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Exam 9: Interest Rate Risk II

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Question 31

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Modified Duration, semi-annual $M D = \frac { D } { \left( 1 + \frac { 1 } { 2 } R \right) } = \frac { 7.50 } { ( 1.05 ) } = 7.143$ Dollar Duration $\text { Dollar Duration } = M D \times P = 7.143 \times 100,000 = 714,300$ Change in Price $\Delta P = - \text { Dollar Duration } \times \Delta R = 714,300 \times 0.04 = - 28,572$ New Price $100,000 - 28,572 = \$ 71,428$ -What is the duration of an 8 percent annual payment two-year note that currently sells at par?

A) 2 years.
B) 1.75 years.
C) 1.93 years.
D) 1.5 years.
E) 1.97 years.

F) B) and D)
G) B) and E)

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Question 32

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-What will be the impact, if any, on the market value of the bank's equity if all interest rates increase by 75 basis points?

A) The market value of equity will decrease by $15,750.
B) The market value of equity will increase by $15,750.
C) The market value of equity will decrease by $426,825.
D) The market value of equity will increase by $426,825.
E) There will be no impact on the market value of equity.

F) A) and D)
G) B) and E)

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Question 33

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$\left[ D _ { A } - D _ { L } k \right] = \left[ 0.955 - 0.354 \times \left( \frac { 1,710 } { 1,730 } \right) \right] = [ 0.955 - 0.350 ] = 0.605$ Consider a five-year, 8 percent annual coupon bond selling at par of $1,000. -What is the duration of this bond?

-What is the leverage-adjusted duration gap of the FI?

The leverage adjusted duration of a typical depository institution is positive.

Marking-to-market accounting is a market value accounting method that reflects the purchase prices of assets and liabilities.

In most countries FIs report their balance sheet using market value accounting.

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

In duration analysis, the times at which cash flows are received are weighted by the relative importance in present value terms of the cash flows arriving at each point in time.

Immunization of an FIs net worth requires the duration of the liabilities to be adjusted for the amount of leverage on the balance sheet.

The duration of a portfolio of assets can be found by calculating the book value weighted average of the durations of the individual assets.

Immunizing the net worth ratio requires that the duration of the assets be set equal to the duration of the liabilities.

Duration is related to maturity in a linear manner through the interest rate of the asset.

The immunization of a portfolio against interest rate risk means that the portfolio will neither gain nor lose value when interest rates change.

Duration is related to maturity in a nonlinear manner through the current yield to maturity of the asset.

Immunizing net worth from interest rate risk using duration matching requires that the duration match must be realigned periodically as the maturity horizon approaches.

$\begin{array} { | l | l | l | l | l | } \hline \text { Rate } & \text { Maturity } & \text { Ask } & \text { Change } & \text { Ask yield } \\\hline 7.1250 & \text { Oct 15,2005 } & 102 : 08 & - 1 & 5.9156 \\\hline\end{array}$ -If yields increase by 10 basis points, what is the approximate price change on the $100,000 Treasury note? Use the duration approximation relationship.

The use of duration to predict changes in bond prices for given changes in interest rate changes will always underestimate the amount of the true price change.

Investing in a zero-coupon asset with a maturity equal to the desired investment horizon is one method of immunizing against changes in interest rates.

First Duration, a securities dealer, has a leverage-adjusted duration gap of 1.21 years, $60 million in assets, 7 percent equity to assets ratio, and market rates are 8 percent. -What is the impact on the dealer's market value of equity per $100 of assets if the change in all interest rates is an increase of 0.5 percent [i.e., ΔR = 0.5 percent]