# Compound the monthly returns to make them quarterly [closed]

How can someone make the Kenneth French library data returns quarterly from monthly? Since they are not loq returns, then you need to compound returns rather than summing them up. I want to make the returns of the SML, HML, the industry portfolio and the risk free that he uses, as quarterly returns. Does anybody know how you can deal with such a problem in R?

• Wll I can not understand how can i convert monthly to quarterly data. I only know that the best way to deal with this problem is to convert annual data to quarterly data. Specifically, if $x$ is the yearly return of a stock, then I can use the formula: $$r_{\text{quarter}}=\left(1+\frac{x}{100}\right)^{3/12}-1$$ May 7, 2020 at 11:41

## 1 Answer

You add 1 to every monthly return of a given quarter, take the product of those returns, and then subtract 1.

In R (without any package): Suppose r are the monthly returns, and dt are the timestamps.

r <- rep(0.01, 12)
dt <- seq(from = as.Date("2020-1-1"),
to = as.Date("2020-12-1"),
by = "1 month")

tapply(r,
paste(as.POSIXlt(dt)\$year + 1900, quarters(dt)),
FUN = function(x) prod(x + 1) - 1)
## 2020 Q1 2020 Q2 2020 Q3 2020 Q4
##  0.0303  0.0303  0.0303  0.0303


If you prefer the convenience of packages:

library("NMOF")  ## for function 'French'
library("PMwR")  ## for function 'returns'

P <- French(dest.dir = tempdir(),
dataset = "F-F_Research_Data_Factors_CSV.zip",
weighting = "value", frequency = "monthly",
price.series = TRUE)

head(P)
##              Mkt-RF       SMB      HML       RF
## 1926-06-30 1.000000 1.0000000 1.000000 1.000000
## 1926-07-31 1.029600 0.9770000 0.971300 1.002200
## 1926-08-31 1.056781 0.9633220 1.011997 1.004706
## 1926-09-30 1.060586 0.9506061 1.012099 1.007016
## 1926-10-31 1.026223 0.9509864 1.017260 1.010239
## 1926-11-30 1.052186 0.9490844 1.013700 1.013371

returns(P, t = as.Date(row.names(P)), period = "quarterly")
##                Mkt-RF         SMB        HML          RF
## 1926-09-30  0.0605859 -0.04939385  0.0120987  0.00701632
## 1926-12-31  0.0180728 -0.00200016  0.0013818  0.00912759
## 1927-03-31  0.0425284 -0.02248889  0.0526542  0.00812182
## 1927-06-30  0.0344638  0.02324739  0.0394452  0.00812182
## 1927-09-30  0.1457918 -0.07356559 -0.0548306  0.00792060
## 1927-12-31  0.0411792  0.05924812 -0.0563754  0.00681538


(disclosure: I am the maintainer of packages NMOF and PMwR.)

• thank you very much! May 7, 2020 at 12:34