How do I calculate a compounding return in a vector indexed to 100?

Question

I have the following dataframe:

dat <- tibble::tribble(    ~date     ,  ~pct_monthly_return,
                           2021-01-31,   0.0023,
                           2021-02-28,   0.01,
                           2021-03-31,   0.035)

I would like to create a new column called index which starts at 100 a month before the dataframe starts (i.e. 2020-12-31 in my example). The index of 100 must then be compounded by pct_monthly_return variable so that I can see how the index grows over time.

The result should produce the following dataframe:

date                   pct_monthly_return   index
2020-12-31             0                    100 
2021-01-31             0.0023               100.23
2021-02-28             0.01                 101.2323
2021-03-31             0.035                104.7754

Answer 1

We can take the cumulative product of the returns expressed as coefficients, i.e. 1 + pct_monthly_return

dat$index = 100 * cumprod(1+dat$pct_monthly_return)

Then to add the header row you described:

rbind(data.frame(date = "2020-12-31", index = 100, pct_monthly_return = 0), 
      dat)

        date    index pct_monthly_return
1 2020-12-31 100.0000             0.0000
2 2021-01-31 100.2300             0.0023
3 2021-02-28 101.2323             0.0100
4 2021-03-31 104.7754             0.0350

Sample data

dat <- tibble::tribble(    ~date     ,  ~pct_monthly_return,
                           "2021-01-31",   0.0023,
                           "2021-02-28",   0.01,
                           "2021-03-31",   0.035)

Answer 2

Base R:

Use sapply and cumprod:

> cbind(dat, index=as.vector(sapply(dat[,-1] + 1, cumprod) * 100))
        date pct_monthly_return    index
1 2021-01-31             0.0023 100.2300
2 2021-02-28             0.0100 101.2323
3 2021-03-31             0.0350 104.7754
> 

Or even better:

> cbind(dat, index=cumprod(1 + dat$pct_monthly_return) * 100)
        date pct_monthly_return    index
1 2021-01-31             0.0023 100.2300
2 2021-02-28             0.0100 101.2323
3 2021-03-31             0.0350 104.7754
> 

Answer 3

Base R solution:

# Import data: df => data.frame
df <- structure(list(date = structure(c(18658L, 18686L, 18717L), class = c( 
"Date")), pct_monthly_return = c(0.0023, 0.01, 0.035)), class = "data.frame", row.names = c(NA, 
-3L))

# Add new row calculate index: res => data.frame
res <- transform(
  rbind(
    data.frame(
      date = as.Date("2020-12-31"),
      pct_monthly_return = 0.000
    ),
    df
  ),
  index = 100 * cumprod(1 + pct_monthly_return)
)

Tidyverse solution:

# Import and initialise package: 
library(tidyverse)

# Import tibble: df1 => tibble
df1 <- structure(list(date = structure(c(18658L, 18686L, 18717L), class = c("Date")), pct_monthly_return = c(0.0023, 0.01, 0.035)), row.names = c(NA, -3L), 
class = c("tbl_df", "tbl", "data.frame"))

# Calculate answer: res1 => tibble
res1 <- tibble(date = as.Date("2020-12-31"),
  pct_monthly_return = 0.000) %>%
  bind_rows(., df1) %>% 
  mutate(index = 100 * cumprod(1 + pct_monthly_return))

data.table solution:

# Import and intialise data.table package: 
library(data.table)

# Import data: dat => data.table
dat <- structure(list(date = structure(c(18658, 18686, 18717), class = "Date"), 
pct_monthly_return = c(0.0023, 0.01, 0.035)), row.names = c(NA, 
-3L), class = c("data.table", "data.frame"), 
.internal.selfref = <pointer: 0x000002704fbd1ef0>)

# Add row and calculate index: dat_res => data.table
dat_res <- rbindlist(
  list(
    dat1 = data.table(
      date = as.Date("2020-12-31"),
      pct_monthly_return = 0.000
    ),
    dat
  )
)[,index := 100 * cumprod(1 + pct_monthly_return),]

Answer 4

This can be done even with a simple while loop:

#Assuming you'll always want the first date to be the first row of the new data frame

rbind(data.frame(date=dat$date[1], pct_monthly_return = 0), dat)-> dat

index <- c(100)

i <- 2

while (i <=nrow(dat)) {
  index[i] <- (1+dat$pct_monthly_return[i])* index[i-1]
  
  i<- i+1
}

dat$index <- index

> dat
        date pct_monthly_return    index
1 2021-01-31             0.0000 100.0000
2 2021-01-31             0.0023 100.2300
3 2021-02-28             0.0100 101.2323
4 2021-03-31             0.0350 104.7754

Sample data:

dat <- tibble::tribble(    ~date     ,  ~pct_monthly_return,
                           "2021-01-31",   0.0023,
                           "2021-02-28",   0.01,
                           "2021-03-31",   0.035)