In portfolio risk minimization, the inverse covariance matrix of returns is often unknown and has to be estimated in practice. Yet the eigenvalues of the sample covariance matrix are often overdispersed, leading to severe estimation errors in the inverse covariance matrix. To deal with this problem, we propose a general framework by shrinking the sample eigenvalues based on the Schatten norm. The proposed framework has the advantage of being computationally efficient as well as structure-free. The comparative studies show that our approach behaves reasonably well in terms of reducing out-of-sample portfolio risk and turnover.

Consistent with theories on the equilibrium matching between capital structure and employee job risk aversion, we find a robust, positive association between a firm’s leverage and its employees’ family labor income diversification. Higher-Leverage firms also recruit new employees with greater income diversification. For identification, we exploit two policy shocks that exogenously change employee income diversification and firm leverage, respectively. Individual employee-level tests further reveal that workers with differential risk attitudes adjust their job choices and household labor income portfolios in response to significant shifts in their employers’ leverage. Finally, human bankruptcy costs contribute to the general level of corporate risk-taking.

A country’s economic growth exhibits a significant response to sovereign rating changes: a one-notch upgrade (downgrade) causes an increase (decline) of about 0.6% (0.3%) in re-rated countries’ five-year average annual growth rates. The results hold after accounting for other determinants of economic growth and potential endogeneity problems, and are robust to the use of quarterly data. Changes in country rating affect economic growth via the interest-rate and capital-flow channels: narrower sovereign bond yield spreads and increased capital inflows are associated with upgrades, which stimulate re-rated countries’ economic performance, and the converse holds for downgrades.

Sovereign credit rating changes have an influence on real private investment of re-rated countries. We find significant increases in private investment growth following upgrades in sovereign ratings. These increases, however, are transitory. We also find significant, temporary declines in private investment growth following sovereign rating downgrades. The results hold after accounting for re-rated countries’ growth opportunities, endogeneity, and other factors that could affect private investment. The irreversible nature of investment may be the explanation for the temporary changes in the growth rates of physical capital investment associated with revisions in sovereign credit ratings.