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The Risk Parity portfolio will be equal weighted if the assets have uniform correlation and equal variance. This would be the case for the shrunk covariance matrix if the shrinkage coefficient used equals unity. In sklearn, you can check the shrinkage coefficient for the Ledoit-Wolf shrinkage after fitting it from the instance's .shrinkage_ attribute. If the ...


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OK, so think of it this way... Your standard (Markowitz) covariance matrix is a sample observation. That may or not be close to the population sigmas and correlations of your sampled markets. Even if close, the sample-vs-population errors will create asset allocation errors. The identity matrix here is the "complete strategic ignorance" covariance ...


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You can think of it in Bayesian terms. To start with, knowing nothing at all about stocks, you might assume that stock returns are i.i.d with unit variance. This would be your prior. It is very simple and is well behaved because the identity is invertible. Then you would gather some empirical data on stock returns and measure the actual variances and ...


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Generally it is better to shrink the covariance matrix—since the variances of your data probably vary a lot, and the correlation matrix treats them all as essentially equal variance, you throw out the baby with the bath water by pausing to the correlation matrix. In effect, when you shrink the correlation matrix, you correct a lot of stuff that is not ...


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Let your linear system be defined by the latent multivariate state variable $x_t$, progressing in an AR(1) fashion, and let your observation at time step $t$ be linear in the latent state: $$ \begin{align} x_{t+1}&=Ax_t+u_t\\ y_{t}&=Hx_t+v_t\\ \end{align} $$ with $u_t\sim N(0,Q)$ and $v_t\sim N(0,R)$ time-and-state-independent process noise. Let $K_t$...


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Hi: Exponential smoothing weights observations by taking a weighted combination of the old estimate and the new. So, if you denote your original matrix ( or current covariance matrix ) as $R_t$ and your new one as $R^{*}_t$, then exponential smoothing does $R_{t+1} = \lambda R_{t} + (1- \lambda) R^{*}_t $. But there are two issues with doing this update. ...


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Yes all you have to do is estimate the Black Litterman covariance matrix that includes investor views using a shrinkage estimator. Covariance shrinkage like Ledoit Wolf is an old technique, however, that has been outperformed by the denoised or detoned covariance matrix estimated by random matrix theory, as well as the nested clustered optimization (NCO) ...


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