Questions:
What is the formula for a continuously compounded return?

The stock price of Microsoft went from $109.86 to $138.78 in 2024. Amazon’s stock jumped from $88 to $129 and Meta’s stock increased from $152 per share to $177. Which stock had the highest continuously compounded return?

Reference answers:
# Formula

Continuously compounded return can be calculated using the following formula

Continuously compounded return = rt,t+1 = ln[P1 / P0]

- rt,t+1 is the continuously compounded return.
- P1 is the price at the end of the period.
- P0 is the price at the beginning of the period.

# Microsoft

P1 = $138.78
P0 = $109.86

rt,t+1 = ln[P1 / P0]
rt,t+1 = ln[$138.78 / $109.86]
rt,t+1 = ln[1.2632]
rt,t+1 = 0.2336 = 23.36%

# Amazon

P1 = $129
P0 = $88

rt,t+1 = ln[P1 / P0]
rt,t+1 = ln[$129 / $88]
rt,t+1 = ln[1.4659]
rt,t+1 = 0.3825 = 38.25%


# Meta

P1 = $177
P0 = $152

rt,t+1 = ln[P1 / P0]
rt,t+1 = ln[$177 / $152]
rt,t+1 = ln[1.1645]
rt,t+1 = 0.1523 = 15.23%

# Result

Amazon had the highest continuously compounded return last year.