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Volatility Risk Metrics
import numpy
import numpy.random as nrand
def vol(returns):
# Return the standard deviation of returns
return numpy.std(returns)
def beta(returns, market):
# Create a matrix of [returns, market]
m = numpy.matrix([returns, market])
# Return the covariance of m divided by the standard deviation of the market returns
return numpy.cov(m)[0][1] / numpy.std(market)
# Example usage
r = nrand.uniform(-1, 1, 50)
m = nrand.uniform(-1, 1, 50)
print("vol =", vol(r))
print("beta =", beta(r, m))
@WilliamJosephKlubinski

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@WilliamJosephKlubinski WilliamJosephKlubinski commented Dec 16, 2019

Hi Stuart,

In line 14: return numpy.cov(m)[0][1] / numpy.std(market) you should replace the .std with .var. The division in Beta is done with the variance of the market and not standard deviation. Thus, return numpy.cov(m)[0][1] / numpy.var(market)

In the current form, Beta is significantly affecting the results of the Treynor ratio.

PS. It can also be easily tested in Excel e.g. =COVARIANCE.P(range_of_the_fund,range_of_the_market)/VAR.P(range_of_the_market)

Hope it helps. Thanks
William Klubinski

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