Risk pooling, leverage, and the business cycle

This paper investigates the interdependence between the risk-pooling activity of the financial sector and: output, consumption, risk-free rate, and Sharpe ratio in a dynamic general equilibrium model of a productive economy. Due to their exposure to idiosyncratic shocks and market segmentation, heterogeneous households/entrepreneurs (h/entrepreneurs) are willing to mitigate their risk through a financial sector. The financial sector pools risky claims issued by different firms within its assets, faces an associated intermediation cost and, via leverage, provides a risk-free asset to h/entrepreneurs. Exogenous systematic shocks change the relative size of the financial sector, and thus the equilibrium amount of pooled risk, making financial leverage state-dependent and counter-cyclical. We study how this mechanism endogenously channels amplification of consumption and mitigation of output fluctuations. In equilibrium, financial sector leverage also determines counter-cyclical Sharpe ratios and pro-cyclical riskfree interest rates. Last, we investigate the relationship between the size of the financial sector, leverage, and welfare. We show that limiting financial sector leverage determines a sub-optimal pooling of idiosyncratic risk but fosters the growth rate of the h/entrepreneurs' consumption. On the other side, when the financial sector is too large, it destroys too many resources after intermediation costs. Therefore, the h/entrepreneurs benefit the most when the financial sector is neither too small nor too big.