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pythonmatrixmultiplication
P Micallef
P Micallef

Reputation: 17

Python - Marginal contribution to risk

Can somebody help with the below as i have been struggling for sometime.

Marginal contribution to risk= To find the marginal contribution of each asset, take the cross-product of the weights vector and the covariance matrix divided by the portfolio standard deviation.

Now multiply the marginal contribution of each asset by the weights vector to get total contribution. We can then sum the asset contributions and make sure it’s equal to the total portfolio standard deviation.

Relativeweights = np.array([0.02, -0.025, -0.015, 0.0, 0.02,0,0,0])
cov_matrix_a= 8x8 matrix
Port_volatility= 0.05882615906289199

So i have tried the following code;

MCTAR=(np.dot(Relativeweights,cov_matrix_a))/Port_volatility
TCTPR=MCTAR*Relativeweights
np.sum(TCTPR, axis=0)

This doesn't sum to the portfolio volatility so not sure what is wrong?

Any help appreciated. Thanks

Full code below;

Pull in returns from csv file

import numpy as np
import ST as STPL
Assetreturns = STPL.get_Asset_returns()

Construct a covariance matrix for the portfolio's daily returns with the .cov() method

cov_matrix_Assetreturns = Assetreturns.cov()
cov_matrix_Assetreturns

Annualise the daily covariance matrix with the standard 252 trading days

cov_matrix_a = cov_matrix_Assetreturns * 252
cov_matrix_a

Assign relative weights

Relativeweights = np.array([0.02, -0.025, -0.015, 0.0, 0.02,0,0,0])
Relativeweights

Assign portfolio weights

Portweights = np.array([0.49, 0.15, 0.125, 0.215, 0.02, 0, 0,0])
Portweights

The standard deviation of a portfolio is just a square root of its variance

Port_volatility = np.sqrt(np.dot(Portweights.T, np.dot(cov_matrix_a, Portweights)))
Port_volatility

Marginal contribution of each asset, take the cross-product of the weights vector and the covariance matrix divided by the portfolio standard deviation.

MCTAR=(np.dot(Relativeweights,cov_matrix_a))/Port_volatility

Now multiply the marginal contribution of each asset by the weights vector to get total contribution. We can then sum the asset contributions and make sure it’s equal to the total portfolio standard deviation.

TCTPR=MCTAR*Relativeweights

np.sum(TCTPR, axis=0)

Upvotes: 2

Views: 6285

Answers (1)

Srinivas P
Srinivas P

Reputation: 108

If you equate Relativeweights = Portweights, then the multiplications work out to the answer you expect.

Upvotes: 1

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