Effective Annual Rate of Return Question

CFA Level I Quant
#1

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!

Please help a brain-dead man

#2

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.

Hope this helps.

#3

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.

#4

how to get the 7.71%?

thanks

#5

Turn each rate into a decimal, add 1.0 to each, multiply across, then subtract 1.0.

#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?

#7

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.

#8

Thank you!

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