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)
I need to calculate daily gain/loss (%) - i.e. what is the gain it has from 10.25 to 11.26 then from 11.26 to 14 etc.
Is there a function to calculate this automatically?
Using your sample data, I think you mean the following:
a <- c(10.25, 11.26, 14, 13.56)
> diff(a)/a[-length(a)]
[1] 0.09853659 0.24333925 -0.03142857
diff returns the vector of lagged differences and a[-length(a)] drops the last element of a.
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.