Imagine a bank that has raised $600M in funds (total funding raised) and invested these funds in a moderate-risk strategy. In this strategy, the assets (loans) generate a return equal to 6% with probability 95% and there is a 5% chance that the assets generate a return equal to -25%. For simplicity, there is only two dates in this example (today and tomorrow). The lender invests its funds today and the return on this strategy is delivered tomorrow (cash flows only take place tomorrow). Both the lender and the government do not discount tomorrow's cash flows (independently of their risk). Regulators collected the following additional information on the bank: 89 percent of the funds raised by the lender are deposits paying no interest. • 50 percent of the deposits are insured by the deposit insurance fund, the remaining 50 percent of deposits are uninsured and not protected by the deposit insurance fund.

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Imagine a bank that has raised $600M in funds (total funding raised) and invested these funds in a
moderate-risk strategy. In this strategy, the assets (loans) generate a return equal to 6% with
probability 95% and there is a 5% chance that the assets generate a return equal to -25%. For
simplicity, there is only two dates in this example (today and tomorrow). The lender invests its funds
today and the return on this strategy is delivered tomorrow (cash flows only take place tomorrow).
Both the lender and the government do not discount tomorrow's cash flows (independently of their
risk).
Regulators collected the following additional information on the bank:
• 89 percent of the funds raised by the lender are deposits paying no interest.
• 50 percent of the deposits are insured by the deposit insurance fund, the remaining 50 percent
of deposits are uninsured and not protected by the deposit insurance fund.
The government wants to eliminate any subsidy created by deposit insurance to the bank and is
charging the bank a deposit insurance premium tollay.
Calculate the (dollar) value of the deposit insurance premium today that would achieve this goal.
O
5.1
8.6
2.1
4.2
2.6
Transcribed Image Text:Imagine a bank that has raised $600M in funds (total funding raised) and invested these funds in a moderate-risk strategy. In this strategy, the assets (loans) generate a return equal to 6% with probability 95% and there is a 5% chance that the assets generate a return equal to -25%. For simplicity, there is only two dates in this example (today and tomorrow). The lender invests its funds today and the return on this strategy is delivered tomorrow (cash flows only take place tomorrow). Both the lender and the government do not discount tomorrow's cash flows (independently of their risk). Regulators collected the following additional information on the bank: • 89 percent of the funds raised by the lender are deposits paying no interest. • 50 percent of the deposits are insured by the deposit insurance fund, the remaining 50 percent of deposits are uninsured and not protected by the deposit insurance fund. The government wants to eliminate any subsidy created by deposit insurance to the bank and is charging the bank a deposit insurance premium tollay. Calculate the (dollar) value of the deposit insurance premium today that would achieve this goal. O 5.1 8.6 2.1 4.2 2.6
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