Precautionary saving and changes in risk correlation

This note analyzes the effect of a change in the covariance between labor income risk and interest rate risk on the threshold level for prudence ensuring positive precautionary saving, recently derived by Baiardi, Magnani and Menegatti (2014). We show that this effect is different in different cases. An increase in the covariance between the two risks decreases (increases) the threshold level when the variance of labor income is smaller (larger) than the variance of the return on saving. An interpretation of these results in terms of elasticity of total variance with respect to saving is provided.