R5.9 A random walk on Wall Street? The "random walk" theory of stock prices holds that price movements in disjoint time periods are independent of each other. Suppose that we record only whether the price is up or down each year, and that the probability that our portfolio rises in price in any one year is 0.65. (This probability is approximately correct for a portfolio containing equal dollar amounts of all common stocks listed on the New York Stock Exchange.) (a) What is the probability that our portfolio goes up for three consecutive years? (b) What is the probability that the portfolio's value moves in the same direction (either up or down) for three consecutive years?
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Given that the probability of the portfolio rising in price in one year is 0.65, the probability of it going down in one year is 0.35. Therefore, the probability of the portfolio going up for three consecutive years is 0.65^3 = 0.274625. Show more…
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II. Proponents of the random walk theory of stock prices hold that predictions of whether a stock will do better or worse than the market in the short run (for example: one month) are no better than could be obtained by flipping a fair coin. Suppose that each of 100 different analysts select 8 stocks that they predict will beat the market next month. A. What is the probability that no analyst gets 8 winners assuming the validity of the random walk theory. B. What is the probability that at least one analyst gets 8 winners assuming the validity of the random walk theory. C. State the assumptions you made in answering part A.
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Historically, the likelihood for a stock going up in a particular year is 53% - a little better than a coin flip. According to Investopedia, there seems to be a January Effect in the stock market. If there is a January rally, then the probability that the market will have a good year is 60%. Statistics also show that the probability of a January rally is 62%. (a) What is the probability that there is a January rally followed by a good year? (b) If the yearly performance is in positive territory, what is the probability that there was no January rally? (c) What is the probability of encountering a bear market in both January and the whole year? (d) Are the two events "January rally" and "Good year" independent? Mutually exclusive? Why?
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