Question 1

Duration gap analysis:

Accepted Answer

Duration gap analysis applies the concept of duration to the bank's entire balance sheet, comparing the duration of assets and liabilities to determine the bank's exposure to interest rate risk. It measures the difference between the durations of a bank's assets and liabilities and indicates the sensitivity of the bank's net worth to changes in interest rates.

Question 2

Which of the following is true regarding duration gap analysis?

Accepted Answer

Duration gap analysis is a tool used by banks to manage interest rate risk. The magnitude of the duration gap indicates the level of interest rate risk, management can adjust the duration gap based on their interest rate outlook, and a positive duration gap implies that the bank's market value of equity decreases when interest rates rise.

Question 3

Which of the following allows a security's cash flows to change when interest rates change?

Accepted Answer

Effective duration measures the sensitivity of a security's price to changes in interest rates, taking into account the potential changes in cash flows due to changes in interest rates. Modified duration and Macaulay's duration do not take into account changes in cash flows, and balance sheet duration and income statement duration are not commonly used measures in finance.

Question 4

Macaulay's duration:

Accepted Answer

Macaulay's duration is a measure of the average time it takes to receive cash flows from a bond (including interest and principal payments), weighted by the present value of those cash flows. It is a useful tool for estimating the sensitivity of a bond's price to changes in interest rates. Therefore, choice A, which states that Macaulay's duration is a weighted average of the time until cash flows are received, is the correct answer. Choice B is incorrect, as duration can be equal to, greater than, or less than maturity, depending on the characteristics of the bond. Choice C is also incorrect, as duration can be equal to maturity in some cases. Choice D is partially correct, as duration can help estimate how a bond's price will change in response to changes in interest rates, but it is not a direct indicator. Choice E is incorrect, as duration is not used to estimate when options will be exercised.

Question 5

Which of the following would generally be considered price sensitive?

Accepted Answer

A 20-year zero coupon bond is generally considered price sensitive because its value is highly susceptible to changes in interest rates. Unlike instruments that involve short-term borrowing or lending (such as Fed funds purchased, Fed funds sold, and repurchase agreements) or demand deposits which do not have a maturity date, the value of a long-term bond like a zero coupon bond fluctuates significantly with interest rate movements.

Question 6

A 30-year zero coupon bond with a face value of $5,000 is currently selling for $1,156.88 and has a market rate of interest of 5%. Using the bond's modified duration, what is the approximate change in the price of the bond if interest rates fall to 4.25%?

Accepted Answer

The answer of A 30-year zero coupon bond with a...

Question 7

Use the following bank information for questions .
 $\begin{array}{|l|l|l|l|l|l|l|l|}
\hline &\begin{array}{c}
\text { Market } \
\text { Value }
\end{array} &\text { Rate } & \begin{array}{c}
\text { Duration } \
\text { (Years) }
\end{array} & \begin{array}{c}\text { Liabilities }\
\text { and } \
\text { Equity }
\end{array} & \begin{array}{c}
\text { Market } \
\text { Value }
\end{array} & \text { Rate } & \begin{array}{c}
\text { Duration } \
\text { (Years) }
\end{array} \
\hline\text { Cash } & \$  150 & && \text {Time Deposits } & \$  500 & 4 \% & 1.25 \
\hline \text { Loans } & \$  675 & 10 \% & 2.50 &\text { CDs } & \$  400 & 6 \% & 3.00 \
\hline\text { T-Bonds }&\$175&5\%&5.00&\text { Equity }&\$100&&\
\hline\text { Total }&\$1,000&&&&\$1,000\
\hline
\end{array}$
-What is the weighted average duration of assets?

Accepted Answer

The weighted average duration of assets is calculated by multiplying the duration of each asset by its proportion of the total market value and then summing these products. For cash, loans, and T-bonds, the calculation is as follows: $(150/1000)*0 + (675/1000)*2.5 + (175/1000)*5 = 0 + 1.6875 + 0.875 = 2.5625$ years.

Question 8

A 10-year annual coupon bond is currently selling for its par value of $1,000 with an annual yield of 5%. If the bond is callable at par, what is the effective duration of the bond, if the interest rates change by 1%? The price of the bond at a 6% interest rate equals $926.40.

Accepted Answer

The answer of A 10-year annual coupon bond is currently...

Question 9

Put the following steps in duration gap analysis in the proper order.
I.	Estimate the economic value of assets, liabilities and equity.
II.	Forecast the change in the economic value of equity for various interest rates.
III.	Forecast future interest rates.
IV.	Estimate the duration of assets and liabilities.

Accepted Answer

First, forecast future interest rates (III), then estimate the economic value of assets, liabilities, and equity (I), followed by estimating the duration of assets and liabilities (IV), and finally forecast the change in the economic value of equity for various interest rates (II).

Question 10

EVE analysis: is essentially a _____________ analysis.

Accepted Answer

The answer of EVE analysis: is essentially a _____________ analysis.
...

Question 11

Modified duration:

Accepted Answer

Modified duration directly indicates the percentage change in the price of a security for a 1% change in yield (interest rates), not when options will be used or that it's always greater than maturity.

Question 12

Effective duration:

Accepted Answer

The answer of Effective duration:
...

Question 13

What does a bank's duration gap measure?

Accepted Answer

The duration gap measures the difference in the duration of a bank's assets and its liabilities. A positive duration gap indicates that the bank's assets have a longer duration than its liabilities, making the bank more sensitive to interest rate increases, and vice versa.

Question 14

Which of the following is false regarding duration gap analysis?

Accepted Answer

Duration gap analysis is primarily used to assess the potential change in a bank's market value of equity, not its net interest income.

Question 15

A bond has a Macaulay's duration of 26.56 years. If rates rise from 6.25% to 6.50%, the bonds price will:

Accepted Answer

The bond's price will decrease if interest rates rise. Macaulay's duration can be used to estimate the percentage change in a bond's price for a given change in interest rates. The formula for the approximate percentage change in price is: -Duration × Change in interest rate. Here, the duration is 26.56 years, and the interest rate increases by 0.25% (from 6.25% to 6.50%), so the bond's price will decrease by approximately 6.25% (26.56 × 0.25% ≈ 6.64%, but the closest option given is 6.25%).

Question 16

A bond has a Macaulay's duration of 21 years. If rates rise from 5% to 5.5%, the bonds price will:

Accepted Answer

When interest rates rise, bond prices generally fall. The magnitude of the change in price is determined by the duration of the bond. A 1% increase in interest rates would result in approximately a 21% decrease in the bond price (21 years of duration). Therefore, a 0.5% increase in rates would result in approximately a 10.5% decrease in the bond price, which rounds to 10%.

Question 17

A 20-year annual coupon bond is currently selling for its par value of $10,000 with an annual yield of 7%. If the bond is callable at par, what is the effective duration of the bond, assuming rates change by 2%? The price of the bond at a 9% interest rate equals $8,174.29.

Accepted Answer

Effective duration = (P- - P+) / (2 * Δy * P0), where P- is the price if yield decreases, P+ is the price if yield increases, Δy is the change in yield, and P0 is the current price. Given P+ = $8,174.29, P0 = $10,000, and Δy = 2% or 0.02, we need to find P-. Since the bond is at par and callable at par, its price won't increase above $10,000 (the call feature caps the price). Thus, P- = P0 = $10,000. Plugging into the formula: Effective duration = ($10,000 - $8,174.29) / (2 * 0.02 * $10,000) = $1,825.71 / $400 = 4.56 years.

Question 18

Which of the following is likely to have a negative effective duration?

Accepted Answer

A high coupon, interest only mortgage-backed security that is pre-paying at a high rate is likely to have a negative effective duration due to the high prepayment rate, which shortens the expected cash flows and causes the security's price to rise less in response to a decrease in interest rates.

Question 19

A bond has a Macaulay's duration of 10.7 years. If rates fall from 7% to 6%, the bonds price will:

Accepted Answer

The bond's price will increase by approximately 10% because Macaulay's duration can be used to estimate the percentage change in a bond's price for a 1% change in yield. A duration of 10.7 years means a 1% decrease in yield (from 7% to 6%) would lead to approximately a 10.7% increase in the bond's price.

Question 20

A 20-year zero coupon bond with a face value of $1,000 is currently selling for $214.55 and has a market rate of interest of 8%. Using the bond's modified duration, what is the approximate change in the price of the bond if interest rates rise to 9%?

Accepted Answer

First, calculate the bond's modified duration:

$$	ext{Modified Duration} = \frac{	ext{Macaulay Duration}}{(1 + r)}$$

where $r$ is the market rate of interest and the Macaulay Duration is:

$$	ext{Macaulay Duration} = \frac{20}{(1 + r)^{20}}$$

Plugging in $r = 8\%$:

$$	ext{Macaulay Duration} = \frac{20}{(1 + 0.08)^{20}} \approx 11.10$$

Then, solve for the approximate change in price:

$$	ext{Approximate Price Change} = -	ext{Modified Duration} 	imes 	ext{Change in Yield} 	imes 	ext{Original Price}$$

where the change in yield is:

$$	ext{Change in Yield} = 0.09 - 0.08 = 0.01$$

Plugging in the values:

$$	ext{Approximate Price Change} = -11.10 	imes 0.01 	imes 214.55 \approx -\$39.73$$

Therefore, the price of the bond is expected to decrease by approximately $39.73 if the interest rate rises to 9%. The answer is (C).

Quiz 8: Managing Interest Rate Risk: Duration Gap and Economic Value of Equity