Many researchers and practitioners argue that a long-term return forecast would be overestimated if it is based on the arithmetic mean of the past returns and underestimated based on a geometric mean. Using 80 years' historical returns to forecast the next 25-year future return, Jacquier, Kane, and Marcus (2003) suggest the following weighted scheme:
The following program reflects the preceding equation:
import numpy as np
import pandas as pd
from matplotlib.finance import quotes_historical_yahoo_ochl as getData
#
# input area
ticker='IBM' # input value 1
begdate=(1926,1,1) # input value 2
enddate=(2013,12,31) # input value 3
n_forecast=25 # input value 4
#
def geomean_ret(returns):
product = 1
for ret in returns:
product *= (1+ret)
return product ** (1.0/len(returns))-1
#
x=getData(ticker,begdate,enddate,asobject=True, adjusted=True)
logret = np.log(x.aclose[1:]/x.aclose[:-1])
date=[]
d0=x.date
for i in range...