Fin 4243 final

Suppose that the yields-to-maturity on three-year and four-year zero-coupon bonds are 4% and 5%, respectively, stated on a semiannual bond basis. An analyst would like to know the “3y1y” implied forward rate, which is the implied one-year forward yield three years into the future.

Find IFR:  (IFR = the implied one-year forward rate three years into the future)

Enter your answer as a percentage.

8.03

A 6% annual coupon corporate bond with 5 years remaining to maturity is trading at a price of 102.

The 4% annual coupon government bond with 5 years remaining to maturity is trading at a price of 101. 

Find:
Calculate the G-spread.

Enter your answer in basis points.

175.45

Problem 5.3.1.0.1.P Macaulay Duration
Given:
A 3-year 0% annual coupon bond has a yield-to-maturity of 5%. 

Find:
Macaulay Duration (MacDur)

Enter your answer in years.

3

Problem 5.3.1.0.2.P Macaulay Duration
Given:
A 3-year 4% annual coupon bond has a yield-to-maturity of 5%. 

Find:
Macaulay Duration (MacDur)

Enter your answer in years.

2.8844

A 10-year 8% annual coupon bond has a yield-to-maturity of 6% and Macaulay duration of 7.4450 years.

Find:
Modified Duration

Enter your answer in years.

7.0236

A 10-year 8% annual coupon bond has a yield-to-maturity of 10% and Macaulay duration of 7.0439 years.

Find:
Expected change in the price of a bond if interest rates change by 25 basis points.

Enter your answer as a percentage.

1.6009

A 5-year 7% annual coupon bond has a yield-to-maturity of 5%. 

Find:
Effective Duration given a 25 bps change in yield-to-maturity.

Enter your answer in years.

4.2049

A 5-year 4% annual coupon bond has a yield-to-maturity of 5%. 

Find:
Approximate Modified Duration given a 5 bps change in yield-to-maturity.

Enter your answer in years.

4.4003

A 5-year 4% annual coupon bond has a yield-to-maturity of 5%. 

Find:
Approximate Macaulay Duration given a 5 bps change in yield-to-maturity.

Enter your answer in years.

4.6203

A 5-year 7% annual coupon bond has a yield-to-maturity of 5%. 

Find:
Effective Duration given a 25 bps change in yield-to-maturity.

Enter your answer in years.

4.2049

Which of the following statements about duration is correct? A bond’s:

Modified duration cannot be larger than its Macaulay duration (assuming a positive yield-to-maturity).

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?

Reinvestment of coupon payments

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:

assumes a parallel shift to the yield curve.

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

convexity

Empirical duration is likely the best measure of the impact of yield changes on portfolio value, especially under stressed market conditions, for a portfolio consisting of:

25% AAA rated sovereign bonds, 25% AAA rated corporate bonds, and 50% high-yield (i.e., speculative-grade) corporate bonds, all from various euro area sovereign and corporate issuers.

A manufacturing company receives a ratings upgrade and the price increases on its fixed-rate bond. The price increase was most likely caused by a(n):

decrease in the bond’s credit spread.

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

reduces the effective duration of the bond.

The holding period for a bond at which the coupon reinvestment risk offsets the market price risk is best approximated by:

Macaulay duration.

When the investor’s investment horizon is less than the Macaulay duration of the bond she owns:

market price risk dominates, and the investor is at risk of higher rates.

Which of the following statements about Macaulay duration is correct?

A bond’s Macaulay duration is inversely related to its yield-to-maturity.

Suppose an investor holds the following portfolio of two zero-coupon bonds:
A 1-year zero-coupon bond.
A 30-year zero-coupon bond.

The weights of the bonds are as follows:
Bond 1: 25%
Bond 30: 75%

Find:
Using Approach 2, find the Macaulay Duration of the Bond Portfolio.

Enter your answer in years.
Round your answer to the nearest ten-thousandth of a year (0.0000).

22.75

A bond with exactly 10 years remaining until maturity offers a 5% coupon rate with annual coupons and is priced at a yield-to-maturity of 4%.

Find:
Price value of a basis point (PVBP).

Enter your answer as a decimal.
Round your answer to 4 digits past the decimal (0.0000).

0.0851

A bond with exactly 9 years to maturity, a $1000 par value, a 9% coupon paid annually, and 9% yield to maturity.

Find:
The bond’s approximate convexity given a 50 basis point change in annual yield.

Enter your answer as a decimal.
Round your answer to 2 digits past the decimal (0.00).

48.76

A bond with exactly 9 years to maturity, a $1000 par value, a 9% coupon paid annually, and 9% yield to maturity.

Find:
The bond’s price change using approximate convexity given a 50 basis point increase in annual yield.

Enter your answer as a percentage.
Round your answer to the nearest hundredth of a percent (0.00%).

-2.94

Credit risk of a corporate bond is best described as the:

risk of loss resulting from the issuer failing to make full and timely payments

The two components of credit risk are default probability and:

loss severity.

The risk that the price at which investors can actually transact differs from the quoted price in the market is called:

market liquidity risk.

Credit spreads are most likely to widen:

in periods of heavy new issue supply and low borrower demand.

An issuer credit rating usually applies to a company’s:

senior unsecured debt.

The priority of claims for senior subordinated debt is:

lower than for senior unsecured debt.

Which of the following statements about credit ratings is most accurate?

Credit ratings can migrate over time.

The factor that most likely results in corporate credit spreads widening is:

weakening economic conditions.

Which of the following corporate debt instruments has the highest seniority ranking?

Second lien

A senior unsecured credit instrument holds a higher priority of claims than one ranked as:

senior subordinated.

According to the "Sources of Return" notes, what occurs to a bond purchased at a discount as its carrying value is "pulled to par" over time?

The amortization of the discount brings the return in line with the market discount rate.

Question: Which duration measure is defined as the "weighted average time to receipt of cash flows" and serves as the mathematical basis for calculating annual modified duration?

Macaulay Duration

Question: What is the primary conceptual difference between Modified Duration and Effective Duration?

Modified duration is a "yield duration" based on the bond's own YTM, while Effective duration is a "curve duration" based on a benchmark yield curve.

Why is Effective Duration (EffDur) considered the only appropriate measure of interest rate risk for bonds with embedded options?

Because changes in benchmark rates can change the timing and amount of the bond's future cash flows.

Beyond parallel shifts, what specific type of risk do key rate durations (partial durations) help an analyst identify?

Shaping risk (e.g., the yield curve becoming steeper or flatter).

Based on the "Properties of Bond Duration" notes, which of the following is an established rule for duration?

With other factors held constant, duration is higher when the bond's yield-to-maturity is lower.

What is the primary limitation of calculating portfolio duration as the weighted average of the individual bond durations?

It implicitly assumes a parallel shift in the yield curve.

In the United States, money duration is commonly called "dollar duration." What does the related "PV01" (PVBP) statistic represent?

The estimated change in the full bond price given a 1 basis point (0.01%) change in the yield-to-maturity.

In the formula for Approximate Convexity, what is the mathematical effect of the [∆Yield]^2 term in the denominator?

It captures the "curviness" or secondary effect of the price-yield relationship.

For a callable bond, what occurs to "Effective Convexity" when the benchmark yield is low and the bond is likely to be called?

The effective convexity becomes negative, meaning price appreciation is limited as rates fall.

How does the term structure of yield volatility affect a bond's interest rate risk?

It implies that short-term and long-term yields may have different levels of volatility, which duration alone may not capture.

If an investor has a "positive duration gap" (Macaulay Duration > Investment Horizon), what is their primary risk?

Market price risk dominates; the investor is at risk of higher interest rates.

According to the "Credit and Liquidity Risk" notes, how do duration and convexity apply when a bond's credit spread changes rather than the benchmark yield?

The same duration and convexity statistics apply for a change in the spread as for a change in the benchmark yield.

Why might an analyst use "Empirical Duration" rather than "Analytical Duration" for a portfolio of high-yield corporate bonds?

Empirical duration uses historical market data to capture how prices actually move, which may differ from theoretical pricing models.

Which credit-related risk specifically refers to the risk that a bond issuer's creditworthiness will deteriorate, causing yield spreads to widen and bond prices to fall?

Credit migration or downgrade risk

How is "expected loss" calculated when summarizing credit risk for a debt instrument?

Default Probability × Loss Severity

In a typical corporate capital structure, which of the following debt types generally holds the highest priority of claim on an issuer's assets?

First lien loan

Why might a junior creditor (such as a subordinated bondholder) receive a recovery in a bankruptcy reorganization even if senior creditors are not paid in full?

The various classes of claimants agree to a compromise to avoid a protracted legal process

Which term describes the rating agency practice of adjusting a specific bond's rating higher or lower than the issuer's overall credit rating based on its seniority or collateral?

Notching

Which of the following is a recognized risk or limitation of relying solely on credit ratings from agencies?

Ratings can be lagging indicators that do not change as quickly as market prices

Within the "Four Cs" framework, which "C" refers to the borrower's ability to make its debt payments on time and is typically assessed through industry structure and financial statement analysis?

Capacity

In credit analysis, assessing management's "Character" involves looking at which of the following?

Management's track record and the use of aggressive accounting policies

Which ratio is a key measure of "leverage" used by credit analysts to determine an issuer's ability to pay its debt over time?

Total Debt / EBITDA

If an analyst observes that a company has a much higher "Total Debt/EBITDA" and a lower "EBITDA Interest Coverage" than its industry median, the company most likely has:

Lower credit quality and higher risk of default than its peers

How do credit spreads typically react during a period of financial distress or a weakening economy?

Spreads widen due to increased concerns about creditworthiness and lower market liquidity

When evaluating high-yield (below-investment-grade) bonds, why is "Covenant Analysis" considered more critical than it is for investment-grade bonds?

High-yield issuers often have complex capital structures and higher default risk making legal protections more vital

Which ratio is a key credit measure for revenue-backed non-sovereign (municipal) government bonds to determine if they can cover their obligations?

Debt-service-coverage or DSC ratio