Constructing Momentum Factor in R Studio - Fama & French

Question

I want to construct a momentum factor which is part of Fama and French Regression. We have a monthly data table starting from 1980-12-31 to 2021-12-31, and a time series of stock returns, given as a percentage monthly return. [The Image is showing a simple version of our data table, (where RI - Return Index)]

The definition of the momentum factor is the cumulated total stock return (calculated by the total return index, item RI) from month t-12 to month t-2, where t is the month of the forecasted return. Momentum factor is updated monthly.

I know the code of the cumulated total stock return to be: DS.monthly[, cum_ret := cumprod(RET.USD + 1), by = c("Id", "Date")]

but this would not be the correct way to compute momentum, because of this statement "from month t-12 to month t-2 "

We came up with this new columns for our data set:

DS.monthly %>% setorder(Id, -Date)
DS.monthly[, t_1:=lead(RET.USD/100), by=Id]
DS.monthly[, t_2:=lead(t_1), by=Id]
DS.monthly[, t_3:=lead(t_2), by=Id]
DS.monthly[, t_4:=lead(t_3), by=Id]
DS.monthly[, t_5:=lead(t_4), by=Id]
DS.monthly[, t_6:=lead(t_5), by=Id]
DS.monthly[, t_7:=lead(t_6), by=Id]
DS.monthly[, t_8:=lead(t_7), by=Id]
DS.monthly[, t_9:=lead(t_8), by=Id]
DS.monthly[, t_10:=lead(t_9), by=Id]
DS.monthly[, t_11:=lead(t_10), by=Id]
DS.monthly[, t_12:=lead(t_11), by=Id]
DS.monthly[, cumulative:= ((t_2+1)(t_3+1)(t_4+1)(t_5+1)(t_6+1)(t_7+1)(t_8+1)(t_9+1)(t_10+1)(t_11+1)(t_12+1))]  

where we basically calculate the lagged return for each month and compute the cum_return manually, but it is a very inefficient way.

We had already one code suggestion, but the explanation before from my part was not good so I am not sure if it's the correct way. The suggested code is as below:

as.data.table(DS.monthly |> 
                              arrange(Id, Date) |>
                              group_by(Id) |>
                              mutate(Momentum = slide_dbl(lag(RET.USD), ~ last(cumprod(1 + .x)), .before = 10, .complete = TRUE))) 

Can someone please suggest a solution?

Answer 1

I believe you can leverage shift() and Reduce() here.. data.table::shift() can take a vector of offsets, so that you can get all the offsets from -2 to -12 all at once..

DS.monthly[order(-Date),cumulative:=Reduce(`*`,shift(1+RET.USD/100, -2:-12)), by=Id]

Output:

             Date    Id  RET.USD       RI cumulative
           <Date> <num>    <num>    <num>      <num>
    1: 1980-12-31 90130 4.004682 179.9825         NA
    2: 1981-01-31 90130 4.769887 196.4839         NA
    3: 1981-02-28 90130 8.428463 175.4452         NA
    4: 1981-03-31 90130 3.088209 131.3926         NA
    5: 1981-04-30 90130 2.189597 233.2892         NA
   ---                                              
34999: 2021-08-31 90200 6.481878 220.9295   1.887856
35000: 2021-09-30 90200 2.171489 122.2258   1.861571
35001: 2021-10-31 90200 8.312751 243.9816   1.866157
35002: 2021-11-30 90200 3.388710 134.0194   1.845590
35003: 2021-12-31 90200 1.734986 113.5201   1.844010

Input:

set.seed(123)
Dates= seq(as.Date("1981-01-01"), as.Date("2022-01-01"),by="1 month")-1
IDs = seq(90130, 90200,1)
DS.monthly = data.table(Date=rep(Dates,length(IDs)))
DS.monthly[order(Date),Id:=rep(IDs, length.out=.N)]
DS.monthly[,RET.USD := runif(.N,1,9)]
DS.monthly[,RI := runif(.N,100,250)]