Question

A bank has DA = 2.8 years and DL= 1.2 years. The bank has total equity of $105 million and total assets of $950 million. Interest rates are at 7 percent.

2. If interest rates decrease 100 basis points, what is the predicted dollar change in equity value? (0.2 points)

3. To get DE to equal zero to protect the equity value in the event of an interest rate change, how could the bank change its D_L? (0.2 points)

Answer 1

Asset, A = Liabilities, L + Equity, E

Hence, A = L + E

950 = L + 105

Hence, L = 950 - 105 = $ 845 million

Modified duration, MD = Duration / (1 + interest rate)

MDA = DA / (1 + y) = 2.8 / (1 + 7%) = 2.6168

MDL = DL / (1 + y) = 1.2 / (1 + 7%) = 1.1215

% chnage in interest = reduction by 100 bps = -100 bps = -1%

%change in value of asset = -MDA x % change in interest = - 2.6168 x (-1%) = 2.6168%

%change in value of liabilities = -MDL x % change in interest = - 1.1215 x (-1%) = 1.1215%

Part (a)

Predicted change in equity value = Predicted change in asset value - Predicted change in laibilities vale = A x %change in value of asset - L x %change in value of liabilities = 950 x 2.6168 - 845 x 1.1215% = $ 15.38 million

Part (b)

A = L + E

Hence, DA = L/A x DL + E/A x DE

Hence, to achieve DE = 0

DA = L/A x DL

Or, DL = A x DA / L = 950 x 2.8 / 845 = 3.15 years

The bank needs to increase the duration of its liabilities from 1.2 years to 3.15 years. This can be achieved by replacing the liabilities with higher maturity such that the overall duration of the liabilities increases from 1.2 years to 3.15 years.