So I understand that to calculate the continuously compounded return between 2 prices, all you have to do is log the fraction of the 2 prices. For example:
What I don't get is how come if you take a log of just one price, it gives you a return or percent change as well? I don't know how the interpret the 2.
I am confused because let's say I am working with the CAPM model, which is:
(Excess Stock Return) = Beta0 + Beta1 * (Excess Market Return)
and am given a series of 100 stock prices and want to regress it against the market returns so I can get the Betas. To get the stock returns, I would take the log(price1/price2) and end up with 99 observations. Cool everything makes sense so far.
Now let's say I had two vectors of data, which are price and sales of a product. If I want the elasticity of sales with respect to price, that is, if I want to calculate how much a 1% change in price would affect a ?% change in sales, I would do the log-log regression, i.e. take the log of both price and sales and do a regression. My Beta1 would be the elasticity.
Let's say I have 100 observations of price and 100 observations of sales and I take the log of vectors. I still end up with 100 observations of each.
I don't get how
log(price1/price2) both give me a return or % change? What's the difference between these 2? I get that that
log(price1/price2) tells me the continuously compounded return going from price 2 to price 1. So
log(3/2) = .405 means that the continuously compounded return is 40.5%. So what does
log(price1) tell me aka just