leveraged etf compounding performance lag

letf.R

library(tidyverse)

library(ggplot2)

periods <- 10
trend <- 0
vola <- 0.1

leverage <- 2

ret <- rnorm(10, 0, vola)

return.df <- data.frame(ret) %>% 
  mutate(period = row_number(),
         etf = cumprod(ret+1)-1,
         letf = cumprod(ret*leverage+1)-1,
         expected = etf*leverage) %>% 
  pivot_longer(cols = c(etf, letf, expected), names_to = "series")
  


return.df %>% 
  ggplot(aes(x = period, y = value, color = series)) +
  geom_line()