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Why is there negative covariance between future bond price and intertemporal rate of substitition?

Given bonds are a good consumption hedge, I would think that a higher intertemporal rate of substition (i.e., higher marginal utility from future consumption, i.e., lower incomes in the future) would correspond to a higher bond price. 

I understand why the covariance would be negative for equities, which are a bad consumption hedge - I don’t understand why it would be negative for a default-free bond.

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It because when there is a bad economic time, there is a fly to quality, so demand of default-free bond increase, which increase the price of this bond. Therefore bad economic time will be negatively correlated to bond. 

JPEREZAR wrote:

It because when there is a bad economic time, there is a fly to quality, so demand of default-free bond increase, which increase the price of this bond. Therefore bad economic time will be negatively correlated to bond. 

This would imply that price of default-free bond will go up when economic times are bad in the future (i.e., higher ITS), therefore positive covariance.