replicating momentum strategy - Formation Periods

Question

I am trying to replicate the momentum strategy of the study by Jegadesh and Titman (1993) onyl using data from the past 10 years.I am trying right now to calculate the formation period returns. But I think I have some mistakes. If I go further and then form the portfolios, ranking them, all 4 portfolios show the same returns for each 1-10 ranks. I have a feeling that my mistakes is already here in the formation periods but I dont get it. Maybe somebody can help me a bit. thanks a lot! (the data_subset is my original data with all variables included)

formation_periods <- c(3, 6, 9, 12)

momentum_portfolios <- list()
for (formation_period in formation_periods) {
  
  subset <- data_subset %>% 
    select(PERMNO, Date, Returns, logreturns) %>% 
    arrange(PERMNO, Date)

  subset$sumlogret <- subset %>% 
    group_by(PERMNO) %>% 
    mutate(sumlogret = rollsum(logreturns, formation_period, align = "right", fill = NA)) %>% 
    ungroup() %>% 
    pull(sumlogret)
  
  subset <- subset %>% 
    rename(sumlogreturns = logreturns)
  
  subset$cumret <- exp(subset$sumlogreturns) - 1
  
  momentum_portfolios[[paste0("Formation_", formation_period)]] <- subset
}

here is my following code where I realized that all formation periods have the same numbers in it.

  
  momentum_portfolio <- momentum_portfolios[[paste0("Formation_", formation_period)]]
  
  momentum_portfolio <- momentum_portfolio[!is.na(momentum_portfolio$cumret), ]
  
  momentum_portfolio$momr <- as.numeric(factor(momentum_portfolio$cumret, levels = unique(momentum_portfolio$cumret)))
  momentum_portfolio$momr <- cut(momentum_portfolio$cumret, breaks = quantile(momentum_portfolio$cumret, probs = seq(0, 1, by = 0.1)), labels = FALSE) 
  cat("Formation Period:", formation_period, "\n")
  cat("Examine distribution of cumret by momr:\n")
  print(tapply(momentum_portfolio$cumret, momentum_portfolio$momr, mean)) 
}
tail(momentum_portfolio)
```

Answer 1

You could form the groups inside the main loop, but do it by each Date:

momentum_portfolios <- list()
for (formation_period in formation_periods) { # formation_period=6
  
  subset <- data_subset %>% 
    select(PERMNO, Date, Returns, logreturns) %>% 
    arrange(PERMNO, Date)
  
  subset$sumlogreturns <- subset %>% 
    group_by(PERMNO) %>% 
    mutate(sumlogret = rollsum(logreturns, formation_period, align = "right", fill = NA)) %>% 
    ungroup() %>% 
    pull(sumlogret)
  
  subset$cumret <- exp(subset$sumlogreturns) - 1
  
  subset <- subset %>% dplyr::filter(!is.na(cumret))
  
  subset <- subset %>% 
    group_by(Date) %>% 
  mutate(momr = cut(cumret, 
                           quantile(cumret, seq(0,1,by=.1)), 
                           labels = F, 
                           include.lowest = TRUE))
  
  momentum_portfolios[[paste0("Formation_", formation_period)]] <- subset
}

Then you can calculate the mean of cumret by Date and momr. Finally compute stats by formation_period and momr.

stats = lapply(momentum_portfolios,function(momentum_portfolio){
tail(momentum_portfolio)

sumres = momentum_portfolio %>% group_by(Date,momr) %>% 
  summarise(MeanRet= mean(cumret))
sumres
})

lapply(stats, function(sumres){
  psych::describeBy(sumres$MeanRet,sumres$momr,T,fast=T)
  })

And get for example (the data is real for a sample of random assets):

$Formation_3
     item group1 vars   n          mean         sd         min        max     range          se
X11     1      1    1 163 -0.1406651698 0.10433599 -0.54924523 0.02337787 0.5726231 0.008172225
X12     2      2    1 163 -0.0594150045 0.06424748 -0.31759419 0.05568860 0.3732828 0.005032251
X13     3      3    1 163 -0.0258877359 0.05774981 -0.22716365 0.09620802 0.3233717 0.004523314
X14     4      4    1 163 -0.0006506752 0.05501481 -0.18303160 0.12743288 0.3104645 0.004309093
X15     5      5    1 163  0.0233330867 0.05508793 -0.14573197 0.18195906 0.3276910 0.004314820
X16     6      6    1 163  0.0469287583 0.05746346 -0.13073737 0.25985134 0.3905887 0.004500885
X17     7      7    1 163  0.0711782424 0.06206042 -0.11635815 0.36741241 0.4837706 0.004860947
X18     8      8    1 163  0.1013354021 0.06794467 -0.09081408 0.47001651 0.5608306 0.005321837
X19     9      9    1 163  0.1481222105 0.09273639 -0.04511237 0.70092962 0.7460420 0.007263675
X110   10     10    1 163  0.3806737037 0.43766965  0.03286265 2.82848241 2.7956198 0.034280932