Blue Sunday Bank has a portfolio of loans and securities, as well as deposits an

Question

Blue Sunday Bank has a portfolio of loans and securities, as well as deposits and money market borrowings,

which are expected to produce the following cash inflows and outflows for the bank in the coming 5 years.

Now assume that the bank has total assets of $30 billion and total liabilities of $25 billion, and all asset and

liability cash flows are proportional to the cash flows given in the charts below. How much would the value of the bank

change if interest rates rise from 4.5% to 5.0%? What about if interest rates change from 4.5% to 4.2%?

Assume that the total assets and total liabilities have the same duration profile as the cash flows given in this problem.

Show your calculations in a spreadsheet.

Duration of Total Cash Inflows

Blue Sunday Bank has a portfolio of loans and securities, as well as deposits and money market borrowings,

which are expected to produce the following cash inflows and outflows for the bank in the coming 5 years.

Now assume that the bank has total assets of $30 billion and total liabilities of $25 billion, and all asset and

liability cash flows are proportional to the cash flows given in the charts below. How much would the value of the bank

change if interest rates rise from 4.5% to 5.0%? What about if interest rates change from 4.5% to 4.2%?

Assume that the total assets and total liabilities have the same duration profile as the cash flows given in this problem.

Show your calculations in a spreadsheet.

Duration of Total Cash Inflows

Expected Cash Flow Cash Flow Timeline Current Year Present Value (4.5%) Present Value Weight Duration 1900000 1 Year 1 0.956937799 1818181.818 0.63258399 0.63258399 750000 2 Years 2 0.915729951 686797.4634 0.238951394 0.477902788 350000 3 Years 3 0.876296604 306703.8114 0.106708756 0.320126269 65000 4 Years 4 0.838561344 54506.48733 0.018963962 0.075855849 10000 5 Years 5 0.802451047 8024.510465 0.002791897 0.013959486 2874214.091 1.520428382 Duration is 1.520428 Years Duration of Total Cash Outflows Expected Cash Flow Cash Flow Timeline Current Year Present Value (4.5%) Present Value Weight Duration -1400000 1 Year 1 0.956937799 -1339712.919 0.531606644 0.531606644 -830000 2 Years 2 0.915729951 -760055.8595 0.30159502 0.60319004 -400000 3 Years 3 0.876296604 -350518.6416 0.139088036 0.417264108 -45000 4 Years 4 0.838561344 -37735.26046 0.014973592 0.05989437 -40000 5 Years 5 0.802451047 -32098.04186 0.012736708 0.06368354 -2520120.722 1.675638701 Duration is 1.675639 Years

Explanation / Answer

Soln : Step 1: It has been given that duration of cash inflows, D = 1.520428 years

Duration measures the change in pricing of a security with change in interest rate

i.e., change in price = - Duration *change in interest rate/(1+ interest rate)

We can calculate the change in assets value and liabilities value as per the change in interest rate.

Step 2: We can also ise duration gap analysis concept that says :

Duration gap = Duration of assets - (L/A) * duration of liabilities

L = value of liabilities and A = value of assets

Duration gap = 1.520428 - (25/30)*1.675639 = 0.124062 years

Step 3 , using this duration gap and change in interest rate , we can evaluate the change in value

change in value of bank, N /assets value = -duration gap *change in interest rate/(1+rate)

change in interest rate = 5-4.5 = 0.5% and rate = 4.5%

N = -  0.124062* 0.5%/(1.045) *30 billion = -$17.81 million

Now , again in case interest rate changes from 4.5% to 4.2% = 4.2-4.5 = -0.3%

Again we use duration gap analysis using the change in interest rate as calculated above

N =  -  0.124062* (-0.3%)/(1.045) *30 billion = $10.685 million

Note : Cash inflows = assets and cash outflows = liabilities.

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