The random walk theory of stock prices holds that pricemovements in disjoint tim
ID: 2919217 • Letter: T
Question
The random walk theory of stock prices holds that pricemovements in disjoint time periods are independent of eachother. Suppose that we record only wether the price is up ordown each year, and that the probability that our protfolio risesin price in any one year is 0.65. ( this probability isapproximately correct for a portfolio containing equal dollaramounts of all common stocks listed on the New York StockExchange.) (a.) What is the probability that our portfolio goes up forthree consecutive years? (b.) What is the probability that the portfolio's value movesin the same direction (either up or down) for three consecutiveyears? The random walk theory of stock prices holds that pricemovements in disjoint time periods are independent of eachother. Suppose that we record only wether the price is up ordown each year, and that the probability that our protfolio risesin price in any one year is 0.65. ( this probability isapproximately correct for a portfolio containing equal dollaramounts of all common stocks listed on the New York StockExchange.) (a.) What is the probability that our portfolio goes up forthree consecutive years? (b.) What is the probability that the portfolio's value movesin the same direction (either up or down) for three consecutiveyears?Explanation / Answer
for part a, since we know that the event are independent (by therandom walk theory of stocks), and we know that the probability ofour portfolio rising is .65 for any given year, the probability that it will rise three consecutive years is.65*.65*.65 =.274625 ˜ 27.5% ---------------------------------------------------------------------------------------------------------------- for part b, if it moves in the same direction for three consecutiveyears the only possibilities are that it rises for three straightyears, or it falls for three straight years. We know the probability of it rising for three straight years is.274625 (as determined in part a) so we need to add to that theprobability of it falling for three straight years to find theprobability of either one happening. so the probability of it falling in any one year is 1-.65 = .35 then the probability of it falling for three consecutive years is.35*.35*.35 = .042875 ˜4.3% so the probability of either one happening is .274625 + .042875 =.3175 = 31.75 %