Format date as Year/Quarter

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You need to explicilty Vectorize your function: 

fun_v <- Vectorize(fun, "x")
fun_v(Data$date)
#[1] "01/01" "01/01" "01/01" "01/02" "01/02" "01/02"

However, when it comes to more or less standard tasks (such as datetime manipulations), there’s always a solution already available:

library(zoo)
yq <- as.yearqtr(Data$date, format = "%Y-%m-%d")
yq
#[1] "2001 Q1" "2001 Q1" "2001 Q1" "2001 Q2" "2001 Q2" "2001 Q2"

To convert to your specific format, use 

format(yq, format = "%y/0%q")
#[1] "01/01" "01/01" "01/01" "01/02" "01/02" "01/02"

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