Exam 9: Interest Rate Risk II

Macaulay's Duration $D = \frac { \sum _ { t = 1 } ^ { N } P V _ { t } \times t } { \sum _ { t = 1 } ^ { N } P _ { t } } = \frac { \left[ \frac { 100 } { ( 1.10 ) ^ { 5 } } \times 5 \right] } { \left[ \frac { 100 } { ( 1.10 ) ^ { 5 } } \right] } = \frac { 310.46 } { 62.09 } = 5.00 \text { years }$ The duration of a zero coupon bond is equal to its maturity. -Calculating modified duration involves

First Duration Bank has the following assets and liabilities on its balance sheet Assets Par Amount Rate Liabilities Par Amount Rate 2-year commercial loans, annual fixed rate, at par \ 400 million 10\% 1-year CDs, annual fixed rate, at par \ 450 million 7\% 1-year Treasury bills \ 100 million Net Worth \ 50 million -What is the duration of the commercial loans?

Which of the following is indicated by high numerical value of the duration of an asset?

Setting the duration of the assets higher than the duration of the liabilities will exactly immunize the net worth of an FI from interest rate shocks.

Duration increases with the maturity of a fixed-income asset at a decreasing rate.

What is the effect of a 100 basis point increase in interest rates on the market value of equity of the FI? Use the duration approximation relationship. Assume r = 4 percent.

Perfect matching of the maturities of the assets and liabilities will always achieve perfect immunization for the equity holders of an FI against interest rate risk.

For a given maturity fixed-income asset, duration decreases as the market yield increases.

-What is this bank's interest rate risk exposure, if any?

$D = \frac { \left[ \frac { 80 } { ( 1.08 ) ^ { 1 } } \times 1 \right] + \left[ \frac { 80 } { ( 1.08 ) ^ { 2 } } \times 2 \right] \left[ \frac { 80 } { ( 1.08 ) ^ { 3 } } \times 3 \right] \left[ \frac { 80 } { ( 1.08 ) ^ { 4 } } \times 4 \right] \left[ \frac { 80 + 1,000 } { ( 1.08 ) ^ { 5 } } \times 5 \right] } { 1,000 } = 4.312$ -If interest rates increase by 20 basis points, what is the approximate change in the market price using the duration approximation?

The economic meaning of duration is the interest elasticity of a financial assets price.

Managers can achieve the results of duration matching by using these to hedge interest rate risk.

Assets Amount Rate Duration Cash \ 75 million Loans \ 750 million 12 percent 1.75 years Treasuries \ 175 million 9 percent 7.00 years Liabilities and Equity Time Deposits \ 350 million 7 percent 1.75 years CDs \ 575 million 8 percent 2.50 years Equity \ 75 million -Calculate the duration of the assets to four decimal places.

Larger coupon payments on a fixed-income asset cause the present value weights of the cash flows to be lower in the duration calculation.

The duration of all floating rate debt instruments is

Duration measures the average life of a financial asset.

Fully amortizing loan cash flows: =30,000,000 =0 =6 =2 = Macaulay's Duration $D = \frac { \sum _ { t = 1 } ^ { N } P V _ { t } \times t } { \sum _ { t = 1 } ^ { N } P _ { t } } = \frac { \left[ \frac { 16,363,107 } { ( 1.06 ) ^ { 1 } } \times 1 \right] + \left[ \frac { 16,363,107 } { ( 1.06 ) ^ { 2 } } \times 2 \right] } { 30,000,000 } = 1.4854$ -Calculate the modified duration of a two-year corporate loan paying 6 percent interest annually. The $40,000,000 loan is 100 percent amortizing, and the current yield is 9 percent annually.

-What is the leverage-adjusted duration gap?