Continuously Compounded Rate of Return

Effective Annual Rate = er – 1

=e^0.10 – 1

=10.517%

This means that if 10% was continuously compounded, the effective annual rate will be 10.517%.

We can also perform the reverse calculations. If a portfolio earned 10.517% in one year, then what would be the equivalent continuously compounded rate?

It will be ln(1+r) = ln (1.10517) = 10%

Let’s take another example. An investment of $100 grows to $130 in one year. What is the continuously compounded rate of return?

We can calculate it in two ways. First calculate the return earned, i.e., (130 -100)/100 = 30%. 30% is the holding period return.

The continuously compounded rate of return = ln(1.30) = 26.23%

Alternatively you can simply calculate ln(130/100) = 26.23%

An important property of continuously compounding rates is that they are additive.