No – stocks and bonds are not supposed to move inverse to each other.
Correlation between two asset classes can be represented as a number between 1.0 (perfect correlation) to -1.0 (perfectly inverse correlation), with 0.0 representing the asset classes moving completely independently of each other.
In the real world, correlation between stock and bond returns varies significantly over time, and I don’t think it’s ever been -1.0, which you would need to guarantee that prices of the two asset classes always move in the opposite direction.
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