Moderate return-low risk vs high returns-high risk investments











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To quantify Buffet's #1 rule of investing, "Don't lose money", I take the assumption that % returns of an investment follow a Normal distribution.



Now a high return high risk investment might follow N(mu=50%, sigma=70%) while low return low risk investment follow N(mu=20%, sigma=10%).



from operator import mul
from functools import reduce
from random import gauss
from statistics import median
from typing import List

def avg_cagr(percents: List[int]) -> float:
'''Given (successive) % annual growth rates, returns average Compound Annual Growth Rate'''
amount = reduce(mul, [1+p/100 for p in percents])
amount = amount if amount > 0 else 0 # at worst, complete amount can be lost but can't go negative
return (amount**(1/len(percents)) - 1)*100

def normal_returns(mu: float, sigma: float, years: int = 20, simulations: int = 1000) -> float:
'''Returns net CAGR assuming annual percentage returns follow a Normal distribution'''
return median(avg_cagr([gauss(mu=mu, sigma=sigma) for _ in range(years)) for _ in range(simulations)])


I have simulated normal_returns for various values of mu & sigma (for 20 consecutive years) and plotted a contour plot. We can see here that N(25, 20) handily beats N(60, 80). Plotting code
Contour plot of CAGR









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    down vote

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    To quantify Buffet's #1 rule of investing, "Don't lose money", I take the assumption that % returns of an investment follow a Normal distribution.



    Now a high return high risk investment might follow N(mu=50%, sigma=70%) while low return low risk investment follow N(mu=20%, sigma=10%).



    from operator import mul
    from functools import reduce
    from random import gauss
    from statistics import median
    from typing import List

    def avg_cagr(percents: List[int]) -> float:
    '''Given (successive) % annual growth rates, returns average Compound Annual Growth Rate'''
    amount = reduce(mul, [1+p/100 for p in percents])
    amount = amount if amount > 0 else 0 # at worst, complete amount can be lost but can't go negative
    return (amount**(1/len(percents)) - 1)*100

    def normal_returns(mu: float, sigma: float, years: int = 20, simulations: int = 1000) -> float:
    '''Returns net CAGR assuming annual percentage returns follow a Normal distribution'''
    return median(avg_cagr([gauss(mu=mu, sigma=sigma) for _ in range(years)) for _ in range(simulations)])


    I have simulated normal_returns for various values of mu & sigma (for 20 consecutive years) and plotted a contour plot. We can see here that N(25, 20) handily beats N(60, 80). Plotting code
    Contour plot of CAGR









    share


























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      0
      down vote

      favorite









      up vote
      0
      down vote

      favorite











      To quantify Buffet's #1 rule of investing, "Don't lose money", I take the assumption that % returns of an investment follow a Normal distribution.



      Now a high return high risk investment might follow N(mu=50%, sigma=70%) while low return low risk investment follow N(mu=20%, sigma=10%).



      from operator import mul
      from functools import reduce
      from random import gauss
      from statistics import median
      from typing import List

      def avg_cagr(percents: List[int]) -> float:
      '''Given (successive) % annual growth rates, returns average Compound Annual Growth Rate'''
      amount = reduce(mul, [1+p/100 for p in percents])
      amount = amount if amount > 0 else 0 # at worst, complete amount can be lost but can't go negative
      return (amount**(1/len(percents)) - 1)*100

      def normal_returns(mu: float, sigma: float, years: int = 20, simulations: int = 1000) -> float:
      '''Returns net CAGR assuming annual percentage returns follow a Normal distribution'''
      return median(avg_cagr([gauss(mu=mu, sigma=sigma) for _ in range(years)) for _ in range(simulations)])


      I have simulated normal_returns for various values of mu & sigma (for 20 consecutive years) and plotted a contour plot. We can see here that N(25, 20) handily beats N(60, 80). Plotting code
      Contour plot of CAGR









      share















      To quantify Buffet's #1 rule of investing, "Don't lose money", I take the assumption that % returns of an investment follow a Normal distribution.



      Now a high return high risk investment might follow N(mu=50%, sigma=70%) while low return low risk investment follow N(mu=20%, sigma=10%).



      from operator import mul
      from functools import reduce
      from random import gauss
      from statistics import median
      from typing import List

      def avg_cagr(percents: List[int]) -> float:
      '''Given (successive) % annual growth rates, returns average Compound Annual Growth Rate'''
      amount = reduce(mul, [1+p/100 for p in percents])
      amount = amount if amount > 0 else 0 # at worst, complete amount can be lost but can't go negative
      return (amount**(1/len(percents)) - 1)*100

      def normal_returns(mu: float, sigma: float, years: int = 20, simulations: int = 1000) -> float:
      '''Returns net CAGR assuming annual percentage returns follow a Normal distribution'''
      return median(avg_cagr([gauss(mu=mu, sigma=sigma) for _ in range(years)) for _ in range(simulations)])


      I have simulated normal_returns for various values of mu & sigma (for 20 consecutive years) and plotted a contour plot. We can see here that N(25, 20) handily beats N(60, 80). Plotting code
      Contour plot of CAGR







      python python-3.x random simulation data-visualization





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      edited 44 secs ago

























      asked 6 mins ago









      kamalbanga

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