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Estimation of the covariance matrix of asset returns is crucial to portfolio construction. As suggested by economic theories, the correlation structure among assets differs between emerging markets and developed countries. It is therefore imperative to make rigorous statistical inference on correlation matrix equality between the two groups of countries. However, if the traditional vector-valued approach is undertaken, such inference is either infeasible due to limited number of countries comparing to the relatively abundant assets, or invalid due to the violations of temporal independence assumption. This highlights the necessity of treating the observations as matrix-valued rather than vector-valued. With matrix-valued observations, our problem of interest can be formulated as statistical inference on covariance structures under sub-Gaussian distributions, i.e., testing non-correlation and correlation equality, as well as the corresponding support estimations. We develop procedures that are asymptotically optimal under some regularity conditions. Simulation results demonstrate the computational and statistical advantages of our procedures over certain existing state-of-the-art methods for both normal and non-normal distributions. Application of our procedures to stock market data reveals interesting patterns and validates several economic propositions via rigorous statistical testing.

Firms with higher R&D intensity subsequently experience higher stock returns in international stock markets, highlighting the role of intangible investments in international asset pricing. The R&D effect is stronger in countries where growth option risk is more likely priced, but is unrelated to country characteristics representing market sentiments and limits-of-arbitrage. Moreover, we find that R&D intensity is associated with higher future operating performance, return volatility, and default likelihood. Our evidence suggests that the cross sectional relation between R&D intensity and stock returns is more likely attributable to risk premium than to mispricing.