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Do stock market returns follow a normal distribution?
We all know that stock market returns are not normally distributed. Instead, we think of them as having fat tails (i.e. extreme events happen more frequently than expected). As you can see, on an annual scale, market returns are essentially random and follow the normal distribution relatively well.
Why is the normal distribution not a good model?
There is a probability of about 3.4% that a normally distributed random variable is more than 1.836 standard deviation units above the mean. So at the upper end of the range at least, the normal with the given mean and standard deviation gives a poor fit.
Is normal distribution a good model?
The normal distribution is the most important probability distribution in statistics because it fits many natural phenomena. For example, heights, blood pressure, measurement error, and IQ scores follow the normal distribution.
What is a normal distribution and why is it powerful for forecasting ranges of outcomes?
The higher the standard deviation, the riskier the investment, as it leads to more uncertainty. Hence, the graphical representation of normal distribution through its mean and standard deviation enables the representation of both returns and risk within a clearly defined range.
What are normal stock returns?
The average stock market return is about 10% per year for nearly the last century. The S&P 500 is often considered the benchmark measure for annual stock market returns. Though 10% is the average stock market return, returns in any year are far from average.
How do you check if returns are normally distributed?
For quick and visual identification of a normal distribution, use a QQ plot if you have only one variable to look at and a Box Plot if you have many. Use a histogram if you need to present your results to a non-statistical public. As a statistical test to confirm your hypothesis, use the Shapiro Wilk test.
How is the normal distribution of stock returns?
The skinny middle and the fat tails imply that the normal distribution might not be the best describer of stock returns. Rather, there seem to be 2 regimes — a calm regime where we spend most of the time that is normally distributed (but with a lower volatility than 12%) and a regime with high volatility and terrible returns.
Which is better normal or simulated stock market returns?
The distribution of simulated results matches the S&P 500 actuals significantly better than the normal distribution. This simulation has the leptokurtic shape (high central peak, narrower upper shoulders) characteristic of stock market returns.
When to use lognormal distribution to model stock prices?
Lognormal is extremely useful when analyzing stock prices. As long as the growth factor used is assumed to be normally distributed (as we assume with the rate of return), then the lognormal distribution makes sense. Normal distribution cannot be used to model stock prices because it has a negative side, and stock prices cannot fall below zero.
Which is the best probability distribution for stock market returns?
No wonder that market crashes seem so unforeseeable when such models are used to assign probability values to them. By now, it should be clear that a normal distribution is not exactly a great model for stock returns. Nevertheless, it is the most popular choice of distribution to do exactly that.