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Campbell, Lo and Mac Kinley (1997) stated that „any test of efficiency must assume an equilibrum model that defines normal security returns.

If efficient hypothesis is rejected, this can be because the market is truly inefficient or because an incorrect equilibrum model has been assumed”.

The main advantages of this discrete approach are pedagogical, but it may suggest various generalizations which will contribute to the development of the Calculus of Probability.

The random walk theory has nowadays a practical implication into the financial theory, stating that the stock prices evolve accordingly to a random walk, and thus they are impossible to predict.

Those hypothesis are further presented: is the fact it follows a normal distribution function, except the fact that it represents a white noise, condition that generates a certain formal commonness.

But this may be the cause of appearing certain irregularities with the practice, due to the fact that the normal distribution function covers the whole range of real numbers, and it may result into the fact that there may be a non-zero probability that the price of a security title to be negative.

Consequently, the statistical manner to express the market efficiency is the random walk hypothesis (RWH), which can be formulated in three different sub-hypothesis, respectively: independently and identically distributed increments, independent increments, and uncorrelated increments.

Those sub-hypothesis start from a less broad perspective, getting to a more relaxed and natural perspective.

Forecasting rates of return, thus the attempt to predict the behavior of financial assets, with an increased degree of accuracy, represents one of the most outstanding challenges for the academic and investment area.This theory is consistent with the efficient-market hypothesis.In finance, this theory is mainly linked by the name of Eugene Fama (1965), even if Burton Malkiel (1973) is considered to have strongly developed it.Even Albert Einstein had an important contribution to this theory.The limitations of this theory were already recognized by Einstein and Smoluchowski (1916), but are often disregarded by other writers.

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