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How do bond prices fall in a crisis as of course credit spreads will go up generally but also interest rates plummet meaning surely the bond price rises at the same time?

Does this effect cancel out the reduction in credit quality at all?

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Yes these two forces are in opposition, so the magnitude of each force is what determines the overall movement. If credit spreads move more than interest rates then bond prices will fall overall.

Bonds can also be more sensitive to spreads than to rates, depending on the characteristics (and riskiness) of the bond. So a move in spreads can overshadow a move in underlying rates.

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