Tensor dynamic conditional correlation model: A new way to pursuit "Holy Grail of investing"

Style investing creates asset classes (or the so-called "styles") with low correlations, aligning well with the principle of "Holy Grail of investing" in terms of portfolio selection. The returns of styles naturally form a tensor-valued time series, which requires new tools for studying the dynamics of the conditional correlation matrix to facilitate the aforementioned principle. Towards this goal, we introduce a new tensor dynamic conditional correlation (TDCC) model, which is based on two novel treatments: trace-normalization and dimension-normalization. These two normalizations adapt to the tensor nature of the data, and they are necessary except when the tensor data reduce to vector data. Moreover, we provide an easy-to-implement estimation procedure for the TDCC model, and examine its finite sample performance by simulations. Finally, we assess the usefulness of the TDCC model in international portfolio selection across ten global markets and in large portfolio selection for 1800 stocks from the Chinese stock market.