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Modern Portfolio Theory: Matrix Multiplication without numpy.matmul
Kalinda Vathupola
posted Dec 27, 2017
API Tools and Tips Asset Allocation

I'm currently working on implementing modern portfolio theory in the form of a function that intakes securities with expected returns. It then returns the portfolio weights for the global minimum variance portfolio.

I have already programmed a working function off the Quantopian platform when interfacing with "csv" files. Of issues I cannot resolve, I have the following:

  1. A ndarray initialized by
iota = np.ones((5, 1), int)

cannot be converted to a matrix for conventional matrix multiplication since the result of either

attempt_1 = np.asmatrix(iota)

or

attempt_2 = iota.as_matrix()

is a corrupted matrix that is infinite.

  1. I cannot simply apply the np.matmul function to the ndarrays I wish to multiply as matrices since it is not supported...

Any suggestions for workarounds?

2 responses
Scott Sanderson
Dec 28, 2017

The matrix class in numpy is all-but-deprecated. On python 2.7 (what Quantopian currently supports), the most efficient and idiomatic way to do matrix multiplication on numpy arrays is to use left.dot(right).

For example:

In [21]: m = np.array([[1, 1],  
    ...:               [1, 0]])  
    ...:

In [22]: x = np.array([[1],  
    ...:               [2]])  
    ...:  
    ...:

In [23]: m.dot(x)  
Out[23]:  
array([[3],  
       [1]])

You can also use np.dot(left, right) if you prefer to use a free function instead of a method call.

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Kalinda Vathupola
Dec 28, 2017

Thanks Scott!

Looks like I have more than just my Quantopian code to edit now...

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The material on this website is provided for informational purposes only and does not constitute an offer to sell, a solicitation to buy, or a recommendation or endorsement for any security or strategy, nor does it constitute an offer to provide investment advisory services by Quantopian.

In addition, the material offers no opinion with respect to the suitability of any security or specific investment. No information contained herein should be regarded as a suggestion to engage in or refrain from any investment-related course of action as none of Quantopian nor any of its affiliates is undertaking to provide investment advice, act as an adviser to any plan or entity subject to the Employee Retirement Income Security Act of 1974, as amended, individual retirement account or individual retirement annuity, or give advice in a fiduciary capacity with respect to the materials presented herein. If you are an individual retirement or other investor, contact your financial advisor or other fiduciary unrelated to Quantopian about whether any given investment idea, strategy, product or service described herein may be appropriate for your circumstances. All investments involve risk, including loss of principal. Quantopian makes no guarantees as to the accuracy or completeness of the views expressed in the website. The views are subject to change, and may have become unreliable for various reasons, including changes in market conditions or economic circumstances.