Over the entire 20th century, the real (that is, adjusted for inflation) annual returns (in percent) on U.S. common stocks had mean 8.7 and standard deviation 20.25. The distribution of annual returns on common stocks is roughly symmetric, so the mean return over even a moderate number of years is close to normal. (a) What is the probability (assuming that the past pattern of variation continues) that the mean annual return on common stocks over the next 10 years will be between 5 and 10 (%)? (b) Over the next 10 years, the top 5% of returns would be above what average return?
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
Over the entire 20th century, the real (that is, adjusted for inflation) annual returns (in percent) on U.S. common stocks had mean 8.7 and standard deviation 20.25. The distribution of annual returns on common stocks is roughly symmetric, so the mean return over even a moderate number of years is close to normal.
(a) What is the
(b) Over the next 10 years, the top 5% of returns would be above what average return?
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