Question 1

A bond with a 9-year duration is worth $1,080, and its yield to maturity is 8%. If the yield to maturity falls to 7.84%, you would predict that the new value of the bond will be approximately ________.

Accepted Answer

ΔP/P = −D*(Δy)
D* = D/(1 + y) = 9/1.08 = 8.33
ΔP/P = −D*(Δy) = −8.33(−0.16%) = 1.33%
New price = $1,080(1.01333) = $1,094.40

Question 2

Duration facilitates the comparison of bonds with differing ________.

Accepted Answer

Duration is a measure of the sensitivity of a bond's price to changes in interest rates, and it takes into account the bond's remaining time to maturity. Therefore, it is particularly helpful in comparing bonds with different maturities. Bonds with longer maturities generally have greater durations because they are more sensitive to changes in interest rates over a longer period of time.

Question 3

Compute the modified duration of a 9% coupon, 3-year corporate bond with a yield to maturity of 12%.

Accepted Answer

11eaaae8_8b58_5d67_a4b8_779f95c90d89_TB6474_00 D* = 2.75/1.12 = 2.45

Question 4

An 8%, 30-year bond has a yield to maturity of 10% and a modified duration of 8 years. If the market yield drops by 15 basis points, there will be a ________ in the bond's price.

Accepted Answer

(ΔP/P) = −8(−0.0015) = 0.012

Question 5

An investor who expects declining interest rates would maximize her capital gain by purchasing a bond that has a ________ coupon and a ________ term to maturity.

Accepted Answer

A bond with a zero coupon and a long term to maturity is most sensitive to interest rate changes, meaning its price would increase the most if interest rates decline, maximizing capital gains for the investor.

Question 6

A bond has a maturity of 12 years and a duration of 9.5 years at a promised yield rate of 8%. What is the bond's modified duration?

Accepted Answer

D* = 9.5/1.08 = 8.8 years

Question 7

A bond currently has a price of $1,050. The yield on the bond is 6%. If the yield increases 25 basis points, the price of the bond will go down to $1,030. The duration of this bond is ________ years.

Accepted Answer

ΔP/P = −D*(Δy)
−20/1,050 = −D*(0.25%)
−1.9% = −D*(0.25%)
D* = 7.6
D = D*(1 + y)
D = 7.6(1.0625) = 8.075

Question 8

Which of the following set of conditions will result in a bond with the greatest price volatility?

Accepted Answer

Bonds with a low coupon and a long maturity have the greatest price volatility because they have the longest time until maturity and the lowest interest payments, making them more sensitive to changes in interest rates. A high coupon would provide more stable income and a short maturity would result in the bond paying back the principal sooner, reducing the impact of interest rate changes on the bond's price.

Question 9

A bond has a current price of $1,030. The yield on the bond is 8%. If the yield changes from 8% to 8.1%, the price of the bond will go down to $1,025.88. The modified duration of this bond is ________.

Accepted Answer

ΔP/P = −D*(Δy)
−0.40% = −D*(0.10%)
D* = 0.40%/0.10% = 4

Question 10

To create a portfolio with a duration of 4 years using a 5-year zero-coupon bond and a 3-year 8% annual coupon bond with a yield to maturity of 10%, one would have to invest ________ of the portfolio value in the zero-coupon bond.

Accepted Answer

The duration of the 3-year bond is 2.78, as shown in the table below.
 11eaaae8_8b58_5d68_a4b8_c9770fd5ebad_TB6474_00 Then 5wZ + 2.78(1 − wZ) = 4
2.22wZ = 1.22
wZ = 0.5495

Question 11

A 20-year maturity bond pays interest of $90 once per year and has a face value of $1,000. Its yield to maturity is 10%. You expect that interest rates will decline over the upcoming year and that the yield to maturity on this bond will be only 8% a year from now. Using horizon analysis, the return you expect to earn by holding this bond over the upcoming year is ________.

Accepted Answer

Calculator entries for the price today are N = 20, I/Y = 10, PMT = 90, FV = 1,000, CPT PV 11eaaae8_8b57_e833_a4b8_07a143f09210_TB6474_11 −914.86
calculator entries for the price in 1 year are N = 19, I/Y = 8, PMT = 90, FV = 1,000, CPT PV 11eaaae8_8b58_0f44_a4b8_81a7f42e8dd4_TB6474_11 −1,096.04
Return = 11eaaae8_8b58_0f45_a4b8_558be99eb967_TB6474_11 = 0.2964

Question 12

If you choose a zero-coupon bond with a maturity that matches your investment horizon, which of the following statements is (are) correct?
I. You will have no interest rate risk on this bond.
II. In the absence of default, you can be sure you will earn the promised yield rate.
III. The duration of your bond is less than the time to your investment horizon.

Accepted Answer

I. A zero-coupon bond has no reinvestment risk, as there are no coupon payments to reinvest. Therefore, the only risk is interest rate risk, which is eliminated if the investment horizon and the maturity match.
II. A zero-coupon bond promises to pay a fixed amount at maturity, and as long as there is no default, the investor can be guaranteed to earn the promised yield rate.
III. The duration of a zero-coupon bond is equal to its maturity, which matches the investment horizon in this case. Therefore, the duration is also less than (or equal to) the time to the investment horizon.

Question 13

A bond pays annual interest. Its coupon rate is 9%. Its value at maturity is $1,000. It matures in 4 years. Its yield to maturity is currently 6%.
The modified duration of this bond is ________ years.

Accepted Answer

11eaaae8_8b57_e832_a4b8_09f874ac5d6c_TB6474_00 D* = 3.56/1.06 = 3.36 years

Question 14

A bond pays annual interest. Its coupon rate is 9%. Its value at maturity is $1,000. It matures in 4 years. Its yield to maturity is currently 6%.
The duration of this bond is ________ years.

Accepted Answer

11eaaae8_8b57_c121_a4b8_870be53e92c3_TB6474_00 Duration = 3.56

Question 15

A bank has $50 million in assets, $47 million in liabilities, and $3 million in shareholders' equity. If the duration of its liabilities is 1.3 and the bank wants to immunize its net worth against interest rate risk and thus set the duration of equity equal to zero, it should select assets with an average duration of ________.

Accepted Answer

(50,000,000)(D_A) = (47,000,000)(1.3); D_A= 1.22

Question 16

A perpetuity pays $100 each and every year forever. The duration of this perpetuity will be ________ if its yield is 9%.

Accepted Answer

D = 11eaaae8_8b57_c120_a4b8_c35d128419f9_TB6474_11 = 12.11

Question 17

The historical yield spread between the AA bond and the AAA bond has been 25 basis points. Currently the spread is only 9 basis points. If you believe the spread will soon return to its historical levels, you should ________.

Accepted Answer

If the spread is currently lower than its historical level, the trader should anticipate it to revert to the mean. To profit from this prediction, the trader should buy the cheaper security (AAA) and short the more costly one (AA). By doing so, they will benefit from the spread widening and returning to its historical average.

Question 18

Compute the duration of an 8%, 5-year corporate bond with a par value of $1,000 and yield to maturity of 10%.

Accepted Answer

11eaaae8_8b58_3656_a4b8_796a32ebcd43_TB6474_00

Question 19

When interest rates increase, the duration of a 20-year bond selling at a premium ________.

Accepted Answer

When interest rates increase, bond prices fall, and the duration of a bond decreases. For a bond selling at a premium, which means its price is higher than its face value, the decrease in price is more pronounced. As a result, the duration of a 20-year bond selling at a premium decreases when interest rates increase.

Question 20

The duration of a bond normally increases with an increase in:
I. Term to maturity
II. Yield to maturity
III. Coupon rate

Accepted Answer

The duration of a bond is directly proportional to its term to maturity, meaning that as the maturity increases, so does the duration. However, changes in yield to maturity and coupon rate can have conflicting effects on duration, and the overall impact depends on the specific characteristics of the bond. Therefore, choices II and III cannot be considered reliable predictors of duration changes.

Quiz 11: Managing Bond Portfolios