# Compound annual rate question?

Guys, I came across a question today that I could not woek through, i would appreciate clarification, thanks. An analysis observes the following four annual returns: R1 = +10%, R2 = -15%, R3 = 0%, R4 = +5% The equivalent compound annual rate is; A; -5% B; -0.5% C; 0% D: 7.4% I came up with answer C 0% where as the correct ana=swer is B; -0.5% I would be grateful for the workings on this one, many thanks.

its (1.1*.85*1*1.05)^(1/4)

correct, use geometric average.

i did: (1.1)(.85)(1)(1.05)^.25 - 1 = -0.00459 = approximately -.5% (if rounded) not sure if this is right or not…havent looked through quant in a long time

Thankyou, looking back over the book it is clearly the one to use, hopefully this will have sunk in now…Cheers!

Perdition, It might be helpful to keep in mind that geometric average factors in the effects of compounding so that is the one you generally want to use when calculating historical returns as that is the best reflection of how your investment actually grew/shrunk. If the question is in the context of forward looking, or expected return, arithmetic average would be more appropriate.

Tks Chi, i had remembered the geometric mean formula, but prior to this I was clearly unsure of it’s application. Cheers.