Simulating a Random Walk with a drift (using a for loop)

Question

I am trying to build a simulation of a random walk process with a drift using a loop, however, I am not able to get any outputs and instead I get a length error (number of items to replace is not a multiple of replacement length) which I can't fully understand since I provide a length that will change with how any number of values (N). I am supposed to be able to provide with specific values and then simulate the random walk. Here's my code:

random_walk <- function(prices){
  

  prices <- as.vector(prices)
  
 
  ln_prices <- log(prices)
  
  
  N <- length(prices)
  
 
  phi0 <- (ln_prices[N] - ln_prices[1]) / N
  
  
  sigma <- sd(ln_prices) / sqrt(ln_prices)
  
 
  shock <- rnorm(ln_prices, 0, sigma)
  
 
  rw1 <- c(ln_prices[1])
  
 for (i in 2:N){
  # I calculate the rw value for day t:
  # rw <- drift + shock + rw of yesterday
  rw1 <- rw1 + phi0 + shock

 }
  
}```

Answer 1

You need to return something out of this functions, you can either use return or just call the name of what you want at the last line

random_walk <- function(prices){
  
  
  prices <- as.vector(prices)
  
  
  ln_prices <- log(prices)
  
  
  N <- length(prices)
  
  
  phi0 <- (ln_prices[N] - ln_prices[1]) / N
  
  
  sigma <- sd(ln_prices) / sqrt(ln_prices)
  
  
  shock <- rnorm(ln_prices, 0, sigma)
  
  
  rw1 <- c(ln_prices[1])
  
  for (i in 2:N){
    # I calculate the rw value for day t:
    # rw <- drift + shock + rw of yesterday
    rw1 <- rw1 + phi0 + shock
    
  }
  return(rw1)
}  

price <- c(10,11,9,10.6,10.2,9.8,8.5,8,8.8,11)  

random_walk(prices = price)
#>  [1] 2.5747813 2.2403036 1.8345087 2.9714599 1.4440819 0.8269357 2.0922631
#>  [8] 2.0563724 1.7999183 3.1020998

^{Created on 2021-06-03 by the reprex package (v2.0.0)}

Session info

sessionInfo()
#> R version 4.1.0 (2021-05-18)
#> Platform: x86_64-w64-mingw32/x64 (64-bit)
#> Running under: Windows 10 x64 (build 21390)
#> 
#> Matrix products: default
#> 
#> locale:
#> [1] LC_COLLATE=Portuguese_Brazil.1252  LC_CTYPE=Portuguese_Brazil.1252   
#> [3] LC_MONETARY=Portuguese_Brazil.1252 LC_NUMERIC=C                      
#> [5] LC_TIME=Portuguese_Brazil.1252    
#> 
#> attached base packages:
#> [1] stats     graphics  grDevices utils     datasets  methods   base     
#> 
#> loaded via a namespace (and not attached):
#>  [1] ps_1.6.0          digest_0.6.27     withr_2.4.2       magrittr_2.0.1   
#>  [5] reprex_2.0.0      evaluate_0.14     highr_0.9         stringi_1.6.2    
#>  [9] rlang_0.4.11      cli_2.5.0         rstudioapi_0.13   fs_1.5.0         
#> [13] rmarkdown_2.8     tools_4.1.0       stringr_1.4.0     glue_1.4.2       
#> [17] xfun_0.23         yaml_2.2.1        compiler_4.1.0    htmltools_0.5.1.1
#> [21] knitr_1.33

Answer 2

Let me try to refactor your code a bit, so that it actually returns something:

random_walk <- function(prices){

  #  prices <- as.vector(prices) # You don't need this since you're already passing a vector
  
  ln_prices <- log(prices)
  
  N <- length(prices)
    
  phi0 <- (ln_prices[N] - ln_prices[1]) / N
    
  sigma <- sd(ln_prices) / sqrt(ln_prices)
    
  shock <- rnorm(ln_prices, 0, sigma)
    
  rw1 <- ln_prices[1]
  
  # This for loop is also unnecessary. You're basically adding phi0 + shock N-1 times
  #for (i in 2:N){
  #  # I calculate the rw value for day t:
  #  # rw <- drift + shock + rw of yesterday
  #  rw1 <- rw1 + phi0 + shock
  #  
  #}
  rw.N <- rw1 + (N-1) * (phi0 + shock)
  
  rw.N # Call rw.N to actually return anything  
}