Question 1

a bond with exactly nine years remaining until maturity offers a 3% coupon rate with annual coupons. The bond, with a yield-to-maturity of 5%, is priced at 85.784357 per 100 of par value. The estimated price value of a basis point for the bond is closest to:
A) 0.0086.
B) 0.0648.
C) 0.1295.

Accepted Answer

To calculate the estimated price value of a basis point (PVBP), we need to find the partial derivative of the bond price with respect to the yield-to-maturity (YTM) and multiply it by -0.0001 (this represents a change of one basis point).

PVBP = -0.0001 * (∂Price/∂YTM)

Using a financial calculator or Excel, we can find that the price of the bond is $85.784357 when the YTM is 5%. Then, we can calculate the bond price when the YTM is 5.01% and 5.02%, respectively, to find the partial derivatives.

When YTM = 5.01%, the bond price is $85.677260. 
When YTM = 5.02%, the bond price is $85.570440.

Using these values, we can calculate the PVBP:

PVBP = (-85.677260 + 85.784357) / (0.01 * 85.784357) ≈ 0.0648

Therefore, the estimated price value of a basis point for this bond is 0.0648 or 6.48 cents. The closest choice is B.

Question 2

The "second-order" effect on a bond's percentage price change given a change in yield-to-maturity can be best described as:
A) duration.
B) convexity.
C) yield volatility.

Accepted Answer

The "second-order" effect on a bond's percentage price change given a change in yield-to-maturity is known as convexity. Duration measures the sensitivity of bond price to changes in yield, but it assumes a linear relationship between price and yield, and it may not accurately reflect the actual price change, especially when there are large changes or non-parallel shifts in the yield curve. Convexity, on the other hand, measures the curvature of the price-yield relationship and provides a better approximation of the price change, especially when there are large changes or non-parallel shifts in the yield curve. Yield volatility refers to the magnitude of changes in yield, but it does not capture the curvature of the price-yield relationship.

Question 3

Which of the following sources of return is most likely exposed to interest rate risk for an investor of a fixed-rate bond who holds the bond until maturity?
A) Capital gain or loss
B) redemption of principal
C) reinvestment of coupon payments

Accepted Answer

When an investor holds a fixed-rate bond until maturity, the reinvestment of coupon payments is most likely exposed to interest rate risk. This is because the coupon payments are fixed, and if interest rates rise, the investor may not be able to reinvest the coupon payment at the same rate of return. As a result, the investor may face reinvestment risk and receive a lower return than expected. The capital gain/loss and redemption of principal are not affected by interest rate risk if the bond is held until maturity.

Question 4

an investor purchases a bond at a price above par value. two years later, the investor sells the bond. The resulting capital gain or loss is measured by comparing the price at which
The bond is sold to the:
A) carrying value.
B) original purchase price.
C) original purchase price value plus the amortized amount of the premium.

Accepted Answer

The answer of an investor purchases a bond at a...

Question 5

The following information relates to Problems 
an investor purchases a nine-year, 7% annual coupon payment bond at a price equal to par value. after the bond is purchased and before the first coupon is received, interest rates increase to 8%. The investor sells the bond after five years. assume that interest rates remain unchanged at 8% over the five-year holding period.
-assuming that all coupons are reinvested over the holding period, the investor's five-year horizon yield is closest to:
A) 5.66%.
B) 6.62%.
C) 7.12%.

Accepted Answer

When the bond is purchased at par, the yield to maturity (YTM) is equal to the coupon rate. In this case, the YTM is 7%.

However, when interest rates increase to 8%, the bond's price will decrease in order to compensate investors for the lower coupon payments relative to the new higher interest rates being offered in the market. The extent of the price drop will depend on the remaining time to maturity of the bond, among other factors.

Since the investor sells the bond after five years, there are four years left until maturity. Using a bond calculator, we can determine that the price of the bond decreases to 92.77% of par value in response to the increase in interest rates.

Upon selling the bond after five years, the investor will receive the remaining principal plus the final coupon payment. The total cash flows for the investor will be as follows:

Year 1: Reinvest coupon payment at 8%
Year 2: Reinvest coupon payment at 8%
Year 3: Reinvest coupon payment at 8%
Year 4: Reinvest coupon payment at 8%, receive final coupon payment
Year 5: Sell bond for 92.77% of par value, receive remaining principal

Using these cash flows, we can calculate the investor's five-year horizon yield as 6.62%. This is the annualized return that the investor would earn over the five-year holding period, taking into account all reinvested coupon payments and the final sale price of the bond.

Question 6

Which of the following is most appropriate for measuring a bond's sensitivity to shaping risk?
A) key rate duration
B) effective duration
C) modified duration

Accepted Answer

Key rate duration is the sensitivity to changes in specific key interest rates, which is tied to the shaping risk associated with yield curve movements. This makes it the most appropriate measurement for assessing a bond's sensitivity to shaping risk. Effective duration and modified duration are measures of a bond's overall sensitivity to changes in interest rates and are not specifically tied to shaping risk.

Question 7

a bond portfolio consists of the following three fixed-rate bonds. assume annual coupon payments and no accrued interest on the bonds. Prices are per 100 of par value. $$\begin{array} { l r c c c c r } 
\text { Bond } & \text { Maturity } & \begin{array} { c } 
\text { Market } \
\text { Value }
\end{array} & \text { Price } & \text { Coupon } & \begin{array} { c } 
\text { Yield-to- } \
\text { Maturity }
\end{array} & \begin{array} { r } 
\text { Modified } \
\text { Duration }
\end{array} \
\hline \text { A } & \text { 6 years } & 170,000 & 85.0000 & 2.00 \% & 4.95 \% & 5.42 \
\text { B } & 10 \text { years } & 120,000 & 80.0000 & 2.40 \% & 4.99 \% & 8.44 \
\text { C } & 15 \text { years } & 100,000 & 100.0000 & 5.00 \% & 5.00 \% & 10.38 \
\hline
\end{array}$$ The bond portfolio's modified duration is closest to:
A) 7.62.
B) 8.08.
C) 8.20.

Accepted Answer

The answer of a bond portfolio consists of the following...

Question 8

a bond is currently trading for 98.722 per 100 of par value. if the bond's yield-to-matu- rity (YtM) rises by 10 basis points, the bond's full price is expected to fall to 98.669. if The bond's YtM decreases by 10 basis points, the bond's full price is expected to increase To 98.782. The bond's approximate convexity is closest to:
A) 0.071.
B) 70.906.
C) 1,144.628.

Accepted Answer

The approximate convexity of a bond can be calculated using the formula: Convexity ≈ [(P- + P+ - 2P0) / (2 * P0 * Δy^2)], where P- is the price if the yield decreases, P+ is the price if the yield increases, P0 is the original price, and Δy is the change in yield in decimal form. Given P- = 98.782, P+ = 98.669, P0 = 98.722, and Δy = 0.001 (10 basis points = 0.1% = 0.001), substituting these values into the formula gives a convexity close to 70.906.

Question 9

Which of the following statements about Macaulay duration is correct?
A) a bond's coupon rate and Macaulay duration are positively related.
B) a bond's Macaulay duration is inversely related to its yield-to-maturity.
C) The Macaulay duration of a zero-coupon bond is less than its time-to-maturity.

Accepted Answer

Macaulay duration measures the weighted average time until a bond's cash flows are received, and it decreases as the yield to maturity increases because higher discount rates reduce the present value of later cash flows more than that of earlier cash flows. This makes the duration, or the weighted average time until cash flows, shorter.

Question 10

Using the information below, which bond has the greatest money duration per 100 of par value assuming annual coupon payments and no accrued interest? $\begin{array} { l r c c c c } 
\hline \text { Bond } & \begin{array} { c } 
\text { Time-to- } \
\text { Maturity }
\end{array} & \begin{array} { c } 
\text { Price Per } 100 \
\text { of Par Value }
\end{array} & \text { Coupon Rate } & \begin{array} { c } 
\text { Yield-to- } \
\text { Maturity }
\end{array} & \begin{array} { c } 
\text { Modified } \
\text { Duration }
\end{array} \
\hline \text { A } & 6 \text { years } & 85.00 & 2.00 \% & 4.95 \% & 5.42 \
\text { B } & 10 \text { years } & 80.00 & 2.40 \% & 4.99 \% & 8.44 \
\text { C } & 9 \text { years } & 85.78 & 3.00 \% & 5.00 \% & 7.54 \
\hline
\end{array}$
A) bond a
B) bond b
C) bond C

Accepted Answer

Bond B has the greatest modified duration of 8.44, which indicates it has the greatest sensitivity to interest rate changes and thus the greatest money duration per 100 of par value.

Question 11

a "buy-and-hold" investor purchases a fixed-rate bond at a discount and holds the securi- ty until it matures. Which of the following sources of return is least likely to contribute to The investor's total return over the investment horizon, assuming all payments are made as Scheduled?
A) Capital gain
B) Principal payment
C) reinvestment of coupon payments

Accepted Answer

A "buy-and-hold" investor who purchases a fixed-rate bond at a discount and holds the security until it matures is likely to receive a return from the coupon payments and the principal payment. However, capital gain is least likely to contribute to the investor's total return, as the investor is holding the security until maturity and not intending to sell it before then.

Question 12

an investor buys a 6% annual payment bond with three years to maturity. The bond has a yield-to-maturity of 8% and is currently priced at 94.845806 per 100 of par. The bond's Macaulay duration is closest to:
A) 2.62.
B) 2.78.
C) 2.83.

Accepted Answer

The Macaulay duration of a bond is the weighted average time until the bond's cash flows are received, and it is a measure of the bond's interest rate sensitivity. To calculate it for a bond paying annual coupons, you can use the formula that accounts for the present value of each cash flow (both the annual coupon payments and the principal repayment at maturity), weighted by the time until each cash flow occurs, and then divided by the bond's current price. Given the bond's annual coupon rate (6%), yield to maturity (8%), maturity (3 years), and price (94.845806), when you perform the calculation, you will find that the Macaulay duration is closest to the value given in option C, which is 2.83. This calculation involves discounting each of the bond's cash flows back to their present value using the yield to maturity, multiplying each by the time until it is received, summing these values, and then dividing by the current bond price.

Question 13

The following information relates to Problems 
an investor purchases a nine-year, 7% annual coupon payment bond at a price equal to par value. after the bond is purchased and before the first coupon is received, interest rates increase to 8%. The investor sells the bond after five years. assume that interest rates remain unchanged at 8% over the five-year holding period.
-The capital gain/loss per 100 of par value resulting from the sale of the bond at the end of the five-year holding period is closest to a:
A) loss of 8.45.
B) loss of 3.31.
C) gain of 2.75.

Accepted Answer

When interest rates increase, the value of a bond decreases. Since the investor purchased the bond at par value, the initial price was 100. When interest rates increase to 8%, the market value of the bond drops to $92.59 (using the bond pricing formula: PV = C[1 - 1/(1+r)^n]/r + FV/(1+r)^n, where PV is the present value or price of the bond, C is the coupon payment, r is the discount rate, n is the number of periods, and FV is the face value or par value of the bond).

After five years, the bond will have four years until maturity. Using the bond pricing formula, the price of the bond after five years with an 8% discount rate is $94.19. The capital gain/loss per 100 of par value is the difference between the selling price of the bond ($94.19) and the purchase price of the bond ($100), which is a loss of $5.81.

Therefore, the capital gain/loss per 100 of par value resulting from the sale of the bond at the end of the five-year holding period is closest to a loss of 3.31 ($5.81 / $100) which is option B.

Question 14

The following information relates to Problems 
an investor purchases a nine-year, 7% annual coupon payment bond at a price equal to par value. after the bond is purchased and before the first coupon is received, interest rates increase to 8%. The investor sells the bond after five years. assume that interest rates remain unchanged at 8% over the five-year holding period.
-Per 100 of par value, the future value of the reinvested coupon payments at the end of the holding period is closest to:
A) 35.00.
B) 40.26.
C) 41.07.

Accepted Answer

The future value of the reinvested coupon payments can be calculated using the formula for the future value of an annuity. Given a 7% annual coupon on a $100 par value bond, the annual coupon payment is $7. These payments are reinvested at the new interest rate of 8% for the duration of the holding period, which is 5 years. The future value of these reinvested coupons is calculated as: FV = P * [(1 + r)^n - 1] / r, where P is the payment ($7), r is the annual interest rate (8% or 0.08), and n is the number of periods (5 years). Plugging in these values gives: FV = $7 * [(1 + 0.08)^5 - 1] / 0.08, which equals approximately $41.07.

Question 15

Which of the following statements about duration is correct? a bond's:
A) effective duration is a measure of yield duration.
B) modified duration is a measure of curve duration.
C) modified duration cannot be larger than its Macaulay duration (assuming a positive yield-to-maturity).

Accepted Answer

Modified duration, which adjusts Macaulay duration for the interest rate, cannot exceed Macaulay duration when the yield-to-maturity is positive. This is because modified duration accounts for the change in interest rates, effectively providing a more accurate measure of interest rate risk.

Question 16

a limitation of calculating a bond portfolio's duration as the weighted average of the yield durations of the individual bonds that compose the portfolio is that it:
A) assumes a parallel shift to the yield curve.
B) is less accurate when the yield curve is less steeply sloped.
C) is not applicable to portfolios that have bonds with embedded options.

Accepted Answer

Assumes a parallel shift to the yield curve.

Question 17

an investor buys a three-year bond with a 5% coupon rate paid annually. The bond, with a yield-to-maturity of 3%, is purchased at a price of 105.657223 per 100 of par value. Assuming a 5-basis point change in yield-to-maturity, the bond's approximate modified Duration is closest to:
A) 2.78.
B) 2.86.
C) 5.56.

Accepted Answer

First, we need to calculate the bond's present value factor:

PV Factor = (1 + Yield) ^ (-Number of periods) = (1 + 0.03) ^ (-3) = 0.942596

Next, we can calculate the bond's full price:

Full Price = Annual Coupon Payment x PVIFA(Yield, Number of periods) + Par Value x PV Factor
Full Price = 5 x 2.870772 + 100 x 0.942596
Full Price = 18.539352 + 94.2596
Full Price = 112.798952

The bond's modified duration can then be calculated as:

Modified Duration = (-1 / Full Price) x [PVIFA(Yield + 0.0005, Number of periods) - PVIFA(Yield - 0.0005, Number of periods)]
Modified Duration = (-1 / 112.798952) x [2.827275 - 2.91457]
Modified Duration = (-0.008859) / (112.798952)
Modified Duration = -0.0000785 or approximately 2.78

Therefore, the closest choice is A.

Question 18

The interest rate risk of a fixed-rate bond with an embedded call option is best measured by:
A) effective duration.
B) modified duration.
C) Macaulay duration.

Accepted Answer

Effective duration measures the sensitivity of a bond's price to changes in interest rates, taking into account any embedded options such as call options. Modified duration and Macaulay duration also measure interest rate risk, but do not fully capture the impact of embedded options. Therefore, effective duration is the best choice for measuring interest rate risk of a fixed-rate bond with an embedded call option.

Question 19

a Canadian pension fund manager seeks to measure the sensitivity of her pension lia- bilities to market interest rate changes. The manager determines the present value of the Liabilities under three interest rate scenarios: a base rate of 7%, a 100 basis point increase In rates up to 8%, and a 100 basis point drop in rates down to 6%. The results of the Manager's analysis are presented below: $\begin{array} { l c } 
\hline\text { Interest Rate Assumption } & \text { Present Value of Liabilities } \
\hline 6 \% & \text { CAD510.1 million } \
7 \% & \text { CAD455.4 million } \
8 \% & \text { CAD373.6 million } \
\hline
\end{array}$ The effective duration of the pension fund's liabilities is closest to:
A) 1.49.
B) 14.99.
C) 29.97.

Accepted Answer

Effective duration can be calculated using the formula: $\frac{V^{-} - V^{+}}{2 \times V^{0} \times \Delta y}$, where $V^{-}$ is the value if rates decrease, $V^{+}$ is the value if rates increase, $V^{0}$ is the value at the current rate, and $\Delta y$ is the change in yield (in decimal form). Plugging in the given values: $\frac{510.1 - 373.6}{2 \times 455.4 \times 0.01}$ = 14.99.

Question 20

assuming no change in the credit risk of a bond, the presence of an embedded put option:
A) reduces the effective duration of the bond.
B) increases the effective duration of the bond.
C) does not change the effective duration of the bond.

Accepted Answer

The presence of an embedded put option provides the bondholder with the right to sell the bond back to the issuer at a pre-determined price. This feature effectively limits the potential downside risk of the bondholder. As a result, the price of the bond will be less sensitive to changes in interest rates, which decreases the effective duration of the bond.

Quiz 5: Understanding Fixed Income Risk and Return

a bond with exactly nine years remaining until maturity offers a 3% coupon rate with annual coupons. The bond, with a yield-to-maturity of 5%, is priced at 85.784357 per 100 of par value. The estimated price value of a basis point for the bond is closest to:

The "second-order" effect on a bond's percentage price change given a change in yield-to-maturity can be best described as:

Which of the following sources of return is most likely exposed to interest rate risk for an investor of a fixed-rate bond who holds the bond until maturity?

an investor purchases a bond at a price above par value. two years later, the investor sells the bond. The resulting capital gain or loss is measured by comparing the price at which The bond is sold to the:

Which of the following is most appropriate for measuring a bond's sensitivity to shaping risk?

Which of the following statements about Macaulay duration is correct?

a "buy-and-hold" investor purchases a fixed-rate bond at a discount and holds the securi- ty until it matures. Which of the following sources of return is least likely to contribute to The investor's total return over the investment horizon, assuming all payments are made as Scheduled?

an investor buys a 6% annual payment bond with three years to maturity. The bond has a yield-to-maturity of 8% and is currently priced at 94.845806 per 100 of par. The bond's Macaulay duration is closest to:

Which of the following statements about duration is correct? a bond's:

a limitation of calculating a bond portfolio's duration as the weighted average of the yield durations of the individual bonds that compose the portfolio is that it:

an investor buys a three-year bond with a 5% coupon rate paid annually. The bond, with a yield-to-maturity of 3%, is purchased at a price of 105.657223 per 100 of par value. Assuming a 5-basis point change in yield-to-maturity, the bond's approximate modified Duration is closest to:

The interest rate risk of a fixed-rate bond with an embedded call option is best measured by:

assuming no change in the credit risk of a bond, the presence of an embedded put option: