# shrinking covariance matrix for assets coming from different asset class

I learned a way of shrinking the covariance matrix to get more robust portfolio optimization performance. Yet in the note #4, it says,

The constant correlation model would not be appropriate if the assets came from different asset classes, such as stocks and bonds. But in such cases more general models for the shrinkage target are available.

Does anyone know any such "more general models"? Thanks.

• Instead of the model "all stocks i,j have the same correlation $\phi$" we would need to implement the model "the correlation between any two stocks is $\phi$, the correlation between any two bonds is $\psi$ and the correlation between a stock and a bond is $\eta$. So we would have three parameters in the correlation matrix model (that we shrink towards) rather than one. How to actually implement this mathematically I know not. Mar 9 '18 at 17:57
• @AlexC, thanks! Do you know of any paper on this question? Mar 9 '18 at 21:49
• No, because the whole subject of stock-bond correlation is a literature in and of itself. So the covariance of any stock to any bond is a function of each asset to its asset class, plus a time-varying cross-asset-class covariance. The latter is easiest thought-of as the effect of 1bp on yields to % change in stocks (and vice versa). This translates to a decomposition of nominal interest rates: how much is stronger growth, how much is tighter monetary policy, and how much is inflationary pressures? If you can't exogenously model that, then stock:bond correlation is noise, seen only ex-post. Feb 4 at 2:25