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

A more detailed example with multiple time series:

############ Vector  ############

vPrice <- (10.25, 11.26, 14, 13.56) 
n = length(vPrice)

#Log returns

log_ret <- diff(log(vPrice)) # or = log(vPrice[-1]/vPrice[-n]) because "..[-i]" removes the i'th item of the vector
log_ret

#Simple returns

simple_ret <- diff(vPrice)/vPrice[1:(n-1)] # or = diff(vPrice)/vPrice[-n]
simple_ret


############ Multiple Time series ############

head(EuStockMarkets)

mPrice <-  EuStockMarkets
n = dim(mPrice)[1] #Nb rows

log_ret <- diff(log(mPrice))
head(log_ret)

simple_ret <- diff(mPrice)/mPrice[1:(n-1),]
head(simple_ret)


#Total Returns

total_log_ret <- colSums(log_ret,2) #just a sum for log-returns
total_log_ret
total_Simple_ret <- apply(1+simple_ret, 2, prod)-1 # product of simple returns
total_Simple_ret

##################

#From simple to log returns 
all.equal(log(1+total_Simple_ret),total_log_ret) #should be true

#From Log to simple returns 
all.equal( total_Simple_ret,exp(total_log_ret)-1) #should be true

Answer 2

You can do this:

(PRICE / lag(PRICE)-1) * 100

Answer 3

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.

Answer 4

You may find the functions in quantmod relevant for your work:

> require(quantmod)
> Delt(a)
     Delt.1.arithmetic
[1,]                NA
[2,]        0.09853659
[3,]        0.24333925
[4,]       -0.03142857

Answer 5

You can also use the exact relationship that returns are equal to the exponent of log returns minus one. Thus, if Prices contains your prices, the following will give you your returns:

Returns = exp(diff(log(Prices))) - 1

Note that this is an exact relationship, rather than the approximate relationship given in the answer by @PBS.

Answer 6

Another possibility is the ROC function of the TTR package:

library(TTR)
a <- c(10.25, 11.26, 14, 13.56)
ROC(a, type = "discrete")
## [1]          NA  0.09853659  0.24333925 -0.03142857

type = continuous (which is also the default) gives log-returns:

ROC(a)
## [1]          NA  0.09397892  0.21780071 -0.03193305