A bond with a face value of $1,000 pays a fixed coupon of 5% annually. If market interest rates rise from 5% to 7%, what happens to the bond's market price and why?
AThe bond's price falls to exactly $0, because a bond paying below the current market rate becomes worthless to all investors
BThe bond's price rises above $1,000, because investors prefer the safety of owning a bond that was issued when rates were lower
CThe bond's price falls below $1,000, because newly issued bonds now offer 7% coupons, making the existing 5% coupon less attractive — investors will only buy the older bond at a discount that compensates for the lower coupon
DThe bond's price stays at $1,000, because the coupon rate is fixed and contractually guaranteed regardless of what happens in the broader market
Correct answer: .
Bond prices and market interest rates move inversely. When market rates rise above a bond's coupon rate, the bond's fixed cash flows become less valuable relative to new bonds offering higher coupons. Investors will only purchase the older bond at a price below par (a discount) that effectively raises its yield to match the new market rate. The option claiming the price rises confuses safety preference with yield mechanics. The option claiming the price stays at par ignores the time value of money — a fixed-coupon bond's market price fluctuates with rate changes even though its coupon payments remain the same. The option claiming the bond becomes worthless is extreme; the bond still pays $50 per year and returns $1,000 at maturity, so it has value — just less than before.
Source: SEC, Investor.gov, 'Bonds'; CFA Institute, Fixed-Income: Basic Concepts
What does a bond's yield to maturity (YTM) represent, and how does it differ from the bond's coupon rate?
AYTM and coupon rate are identical for all bonds trading in the secondary market; the distinction only exists for bonds held from original issuance to maturity
BYTM is the total annualised return an investor will earn if they buy the bond at its current market price and hold it to maturity, assuming all coupons are reinvested at the YTM rate — it accounts for the purchase price, coupon payments, and the return of face value, while the coupon rate is simply the fixed annual interest payment expressed as a percentage of the bond's face value
CYTM is the annual coupon payment divided by the bond's current market price, making it the same as the current yield but expressed on a different time basis
DYTM measures only the capital gain or loss on the bond and excludes coupon income entirely, while the coupon rate captures the income component
Correct answer: .
Yield to maturity is the internal rate of return that equates the present value of all future cash flows from a bond (coupons plus the face value returned at maturity) to its current market price. It differs from the coupon rate because the coupon rate is fixed at issuance as a percentage of face value, while YTM changes with the bond's market price and captures the full economic return including any premium or discount to par. The option claiming YTM equals coupon rate is only true when the bond trades at exactly par. The option equating YTM with current yield is incorrect — current yield is coupon divided by price but ignores the capital gain or loss at maturity and the time value of money. The option limiting YTM to capital gains misses the fact that YTM explicitly incorporates coupon payments into its calculation.
Source: CFA Institute, Fixed-Income: Pricing and Valuation
An investor must choose between two bonds with identical credit quality and maturity dates: Bond X has a duration of 3 years and Bond Y has a duration of 8 years. If interest rates are expected to rise significantly, which bond carries more price risk and why?
ABond X carries more price risk, because shorter-duration bonds are more volatile since their cash flows are received sooner and are therefore more affected by rate changes
BNeither bond carries price risk because both have fixed coupon payments that are contractually guaranteed regardless of interest rate movements
CBoth bonds carry identical price risk because they have the same credit quality and maturity date, which are the only factors that determine bond price sensitivity
DBond Y carries more price risk, because duration measures a bond's sensitivity to interest rate changes — a higher duration means the bond's price will fall more for a given increase in rates
Correct answer: .
Duration is a measure of a bond's price sensitivity to changes in interest rates. A bond with a duration of 8 years will experience roughly 8% price change for each 1% change in interest rates, compared to roughly 3% for a bond with a duration of 3 years. When rates rise, the longer-duration Bond Y will therefore fall in price significantly more than Bond X. The option claiming shorter-duration bonds are more volatile reverses the relationship. The option claiming maturity alone determines sensitivity ignores coupon structure — two bonds with the same maturity but different coupon rates have different durations. The option claiming no price risk confuses the certainty of coupon payments with the certainty of the bond's market price, which fluctuates with rates.
Source: CFA Institute, Understanding Fixed-Income Risk and Return; Macaulay duration concept
Interest rate risk and credit (default) risk are two distinct risks that affect bond investors. Which statement correctly distinguishes them?
ACredit risk describes the risk that a bond's market price will fall as market interest rates rise, while interest rate risk describes the risk that the issuer will fail to make its promised interest or principal payments
BInterest rate risk is the risk that a bond's market price will change as prevailing market interest rates move, while credit risk is the risk that the issuer defaults on its promised interest or principal payments; a bond can carry heavy exposure to one of these risks with almost none of the other
CBoth risks measure the same underlying exposure, because a rise in market interest rates always signals that the issuer's ability to repay its debt is deteriorating
DInterest rate risk applies only to bonds issued by national governments, while credit risk applies only to bonds issued by corporations, since governments cannot default and corporations are unaffected by market rate movements
Correct answer: .
Interest rate risk and credit risk are separate dimensions of bond risk that can move independently. Interest rate risk affects a bond's market price purely because prevailing rates in the broader market shift, regardless of the issuer's financial health — a highly creditworthy government bond still loses market value when rates rise. Credit risk, by contrast, concerns whether the specific issuer will actually make its promised coupon and principal payments, driven by that issuer's own financial condition. A long-dated, highly-rated government bond can carry substantial interest rate risk with almost no credit risk, while a short-dated bond from a financially troubled company can carry heavy credit risk with little interest rate risk. The option reversing the two definitions swaps which risk concerns price movement versus which concerns default. The option claiming they measure the same exposure wrongly assumes rate moves always reflect issuer-specific deterioration, when rates are driven by broad macroeconomic factors unrelated to any single issuer. The option restricting each risk type to one category of issuer is incorrect — corporate bonds are exposed to interest rate risk just as government bonds are, and governments can and do default on debt, particularly in foreign currency.
Source: CFA Institute, Fixed-Income: Risks (credit risk vs. interest rate risk)
A zero-coupon bond makes no periodic interest payments to the bondholder during its term. How does an investor who holds one to maturity actually earn a return?
AThe bond pays a single large coupon payment exactly halfway through its term instead of the usual periodic schedule, and that one payment is the investor's entire return
BThe issuer pays a variable amount each year tied to its own stock price performance, replacing the fixed coupon that a standard bond would pay
CThe investor earns no return at all unless the bond is resold before maturity, at a price set purely by speculative demand with no relationship to face value
DThe bond is issued and typically trades at a price below its face value, and the investor's return comes entirely from that built-in discount — the difference between the discounted purchase price and the full face value repaid at maturity
Correct answer: .
A zero-coupon bond is sold at a price well below its face value and pays no periodic interest during its life; the entire return to the holder comes from the gradual accretion of that discount toward full face value, which is paid out as a single lump sum at maturity. For example, a bond with a $1,000 face value might be issued at $700, and the $300 difference represents the investor's total return over the bond's term, functioning economically like compound interest even though no cash changes hands until maturity. The option describing a single mid-term coupon payment is incorrect because zero-coupon bonds are defined precisely by having no coupon payments at any point, including mid-term. The option describing a stock-like variable payment confuses a zero-coupon bond with an equity instrument; a zero-coupon bond's face value and maturity date are fixed and contractual. The option claiming there is no return without a resale ignores that the maturity repayment itself constitutes the return — resale before maturity is optional, not required, to realize value from the built-in discount.
Source: SEC, Investor.gov, 'Zero-Coupon Bond'; CFA Institute, Fixed-Income: Introduction to Bond Valuation
A bond has a fixed coupon rate of 4%. Comparing that coupon rate to the prevailing market interest rate for newly issued bonds of similar credit quality and maturity, under which condition will this bond trade at a premium (a market price above its face value)?
AWhen the prevailing market rate for comparable bonds is below the bond's 4% coupon, making its fixed payments more attractive than newly issued bonds, so investors bid its price above face value
BWhen the prevailing market rate for comparable bonds is above the bond's 4% coupon, since a higher market rate always pushes the price of an existing bond upward to match the new rate
COnly when the bond is issued directly by a national government, regardless of where its coupon rate sits relative to the current market rate
DOnly during the bond's final year before maturity, when its market price is mechanically forced to converge upward toward a premium
Correct answer: .
A bond trades at a premium when its fixed coupon rate is more attractive than what new bonds of similar risk and maturity are currently offering. If comparable newly issued bonds only offer a 3% coupon while this bond locks in 4%, investors are willing to pay more than face value to capture that above-market income stream, bidding the price up until its yield to maturity converges toward the prevailing market rate. The reverse situation — market rates above the bond's coupon — would push the price below face value into a discount, not a premium, so the option claiming a higher market rate always pushes price upward has the direction backwards. The option tying premium pricing to government issuance alone is incorrect because par, premium, and discount pricing is driven by the relationship between a bond's own coupon and prevailing market rates, not by the type of issuer. The option claiming premiums only occur in the final year before maturity is also wrong; while a premium bond's price does converge toward par as maturity approaches, the premium itself is created by the coupon-versus-market-rate relationship and can exist for the bond's entire life.
Source: CFA Institute, Fixed-Income: Pricing and Valuation (par, premium, and discount bonds)
A bond investor plans to reinvest each coupon payment as it's received. If market interest rates fall significantly after the bond is purchased, which risk does this reinvestment plan expose the investor to, and how does that risk differ from the interest-rate risk affecting the bond's own market price?
AThe same interest-rate risk that affects the bond's price, since a falling market rate always causes both the bond's price and its coupon payments to decline by the same proportion
BCredit risk, because falling market rates are typically a sign that the issuer's financial condition is weakening and less able to support future payments
CReinvestment risk — the risk that future coupon payments (and, at maturity, the returned principal) will have to be reinvested at the now-lower prevailing rate, reducing the investor's overall realized return; this is distinct from price risk, which concerns the bond's own market value moving in the opposite direction as rates fall
DCurrency risk, because a decline in domestic interest rates is assumed to automatically weaken the currency the coupon payments are denominated in
Correct answer: .
Reinvestment risk is the risk that cash flows received from a bond — its periodic coupons and, at maturity, its returned principal — will have to be reinvested at a lower rate than the one originally earned, if market rates have fallen in the meantime. This directly reduces the investor's total realized return compared to what a simple yield-to-maturity calculation assumed at purchase, since that calculation implicitly assumes coupons are reinvested at the original rate. This is the mirror image of price (interest-rate) risk: when rates fall, the bond's own market price actually rises, benefiting a holder who sells, while the coupons received along the way now earn less when reinvested — the two risks move in opposite directions from the same rate change. The option claiming the bond's price and its coupons decline together is incorrect because falling rates raise a fixed-coupon bond's price, not lower it. The option invoking credit risk wrongly assumes market-wide rate movements reflect one issuer's financial health. The option invoking currency risk introduces a mechanism, exchange rates, that has no necessary relationship to a change in domestic interest rates.
Source: CFA Institute, Understanding Fixed-Income Risk and Return (reinvestment risk)
Independent credit rating agencies assign ratings to bonds based on the issuer's perceived ability to meet its debt obligations. What is the fundamental distinction between an 'investment-grade' bond and a 'speculative-grade' (high-yield, or 'junk') bond, and why do speculative-grade bonds typically offer higher yields?
AInvestment-grade bonds are always shorter-term than speculative-grade bonds, and the higher yield on speculative-grade bonds simply compensates investors for tying up their money over a longer horizon
BThe distinction reflects the rating agencies' assessment of default risk: investment-grade issuers are judged to have a stronger capacity to meet their obligations, while speculative-grade issuers are judged to carry meaningfully higher default risk, and the higher yield compensates investors for bearing that additional risk
CCredit ratings measure only the size of a bond's coupon payment, so a 'speculative-grade' label simply means the bond happens to pay a larger coupon in dollar terms
DThe distinction is set entirely by whether the bond is traded on a public exchange or privately between institutions, unrelated to the issuer's financial condition
Correct answer: .
Credit rating agencies evaluate an issuer's financial strength and likelihood of meeting its debt obligations, then assign a rating that sorts bonds into investment-grade (judged to carry relatively low default risk) or speculative-grade, also called high-yield or junk (judged to carry meaningfully higher default risk). Because investors bear more risk of missed payments or default when holding speculative-grade debt, the market demands a higher yield on those bonds as compensation — this extra yield above a comparable, safer benchmark is effectively the price of accepting greater credit risk. The option tying the distinction to maturity length is incorrect; investment-grade and speculative-grade bonds exist across short, medium, and long maturities, and the rating itself says nothing about term length. The option claiming ratings measure coupon size confuses the rating, a judgment about repayment capacity, with the coupon, a contractual payment amount set at issuance that can be any size regardless of rating. The option tying the distinction to exchange listing versus private trading describes a completely different characteristic unrelated to credit quality.
Source: SEC, Investor.gov, 'Bonds' (credit ratings); CFA Institute, Fixed-Income: Credit Analysis
A corporate bond includes a call provision, giving the issuer the right to redeem it before maturity at a specified call price. Under what circumstance is the issuer most likely to exercise this call, and what risk does that create for the bondholder?
AThe issuer is most likely to call the bond after market interest rates have fallen well below the bond's coupon rate, since it can then refinance by issuing new debt at the lower rate; this leaves the bondholder holding cash that must now be reinvested at the new, lower prevailing rates
BThe issuer is most likely to call the bond after market interest rates have risen well above the bond's coupon rate, since the issuer benefits from locking bondholders into a below-market payment for as long as possible
CThe decision to call is unrelated to interest rates and instead depends solely on the issuer's stock price reaching a predetermined threshold
DCalling a bond exposes the bondholder to the same type of risk as a missed coupon payment, since both events represent the issuer failing to honor the original terms of the bond
Correct answer: .
A call provision gives the issuer, not the bondholder, the option to redeem the bond early, and issuers act in their own economic interest when deciding whether to exercise it. When market rates fall well below the bond's original coupon, the issuer can call the existing high-coupon debt and replace it by issuing new bonds at the now-lower rate, reducing its own borrowing cost. For the bondholder, this is unwelcome precisely when it happens: the bond is taken away at the moment its high fixed coupon is most valuable, and the resulting cash must be reinvested at the new, lower rates — a version of reinvestment risk specific to callable bonds, often called call risk. The option describing a call when rates rise has the incentive backwards; issuers have no financial reason to refinance into a higher rate. The option tying the call decision to the issuer's stock price ignores that call provisions are contractually tied to bond terms and rate conditions, not equity performance. The option equating a call with a missed payment confuses two very different events: a call is a contractually permitted early redemption at a specified price, while a missed payment is a default.
Source: CFA Institute, Fixed-Income: Introduction to Asset-Backed and Callable Bonds; SEC, Investor.gov, 'Callable or Redeemable Bonds'
Under a 'normal' yield curve, yields on longer-maturity bonds of the same credit quality are higher than yields on shorter-maturity bonds, compensating investors for tying up their money longer and for greater uncertainty further into the future. What does an 'inverted' yield curve describe, and why has it historically drawn close attention from economists and investors?
AAn inverted yield curve describes long-maturity yields rising even further above short-maturity yields than usual, representing an extreme version of the normal pattern rather than a genuinely different shape
BAn inverted yield curve is simply the same set of yields as a normal curve, plotted on a reversed axis for presentation purposes, with no actual difference in the ordering of the yields themselves
CAn inverted yield curve occurs only within municipal bond markets and has no equivalent concept in the market for government or corporate bonds
DAn inverted yield curve describes the less common situation where short-maturity yields exceed longer-maturity yields; historically, in the United States, an inverted Treasury yield curve has preceded most recessions by a lag of many months to roughly two years, which is why it has been treated as a closely watched, though imperfect, historical signal
Correct answer: .
An inverted yield curve reverses the usual ordering: short-maturity bonds yield more than longer-maturity bonds of the same credit quality, which is unusual because investors normally require extra compensation for locking up money longer. This shape has been studied extensively because, looking at historical U.S. Treasury data, an inverted curve has preceded most recessions over the past several decades, typically by a lag ranging from several months to around two years, making it one of the most closely tracked (though not perfectly reliable) leading indicators economists and investors monitor. The option describing an inverted curve as an extreme version of the normal pattern gets the shape backwards — inversion means the ordering of short versus long yields flips, not merely stretches. The option claiming it is just a plotting artifact ignores that the underlying yields themselves, not just their visual presentation, actually change relative order. The option restricting inversion to municipal bonds is incorrect; the concept and its historical significance apply most prominently to the government (Treasury) yield curve and can occur in corporate yield curves as well.
Source: Federal Reserve Bank of New York, research on the yield curve as a recession indicator; CFA Institute, Fixed-Income: The Term Structure of Interest Rates
In the United States, interest income from most municipal bonds (issued by state and local governments) receives distinct federal tax treatment compared to interest income from corporate bonds. What is that treatment, and why does it matter when comparing the stated yields of the two bond types?
AInterest from municipal bonds is fully taxable at the federal level in exactly the same way as corporate bond interest, so there is no meaningful tax difference to account for when comparing their yields
BInterest from municipal bonds is entirely exempt from both federal and every state's income tax for every investor, regardless of which state issued the bond or where the investor lives
CInterest from most municipal bonds is generally excluded from federal taxable income, which is why municipal bonds typically carry lower stated yields than comparably rated corporate bonds; investors calculate a 'tax-equivalent yield' to compare the two fairly, since a municipal bond's after-tax return can exceed a higher-stated corporate yield once the corporate bond's taxable interest is accounted for
DThe federal tax exemption applies to any capital gain earned from selling a municipal bond before maturity, but the periodic interest payments themselves remain fully taxable at the federal level
Correct answer: .
Interest paid on most municipal bonds is generally excluded from federal taxable income, a structural feature that lets municipal issuers offer lower stated coupon rates than a corporate issuer of comparable credit quality would need to offer, since investors are still earning a competitive after-tax return. To compare the two fairly, investors calculate a tax-equivalent yield for the municipal bond — grossing its yield up by the investor's marginal tax rate — which can show that a lower-stated municipal yield actually beats a higher-stated, fully taxable corporate yield once taxes are factored in. The option claiming municipal interest is fully taxable ignores this exclusion entirely. The option claiming a blanket exemption from every state's income tax overstates the exemption; the federal exclusion is the general rule, but state-level tax treatment varies, and an investor's own state typically only exempts bonds issued within that state. The option reversing which part is exempt is also wrong: the periodic interest is the piece that generally receives the federal exclusion, while capital gains from selling a municipal bond before maturity are generally still taxable.
Source: IRS, Publication 550, 'Investment Income and Expenses' (tax-exempt interest); SEC, Investor.gov, 'Municipal Bonds'
Duration provides a linear approximation of how much a bond's price will change for a given change in interest rates. For a large change in rates, this linear approximation becomes increasingly inaccurate, because the true relationship between bond prices and yields is curved rather than a straight line. What does 'convexity' measure in this context, and what does it imply about duration-only price estimates?
AConvexity measures the trend in an issuer's credit rating over time, and it implies that duration-only estimates ignore the issuer's changing ability to repay its debt
BConvexity measures the curvature of the price-yield relationship — essentially, the rate at which duration itself changes as yields change — and because that curve bows in a way that favors the bondholder for most conventional bonds, duration-only estimates tend to understate the actual price increase when yields fall and overstate the actual price decline when yields rise; a convexity adjustment corrects for this
CConvexity is simply another name for duration, describing the exact same sensitivity measure using a different unit of measurement
DConvexity only has meaning for zero-coupon bonds and is entirely irrelevant to bonds that pay regular coupons
Correct answer: .
Duration approximates the price-yield relationship with a straight line drawn tangent to the bond's actual, curved price-yield curve; that approximation is reasonably accurate for small rate changes but drifts increasingly off-target as the rate change grows larger. Convexity measures the curvature of that true relationship — how much duration itself shifts as yields move — and because the price-yield curve for most conventional, non-callable bonds bows in a favorable direction, duration alone tends to understate how much the price actually rises when yields fall, and overstate how much the price actually falls when yields rise. Adding a convexity term to the duration-based estimate corrects both of these directional errors and produces a more accurate price estimate for large rate moves. The option tying convexity to credit rating trends confuses it with a completely different risk dimension. The option equating convexity with duration ignores that convexity specifically captures the second-order curvature that duration, a first-order measure, does not. The option restricting convexity to zero-coupon bonds is incorrect; convexity is a property of the price-yield curve for coupon-paying bonds as well, and in fact plain-vanilla zero-coupon bonds are often used as an example of especially high convexity, not an exception to it.
Source: CFA Institute, Understanding Fixed-Income Risk and Return (convexity)
A corporate bond and a government (Treasury) bond of the same maturity are compared, and the corporate bond offers a higher yield. What does this yield difference (the 'credit spread') primarily compensate the investor for, and why is the Treasury yield typically treated as the risk-free benchmark in this comparison?
AThe credit spread primarily compensates the investor for taking on the corporate issuer's default (credit) risk; the domestic government bond is treated as the benchmark because it carries negligible default risk domestically, backed by the government's taxing and currency-issuing power, so a wider spread signals the market is demanding more compensation for additional default risk
BThe credit spread exists purely to compensate for currency risk, since the two bonds are assumed to be denominated in different currencies whenever a spread is observed
CThe credit spread reflects only a difference in how frequently each bond pays coupons, since more frequent coupon payments mechanically require a lower stated yield
DThe credit spread exists because corporate bonds always have shorter maturities than government bonds of comparable structure, so the spread is simply a maturity premium rather than a credit-related premium
Correct answer: .
The credit spread is the extra yield a corporate bond must offer over a government bond of the same maturity to compensate investors for bearing the corporate issuer's default risk — the possibility that it fails to make its promised payments. A domestic government bond is treated as the risk-free benchmark for this comparison because it is backed by the government's power to tax and, for its own currency, to issue more of that currency, making its domestic default risk negligible in practice; the corporate bond carries no such backing, so the market prices in a premium proportional to the perceived likelihood and severity of default. A widening spread signals the market demands more compensation for that credit risk, while a narrowing spread signals more confidence in the issuer. The option attributing the spread to currency risk assumes a mismatch in currency denomination that isn't part of this comparison — both bonds are assumed to be in the same currency. The option tying the spread to coupon frequency confuses a payment-timing detail with a fundamental risk premium. The option tying the spread to maturity length is incorrect because credit spreads are compared at the same maturity precisely to isolate the credit-risk difference from any maturity-related effect.
Source: CFA Institute, Fixed-Income: Credit Analysis (credit spreads); Federal Reserve, 'Treasury Yield Curve' data description
A fixed-income analyst calculates a bond's Macaulay duration as 7.2 years, with a yield to maturity of 6% compounded semiannually. Which statement correctly describes how modified duration relates to this Macaulay duration figure, and what modified duration is actually used for?
AModified duration equals Macaulay duration divided by one plus the yield per compounding period (here, one plus half of the 6% annual yield), and it approximates the percentage change in the bond's price for a given change in yield — a different measure from Macaulay duration, which instead measures the weighted-average time, in years, until the bondholder receives the bond's cash flows
BMacaulay duration and modified duration are identical in both formula and meaning; the two names simply reflect which textbook or curriculum introduced the term first, with no real difference between them
CModified duration is calculated by multiplying Macaulay duration by the annual yield to maturity, and like Macaulay duration it measures the weighted-average time until the bond's principal is fully repaid
DModified duration can only be applied to zero-coupon bonds, since coupon-paying bonds require effective duration instead to estimate how their price responds to a change in yield
Correct answer: .
Macaulay duration is a time-based measure: it is the weighted-average time, in years, until a bondholder receives the bond's cash flows, where each cash flow's time is weighted by the present value of that cash flow as a share of the total bond price. Modified duration converts this time measure into a price-sensitivity measure by dividing Macaulay duration by one plus the yield per compounding period — here, one plus half of the 6% annual yield, since the bond compounds semiannually. The resulting figure approximates the percentage change in the bond's price for a 1% (100 basis point) change in yield, which is the figure analysts actually use to estimate price risk. The option claiming the two measures are identical ignores that they answer different questions — one measures time, the other measures price sensitivity — and that modified duration is mathematically derived from, and numerically smaller than, Macaulay duration for any bond with a positive yield. The option describing multiplication by the yield, rather than division by one plus the per-period yield, inverts the actual formula and also mischaracterizes modified duration as a time measure when it is a sensitivity measure. The option restricting modified duration to zero-coupon bonds has the exam point backwards: modified duration works for any option-free bond with fixed cash flows, coupon-paying or not; it is bonds with embedded options (callable, putable, mortgage-backed, convertible) that require effective duration instead, because their cash flows can change as yields move.
Source: CFA Institute, Fixed Income: Understanding Fixed-Income Risk and Return (Macaulay duration and modified duration)
A Treasury Inflation-Protected Security (TIPS) has a fixed coupon rate set at auction. Over the life of the bond, how does TIPS protect an investor's purchasing power against inflation, and what happens to its cash flows as the Consumer Price Index for Urban Consumers (CPI-U) rises?
AThe coupon rate itself rises automatically whenever CPI-U rises, while the bond's principal stays fixed at its original face value for the entire life of the bond
BTIPS pay no periodic coupon at all; all inflation protection comes from a single lump-sum adjustment paid out only when the bond matures
CTIPS protection works by letting the investor redeem the bond early, without penalty, any time cumulative inflation since issuance exceeds the bond's fixed coupon rate
DThe bond's principal is adjusted upward as CPI-U rises (and downward if CPI-U falls), and because each coupon payment is the fixed coupon rate applied to the current, inflation-adjusted principal, both the principal and the dollar coupon amount rise with inflation; at maturity the investor receives the greater of the inflation-adjusted principal or the original face value
Correct answer: .
TIPS protect purchasing power by adjusting the bond's principal itself, rather than its coupon rate, to inflation: the Treasury computes an index ratio by dividing the current CPI-U level by the CPI-U level that applied when the security was issued, and applies that ratio to the original face value to produce the current, inflation-adjusted principal. The coupon rate stays fixed at whatever level was set at auction, but because that fixed rate is applied to a principal that grows with inflation, the actual dollar coupon payment rises along with the principal. At maturity, the investor is protected on the downside too: they receive the greater of the inflation-adjusted principal or the original face value, so deflation cannot reduce the final payout below par. The option claiming the coupon rate itself rises has the mechanism backwards — the rate is fixed and the principal is what moves. The option claiming TIPS pay no periodic coupon ignores that TIPS pay interest on a regular schedule, just calculated on a principal that changes over time, not as a single payment at maturity. The option describing a penalty-free early redemption right invents a feature TIPS do not have; inflation protection works entirely through the principal-indexing mechanism described above, with no early-redemption trigger tied to cumulative inflation.
Two competing theories attempt to explain why Treasury yield curves are typically upward-sloping. Under the pure expectations theory, a long-term bond's yield reflects only the market's expectations of future short-term rates, with no inherent bias toward any particular slope. How does the liquidity preference (liquidity premium) theory modify this explanation, and what does that imply about reading an upward-sloping curve purely as a rate forecast?
ALiquidity preference theory argues that investors prefer longer maturities because they are easier to trade and more liquid than short-term instruments, which pushes long-term yields below short-term yields
BLiquidity preference theory replaces expectations entirely, arguing that expected future short-term rates play no role whatsoever in determining any point on the yield curve
CLiquidity preference theory adds that investors require a premium, increasing with maturity, to compensate for the greater interest rate risk of holding longer-term bonds; because this premium layers on top of rate expectations, an upward-sloping curve can appear even when the market expects future short-term rates to stay flat or decline modestly, so the slope alone cannot be read as a pure forecast of rising rates
DLiquidity preference theory applies only to corporate bonds and has no bearing on the shape of the US Treasury yield curve, which pure expectations theory alone fully explains
Correct answer: .
The pure expectations theory holds that a long-term yield is simply a reflection of expected future short-term rates, with no systematic tilt toward an upward or downward slope — an upward-sloping curve under this theory means the market expects short-term rates to rise, period. Liquidity preference theory builds on top of this by adding that investors demand a premium for tying up money for longer, since longer-maturity bonds carry greater interest rate risk; this premium generally increases with maturity. Because the observed yield curve therefore reflects both expected future rates and this added premium, an upward slope no longer has to mean the market expects rates to rise — it can appear even when short-term rates are expected to stay flat or decline modestly, as long as the liquidity premium is large enough to push long-term yields above short-term ones anyway. This is exactly why the slope alone cannot be read as a pure, unbiased forecast once a liquidity premium is layered in. The option about investors preferring longer maturities for liquidity gets the actual claim backwards: liquidity preference theory says investors need to be paid extra to accept the lower liquidity and higher rate risk of long-term bonds, which pushes long-term yields up, not down. The option claiming expectations play no role at all ignores that liquidity preference theory is explicitly an addition to, not a replacement for, the expectations component. The option restricting the theory to corporate bonds is incorrect; it is a general theory of the term structure that applies to Treasury yields just as much as to corporate debt.
Source: CFA Institute, Fixed Income: The Term Structure and Interest Rate Dynamics (pure expectations theory and liquidity preference theory)
A floating-rate note (FRN) pays a coupon equal to a reference rate (such as SOFR) plus a fixed spread, reset quarterly. A fixed-rate bond of the same five-year maturity, issued on the same day, pays a constant coupon set at issuance. If market interest rates rise sharply the day after both bonds are issued, how would you expect their prices to react differently, and why?
AThe floating-rate note's price would stay close to par, because its coupon resets to the new, higher reference rate at the next quarterly reset date, keeping it competitive with newly issued debt; the fixed-rate bond's price would fall, because its coupon is locked in and becomes less attractive relative to newly issued bonds now offering higher coupons
BBoth bonds' prices would fall by roughly the same amount, since interest rate risk depends only on time to maturity, and both bonds share the same five-year maturity regardless of how their coupons are structured
CThe floating-rate note's price would fall further than the fixed-rate bond's, because resetting the coupon introduces uncertainty that the market penalizes more heavily than a bond with a known, fixed coupon
DBoth bonds' prices would rise, since rising market interest rates always increase the present value of a bond's future cash flows regardless of whether its coupon is fixed or floating
Correct answer: .
A floating-rate note's price stays close to par through rate moves because its coupon is not locked in: at each reset date, here quarterly, the coupon recalculates to the then-current reference rate plus the fixed spread, so the note's effective duration is approximately the time remaining until its next reset — a few months at most — rather than its full five-year maturity. A tiny duration means a tiny price reaction to a change in rates. The fixed-rate bond, by contrast, locked in its coupon at issuance and keeps paying that same coupon regardless of where rates move, so its duration is close to its full maturity; when market rates rise, newly issued bonds offer higher coupons, making the existing fixed coupon relatively less attractive and pushing its price down to compensate. The option claiming both bonds fall by the same amount ignores that interest rate risk (duration) depends on how and when the coupon resets, not purely on stated maturity — this is precisely why the floating-rate note and the fixed-rate bond, despite sharing a five-year maturity, have very different durations. The option claiming the floating-rate note falls further has the comparison backwards; resetting the coupon to match the market is what protects its price, not what penalizes it. The option claiming both bonds' prices would rise contradicts the basic inverse relationship between bond prices and yields, which still applies to the small remaining duration on the floating-rate note and fully applies to the fixed-rate bond.
Source: WisdomTree, "An Introduction to U.S. Floating Rate Treasury Notes"; CFA Institute, Fixed Income: Fixed-Income Instrument Features
A corporate bond with a semiannual coupon last paid interest two months ago, with its next coupon due in four months. A buyer and seller agree on a quoted (clean) price of 98.00. What additional amount does the buyer actually pay at settlement beyond this quoted price, and what is that total settlement amount called?
AThe buyer pays exactly 98.00 with nothing added, because the clean price already includes any interest the seller is owed for the two months since the last coupon
BThe buyer pays 98.00 minus a deduction representing the seller's forfeited claim to the two months of interest already earned, since that interest now belongs entirely to the buyer as the bond's new owner
CThe buyer pays 98.00 plus the full amount of the next coupon payment due in four months, since the seller must be compensated upfront for the entire remaining coupon period
DThe buyer pays 98.00 plus accrued interest — the portion of the upcoming coupon the seller has earned for the two months already elapsed since the last payment — and this total amount actually exchanged at settlement is called the dirty (or full) price; the quoted 98.00 is the clean price, which excludes this accrued interest
Correct answer: .
Between coupon dates, a bond continuously accrues interest that has been earned by whoever holds it but has not yet been paid out, since coupons are only disbursed on their scheduled dates. Here, the seller held the bond for the two months since the last coupon, so the seller has earned, but not yet received, two months' worth of that semiannual coupon. To compensate the seller for this earned-but-unpaid interest, the buyer pays the quoted clean price of 98.00 plus this accrued interest; the resulting total is called the dirty price (also called the full or invoice price), which is the amount that actually changes hands at settlement, while the clean price of 98.00 is simply the quoted figure that excludes accrued interest and is typically what's displayed in US bond quotes. The option claiming nothing is added gets the clean/dirty distinction backwards — the clean price is defined as excluding accrued interest, not including it. The option describing a deduction has the direction of the adjustment backwards: the seller is compensated with an addition for interest already earned, not penalized with a subtraction. The option describing payment of the entire next coupon upfront overstates the adjustment enormously; the buyer only owes the seller the two months of interest already accrued, not the full six-month coupon, since the buyer will be the one to collect that full coupon directly from the issuer in four months and is only owed compensation for the two months they did not hold the bond.
Source: CFA Institute, Fixed Income: Introduction to Fixed-Income Valuation (accrued interest, flat/clean price vs full/dirty price)
A corporate bond's indenture includes a sinking fund provision, requiring the issuer to retire a portion of the bond issue's principal at scheduled intervals before the final maturity date, often by purchasing and retiring bonds in the open market or through a lottery call to a randomly selected group of bondholders. From the perspective of a bondholder, what is the primary effect of this provision?
AIt guarantees that every bondholder's bonds will be redeemed on the same date, eliminating any uncertainty about which bonds are retired early
BIt increases the bond's exposure to credit risk, since the issuer sets aside cash that could otherwise be used to pay bondholders in default
CIt reduces the risk that the issuer will be unable to repay the full principal at the final maturity date, because a portion of the debt is steadily retired beforehand -- in exchange, investors typically accept a somewhat lower yield than on an otherwise comparable bond without this feature
DIt transfers responsibility for the bond's interest payments from the issuer to an independent sinking fund trustee for the remainder of the bond's life
Correct answer: .
A sinking fund provision requires the issuer to retire part of the outstanding bonds on a scheduled basis before final maturity, typically by buying bonds in the open market or calling a randomly selected portion from bondholders at a set price. Because a share of the principal is paid down gradually rather than all being due in one lump sum at maturity, the issuer's repayment burden at the final maturity date is smaller and more manageable, which reduces the risk that it cannot repay bondholders in full -- investors accept a somewhat lower yield in exchange for this added safety. The option describing a guaranteed single redemption date for every bondholder is wrong because many sinking fund structures use a lottery selecting only some bonds for early retirement at each interval, leaving other holders uncertain whether their specific bonds will be called next; this creates its own reinvestment risk rather than eliminating uncertainty. The option linking the provision to increased credit risk reverses the actual effect: setting cash aside to retire debt early is a protective measure for bondholders, not a diversion of funds that would otherwise go to them. The option describing a transfer of interest-payment responsibility to a trustee confuses the trustee's administrative role in managing the fund and executing redemptions with the issuer's own continuing legal obligation to pay interest, which does not change.
Source: CFA Institute, Fixed Income: Fixed-Income Securities -- Defining Elements (sinking fund provisions)
A putable bond gives its holder the right, but not the obligation, to sell the bond back to the issuer at a predetermined price on specified dates before maturity. Compared to an otherwise identical plain-vanilla bond with no such feature, how does the putable feature affect the bond from the investor's perspective, and under what market condition is the investor most likely to exercise it?
AThe put option protects the investor against a decline in the bond's market price, most valuable when market interest rates have risen well above the bond's coupon rate -- in exchange for this protection, the bond typically carries a lower yield (or higher price) than the equivalent plain bond
BThe put option protects the issuer against having to refinance at a higher rate, most valuable to the issuer when market interest rates fall well below the bond's coupon rate
CThe put option has no effect on the bond's price relative to a plain-vanilla bond, since it is the opposite of a call option and the two features exactly cancel out whenever both are present
DThe put option obligates the investor to purchase additional bonds from the issuer at the original issue price whenever interest rates rise, in order to maintain the issuer's funding level
Correct answer: .
A putable bond is the mirror image of a callable bond: here the right to force early redemption belongs to the bondholder rather than the issuer. If market interest rates rise well above the bond's coupon rate after issuance, the bond's market price falls below par, since newly issued bonds now offer more attractive income; a bondholder holding the put option can instead force the issuer to redeem the bond at the predetermined put price, typically par, protecting against that price decline. Because this feature benefits the investor rather than the issuer, investors pay for it by accepting a lower yield (equivalently, a higher price) than they would demand on an identical bond without the put. The option describing protection for the issuer against refinancing at a higher rate describes the logic of a call provision, which benefits the issuer when rates fall, not a put provision exercised by the investor when rates rise -- these are opposite features with opposite beneficiaries. The option claiming the put has no net price effect is wrong because options have value on their own regardless of whether a bond also happens to carry an unrelated call feature; a put option embedded alone still raises the bond's value versus an option-free bond, it does not need a call option present to cancel out. The option describing an obligation for the investor to buy more bonds misstates what a put option is entirely; it is a right for the investor to sell the bond already held back to the issuer, not an obligation to purchase anything further.
Source: CFA Institute, Fixed Income: Introduction to Bonds with Embedded Options (putable and callable bonds)
A residential mortgage-backed security (MBS) pools together thousands of individual home mortgages and passes the mortgage payments through to investors. Homeowners in the underlying pool have the right to repay their mortgages early, in full or in part, at any time -- most commonly by refinancing when mortgage rates fall. How does this prepayment feature affect an MBS investor, and how does that risk differ from a bond's ordinary credit (default) risk?
APrepayment risk is identical to default risk, since in both cases the investor ultimately receives less total cash than originally promised by the mortgage pool
BPrepayment risk only matters when interest rates rise, since rising rates are what cause homeowners to refinance their mortgages into new loans
CPrepayment risk is eliminated entirely once a mortgage pool is securitized into an MBS, because the securitization process transfers all mortgage-related risk to the loan originator
DPrepayment risk is a timing risk, not a repayment risk: investors generally still receive their principal back, but a wave of refinancing when rates fall returns principal earlier than expected, forcing investors to reinvest it at the new, lower prevailing rates -- a different problem from a borrower failing to repay at all
Correct answer: .
Prepayment risk arises because the homeowners whose mortgages back the security can repay principal ahead of schedule, most commonly by refinancing into a new mortgage once rates fall enough to make that worthwhile. For the MBS investor, this means principal that was expected to arrive later, continuing to earn the original, now-attractive coupon, instead arrives early and must be reinvested at the new, lower market rates -- the money itself is not lost, only its timing and its future earning power change. This is fundamentally different from credit (default) risk, where the concern is whether the borrower repays at all; prepayment risk assumes repayment happens, just earlier than planned, which is precisely why it is often described as a form of reinvestment risk rather than a form of credit risk. The option equating prepayment risk with default risk collapses this exact distinction, when the whole point of the terminology is to separate repaid-early from not-repaid. The option limiting prepayment risk to rising-rate environments has the direction backwards: homeowners refinance, and prepayments accelerate, when rates fall, not when they rise -- rising rates actually tend to slow prepayments (a related risk called extension risk), the opposite problem. The option claiming securitization eliminates prepayment risk is wrong because pooling individual mortgages into a security does not change any underlying borrower's contractual right to prepay; it merely passes that same risk through to whoever holds the security, which is exactly why MBS investors must account for it.
Source: SEC Investor.gov, 'Mortgage-Backed Securities and Collateralized Mortgage Obligations'
A company issues two types of bonds on the same day: senior bonds and subordinated bonds. Both bonds have the same maturity date, but they rank differently in the event the company becomes insolvent. What does 'subordinated' mean in this context, and why do subordinated bonds typically offer a higher yield than the same issuer's senior bonds?
ASubordinated bonds are repaid before senior bonds in bankruptcy, which is why they typically pay a lower yield to compensate senior bondholders for taking on less protection
BSubordinated bondholders are paid only after senior bondholders have been repaid in full, so they bear a higher risk of loss if the company's assets are insufficient to cover all its debts -- the higher yield compensates investors for taking on that additional risk
CSubordinated bonds are backed by a specific pledged asset, while senior bonds are entirely unsecured, which is why subordinated bondholders demand a higher yield for giving up that asset-backed protection
DThere is no practical difference in repayment priority between senior and subordinated bonds from the same issuer; the term 'subordinated' refers only to the order in which the bonds were originally issued, not to their claim priority in bankruptcy
Correct answer: .
When an issuer's debt is split into senior and subordinated tranches, the ranking determines the order in which bondholders are paid out of the issuer's remaining assets if it becomes insolvent. Senior bondholders are repaid first, and only after their claims are satisfied in full do subordinated bondholders receive anything from what remains; if the issuer's assets fall short, subordinated holders absorb losses before senior holders do. Because this lower claim priority means a higher probability of partial or total loss in a default scenario, investors demand a higher yield on subordinated bonds to compensate for that added risk, all else equal. The option reversing the payment order is simply backwards: subordinated means paid later, not earlier, which is the entire reason the yield premium exists in the first place. The option describing subordination as a matter of collateral confuses an unrelated feature (secured versus unsecured debt, which depends on whether specific assets are pledged) with seniority (which depends on contractual claim priority); a bond can be both unsecured and senior, or secured and still outrank some other unsecured tranche, depending on the issuer's specific debt structure. The option claiming seniority is just about issuance order is incorrect; seniority and subordination are terms defined by the bond's own legal indenture establishing claim priority, not by which bond happened to be sold to investors first or second.
Source: CFA Institute, Fixed Income: Introduction to Fixed-Income Issuance (seniority ranking in bankruptcy)
A bond investor is comparing three portfolio construction strategies, all built to have the same overall portfolio duration: a 'bullet' strategy concentrates holdings around a single target maturity; a 'barbell' strategy holds only short-maturity and long-maturity bonds, with nothing in between; and a 'laddered' strategy spreads holdings evenly across many maturities from short to long. Even though all three can be built to share the same portfolio duration, which strategy is generally understood to have the highest convexity, and why does that distinction matter to the investor?
AThe barbell strategy generally has the highest convexity among the three, because convexity rises with the dispersion of a portfolio's cash flows around its average maturity, and the barbell's two extreme maturities are the most dispersed -- higher convexity means the portfolio benefits more from a large rate move in either direction than a same-duration bullet or ladder would
BThe bullet strategy generally has the highest convexity, because concentrating every bond around a single maturity date eliminates the reinvestment-rate uncertainty that otherwise reduces a portfolio's convexity
CThe laddered strategy generally has the highest convexity, because spreading maturities evenly guarantees the smallest possible duration for any given level of yield, and duration and convexity always move in the same direction
DAll three strategies always have identical convexity whenever their durations are matched, because duration alone fully determines a bond portfolio's price sensitivity to any size of interest rate change
Correct answer: .
Convexity measures how much a bond portfolio's price-yield relationship curves away from the straight-line approximation that duration provides, and that curvature tends to increase with the dispersion of a portfolio's cash flows around its average (duration-weighted) maturity. A barbell's two clusters of bonds sit at the extremes, far from the portfolio's average maturity, producing more dispersion -- and therefore more convexity -- than a bullet, whose cash flows are concentrated tightly around one point with very little dispersion, or a ladder, whose cash flows sit between those two extremes. Higher convexity benefits an investor on large interest-rate moves in either direction, since the portfolio gains more when rates fall and loses less when rates rise than a lower-convexity, same-duration alternative would, which is why an investor who expects rates to become more volatile might favor a barbell. The option crediting the bullet with the highest convexity is backwards: concentrating cash flows around a single date is exactly the structure that produces the least dispersion and the least convexity, not the most. The option attributing high convexity to the ladder's 'smallest possible duration' both misdescribes the ladder (a ladder's duration depends entirely on its chosen maturity range, not some automatic minimum) and wrongly asserts that duration and convexity always move together, when the whole point of this comparison is that portfolios can share an identical duration while differing meaningfully in convexity. The option claiming all three must have identical convexity whenever duration is matched ignores convexity entirely as a separate, second-order measure of price sensitivity -- if duration alone fully captured price sensitivity, convexity would have no reason to exist as a distinct concept.
Source: CFA Institute, Fixed Income: Yield-Based Bond Convexity and Portfolio Construction (bullet, barbell, and laddered portfolios)
A callable corporate bond was issued with a 7% coupon and is first callable in three years at a price of 102. Market interest rates have since fallen well below 7%, and the bond now trades at a premium price of 108, above its call price. An investor evaluating this bond calculates both its yield to maturity (YTM, assuming it is held to its final maturity date) and its yield to call (YTC, assuming it is redeemed at the first call date). Which of the following correctly describes the relationship between these two figures and why?
AYTC will be higher than YTM, because the call price of 102 is itself higher than the bond's original face value of 100, which mechanically raises any yield calculation that assumes redemption at that price
BYTM and YTC must always be mathematically identical for any bond, since both are simply the bond's current coupon rate expressed as a yield
CYTC will be lower than YTM in this case, because the bond trades at a premium above its call price, which signals that the issuer is likely to call the bond early -- once called, the investor loses the remaining years of above-market coupon payments that the YTM calculation otherwise assumes they would keep collecting
DYTC cannot be calculated at all unless the issuer has already announced its intention to call the bond, since yield to call requires certainty about the exact redemption date
Correct answer: .
When a callable bond trades at a premium above its call price, as this one does at 108 against a 102 call price, that premium itself signals that the market expects the issuer to call the bond, because market rates have fallen well below the bond's 7% coupon and refinancing at the lower rate benefits the issuer. Yield to call measures the bond's return assuming redemption at the first call date and call price, while yield to maturity assumes the investor keeps collecting the full 7% coupon all the way to the final maturity date; since the call cuts that above-market coupon stream short and returns principal earlier at a price below the bond's current trading price, YTC comes out lower than YTM in this premium-trading scenario, making YTC the more realistic estimate of what the investor can actually expect to earn. The option claiming YTC is higher because the call price exceeds face value confuses the call price's relationship to par with its relationship to the bond's current trading price; what matters here is that the bond's market price exceeds the call price, not that the call price exceeds 100. The option claiming the two yields are always identical ignores that they are built on entirely different assumed cash flow streams and holding periods; they coincide only in the special case where the bond is priced exactly at the call price with no premium or discount. The option claiming YTC cannot be calculated without a confirmed call announcement misunderstands the measure: yield to call is a hypothetical, assumption-based calculation used precisely because the investor does not yet know whether the issuer will call, not a figure that requires the call to already be confirmed.
Source: CFA Institute, Fixed Income: Yield Measures for Fixed-Rate Bonds (yield to call vs. yield to maturity for premium callable bonds)
A step-up bond is structured so that its coupon rate increases according to a predetermined schedule fixed at issuance -- for example, starting at 3% for the first two years, then rising to 4% for the next two years, and so on until maturity. Compared to a plain fixed-rate bond issued at the same time with the same maturity, what is a true statement about a step-up bond?
AA step-up bond's coupon increases are triggered automatically whenever market interest rates rise, making it functionally identical to a floating-rate note tied to a market reference rate
BA step-up bond typically starts with a lower coupon than a comparable plain fixed-rate bond, since part of the investor's compensation is deferred into the later, higher scheduled coupons -- and if the step-up bond is also callable, issuers often call it before the higher coupons take effect, which can leave investors with more call risk than an otherwise comparable plain callable bond
CA step-up bond's coupon schedule can be changed by the issuer at any time after issuance, provided the issuer gives bondholders at least 30 days' written notice of the change
DA step-up bond always has a lower duration than a plain fixed-rate bond of the same maturity, because its final coupon is the largest cash flow in both bonds' cash flow streams
Correct answer: .
A step-up bond's entire coupon schedule, including every future increase and its timing, is fixed at the time of issuance and does not depend on how market rates actually move afterward. Because investors know in advance that later coupons will be higher, issuers can typically offer a lower coupon in the bond's early years than they would need to offer on a plain fixed-rate bond paying the same rate every year, with the promise of catching up later. A practical wrinkle is that many step-up bonds are also callable, and issuers of callable step-ups often call the bond right before a scheduled increase takes effect, since paying the higher coupon has become unattractive to them even without any change in market interest rates -- this gives investors in callable step-ups more call risk than they would face on an otherwise similar plain callable bond, whose coupon is constant throughout. The option describing automatic triggers tied to market rates confuses a step-up bond with a floating-rate note; a step-up's schedule is fixed and predetermined, not responsive to actual market rate movements the way a floater's periodic reset is. The option allowing the issuer to change the schedule after issuance with notice is incorrect; the schedule is a contractual term fixed at issuance and is not something the issuer can unilaterally revise later. The option claiming step-ups always have lower duration misstates how duration works; duration depends on the full timing and size of all cash flows relative to the bond's price, and a step-up's exact duration relative to a plain bond of the same maturity depends on the specific schedule, not a fixed rule that it is always lower.
Source: CFA Institute, Fixed Income: Fixed-Income Securities -- Defining Elements (step-up coupon structures)
An investor holds a conventional (non-inflation-linked) bond with a nominal yield to maturity of 6%. Economists estimate that expected inflation over the bond's remaining life is approximately 4%. Using the approximate Fisher relationship, which statement correctly describes the investor's expected real (inflation-adjusted) return, and what happens to that real return if actual inflation turns out higher than the 4% that was expected?
AThe investor's real return is also approximately 6%, since the nominal yield already reflects the bond's full return regardless of what happens to prices in the broader economy
BThe investor's real return is approximately 10%, since expected inflation must be added on top of the nominal yield to find the bond's true purchasing-power return
CThe investor's real return is approximately 4%, since the nominal yield is simply the inflation rate plus a small fixed spread set by the issuer at auction
DThe investor's real return is approximately 2% (roughly the 6% nominal yield minus the 4% expected inflation), and if actual inflation turns out higher than expected, the investor's realized real return falls below that 2% estimate, since the bond's fixed nominal coupon and principal do not adjust upward to compensate for the inflation surprise
Correct answer: .
The approximate Fisher relationship states that a bond's nominal yield is roughly equal to the real (inflation-adjusted) yield plus the expected rate of inflation over the bond's life, so the real yield can be approximated by subtracting expected inflation from the nominal yield: 6% nominal minus 4% expected inflation leaves an expected real return of roughly 2%. Because this bond is a conventional, fixed-coupon instrument rather than an inflation-linked security, its coupon and principal are set in nominal dollar terms and do not adjust if inflation comes in higher than the 4% that was priced in at purchase; if realized inflation exceeds that expectation, the same fixed nominal cash flows buy less in real terms, so the investor's actual real return ends up below the roughly 2% that was originally expected. The option claiming the real return equals the full nominal yield ignores inflation's erosion of purchasing power entirely, treating a nominal figure as if it were already inflation-adjusted. The option adding inflation on top of the nominal yield to reach 10% inverts the relationship; the Fisher relationship subtracts expected inflation from the nominal yield to isolate the real component, it does not add the two together. The option describing the nominal yield as inflation plus a small fixed issuer spread incorrectly equates the real return itself with the inflation rate, when the real return is specifically what remains after inflation is removed from the nominal yield, not the inflation rate itself.
Source: CFA Institute, Economics: Real and Nominal Interest Rates (the Fisher effect)
About Bonds & Fixed Income
A bond is a loan: the issuer promises to pay the holder periodic coupon interest and return the bond's face (par) value at maturity. Because a bond's coupon is usually fixed at issuance, its market price moves inversely to prevailing interest rates — when rates rise, existing bonds paying the old, lower coupon become less attractive and their price falls until their yield to maturity (the total return an investor earns holding the bond to maturity at its current price) lines up with the new market rate, and vice versa when rates fall.
Duration measures how sensitive a bond's price is to a change in interest rates — roughly, the percentage price change for a 1-percentage-point rate move — and, all else equal, rises with a bond's maturity and falls as its coupon rate rises. Duration itself is a linear approximation, understating the price gain when rates fall and overstating the price loss when rates rise; convexity is the second-order correction for that curvature, and matters most for large rate moves. The duration and convexity guide walks through a full price-change estimate using both measures together.
Plotting yield against maturity across bonds of similar credit quality produces the yield curve. A normal curve slopes upward, since lending for longer usually demands a higher yield; when short-term yields rise above long-term ones, the curve inverts — a pattern that has preceded most US recessions historically, though the lead time between inversion and recession has varied widely.