Q1. Using 625 trading days of data, you estimated the daily log return follows a normal distribution with a mean of 5 bps and and a stdev of 125 bps. Q1c. what is the mean log return and stdev of log return over one year period and four year period (assuming 252 trading days per year)? Q1d. based on Q1c what is the probably of losing money (negative log return) or doubling your money (total log return = ln(2)) over 1 year and 4 year period?
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!
Q1. Using 625 trading days of data, you estimated the daily log return follows a
Q1c. what is the mean log return and stdev of log return over one year period and four year period (assuming 252 trading days per year)?
Q1d. based on Q1c what is the probably of losing money (negative log return) or doubling your money (total log return = ln(2)) over 1 year and 4 year period?
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