Different methods to calculate covariance

AI & Machine learning
1

Course Name: Quantitative Portfolio Management, Section No: 2, Unit No: 6, Unit type: Notebook



Hi there,



I noticed that the following two methods for calculating covariance each gives a different result. Can you help to explain why? 



price_returns.cov() * 252



cov_msft_googl = np.cov(

    price_returns['MSFT'], price_returns['GOOGL'], bias=True)*252



Many thanks,

Ryan

2

The reason for the difference in the np.cov() method and DataFrame.cov() is the normalisation.



In both cases, the default normalisation is False (bias = False) and is done by N-1.

where N is the number of observations given.



When you change to bias=True, then normalisation is done by N.



Instead of this line of code: 

cov_msft_googl = np.cov(

    price_returns['MSFT'], price_returns['GOOGL'], bias=True)*252



Use this:

cov_msft_googl = np.cov(

    price_returns['MSFT'], price_returns['GOOGL'], bias=False)*252



You will get the same result using both np.cov() and DataFrame.cov() method.