Suppose that you are the manager of a bank whose $100 billion of assets have an

Question

Suppose that you are the manager of a bank whose $100 billion of assets have an average duration of four years and whose $90 billion of liabilities have an average duration of six years. Conduct a duration analysis for the bank, and show what will happen to the net worth of the bank if interest rates rise by 2 percentage points. What actions could you take to reduce the bank's interest rate risk? Suppose that you are the manger of a bank that has $15 million of fixed-rate assets, $30 million of rate-sensitive assets, $25 million of fixed-rate liabilities, and $20 million of rate-sensitive liabilities. Conduct a gap analysis for the bank, and show what will happen to bank profits if interest rates rise by 5 percentage points. What actions could you take to reduce the bank's interest-rate risk?

Explanation / Answer

Answer (a)

Duration Gap = -1.4 years

Total Value of Assets A = $ 100 Billion

Average duration D(A)= 4 years

Total Value of Liabilities L= $ 90 Billion

Average Duration D(L)= 6 years

Duration Gap can be calculated as follows

Duration Gap D(gap) = D(A) - (L/A) * D(L)

D(gap) = 4 – (90/100) * 6

D(gap) = 4 – 0.9 * 6 = 4 – 5.4 = -1.4 years

If the interest rates have increase by 2% and let us assume that the initial interest was 0%, then effect of change of interest rates can be calculated as follows

Change in Networth/Assets   = - D(gap) + change in interest rates/(1+initial interest rate)

Change in Networth / $ 100 Billion   = -(-1.4) * (0.02 – 0)/(1+0)

Change in Networth / $ 100 Billion = 1.4 * 0.02 = 0.028

Change in Networth = $ 100 Billion * 0.028 = $ 2.8 Billion

Net worth of the bank will increase by $ 2.8 Billion.

To reduce the interest rate risk bank needs to decrease the duration of liabilities to that of assets.

Answer (b)

Fixed rate Assets = $ 15 Million

Rate sensitive Assets = $ 30 Million

Fixed rate liabilities = $ 25 Million

Rate sensitive liabilities = $ 20 Million

Gap = Rate Sensitive Assets - Rate Sensitive Liabilities = $ 30 Million - $ 20 Million = $ 10 Million

Change in interest rate = 5% or 0.05

Change in income = Gap * change in interest rate = $ 10 Million * 0.05 = $ 0.50 Million

Profits increase by $ 0.50 Million

To reduce the interest rate risk, the bank needs to reduce the gap between Rate Sensitive Assets and Rate Sensitive liabilities by either reducing the assets or increasing the liabilities.

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