ratio test which rejects the RWH for weekly US stock returns indexes from 1962 to 1985. In particular, they find that variances grow faster than linearly as the holding period increases, implying positive serial correlation in weekly returns. Oddly enough, Lo and MacKinlay also show that individual stocks generally do satisfy the RWH, a fact that we shall return to below. French and Roll (1986) document a related phenomenon: stock return variances over weekends and exchange holidays are considerably lower than return variances over the same number of days when markets are open. 

This difference suggests that the very act of trading creates volatility, which may well be a symptom of Black’s (1986) noise traders. For holding periods much longer than one week – fcor example, three to five years – Fama and French (1988) and Poterba and Summers (1988) find negative serial correlation in US stock returns indexes using data from 1926 to 1986. Although their estimates of serial correlation coefficients seem large in magnitude, there is insufficient data to reject the RWH at the usual levels of significance. Moreover, a number of statistical artifacts documented by Kim, Nelson and Startz (1991) and Richardson (1993) cast serious doubt on the reliability of these longer-horizon inferences. 

Finally, Lo (1991) considers another aspect of stock market prices long thought to have been a departure from the RWH: long-term memory. Time series with long-term memory exhibit an unusually high degree of persistence, so that observations in the remote past are non-trivially correlated with observations in the distant future, even as the time span between the two observations increases. Nature’s predilection towards long-term memory has been well-documented in the natural sciences such as hydrology, meteorology, and geophysics, and some have argued that economic time series must therefore also have this property. However, using recently developed statistical techniques, Lo (1991) constructs a test for long-term memory that is robust to short-term correlations of the sort uncovered by Lo and MacKinlay (1988), and concludes that, despite earlier evidence to the contrary, there is little support for long-term memory in stock market prices. Departures from the RWH can be fully explained by conventional models of short-term dependence.

Another set of empirical tests of the EMH starts with the observation that in a world without uncertainty the market price of a share of common stock must equal the present value of all future dividends, discounted at the appropriate cost of capital. In an uncertain world, one can generalize this dividend-discount model or present-value relation in the natural way: the market price equals the conditional expectation of the present value of all future dividends, discounted at the appropriate risk-adjusted cost of capital, and conditional on all available information. This generalization is explicitly developed by Grossman and Shiller (1981). LeRoy and Porter (1981) and Shiller (1981) take this as their starting point in comparing the variance of stock market prices to the variance of ex post present values of future dividends. 

If the market price is the conditional expectation of present values, then the difference between the two, that is, the forecast error, must be uncorrelated with the conditional expectation by construction. But this implies that the variance of the ex post present value is the sum of the variance of the market price (the conditional expectation) and the variance of the forecast error. Since volatilities are always non-negative, this variance decomposition implies that the variance of stock prices cannot exceed the variance of ex post present values. Using annual US stock market data from various sample periods, LeRoy and Porter (1981) and Shiller (1981) find that the variance bound is violated dramatically. Although LeRoy and Porter are more circumspect about the implications of such violations, Shiller concludes that stock market prices are too volatile and the EMH must be false. 

These two papers ignited a flurry of responses which challenged Shiller’s controversial conclusion on a number of fronts. For example, Flavin (1983), Kleidon (1986), and Marsh and Merton (1986) show that statistical inference is rather delicate for these variance bounds, and that, even if they hold in theory, for the kind of sample sizes Shiller uses and under plausible data-generating processes the sample variance bound is often violated purely due to sampling variation. These issues are well summarized in Gilles and LeRoy (1991) and Merton (1987). More importantly, on purely theoretical grounds Marsh and Merton (1986) and Michener (1982) provide two explanations for violations of variance bounds that are perfectly consistent with the EMH. Marsh and Merton (1986) show that if managers smooth dividends – a well-known empirical phenomenon documented in several studies of dividend policy – and if earnings follow a geometric random walk, then the variance bound is violated in theory, in which case the empirical violations may be interpreted as support for this version of the EMH.

Alternatively, Michener constructs a simple dynamic equilibrium model along the lines of Lucas (1978) in which prices do fully reflect all available information at all times but where individuals are risk averse, and this risk aversion is enough to cause the variance bound to be violated in theory as well. These findings highlight an important aspect of the EMH that had not been emphasized in earlier studies: tests of the EMH are always tests of joint hypotheses. In particular, the phrase ‘prices fully reflect all available information’ is a statement about two distinct aspects of prices: the information content and the price formation mechanism. Therefore, any test of this proposition must concern the kind of information reflected in prices, and how this information comes to be reflected in prices. Apart from issues regarding statistical inference, the empirical violation of variance bounds may be interpreted in many ways. It may be a violation of EMH, or a sign that investors are risk averse, or a symptom of dividend smoothing. To choose among these alternatives, more evidence is required.paper代写)

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