Investigating stylized facts of asset returns

Stylized facts are statistical properties that appear to be present in many empirical asset returns (across time and markets). It is important to be aware of them because when we are building models that are supposed to represent asset price dynamics, the models must be able to capture/replicate these properties.

In the following recipes, we investigate the five stylized facts using an example of daily S&P 500 returns from the years 1985 to 2018.

Getting ready

We download the S&P 500 prices from Yahoo Finance (following the approach in the Getting data from Yahoo Finance recipe) and calculate returns as in the Converting prices to returns recipe.

We use the following code...