Calculate annualized returns from quarterly observations

Question

I am trying to calculate annualized quarterly returns from two returns series.

Given a vector r_a, it is fairly easy:

r_a <- c(.05, .02, .03, .08, .1,         


        

Answer 1

We can use

apply(mat_ab, 2, function(col_j){
col_j <- as.matrix(col_j)
(prod(1+col_j)^(4/nrow(col_j)))-1
})
#       r_a       r_b 
  0.2491168 0.4773500 

Further, as you can see your code uses a matrix object:

r_a <- c(.05, .02, .03, .08, .1, .04, .06, .08)
r_a <- t(t(r_a))
class(r_a)
# [1] "matrix"

Answer 2

Though there is an accepted answer, I think the following can be of use. nrow is replaced by NROW so as to work both with quarterly returns vectors and matrices.

To see the difference:

nrow(1:10)
#NULL
NROW(1:10)
#[1] 10

And the function becomes

annualized <- function(x, MARGIN = 2){
  f <- function(y) (prod(1 + y)^(4/NROW(y))) - 1
  if(is.null(dim(x)))
    f(x)
  else
    apply(x, MARGIN = MARGIN, f)
}


r_a <- c(.05, .02, .03, .08, .1, .04, .06, .08)
r_b <- c(.1, .1, .1, .1, .1, .1, .1, .12)
mat_ab <- cbind(r_a, r_b)


annualized(r_a)
#[1] 0.2491168

annualized(mat_ab)
#      r_a       r_b 
#0.2491168 0.4773500