1. ## logarithm

Hi,

Could someone please explain me the use of logarithm in formulas. For example, when I compute a return (such as price_new-price_old/price_old), it is suggested that I take the log of the ratio to get the return. What is the advantage of taking the log here?

thanks a lot,

Sam

2. You probably should get a model.

If the "return" over 'n' is 'i', then perhaps:

$\displaystyle NewPrice = (1+i)^{n}*OldPrice$

Solving for i:

$\displaystyle \frac{NewPrice}{OldPrice} = (1+i)^{n}$

$\displaystyle \log\left(\frac{NewPrice}{OldPrice}\right) = \log((1+i)^{n}) = n\log(1+i)$

That's enough. You can see that exponents can lead to logarithms.

On the other hand, perhaps it is thought that NewPrice/OldPrice gets too big too fast and studying the logarithm is more tractable.

On still another hand, there may be some statistical significance and absent the logarithm the statistical measure shows some inappropriate bias. Suffering the logarithm transformation might straighten it out.

In other words, any number of reasons.