How to calculate returns from a vector of prices?

Question

I have to calculate the return of a vector that gives a historical price series of a stock. The vector is of a form:

a <- c(10.25, 11.26, 14, 13.56) 


        

Answer 1

ret<-diff(log(a))

This will give you the geometric returns - return follow a lognormal distribution (lower boundary is -100% since prices are always non-negative), so the ln(prices) follows a normal distribution (therefore you might see returns smaller than -1 or -100%).

For the "normal" range of returns, the difference between the [P(t+1)-P(t)]/P(t) and the LN(P(t+1)/P(t)) should be negligible. I hope this helps.