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Consider a bank that invests an amount y in risky assets (loans) at t=0. At t=2, each unit invested in the risky asset will yield

Consider a bank that invests an amount y in risky assets (loans) at t=0. At t=2, each unit invested in the risky asset will yield R>1 and so investment y will return yR. Banks assets are funded with short-term debt s, long-term debt l and equity e so that: y = s + l + e. The gross interest rate that short-term creditors receive from t=0 to t=1 is 1, the gross interest rate they receive from t=1 to t=2 is rs > 1, and the long-term creditors receive rl at t=2. A fraction of short-term creditors do not rollover their debt at t=1 (i.e. s withdraw), where has (approximation) a Normal distribution N(,). The bank can repay such creditors by liquidating the risky asset. When one unit of the risky asset is liquidated at t=1, it yields R. Suppose y=100, e = 10, s=70, l=20, rl = 1.2, rs = 1.1, = 0.6, = 0.5 and = 0.1.

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