Geometric Random Walk Model

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By: Bob Nau

A "Random walk down Wall Street"

The fact that stock prices behave at least approximately like a (geometric) random walk is the most striking empirical fact about financial markets. But is it or isn't it a true random walk? If it is, then stock prices are inherently unpredictable except in terms of long-run-average risk and return. The best you can hope to do is to correctly estimate the average returns and volatilities of stocks, along with their correlations, and use these statistics to determine efficient portfolios that achieve a desired risk-return tradeoff. You can't hope to beat the market by microanalyzing patterns in stock price movements--you might as well buy-and-hold an efficient portfolio.

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