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Exam 9: Interest Rate Risk II

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Question 51

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

A) True
B) False

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Question 52

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

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B) False

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Question 53

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$\begin{array} { | l | r | c | c | } \hline \text { Assets } & \text { Amount } & \text { Rate } & \text { Duration } \\\hline \text { Cash } & \$ 75 \text { million } & & \\\hline \text { Loans } & \$ 750 \text { million } & 12 \text { percent } & 1.75 \text { years } \\\hline \text { Treasuries } & \$ 175 \text { million } & 9 \text { percent } & 7.00 \text { years } \\\hline \text { Liabilities and Equity } & & & \\\hline \text { Time Deposits } & \$ 350 \text { million } & 7 \text { percent } & 1.75 \text { years } \\\hline \text { CDs } & \$ 575 \text { million } & 8 \text { percent } & 2.50 \text { years } \\\hline \text { Equity } & \$ 75 \text { million } & & \\\hline\end{array}$ -Calculate the duration of the assets to four decimal places.

Fully amortizing loan cash flows: $\begin{array} { | l | l | l | l | l | } \hline \mathrm { PV } = 30,000,000 & \mathrm { FV } = 0 & \mathrm { I } = 6 & \mathrm {~N} = 2 & \mathbf { P M T } = \mathbf { 1 6 , 3 6 3 , 1 0 7 } \\\hline\end{array}$ 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.

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.

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

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

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.

The duration of all floating rate debt instruments is

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

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

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

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

-What is the leverage-adjusted duration gap?

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.

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

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

Duration measures the average life of a financial asset.