Suppose a bank raised $34B in deposits and $4B in equity. The bank invests these funds in mortgages and cash. Each $1.0 invested in mortgages leads to the following cash flows next year: $0.04 with probability = 96% and -$0.03 with probability = 4%. The investment in cash leads to zero cash flows next year. Over the next year, depositors might face liquidity needs. For each depositor, there is a 10% chance that the depositor will withdraw all of its funds from the bank, a 30% chance that the depositor will withdraw 20% of its funds, and a 60% chance that depositor will not need any withdrawal. These liquidity events are (statistically) independent across depositors and there is a large number of depositors. The bank wants to avoid selling mortgages in response to these withdrawals next year. What is the minimum share of the assets that the bank has to invest in cash?