Why do we multiply returns?

I'm teaching our Fundamentals of Performance Measurement course for a client this week and have been asked some interesting questions by the students. One asked why we multiply returns in order to link them. Questions like this require, I believe, a bit of detail in their response, so let's discuss it here.

Let's say that our first quarter returns are as follows:

The rule we apply to compound is to add one to each return, multiply them together, and then subtract one, which results in:

But why? Why is this the right return? And again, why do we multiply?

Well, we are multiplying in order to compound our returns. January sees a return of 10%, which adds 10,000 to the account's market value. February's return is applied to both the starting or base amount (100,000) as well as January's gain (10,000), and March's return goes against the base, January's gain, as well as February's (5,500). This might help:

Questions like the one this student posed requires some thought, and I believe I've represented what happens, though will expand upon this further in our December newsletter.

p.s., to learn more about our training, please contact Patrick Fowler or Chris Spaulding.