Question

QUESTION 11 You are the bank manager of a bank with 10m. capital and 90m. deposits. . Deposits cost you 1% Choice of two assets: safe asset earning 5% risk free b. Risky asset earning 25% and loses 20% with equal probabilities Calculate the expected ROA and ROE for both choices (Hint: Calculate the profits net of deposit interests for the good / bad scenario first. Remember: For owners the loss is limited toequity). If the bank only holds the risk free asset, its ROA is % and the ROE is If the bank only holds the risky asset, its ROA is %and the ROE is To maximize share holder return the bank manager will chose the Would the depositors be happy with 1% interest if they knew what the banker is doing? The interest rate on deposits would profile. Repeat your calculations for the case that the bank uses 30m capital and only 70m deposits. Investing in the risky asset would now have an expected ROA of Sit back and think of the importance of bank equity for the choices that bank managers will make. Which is better for society? Can you see why we need bank regulation? (increase decrease) if the depositors had perfect information about the bank's risk % and ROE of

Answer 1

					Formula
		Deposits	90	M
		Interest to be given on Deposits	1%
A		Total Interest outgo	0.9	M	Deposits * Interest
	Option 1	Invest in Risk free asset	5%
B		Earnings	4.5	M	Deposits * Risk free asset return
	Option 2	Invest in Risky asset
		Earnings (50% chance)	25%
			22.5	M	Deposits* Risky asset earnings
		Loss (50% chance)	20%
			-18	M	negative (Deposits * Risky asset losses)
C		Earnings Adjusted for probabilities	2.25	M	50% * Earnings + 50% * losses
		Equity	10	M	Capital
		Assets	10.9	M	Equity+Liabilities
		Option 1: Hold Risk Free Asset
		Option 1 ROA	33.03%		(Option 1 Earnings - Interest Outgo )/Assets
		Option 1 ROE	36.00%		(Option 1 Earnings - Interest Outgo )/Equity
		Option 2 : Hold Risky Asset
		Option 2 ROA	12.39%		(Option 2 Earnings - Interest Outgo )/Assets
		Option 2 ROE	13.50%		(Option 2 Earnings - Interest Outgo )/Equity
		To maximize the shareholder return, the bank manager will choose the Option 1 to hold the Risk Free Asset
		Repeating Calculations with different ratios of capital and deposits
					Formula
		Deposits	70	M
		Interest to be given on Deposits	1%
A		Total Interest outgo	0.7	M	Deposits * Interest
	Option 1	Invest in Risk free asset	5%
B		Earnings	3.5	M	Deposits * Risk free asset return
	Option 2	Invest in Risky asset
		Earnings (50% chance)	25%
			17.5	M	Deposits* Risky asset earnings
		Loss (50% chance)	20%
			-14	M	negative (Deposits * Risky asset losses)
C		Earnings Adjusted for probabilities	1.75	M	50% * Earnings + 50% * losses
		Equity	30	M	Capital
		Assets	30.7	M	Equity+Liabilities
		Option 1: Hold Risk Free Asset
		Option 1 ROA	9.12%		(Option 1 Earnings - Interest Outgo )/Assets
		Option 1 ROE	9.33%		(Option 1 Earnings - Interest Outgo )/Equity
		Option 2 : Hold Risky Asset
		Option 2 ROA	3.42%		(Option 2 Earnings - Interest Outgo )/Assets
		Option 2 ROE	3.50%		(Option 2 Earnings - Interest Outgo )/Equity