I’m reviewing some areas and my brain is so jumbled with other topics that I can’t seem to figure out this easy one!
Quarterly holding period returns over six quarters are 1.5%, 2.0%, -0.9%, 4.4%, 2.3%, and -1.7%. The effective annual rate of return is:
5.08%
5.14%
5.06%"
I know the answer is 5.08%, but I can’t figure out how! The explanation states to first get the HPR, which is 7.71% But getting the effective annual rate of return = (1.0771)4/6; I can’t seem to figure out why I’m supposed to do the 4/6 part of the problem!
Because the Holding Period happens to be 6 quarters (1.5 years), so if you are asked to calculate the annual effective return, then adjust annualize the compounded return:
You can also use years (1.0771)1/1.5
or quarters as said above (1.0771)4/6
or months… (1.0771)12/18
or days… (1.0771)360/540
whatever you want, but keep the proportions correct.
You’ve been given 6 quarterly returns, so the 7.71% is the return for 6/4 years. To get to the equivalent annual rate, you raise 1.0771 to the power of 4/6.
Why don’t they raise it to the power of 1/6 as a geometric mean? Am I right that the reason behind is that a geometric mean is used only for multi-year returns? As we have 1,5 years period, we simply multiply HPR of each subperiod?
For a period of T years, you would take 1/T as a geometric mean to come up with an annual rate. In this case, we have 6 quarterly periods or T=1.5 years, so we use 1/T = 1/1.5.