FAQ: Mean-Variance Portfolio Optimization - Efficient Frontier III

This community-built FAQ covers the “Efficient Frontier III” exercise from the lesson “Mean-Variance Portfolio Optimization”.

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This exercise can be found in the following Codecademy content:

Analyze Financial Data with Python

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Sorry if this question may be easy, I might overlook something in the course.
I was going through the rf.py and I am not sure what are the maths behind the optimal portfolio calculation.
In the function optimal_portfolio,
m1 = np.polyfit(returns, risks, 2)
x1 = np.sqrt(m1[2] / m1[0])
wt = solvers.qp(opt.matrix(x1 * S), -pbar, G, h, A, b)[‘x’]

After the polynomial fitting, why would we calculate x1 that way, and use that as mu for the quadratic programing function for optimal portfolio? Here what is the definition of optimal portfolio (e.g. highest sharpe ratio)?
Thanks a lot for any help. :smile:


I have tried to use the random_portfolios and optimal_portfolio functions with my data set.

The random_portfolios works fine, but when I try to run the optimal_portfolio function, I get the following error:

AttributeError: ‘DataFrame’ object has no attribute ‘as_matrix’

Was wondering if anyone possibly had any advice?

Please refer to the documentation of pandas.DataFrame.as_matrix.
“Deprecated since version 0.23.0”
As suggested in pandas documentation, you may consider using pandas.DataFrame.to_numpy instead.

I want to use the optimal_portfolio function in a project who should I credit