In the context of finance, suppose there is a dataframe of asset weights and a panel of daily covariance matrix:
w = pd.DataFrame({'Date':pd.to_datetime(['2016-01-01','2016-01-02','2016-01-03']),'A1':[0.3,0.1,0.1],'A2':[0.4,0.4,0.4]}).set_index(['Date'])
covar = [[[0.000087,0.000017],[0.000087,0.000017],[0.000087,0.000017]],[[0.000017,0.00019],[0.000017,0.00019],[0.000017,0.00019]]]
covPanel = pd.Panel(covar, items=['A1', 'A2'], major_axis=pd.to_datetime(['2016-01-01','2016-01-02','2016-01-03']), minor_axis=['A1', 'A2'])
To calculate the 1-day portfolio variance, the below function can be used:
def portVar(w,sigma):
return w.dot(sigma.dot(w))
I can apply the last row of weights to the covariance matrix each day to get daily variance:
out = covPanel.apply(lambda cov1: portVar(w.iloc[-1,:],cov1),axis = [2,0])
But how do I apply the above function to the dataframe and covariance matrix pairwise, for every day (without loop)?
In other words, something like:
pd.ApplyPairwise(portVar,w,covPanel)
and return the daily variance just as "out" above?
option 1
rewrite portVar
pass entire panel to the function being applied and use xs to get the appropriate cross section for that particular date's weight. The date is in the name attribute.
def portVar(w, sigma):
s = sigma.xs(w.name, axis='major')
return w.dot(s.dot(w))
w.apply(portVar, 1, sigma=covPanel)
Date
2016-01-01 0.000042
2016-01-02 0.000033
2016-01-03 0.000033
dtype: float64
option 2
numpy broadcasting
cv = covPanel.values
wv = w.values
pd.Series(((wv[None, :] * cv).sum(-1).T * wv).sum(1), w.index)
Date
2016-01-01 0.000042
2016-01-02 0.000033
2016-01-03 0.000033
dtype: float64
response to comment
A generic python way to do things pair wise is zip
I'll use a list comprehension to produce a the list we're looking for. Note the transpose on the panel object to ensure the dates are the first dimension.
def portVar(w,sigma):
return w.dot(sigma.dot(w))
[portVar(w_, s_) for w_, s_ in zip(w.values, covPanel.transpose(1, 0, 2).values)]