Use the Monotonicity Theorem to show that all risk-free assets must have the same return rate. Theorem

Use the Monotonicity Theorem to show that all risk-free assets must have the same return rate.

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Theorem (Monotonicity) If portfolios A and B are such that at every possible state of the market at time T, portfolio A is worth at least as much as portfolio B, then at any prior time t < T portfolio A is worth at least as much as portfolio B. Moreover, if portfolio A is worth more than B in some states of the world at time T, then at any prior time t