Python for Finance

Chapter 9
The output is shown here:
Another argument against using standard deviation in the Sharpe ratio is that it
considers the deviations in both directions, below and above the mean. Nevertheless,
we know that investors worry more about the downside risk (deviation below mean
return). The second issue for the Sharpe ratio is that for the numerator, we compare
mean returns with a risk-free rate. Nevertheless, for the denominator, the deviations
are from the mean return instead of the same risk-free rate. To overcome those two
shortcomings, a so-called Lower Partial Standard Deviation (LPSD) is developed.
Assume we have n returns and one risk-free rate (Rf). Assume further that there are
m returns that are less than this risk-free rate. We estimate LPSP by using only those
m returns and it is defined here:
The following program shows how to estimate LPSD for a given set of returns:
import scipy as sp
import numpy as np
mean=0.15;
Rf=0.01
std=0.20
n=200
sp.random.seed(3412)
x=sp.random.normal(loc=mean,scale=std,size=n)
def LPSD_f(returns, Rf):
y=returns[returns-Rf<0]
m=len(y)
total=0.0
for i in sp.arange(m):
total+=(y[i]-Rf)**2
return total/(m-1)
answer=LPSD_f(x,Rf)
print("LPSD=",answer)
('LPSD=', 0.022416749724544906)
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