Are stock returns normally distributed?

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.

Are log returns normal?

Therefore log returns have a normal distribution. The returns of an index — which is the weighted average of a number of assets — has even more reason to be normal. Even if the returns of the individual assets were not normal, the averaging over assets would mean that the index returns would be normal.

Why we use log normal distribution?

Lognormal distribution plays an important role in probabilistic design because negative values of engineering phenomena are sometimes physically impossible. Typical uses of lognormal distribution are found in descriptions of fatigue failure, failure rates, and other phenomena involving a large range of data.

Why stock return distribution is not a normal curve?

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.

Are returns normal?

Stock returns are roughly normal after all and a lot of the benefits of investment theory such as diversification hold true even in a world of less than normal stock returns and fat tails (perhaps even more so).

What does it mean if returns are normally distributed?

If returns are normally distributed, more than 99 percent of the returns are expected to fall within three standard deviations of the mean. These characteristics of the bell shaped normal distribution allow analysts and investors to make statistical inferences about the expected return and risk of stocks.

What do log returns tell us?

Log-return is just another measure of return, so it tells you all of the information that’s usually contained in any measure of return. The mathematics are different, however, and more conclusions can be drawn from that.

Do stock prices follow a normal distribution?

While the returns for stocks usually have a normal distribution, the stock price itself is often log-normally distributed. This is because extreme moves become less likely as the stock’s price approaches zero. For example, a 10-cent price change corresponds to a hefty 5 percent if the stock is only $2. …

What does it mean when returns are normally distributed?

The normal distribution is the probability distribution that plots all of its values in a symmetrical fashion with most of the results situated around the probability’s mean.

Why is return important?

Return on investment, better known as ROI, is a key performance indicator (KPI) that’s often used by businesses to determine profitability of an expenditure. It’s exceptionally useful for measuring success over time and taking the guesswork out of making future business decisions.