Annualising negative daily returns.

Hi guys, I hope you can help me out so thanks for your time.

I have encountered a problem in class where we were given daily average returns as a percentage, lets say x%, now I have annualised this using:

((((x/100)+1)^365)-1)*100

which I hope is right.

But, some of these daily returns are negative, -x%. So I am basically wondering if the formula I have used so far is right, and if you can use the same formula for the negative returns or is there anything you have to change in case of negative returns?

Thanks for your time.

Re: Annualising negative daily returns.

In actuarial notation the expression

$\displaystyle \displayformat \left(1+\frac{i^{(365)}}{365}\right)^{365}$

gives the accumulated value of a yearly nominal percentage compounded daily, whether or not $\displaystyle i$ is positive or negative. However, in order to extract the percentage of gain or loss over an annum, the formula must change. If $\displaystyle x$ is positive, and given as a percentage, then your formula works. However, for negative $\displaystyle x$,

$\displaystyle \displaystyle (1-\left(1-\frac{x}{100}\right)^{365})*100$

gives the annual loss as a percentage, where x is a positive percentage corresponding to -x%.

P.S. Multiplying by 100 to make "percentages" makes me cry on the inside.