Doubts

04 - Exercise Set - 6)

04 - Exercise Set - 6)

by Julian Hildebrandt -
Number of replies: 2

Hello Julio,

I have a question about annualising multi‑year returns. In the video lecture, we simplified annualizing returns by dividing or multiplying (e.g., dividing a total return by the number of years).
However, in our Exercise Set the annual return is calculated as:

(1+Total 2‑year return)1/2−1(1 + \text{Total 2‑year return})^{1/2} - 1


which gives 7.47% instead of simply 15.50%÷2=7.75%15.50\% ÷ 2 = 7.75\%.
Could you please explain why we use this compound annual growth rate (CAGR) formula rather than a simple division?
What is the intuition behind compounding in this context, and when should we choose one method over the other?

Thank you for your clarification!


In reply to Julian Hildebrandt

Re: 04 - Exercise Set - 6)

by Julio Crego -

Very good question without a very good answer. 

We use simple multiplication or division when we want to get the APR (or we use log returns) and this other formula to get the EAR. 

In this case, the reinvestment decision takes place at the end of the year, so we have yearly compounding. Hence, we get the EAR. 

In general, if we want to compare different investments, especially with reinvestment, we use the EAR. 

We use APR to report to clients, etc, who might have a harder time understanding what the rate implies for the periodic payment. 

For the midterm and final exams, use the formula in the exercise set.