First moment: Mu

You can calculate the average historical return of a stock by using numpy's mean() function.

When you are calculating the average daily return of a stock, you are essentially estimating the first moment ( $ \mu $ ) of the historical returns distribution.

But what use are daily return estimates to a long-term investor? You can use the formula below to estimate the average annual return of a stock given the average daily return and the number of trading days in a year (typically there are roughly 252 trading days in a year):

$$ \text{Average Annualized Return} = ( ( 1 + \mu ) ^ {252}) - 1 $$

The StockPrices object from the previous exercise is stored as a variable.

This exercise is part of the course

Introduction to Portfolio Risk Management in Python

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Exercise instructions

Import numpy as np.
Calculate the mean of the 'Returns' column to estimate the first moment ( $ \mu $ ) and set it equal to mean_return_daily.
Use the formula to derive the average annualized return assuming 252 trading days per year. Remember that exponents in Python are calculated using the ** operator.

Hands-on interactive exercise

Have a go at this exercise by completing this sample code.

# Import numpy as np
import ____ as ____

# Calculate the average daily return of the stock
mean_return_daily = ____(StockPrices['Returns'])
print(mean_return_daily)

# Calculate the implied annualized average return
mean_return_annualized = ((____+____)**____)-____
print(mean_return_annualized)

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