calculating_the_strategy_risk_in_practice.py

def binHR(sl,pt,freq,tSR):
    '''
Given a trading rule characterized by the parameters{sl,pt,freq},
what's the min precision p required to achieve a sharpe ratio tSR?
1)Inputs
sl: stop loss threshold
pt:profit taking threshold
freq:number of bets per year
tSR: target annual sharpe ratio
2)output
p: the min precision rate p required to achieve tSR
'''
    a=(freq+tSR**2)*(pt-sl)**2
    b=(2*freq*sl-tSR**2*(pt-sl))*(pt-sl)
    c=freq*sl**2
    p=(-b+(b**2-4*a*c)**.5)/(2.*a)
    return p

#---------------------------------------
import numpy as np,scipy.stats as ss
#----------------------------------
def mixGaussians(mu1,mu2,sigma1,sigma2,prob1,nObs):
    #Random draws from a mixture of gaussians
    ret1=np.random.normal(mu1,sigma1,size=int(nObs*prob1))
    ret2=np.random.normal(mu2,sigma2,size=int(nObs)-ret1.shape[0])
    ret=np.append(ret1,ret2,axis=0)
    np.random.shuffle(ret)
    return ret

#----------------------------------------
def probFailure(ret,freq,tSR):
    # Derive probability that strategy may fail
    rPos,rNeg=ret[ret>0].mean(),ret[ret<0].mean()
    p=ret[ret>0].shape[0]/float(ret.shape[0])
    thresP=binHR(rNeg,rPos,freq,tSR)
    risk=ss.norm.cdf(thresP,p,p*(1-p))# approximation to bootstrap
    return risk

#----------------------------------------
def main():
    #1) parameters
    mu1,mu2,sigma1,sigma2,prob1,nObs=.05,-.1,.05,.1,.75,2600
    tSR,freq=2.,260
    #2) Generate sample from mixture
    ret=mixGaussians(mu1,mu2,sigma1,sigma2,prob1,nObs)
    #3) compute prob failure
    probF=probFailure(ret,freq,tSR)
    print('prob strategy will fail',probF)
    return
#--------------------------------
if __name__=='__main__':main()