Impact of Ledoit-Wolf covariance estimation

[alexander-myltsev]

Hi @Marigold,

You suggested to implement Ledoit-Wolf covariance estimation at the end of modern-portfolio-theory.ipynb.

I read the paper. The shrinkage ratio of F estimator should go to zero when there are 11 assets (like there is at the modern-portfolio-theory.ipynb) or so. Hence the result Covariance Matrix equals to Sample Covariance Matrix. To show the benefit they made an estimation for ~900 assets having monthly historical data. I wonder what impact do you expect to achieve by implementing the method at the universal-portfolios?

[Marigold]

You're absolutely correct. I tried Ledoit-Wolf and the impact is minimal on a universe of ~10 assets. It might even screw up your optimization if you have assets with ~1 correlation in there (e.g. QQQ and TQQQ). There's even a cooler paper https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3530390 with a similar, theoretically sound idea, but its impact is negligible too. The most critical thing is to get your mean estimates right... or at least not too wrong which is where Black-litterman or other regularization approaches comes to play.

[alexander-myltsev]

OK. Thanks for your reply. Did you try Black-Litterman? What's the impact?

[alexander-myltsev]

@Marigold would you answer ⬆️ ?

[Marigold]

I haven't implemented it, BL is just a framework, you still need to come up with return estimates. I'm for instance using an assumption of constant Sharpe ratio across all assets (i.e. return = sharpe * volatility) and then put it into MPT optimization. That gives reasonable allocation across assets (I believe it even has a name, just don't remember what it was). Pretty much all experiments where I estimated expected returns failed.