I need to work out a value S(n) based on the equation
s(n) = (1 + r(1))(1+r(2))...(1+r(n))
The value of
S(after N days) = (1+r(after 1 day))*(1+r(after 2 days))...(1+r(after N days))
with r coming from:
r = return_daily + sig_daily
but calculated D times (see code below, D is calculated once for each day and is a random value)
I'm just not too sure how to implement the equation including a changing variable(r changes daily).
Thanks for any help
Relevant Code:
#import all modules required
import numpy as np # using different notation for easier writting
import scipy as sp
import matplotlib.pyplot as plt
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#collect variables provided by the user
period = 63 # can be edited to an input() command for variable periods.
Return_annual = np.arange(0.00,0.15,0.05) # creates an array ??? not sure if helpful
sig_annual = np.arange(0.01,0.31,0.01) #use .31 as python doesnt include the upper range value.
#functions for variables of daily return and risk.
Return_daily = (1/252)*R_annual
sig_daily = (1/(np.sqrt(252)))*sig_annual
D=np.random.normal(size=period)
r_i=Return_daily + sig_daily # must be calculated D times
