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the diversifiable cash flow

SPOE resolution has two advantages over MPOE. First, the diversifiable cash flow |$\Delta $| can be shared across the two subsidiaries. We initially focus on the case in which the two jurisdictions always share |$\Delta $| equally.18 In this case, SPOE raises the minimum cash flow received by each subsidiary at date |$1$| from |$C_{1}^{L}$| to |$C_{1}^{L}+\Delta /2$|⁠. Second, even without redundant systems, each subsidiary can always roll over an amount |$\overline{p}_{2}V$| of short-term debt at date |$1$| since the two subsidiaries are not separated under an SPOE resolution. Hence, under SPOE resolution each subsidiary can issue more safe short-term debt, generating larger benefits from liquidity creation. The maximum face value of safe short-term debt (imposing losses on long-term claims in a resolution, if necessary) of each subsidiary under SPOE is \begin{align} R_{1}^{\text{SPOE}}=C_{1}^{L}+\Delta /2+\overline{p}_{2}V>R_{1}^{ \text{MPOE}}. \end{align}(1)

TLAC is required if |$F>(1+\gamma )(C_{1}^{L}+\Delta /2+\overline{p}_{2}V)$|⁠, which we assume is the case, and is raised by the global holding company through a combination of subordinated long-term debt and equity. It is again privately optimal for the global holding company to issue subordinated long-term debt with a face value that is at least as large as the amount of cash that is carried forward by the two subsidiaries when they receive the high cash flow: |$R_{LT}^{\text{SPOE}}\geq 2C_{1}^{H}+\Delta -2R_{1}^{ \text{SPOE}}\equiv \hat{R}_{LT}^{\text{SPOE}}$|⁠. We summarize the above discussion in the following lemma.