Question

Suppose that a bank has $10 billion of 1-year loan and $15 billion of 5-year loan. These are financed by $15 billion of 1-year deposit and $7 billion of 5-year deposit. The bank has equity totaling $2 billion and its ROE (return on equity) before tax is currently 10%.

- What is the bank’s asset-liability mismatch?
- What is the profit before tax?
- Let
*X*% be the rise in interest rates next year so that the bank’s ROE will be reduced to half. What is the value of*X*?

Answer #1

as explained below

**Explanation:**

bank currently has $ 10 billion of one year $15 billion of 1 year deposit and $15 billion 5 year loan and $7 billion of 5 year loan

thus since after one year $ 10 billion of one year loan will be repaid whilst $15 billion of one year deposit will be withdrawn the bank has an asset liabilty mismatch of $5 billion

the bank current roe after tax = 10%*2 billion = 0.24 billion

since an x % change in the interest rate would lead to after tax losses $5 billion *x/100*(100-10)% = 5*0.01x *0.9 = 0.045x

therefore roe would become 0 when 0.045x = 0.24

x = 5.33%

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