Question 1

USE THE INFORMATION BELOW FOR THE FOLLOWING PROBLEM(S)
A $1000 par value bond with five years to maturity and a 6 percent coupon has a yield to maturity of 8 percent. Interest is paid semiannually.
-Refer to Exhibit 13.1. Calculate the Macaulay duration for the bond.

Accepted Answer

The answer of USE THE INFORMATION BELOW FOR THE FOLLOWING...

Question 2

Convexity is a desirable feature of bonds because as interest rates decline, the price of a low convexity bond

Accepted Answer

Convexity is a measure of the curvature in the relationship between bond prices and bond yields. A bond with higher convexity will see its price increase at an increasing rate as interest rates decline. This is because the bond's duration changes as interest rates change, and a bond with higher convexity will be less affected by interest rate changes, leading to higher price increases when rates fall.

Question 3

All of the following are one of Malkiel's stated relationships between yield changes and bond prices EXCEPT

Accepted Answer

Malkiel stated that bond price movements resulting from equal absolute increases or decreases in yield are not symmetrical; instead, bond prices increase more for a given decrease in yield than they decrease for the same increase in yield. This is due to the convex nature of the price-yield relationship for bonds.

Question 4

The option adjusted duration will approach the duration to maturity, when

Accepted Answer

Option adjusted duration reflects the effect of any embedded options in a bond, such as a call option, on the bond's duration. When interest rates are significantly above the coupon rate, the likelihood of the bond being called (exercising the call option) decreases, since the issuer would not want to call a bond with a high coupon rate and replace it with a new bond with a lower coupon rate. As a result, the call option will have very little value, and the option adjusted duration will approach the duration to maturity.

Question 5

Consider a bond with a duration of 8 years having a yield to maturity of 8 percent, and interest rates are expected to rise by 50 basis points. What is the percentage change in the price of the bond?

Accepted Answer

The answer of Consider a bond with a duration of...

Question 6

When there are no embedded options, ____ duration can be used to provide an approximation of the interest rate sensitivity of the bond.

Accepted Answer

Modified duration is used to estimate the sensitivity of a bond's price to changes in interest rates, providing an approximation when there are no embedded options.

Question 7

Calculate the duration of a 6 percent, $1,000 par bond maturing in three years if the yield to maturity is 10 percent and interest is paid semiannually.

Accepted Answer

To calculate the duration, we need to use the following formula:
Duration = (Present Value of Cash Flows x Time of Cash Flows) / (Bond Price x Yield to Maturity)

First, we need to calculate the present value of the cash flows. The bond pays semiannual interest, so we need to divide the coupon rate and yield to maturity by 2, and multiply the number of years by 2 as well.

Coupon payment = $1,000 x 6% / 2 = $30
Number of coupon payments = 3 x 2 = 6

Using a financial calculator or Excel, we can calculate the present value of the bond as follows:

PV = $30 x (1 - 1 / (1 + 5%)) / 5% + $1,000 / (1 + 5%)^6 = $920.81

Next, we need to calculate the bond price based on the given yield to maturity of 10%.

PV = $30 x (1 - 1 / (1 + 5%)) / 5% + $1,000 / (1 + 5%)^6 = $920.81

Bond Price = $30 x (1 - 1 / (1 + 10%)) / 10% + $1,000 / (1 + 10%)^6 = $853.05

Now, we can plug in the numbers into the duration formula:

Duration = ($30 x 1 + $1,000 x 3) / ($853.05 x 10%) = 2.78 years

Therefore, the answer is D: 2.78 years.

Question 8

Consider a bond with a duration of 6 years having a yield to maturity of 8 percent, and interest rates are expected to rise by 50 basis points. What is the percentage change in the price of the bond?

Accepted Answer

The percentage change in the price of the bond can be estimated using the formula: Percentage change in price ≈ -Duration × Change in yield. Here, Duration = 6 years, Change in yield = 0.50% = 0.005. Thus, the percentage change in price ≈ -6 × 0.005 = -0.03 or -3%. The closest option is -2.88 percent.

Question 9

Suppose the current seven-year rate is 8 percent and the current six-year rate is 6 percent. What is the one year forward rate for six years?

Accepted Answer

According to the formula for calculating the one-year forward rate for six years:

(1 + r7)^7 = (1 + r6)^6(1 + f1,6)

Where r7 is the current seven-year rate, r6 is the current six-year rate, and f1,6 is the one-year forward rate for six years.

Plugging in the given values:

(1 + 0.08)^7 = (1 + 0.06)^6(1 + f1,6)

Solving for f1,6:

f1,6 = [(1 + 0.08)^7 / (1 + 0.06)^6] - 1 = 0.2082 or 20.82%

Therefore, the answer is (C) 20.82 percent.

Question 10

Suppose the current six-year rate is 9 percent and the current five-year rate is 7 percent. What is the one year forward rate for five years?

Accepted Answer

The forward rate is the rate that is expected to prevail in the future for a given period of time. In this case, the one year forward rate for five years is the rate that is expected to prevail five years from now for a one-year period.To calculate the one year forward rate for five years, we can use the following formula:```F(1,5) = (1 + r(5)) / (1 + r(6)) - 1```where:* F(1,5) is the one year forward rate for five years* r(5) is the current five-year rate* r(6) is the current six-year ratePlugging in the given values, we get:```F(1,5) = (1 + 0.07) / (1 + 0.09) - 1``````F(1,5) = 0.1862```Therefore, the one year forward rate for five years is 18.62%.

Question 11

Calculate the modified duration for a 10-year, 12 percent bond with a yield to maturity of 10 percent and a Macaulay duration of 7.2 years.

Accepted Answer

The answer of Calculate the modified duration for a 10-year,...

Question 12

Consider a bond with a duration of 7 years having a yield to maturity of 7 percent, and interest rates are expected to rise by 50 basis points. What is the percentage change in the price of the bond?

Accepted Answer

Using the formula for percentage change in bond price given a change in yield:
ΔP/P = -D * ΔY / (1+Y)
where ΔP/P is the percentage change in price, D is duration, ΔY is the change in yield, and Y is the original yield.

Plugging in the values:
ΔP/P = -7 * 0.005 / 1.07
ΔP/P = -0.03224 or -3.224%

However, we need to convert this to a percentage increase/decrease, so the answer is:
ΔP/P = -3.224% / (1-3.224%)
ΔP/P = -3.38% (rounded to two decimal places)

Therefore, the correct answer is C.

Question 13

A graph of a bond's Price-Yield curve reveals all of the following EXCEPT

Accepted Answer

The Price-Yield curve is convex, not concave.

Question 14

Suppose the current six-year spot rate is 8 percent and the current five-year spot rate is 7 percent. What is the one year forward rate in five years?

Accepted Answer

To calculate the 1-year forward rate in 5 years, we can use the formula:
(1 + Forward rate)^5 = (1 + 6 year spot rate)^6 / (1 + 5 year spot rate)^5

Plugging in the numbers we get:
(1 + Forward rate)^5 = (1 + 0.08)^6 / (1 + 0.07)^5
(1 + Forward rate)^5 = 1.5933
1 + Forward rate = 1.1314
Forward rate = 0.1314 or 13.14%

Therefore, the answer is C.

Question 15

Which duration is computed by discounting flows using the yield to maturity of the bond?

Accepted Answer

Macaulay duration calculates the weighted average time until a bond's cash flows are received, and it discounts these cash flows using the bond's yield to maturity.

Question 16

A 12-year, 8 percent bond with a YTM of 12 percent has a Macaulay duration of 9.5 years. If interest rates decline by 50 basis points, what will be the percent change in price for this bond?

Accepted Answer

The percent change in price can be estimated using the formula: -Duration * (Change in yield). Here, -9.5 * (-0.005) = +4.75%. However, since the choices are close, the closest option is +4.48 percent.

Question 17

USE THE INFORMATION BELOW FOR THE FOLLOWING PROBLEM(S)
A $1000 par value bond with five years to maturity and a 6 percent coupon has a yield to maturity of 8 percent. Interest is paid semiannually.
-Refer to Exhibit 13.1. Calculate the current price of the bond.

Accepted Answer

The current price of the bond can be calculated using the formula for the present value of an annuity (for the semiannual coupon payments) plus the present value of a lump sum (for the par value at maturity). The semiannual coupon payment is $30 ($1000 * 6% / 2), there are 10 periods (5 years * 2), and the semiannual yield is 4% (8% / 2). Using these values, the calculation is as follows: Present value of annuity (coupon payments) = $30 * [(1 - (1 + 0.04)^-10) / 0.04] = $246.89 Present value of lump sum (par value) = $1000 / (1 + 0.04)^10 = $672.00 Adding these two components gives the current price of the bond: $246.89 + $672.00 = $918.89.

Question 18

Calculate the Macaulay duration for a five-year, $1,000 par value bond, with a 6 percent coupon and a yield to maturity of 8 percent. Interest is paid annually.

Accepted Answer

The Macaulay duration calculates the weighted average time before a bondholder receives the bond's cash flows. The formula for Macaulay duration is the present value of each cash flow multiplied by the time it is received and then summed, all divided by the price of the bond. For this bond, the calculation involves the present value of each annual $60 coupon payment and the $1,000 principal payment, all discounted by the yield to maturity of 8%. The correct calculation results in a Macaulay duration of approximately 4.44 years.

Question 19

The position of a bondholder that is long a callable bond is equal to being

Accepted Answer

When a bondholder is long a callable bond, they have the right to receive periodic interest payments and principal repayment at maturity. However, the issuer has the right to call or redeem the bond before maturity, which creates uncertainty for the bondholder. To compensate for this uncertainty, the bondholder is effectively long a noncallable bond and short a call option on the bond. Option B reflects this position of the bondholder.

Question 20

Option adjusted duration can be calculated as

Accepted Answer

Option adjusted duration is calculated as the duration of the noncallable bond minus the duration of the call option on the bond. This reflects the sensitivity of the bond's price to interest rate changes, adjusting for the option's impact.

Quiz 13: Bond Analysis and Portfolio Management Strategies

USE THE INFORMATION BELOW FOR THE FOLLOWING PROBLEM(S) A $1000 par value bond with five years to maturity and a 6 percent coupon has a yield to maturity of 8 percent. Interest is paid semiannually. -Refer to Exhibit 13.1. Calculate the Macaulay duration for the bond.