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
python python-3.x random simulation data-visualization
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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
python python-3.x random simulation data-visualization
add a comment |
up vote
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
python python-3.x random simulation data-visualization
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
python python-3.x random simulation data-visualization
python python-3.x random simulation data-visualization
edited 44 secs ago
asked 6 mins ago
kamalbanga
2338
2338
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