R translation to Python

Question

I have some code that I wrote in R that I would like to have translated into Python, but am new to python so need a bit of help

The R code basically simulates 250 random normals, and then calculated a geometric mean return of sorts and then a max drawdown, it does this 10000 times and then combines the results, as shown below.

mu <- 0.06
sigma <- 0.20
days <- 250
n <- 10000
v <- do.call(rbind,lapply(seq(n),function(y){
  rtns <- rnorm(days,mu/days,sqrt(1/days)*sigma)
  p.rtns <- cumprod(rtns+1)
  p.rtns.md <- min((p.rtns/cummax(c(1,p.rtns))[-1])-1)
  tot.rtn <- p.rtns[days]-1
  c(tot.rtn,p.rtns.md)
}))

This is my attempt in Python, (if you can make it shorter/more eloquent/more efficient please suggest as answer)

import numpy as np
import pandas as pd
mu = float(0.06)
sigma = float(0.2)
days = float(250)
n = 10000
rtns = np.random.normal(loc=mu/days,scale=(((1/days)**0.5)*sigma),size=days)
rtns1 = rtns+1
prtns = rtns1.cumprod()
totrtn = prtns[len(prtns)-1] -1
h = prtns.tolist()
h.insert(0,float(1))
hdf = pd.DataFrame(prtns)/(pd.DataFrame(h).cummax()[1:len(h)]-1))[1:len(h)]]

and that was as far as I got... wasn't too sure if hdf was correct to get p.rtns.md , and wasnt sure how I would go about simulating this 10000 times.

All suggestions would be greatly appreciated...

Answer 1

I'm unfamiliar with R, but I see some general improvements that could be made to your Python code:

• Use 0.06 without float() around, since Python will infer that a numeric value with a decimal point is a float
  • The last line, h.insert(0,float(1)) can be replaced with h.insert(0,1.0)
• You can reference the last item in an iterable using [-1] , the second-last using [-2] , etc.:
  • totrtn = prtns[-1] -1

Python developers usually choose underscores between words or camelcase. In addition, it is normally preferable to use the full words in your variable names for readability over economy on-screen. For example, some variables here could be renamed to returns and total_returns or totalReturns .

To run your simulation 10000 times, you should use a for loop:

for i in range(10000):
    # code to be repeated 10000 goes in an indented block here
    # more lines in the loop should be indented at same level as previous line
# to mark what code runs after the for loop finishes, just un-indent again
h - prtns.tolist()
...

Answer 2

First, your last line of code:

hdf = pd.DataFrame(prtns)/(pd.DataFrame(h).cummax()[1:len(h)]-1))[1:len(h)]]

can't be right. May be this according to your R code:

hdf = (pd.DataFrame(prtns)/(pd.DataFrame(h).cummax()[1:len(h)])-1)[1:len(h)]

Second, c(1,p.rtns) can be replaced with np.hstack(1, prtns) instead of converting the np.array to list .

Third, looks like you are using pandas just for the cummax() . It is not hard to implement one, like this:

def cummax(a):
    ac=a.copy()
    if a.size>0:
        max_idx=np.argmax(a)
        ac[max_idx:]=np.max(ac)
        ac[:max_idx]=cummax(ac[:max_idx])
    else:
        pass
    return ac

And:

>>> a=np.random.randint(0,20,size=10)
>>> a
array([15, 15, 15,  8,  5, 14,  6, 18,  9,  1])
>>> cummax(a)
array([15, 15, 15, 15, 15, 15, 15, 18, 18, 18])

Take these all together we get:

def run_simulation(mu, sigma, days, n):
    result=[]
    for i in range(n):
        rtns = np.random.normal(loc=1.*mu/days,
                    scale=(((1./days)**0.5)*sigma),
                    size=days)
        p_rtns = (rtns+1).cumprod()
        tot_rtn = p_rtns[-1]-1 
        #looks like you want the last element, rather than the 2nd form the last as you did
        p_rtns_md =(p_rtns/cummax(np.hstack((0.,p_rtns)))[1:]-1).min() 
        #looks like you want to skip the first element, python is different from R for that.
        result.append((tot_rtn, p_rtns_md))
    return result

And:

>>> run_simulation(0.06, 0.2, 250,10)
[(0.096077511394818016, -0.16621830496112056), (0.73729333554192, -0.13566124517484235), (0.087761655465907973, -0.17862916081223446), (0.07434851091082928, -0.15972961033789046), (-0.094464694393288307, -0.2317397117033817), (-0.090720761054686627, -0.1454002204893271), (0.02221364097529932, -0.15606214341947877), (-0.12362835704696629, -0.24323096421682033), (0.023089144896788261, -0.16916790589553599), (0.39777037782177493, -0.10524624505023494)]

The loop is actually not necessary as we can work in two dimension by generating 2D array of Guassian random variable (change size=days to size=(days, n) ). Avoiding the loop will most likely be faster. However, that will require a different cummax() function as this one show here is restricted to 1D. But cummax() in R is restricted to 1D as well (not exactly, if you pass a 2D to cummax() , it will be flattened). So to keep things simple and comparable between Python and R , let's settle for the loop version.