Annualized returns

Introduction to Portfolio Analysis in Python

Charlotte Werger

Data Scientist

Comparing returns

  1. Annual Return: Total return earned over a period of one calendar year

  2. Annualized return: Yearly rate of return inferred from any time period

  3. Average Return: Total return realized over a longer period, spread out evenly over the (shorter) periods.

  4. Cumulative (compounding) return: A return that includes the compounded results of re-investing interest, dividends, and capital gains.

Introduction to Portfolio Analysis in Python

Why annualize returns?

$$ Table of portfolio returns

$$

  • Average return = (100 - 50) / 2 = 25%
  • Actual return = 0% so average return is not a good measure for performance!
  • How to compare portfolios with different time lengths?
  • How to account for compounding effects over time?
Introduction to Portfolio Analysis in Python

Calculating annualized returns

$$

  • N in years: $rate= (1 +Return)^{1/N} -1$

  • N in months: $rate= (1+Return)^{12/N} -1$

  • Convert any time length to an annual rate:

  • Return is the total return you want to annualize.
  • N is number of periods so far.
Introduction to Portfolio Analysis in Python

Annualized returns in python

# Check the start and end of timeseries
apple_price.head(1)

date
2015-01-06    105.05
Name: AAPL, dtype: float64

apple_price.tail(1)

date
2018-03-29    99.75
Name: AAPL, dtype: float64

# Assign the number of months
months = 38
Introduction to Portfolio Analysis in Python

Annualized returns in python

# Calculate the total return
total_return = (apple_price[-1] - apple_price[0]) / 
                apple_price[0]

print (total_return)

0.5397420653068692
Introduction to Portfolio Analysis in Python

Annualized returns in python

# Calculate the annualized returns over months
annualized_return=((1 + total_return)**(12/months))-1
print (annualized_return)

0.14602501482708763

# Select three year period
apple_price = apple_price.loc['2015-01-01':'2017-12-31']
apple_price.tail(3)

date
2017-12-27    170.60
2017-12-28    171.08
2017-12-29    169.23
Name: AAPL, dtype: float64
Introduction to Portfolio Analysis in Python

Annualized return in Python

# Calculate annualized return over 3 years
annualized_return = ((1 + total_return)**(1/3))-1

print (annualized_return)

0.1567672968419047
Introduction to Portfolio Analysis in Python

Let's practice!

Introduction to Portfolio Analysis in Python

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