How can I build a function to calculate weighted standard deviation/coefficient of variation?

I actually want to calculate exponential weighted coefficient of variation. The market volatility is related with normal coefficient of variation. Now I want to see if it is more volatile with more recent price change.

hist_spy = data.history(spy, 'price', 30 , '1m')
std = hist.std()
mean = hist.mean()
cov = std/mean

Could anyone give me some hints to build a weighted one?

2 responses

One can get exponentially weighted values by using the pandas ewmmethod (https://pandas.pydata.org/pandas-docs/stable/reference/api/pandas.DataFrame.ewm.html). So something like this would work.

spy = symbol('SPY')
hist_spy = get_pricing(spy, 'price', 30, '1m')
std = hist_spy.std()
mean = hist_spy.mean()

# adjust the weighting with any of the ewm parameters as desired
# Take only the last value (ie -1)
ewma = hist_spy.ewm(span=1).mean().iat[-1]
cov = std/mean

# The exponentially weighted coefficient of variation
ewm_cov = std/ewma



One can also do something similar but using daily pipeline data and the ExponentialWeightedMovingAverage factor (https://www.quantopian.com/docs/api-reference/pipeline-api-reference#quantopian.pipeline.factors.ExponentialWeightedMovingAverage). No need for a custom factor.

You will need to specify the weighting decay as desired. The pandas documentation has some examples. May want to implement in a notebook first to view the results and verify they are doing what you want.

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Thanks, Dan. I dont know there's such easy way to do it.

ewma = hist_spy.ewm(span=1).mean().iat[-1]
ewmstd = hist_spy.ewm(span=1).std().iat[-1]
ewm_cov = ewmstd/ewma