Branch banks must keep enough money on hand to satisfy customers\' cash demands.
ID: 450017 • Letter: B
Question
Branch banks must keep enough money on hand to satisfy customers' cash demands. Suppose the daily demand for cash at a branch of University Bank follows a lognormal distribution with means and standard deviations as follows (in $1,000s):
Monday= mean $175, std dev $26
Tuesday= mean $ 120, std dev $18
Wednesday= mean $90, std dev $13
Thursday= mean $60, std dev $9
Friday= mean $120 std dev $18
Saturday= mean $140 std dev $21
Sunday= mean $65, std dev $9
An armored truck delivers cash to this bank once a week. The manager of the bank can order any amount of cash she desires for this delivery. Of course, running out of cash in any week is very undesirable as customers of the bank expect to be able to withdraw their deposits on demand. Keeping excessive cash reserves would guard against this situation. However, cash is a noninterest earning asset, so there is an opportunity cost for holding cash reserves.
Suppose the bank manager follows the practice of ordering enough cash to start each week with a balance of $825,000. What is the probability that the bank will run out of money at some point during the week?
What amount of money is needed at the start each week to ensure that there is at most a 0.10% chance of running out of money?
Any help would be appreciated
Explanation / Answer
1. 0.10% is the probability that the bank will run out of money at some point during the week.
2.$ 95,000 amount of money is needed at the start each week to ensure that there is at most a 0.10% chance of running out of money.