READING 46: UNDERSTANDING FIXED INCOME RISK AND RETURN
LOS 46.a: Calculate and interpret the sources of return from investing in a fixed-rate bond.
Question 46.1: Reinvestment risk is least likely:
A) minimized with zero-coupon bond issues.
B) more problematic for those investors with longer time horizons.
C) more problematic when the current coupons being reinvested are relatively small.
C is correct. Reinvestment risk becomes more problematic when the current coupons being reinvested are relatively large.
The intuition of this result is based on the idea of a trade-off between market price risk (the
uncertainty about price due to uncertainty about market YTM) and reinvestment risk (uncertainty about the total of coupon payments and reinvestment income on those payments due to the uncertainty about future reinvestment rates).
short investment horizon: market price risk > reinvestment risk
long investment horizon: reinvestment risk > market price risk
LOS 46.b: Define, calculate, and interpret Macaulay, modified, and effective durations.
Question 46.2: Changes in a fixed-coupon bond's cash flows that result from changes in yield would be reflected in the bond's:
A) effective duration.
B) modified duration.
C) Macaulay duration.
A is correct. Effective duration and effective convexity capture the effects from changes in a bond's cash flows when the yield changes (e.g., an increase in the likelihood of a bond being called when its yield has decreased). For this reason, they are the appropriate measures of interest rate sensitivity for bonds with embedded options.
So far, all of our duration measures have been calculated using the YTM and prices of straight (option-free) bonds. This is straightforward because both the future cash flows and their timing are known with certainty. This is not the case with bonds that have embedded options, such as a callable bond or a mortgage-backed bond. We say mortgage-backed bonds have a prepayment option, which is similar to a call optionon a corporate bond. The borrowers (people who take out mortgages) typically have the option to pay off the principal value of their loans, in whole or in part, at any time. These prepayments accelerate when interest rates fall significantly because borrowers can refinance their home loans at a lower rate and pay off the remaining principal owed on an existing loan. Thus, the pricing of bonds with embedded put, call, or prepayment options begins with the benchmark yield curve, not simply the current YTM of the bond. The appropriate measure of interest rate sensitivity for these bonds is effective duration.
Question 46.3: A bond has an effective duration of 7.5. If the bond yield changes by 100 basis points, the price of the bond will change by:
A) exactly 0.75%.
B) approximately 7.5%.
C) approximately 0.75%.
B is correct. The change in price due to a change in yield is only approximate because the calculation of effective duration does not reflect all of the curvature of the price-yield curve (convexity). It is a linear approximation of a non-linear relation.
Question 46.4: A non-callable bond with 4 years remaining maturity has an annual coupon of 12% and a $1,000 par value. The current price of the bond is $1,063.40. Given a parallel shift in the yield curve of 50 basis points, which of the following is closest to the eective duration of the bond?
A is correct.
Step 1: Find the current yield to maturity of the bond as:
FV = $1,000; PMT = $120; N = 4; PV = –$1,063.40; CPT → I/Y = 10%
Step 2: Compute the price of the bond if rates rise by 50 basis points to 10.5% as:
FV = $1,000; PMT = $120; N = 4; I/Y = 10.5%; CPT → PV = –$1,047.04
Step 3: compute the price of the bond if rates fall by 50 basis points to 9.5% as:
FV = $1,000; PMT = $120; N = 4; I/Y = 9.5%; CPT → PV = –$1,080.11
Step 4: The formula for effective duration is:
(V-–V+) / (2V0Δcurve)
Therefore, effective duration is:
($1,080.11 – $1,047.04) / (2 × $1,063.40 × 0.005) = 3.11
LOS 46.c: Explain why effective duration is the most appropriate measure of interest rate risk for bonds with embedded options
Question 46.5: Effective duration is more appropriate than modified duration as a measure of a bond's price sensitivity to yield changes when:
A) yield curve changes are not parallel.
B) the bond contains embedded options.
C) the bond has a low coupon rate and a long maturity.
B is correct. Effective duration takes into consideration embedded options in the bond. Modied duration does not consider the eect of embedded options. For option-free bonds, modied duration will be similar to effective duration. Both duration measures are based on the value impact of a parallel shift in a at yield curve.
LOS 46.f: Calculate the duration of a portfolio and explain the limitations of portfolio duration
Question 46.6: Portfolio duration most accurately approximates the sensitivity of the value of a bond portfolio to:
A) parallel shifts in the yield curve.
B) increases in the slope of the yield curve.
C) decreases in the slope of the yield curve.
A is correct. Portfolio duration is an approximation of the price sensitivity of a portfolio to parallel shifts of the yield curve (yields for all maturities increase or decrease by equal amounts). Key rate duration may be used to estimate interest rate risk for non-parallel shifts in the yield curve.
The second approach is typically used in practice. Using the durations of individual portfolio bonds makes it possible to calculate the duration for a portfolio that contains bonds with
embedded options by using their effective durations. The weights for the calculation of
portfolio duration under this approach are simply the full price of each bond as a proportion
of the total portfolio value (using full prices). These proportions of total portfolio value are
multiplied by the corresponding bond durations to get portfolio duration.
One limitation of this approach is that for portfolio duration to “make sense” the YTM of
every bond in the portfolio must change by the same amount. Only with this assumption of a
parallel shift in the yield curve is portfolio duration calculated with this approach consistent
with the idea of the percentage change in portfolio value per 1% change in YTM.
LOS 46.g: Calculate and interpret the money duration of a bond and price value of a basis point (PVBP)
Question 46.7: The current price of a $1,000 par value, 6-year, 4.2% semiannual coupon bond is $958.97. The bond's price value of a basis point is
A is correct.
Step 1: Compute the yield to maturity of the bond.
PV = –$958.97, FV = $1,000, PMT = $21, N = 12, CPT I/Y = 2.5%,
Step 2: Multiply by 2 since it is a semiannual bond to get an annualized yield to maturity of 5.0%.
Step 3: Compute the price of the bond at using yield one basis point higher, or 5.01%.
FV = $1,000, PMT = 21, N = 12, I/Y = (5.01 / 2 =) 2.505, CPT PV = –$958.47. The price changes from $958.97 to $958.47, or $0.50.
Question 46.8: Which of the following is an advantage of a callable bond (compared to an identical option-free bond) to an investor?
A) Less reinvestment risk.
B) Higher yield.
C) More convexity
B is correct. An issuer of a callable bond must compensate the bondholder when the issue is sold by offering a higher coupon rate or accepting a lower price than if the call feature was not included. Convexity will typically be much less than for an option-free bond, and reinvestment risk is greater for callable bonds.
LOS 46.i: Estimate the percentage price change of a bond for a specified change in yield, given the bond’s approximate duration and convexity
Question 46.9: For a bond currently priced at $1,018 with an effective duration of 7.48, if the market yield moved down 75 basis points, the new price would be approximately:
B is correct.
%Δprice ≈ –7.48(–0.0075) = 0.0561
$1,018(1 + 0.0561) = $1,075.11
LOS 46.k: Describe the relationships among a bond’s holding period return, its duration, and the investment horizon.
Question 46.10: An investor with an investment horizon of 5 years has purchased a 15-year 6% coupon bond at par. The bond has a modified duration of 9.8. The duration gap for this investor is closest to:
C is correct. The duration gap is calculated as the bond's Macaulay duration minus the investor's investment horizon. Modified duration is Macaulay duration / (1 + YTM), so we can calculate the Macaulay duration as 9.8 × 1.06 = 10.388. The duration gap is 10.388 – 5 = 5.388.
LOS 46.j: Describe how the term structure of yield volatility affects the interest rate risk of a bond.
Question 46.11: The term structure of yield volatility illustrates the relationship between yield volatility and:
A) yield to maturity.
B) Macaulay duration.
C) time to maturity.
C is correct. The term structure of yield volatility refers to the relationship between yield volatility and time to maturity.
The term structure of yield volatility refers to the relation between the volatility of bond
yields and their times to maturity. We have seen that the sensitivity of a bond’s price with
respect to a given change in yield depends on its duration and convexity. From an investor’s
point of view, it’s the volatility of a bond’s price that is of concern. The volatility of a bond’s
price has two components: the sensitivity of the bond’s price to a given change in yield and
the volatility of the bond’s yield.
LOS 46.l: Explain how changes in credit spread and liquidity affect yield-to-maturity of a bond and how duration and convexity can be used to estimate the price effect of the changes
Question 46.12: Which of the following is most accurate about a bond with positive convexity?
A) Price increases and decreases at a faster rate than the change in yield.
B) Positive changes in yield lead to positive changes in price.
C) Price increases when yields drop are greater than price decreases when yields rise by the same amount.
C is correct. A convex price/yield graph has a larger increase in price as yield decreases than the decrease in price when yields increase.
READING 47: FUNDAMENTALS OF CREDIT ANALYSIS
LOS 47.a: Describe credit risk and credit-related risks affecting corporate bonds.
Question 47.1: Shortfall risk is best described as the probability:
A) of a credit rating downgrade due to possible earnings shortfalls.
B) of failing to make a contractually promised payment.
C) that portfolio value will fall below some minimum level at a future date.
C is correct. Choice A is downgrade risk; choice B is default risk.
Default risk is the probability that a borrower (bond issuer) fails to pay interest or repay principal when due
Credit migration risk or downgrade risk is the possibility that spreads will increase because the issuer has become less creditworthy. As we will see later in this topic review, credit rating agencies assign ratings to bonds and issuers, and may upgrade or downgrade these ratings over time
LOS 47.b: Describe default probability and loss severity as components of credit risk.
Question 47.2: Loss severity is most accurately defined as the:
A) percentage of a bond’s value a bondholder will receive if the issuer defaults.
B) amount a bondholder will lose if the issuer defaults.
C) probability that a bond issuer will default.
B is correct. Loss severity is the money amount or percentage of a bond's value a bondholder will lose if the issuer defaults. The percentage of a bond's value a bondholder will receive if the issuer defaults is the recovery rate.
The expected loss is equal to the default risk multiplied by the loss severity. Expected loss
can likewise be stated as a monetary value or as a percentage of a bond’s value.
LOS 47.c: Describe seniority rankings of corporate debt and explain the potential violation of the priority of claims in a bankruptcy proceeding
Question 47.3: Shelby Enterprises recently entered into a new $500 million revolving credit facility. The provisions of the facility require Shelby to repay the loan before any other debt can be retired. In addition, if the company's debt-to-capital ratio is higher than 1.0 or its equity falls below $2 billion, Shelby will be prohibited from paying any dividends. Shelby would most likely agree to these covenants because they reduce:
A) risk to bondholders.
B) the company’s interest cost.
C) risk to shareholders.
B is correct. Shelby's management will agree to the lending covenants to lower the interest rate on the credit facility. The existing bondholders and shareholders may have more risk since their respective interests are subordinate to the credit facility.
Question 47.4: Bert Reed owns a junior secured bond of a firm that has entered bankruptcy proceedings. Mia Tano owns a senior unsecured bond of the same firm. As a result of the bankruptcy, Reed and Tano each recover 80% of the interest and principal owed on their bonds. This outcome is least likely the result of:
A) an order of the bankruptcy court.
B) the pari passu ranking of these creditors.
C) a negotiated settlement among the firm’s creditors
B is correct. Secured creditors have priority of claims over unsecured creditors in a bankruptcy, rather than ranking pari passu with unsecured creditors. However, the priority of claims might not always be followed, either because the creditors have negotiated a different outcome or because a bankruptcy court has ordered one.
Secured debt can be further distinguished as first lien or first mortgage (where a specific asset
is pledged), senior secured, or junior secured debt. Unsecured debt is further divided into
senior, junior, and subordinated gradations. The highest rank of unsecured debt is senior
unsecured. Subordinated debt ranks below other unsecured debt. All debt within the same category is said to rank pari passu, or have same priority of claims. All senior secured debt holders, for example, are treated alike in a corporate bankruptcy.
LOS 47.d: Distinguish between corporate issuer credit ratings and issue credit ratings and describe the rating agency practice of “notching.”
Question 47.5: If an investor wants only investment grade bonds in her portfolio, she would be least likely to purchase a:
A) 2-year municipal bond rated A–.
B) 3-year municipal bond rated BB.
C) 15-year, semiannual coupon corporate bond rated BBB.
B is correct. Investment grade bonds are BBB– and above. This bond is rated BB, which is below BBB–.
LOS 47.e: Explain risks in relying on ratings from credit rating agencies.
Question 47.6: Ann Lloyd, CFA, observes that a 3-year senior unsecured bond of Hawk, Inc. has a rating of Baa3/BBB– and a 3-year senior unsecured bond of Osprey, Inc. has a rating of Ba1/BB+. Based only on this information, Lloyd can most appropriately conclude that:
A) credit risk is greater for the Osprey bond than for the Hawk bond.
B) loss severity is greater for the Osprey bond than for the Hawk bond.
C) the Hawk bond is investment grade and the Osprey bond is non-investment grade.
C is correct. The classifications "investment grade" and "non-investment grade" are based on ratings from recognized credit rating agencies. Bonds rated Baa3/BBB– or higher are classified as investment grade, while bonds rated Ba1/BB+ or lower are classified as non-investment
grade. However, an analyst should not rely exclusively on credit ratings to draw conclusions about the credit risk or loss severity of bond investments.
LOS 47.f: Explain the four Cs (Capacity, Collateral, Covenants, and Character) of traditional credit analysis.
Question 47.7: Which of the following assets is most likely to represent high-quality collateral in credit analysis?
C) Deferred tax assets.
B is correct. Intangible assets that can be sold, such as trademarks, provide collateral of good quality. A credit analyst should view as low-quality collateral any assets that are likely to be written down in value if a firm encounters financial distress, such as goodwill and deferred tax assets.
Collateral analysis is more important for less creditworthy companies. The market value of a company’s assets can be difficult to observe directly. Issues to consider when assessing
collateral values include:
Intangible assets. Patents are considered high-quality intangible assets because they can be more easily sold to generate cash flows than other intangibles. Goodwill is not considered a high-quality intangible asset and is usually written down when company performance is poor.
Depreciation. High depreciation expense relative to capital expenditures may signal that management is not investing sufficiently in the company. The quality of the company’s assets may be poor, which may lead to reduced operating cash flow and potentially high loss severity.
Equity market capitalization. A stock that trades below book value may indicate that company assets are of low quality.
Human and intellectual capital. These are difficult to value, but a company may have intellectual property that can function as collateral.
LOS 47.i: Describe factors that influence the level and volatility of yield spreads
Question 47.8: Recent economic data suggest an increasing likelihood that the economy will soon enter a recessionary phase. What is the most likely effect on the yields of lower-quality corporate bonds and on credit spreads of lower-quality versus higher-quality corporate bonds?
A) Both will increase.
B) Both will decrease.
C) One will increase and one will decrease.
A is correct. During economic contractions, the probability of default increases for lower-quality issues and their yields increase. When investors anticipate an economic downturn, they tend to sell low-quality issues and buy high-quality issues, causing credit spreads to widen.
LOS 47.j: Explain special considerations when evaluating the credit of high yield, sovereign, and non-sovereign government debt issuers and issues.
Question 47.9: A firm is said to have a top-heavy capital structure if a high percentage of its total capital is:
B) short-term debt.
C) secured bank debt.
C is correct. "Top-heavy" refers to a capital structure that includes a high percentage of secured bank debt. A firm with a top-heavy capital structure may be limited in its access to additional bank borrowing, which increases the likelihood of default if the firm encounters financial distress.
High yield companies for which secured bank debt is a high proportion of the capital structure are said to be top heavy and have less capacity to borrow from banks in financially stressful periods. Companies that have top-heavy capital structures are more likely to default and have lower recovery rates for unsecured debt issues.