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Synthetic cash

I’m a little bit confused. When creating synthetic cash position by reducing exposure to equities, do we use betas (target of cash, beta of futures, beta of equities)? Some examples in the curriculum didn’t have betas and used only risk-free rate for creating synthetic position, but one question from MM Mock had betas in the text and they were accordingly used.

Sorry for silly question.

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The examples that dont use beta make the assumption that the betas match.

Thank you!