Implement Mean-Variance Optimization

[carlobortolan]

Implement Mean-Variance Optimization

Description

Implement mean-variance optimization in the portfolio module.

Tasks

• Create mean_variance.rs in the portfolio directory.
• Implement the mean_variance_optimization function.
• Write unit tests for the mean_variance_optimization function.

References

• Modern Portfolio Theory

[SaurabhJamadagni]

Hey @carlobortolan, for mean-variance optimization are we looking write our own numerical code for inverting matrices, using legrange multipliers or was the plan to use some optimization crate in rust that's available? I am open to go either way. Let me know what you had in mind.

[carlobortolan]

Hi @SaurabhJamadagni, I'd say that we don't need to overcomplicate things and can use an existing linear algebra/optimization crate instead of writing our own from scratch.

(I haven't looked into this issue in detail yet, so feel free to see what works best, but maybe https://github.com/dimforge/nalgebra and https://github.com/rust-ndarray/ndarray can be helpful)

Edit: for the options pricing module I followed the same approach and used statrs for distributions instead of writing custom implementations.

[SaurabhJamadagni]

Good to know, thanks @carlobortolan! I wasn't sure how much you would like to be able to have control on performance metrics but I guess implementations could always be swapped out in the future if necessary. But looks good, I'll compare a few options, compare pros and cons if any and list them in this thread for documentation.

[SaurabhJamadagni]

Hey @carlobortolan, I am looking at using ndarray here and argmin wherever needed for this, fyi