CFA Program — Fixed Income

Correct answer: B) The internal rate of return an investor earns if the bond is held to maturity and all coupons are reinvested at the YTM

Yield to maturity is the internal rate of return on a bond's cash flows, assuming the bond is held until maturity and all coupon payments are reinvested at that same rate.

Correct answer: B) Fall below $1,000

Bond prices and market interest rates move inversely. If the market rate rises above the bond's fixed coupon rate, the bond becomes relatively less attractive, causing its price to fall below par ($1,000) so that its yield aligns with the higher market rate.

Correct answer: C) A bond with a lower credit rating (higher default risk)

Bonds with lower credit ratings carry higher default risk, and investors require a higher yield (credit spread) to compensate for that additional risk, all else equal.

Correct answer: B) The bond's approximate sensitivity of price to changes in interest rates

Duration measures the approximate percentage change in a bond's price for a given change in interest rates, serving as a measure of interest rate risk; it is related to but distinct from simple time to maturity.

Correct answer: B) Pays no periodic coupons and is issued at a discount to face value, with the return coming from price appreciation to par

A zero-coupon bond pays no periodic interest; instead, it is sold at a discount to face value, and the investor's return comes from the bond's price appreciating to par value at maturity.

Correct answer: B) A bond that gives the issuer the right to redeem the bond before maturity, typically when interest rates decline

A callable bond gives the issuer the option to redeem the bond before maturity, which issuers often exercise when interest rates fall and they can refinance at a lower rate; this feature is a disadvantage to bondholders and results in the bond typically offering a higher yield than an otherwise similar non-callable bond.

Correct answer: A) A negative (restrictive) covenant.

Negative covenants restrict the issuer from taking certain actions, such as exceeding a specified leverage ratio or issuing additional debt, to protect bondholders, as opposed to positive covenants, which require the issuer to take certain actions (like maintaining insurance or providing financial statements).

Correct answer: B) Excluding accrued interest since the last coupon payment date, which is included in the dirty price.

The clean price excludes accrued interest since the last coupon payment, while the dirty (full) price includes this accrued interest, representing the actual amount a buyer would pay to purchase the bond between coupon dates.

Correct answer: A) Coupon rate is higher than its current market yield to maturity.

A bond trades at a premium (above face value) when its coupon rate exceeds the prevailing market yield to maturity, since investors are willing to pay more for the above-market coupon payments; the reverse relationship holds for bonds trading at a discount.

Correct answer: D) A requirement that the issuer periodically retire a portion of the bond issue before final maturity, reducing the amount outstanding at maturity.

A sinking fund provision requires the issuer to retire a specified portion of the bond issue periodically before the final maturity date, reducing credit risk for remaining bondholders by shrinking the outstanding balance over time.

Correct answer: C) -6.0%

Approximate percentage price change = -Duration x change in yield = -6.0 x 0.0100 = -6.0%, reflecting the inverse relationship between bond prices and yields.

Correct answer: B) A zero-coupon bond with a long maturity.

Longer-maturity, lower-coupon (especially zero-coupon) bonds generally have the highest duration and therefore the greatest interest rate sensitivity, since more of their value depends on cash flows received far in the future, which are more heavily discounted by yield changes.

Correct answer: C) 5.15%

Current yield = Annual coupon / Current price = 50/970 = 5.15%.

Correct answer: A) Lower pre-tax yields than otherwise comparable taxable bonds, since investors are willing to accept a lower stated yield in exchange for the tax exemption.

Because interest income from many municipal bonds is tax-exempt, investors are typically willing to accept a lower stated (pre-tax) yield than they would demand from an otherwise comparable taxable bond, since the after-tax return can still be competitive or superior for investors in higher tax brackets.

Correct answer: D) A call feature requiring the issuer, if it calls the bond early, to compensate bondholders with a redemption price based on the present value of remaining cash flows, discounted at a small spread over a benchmark rate.

A make-whole call provision requires the issuer, upon early redemption, to pay bondholders a redemption price calculated to approximate the present value of the bond's remaining scheduled cash flows, discounted at a small spread over a specified benchmark yield, making early redemption less costly to bondholders than a traditional fixed-price call.

Correct answer: B) The risk that coupon payments will need to be reinvested at a rate lower than the bond's original yield to maturity, reducing the investor's total realized return.

Reinvestment risk arises because coupon payments received over a bond's life must be reinvested, and if prevailing rates have fallen since the bond was purchased, those reinvested coupons will earn less than originally assumed, reducing the investor's total realized (compound) return relative to the quoted yield to maturity.

Correct answer: B) The risk that the issuer will fail to make timely interest or principal payments as contractually promised.

Default risk (credit risk) refers to the possibility that the bond issuer will fail to make scheduled interest or principal payments as promised, distinct from interest rate risk (price sensitivity to rate changes) or call risk (early redemption by the issuer).

Correct answer: A) The market's current expectations of future short-term interest rates.

Under the pure expectations theory, the shape of the yield curve reflects the market's current expectations of future short-term interest rates: an upward-sloping curve implies expectations of rising future short-term rates, while an inverted curve implies expectations of falling rates.

Correct answer: C) Convex (non-linear) and negative

The price-yield relationship is inverse (higher yield → lower price) and convex (the curve bows outward). Convexity means that price increases from a yield decline are larger than price decreases from an equal yield increase.

Correct answer: B) 7.47%

The bond trades at a discount (price < face), so YTM > coupon rate. Using a financial calculator: N=8, PV=-950, PMT=30, FV=1000 -> I/Y = 3.7345% semi-annual -> annualized (x2, bond-equivalent yield) = 7.47%.

Correct answer: A) −2.60%

% price change ≈ −Modified Duration × ΔYield = −5.2 × 0.0050 = −0.026 = −2.60%. Price falls when yields rise.

Correct answer: C) Credit risk and liquidity risk

The spread over the risk-free rate compensates for default risk (credit risk) and the possibility that the bond cannot be sold quickly at a fair price (liquidity risk). Interest rate risk applies to both bonds equally.

Correct answer: B) Lower price and higher yield

The call option benefits the issuer (allows refinancing at lower rates). Investors require compensation for this embedded option risk, resulting in a higher yield and lower price compared to an equivalent non-callable bond.

Correct answer: B) Interest rates fall sharply

When rates fall, homeowners refinance their mortgages at lower rates, accelerating principal prepayments. MBS investors then receive principal earlier than expected and must reinvest at lower prevailing rates.

Correct answer: C) Inversely related -- when YTM rises, the bond's price falls, and vice versa.

Bond prices and yields have an inverse relationship: since a bond's price is the present value of its future cash flows discounted at the market yield, a higher discount rate (yield) results in a lower present value (price), and vice versa.

Correct answer: B) Lower price sensitivity (lower duration) to changes in interest rates than a lower-coupon bond.

Higher-coupon bonds return a larger portion of their cash flows earlier (through coupon payments), reducing the effective weighted-average time to receive cash flows, which results in lower duration and lower interest rate sensitivity compared to a lower-coupon bond of the same maturity.

Correct answer: A) 5.00%

Current yield = Annual coupon payment / Current price = 50/1000 = 5.00%. When a bond is priced at par, its coupon rate, current yield, and yield to maturity are all equal.

Correct answer: D) A lower price (or equivalently, offer a higher yield), since the issuer's call option is valuable to the issuer and a cost to the bondholder.

Because the call option benefits the issuer (who can redeem the bond and refinance at a lower rate if rates fall) at the bondholder's expense, callable bonds trade at a lower price (higher yield) than an otherwise identical option-free bond, to compensate investors for the embedded call risk.

Correct answer: C) Treasury Inflation-Protected Securities (TIPS) or similar inflation-linked bonds.

Inflation-linked bonds, such as U.S. Treasury Inflation-Protected Securities (TIPS), adjust their principal value in line with a specified inflation index (such as the CPI), helping preserve the real (inflation-adjusted) value of the investor's principal and coupon payments.

Correct answer: B) A decrease in the bond's price, as investors demand a higher yield to compensate for increased credit risk.

A credit rating downgrade signals increased default risk, which typically causes investors to demand a higher yield (a wider credit spread) to hold the bond, resulting in a lower bond price, all else equal.

Correct answer: D) 7.69%

Approximate YTM = [Coupon + (Face value - Price)/n] / [(Face value + Price)/2] = [70 + (1,000-950)/10] / [(1,000+950)/2] = [70+5]/975 = 75/975 = approximately 7.69%.

Correct answer: A) The independent supply and demand conditions within each specific maturity segment, since investors and issuers have strong preferences for particular maturity ranges (driven by factors like regulatory or liability-matching needs) and do not readily substitute across segments.

Market segmentation theory holds that the yield curve's shape is determined by the independent supply and demand dynamics within distinct maturity segments (such as short, intermediate, and long-term), since different investors (e.g., banks preferring short maturities, pension funds preferring long maturities) have strong preferences and do not freely substitute across maturity segments, unlike the pure expectations theory's assumption of full substitutability.

Correct answer: D) Investors generally require a liquidity premium to compensate for the greater price volatility and reduced liquidity associated with holding longer-maturity bonds, in addition to any expectations about future short-term rates.

The liquidity preference theory builds on the pure expectations theory by adding that investors typically demand a liquidity premium for holding longer-maturity bonds, which are generally more price-sensitive to interest rate changes and can be less liquid, resulting in yield curves that are typically upward-sloping even when short-term rates are not expected to rise.

Correct answer: C) 6.49%

Bond-equivalent yield (simple annualization) = Holding period yield x (365/days in holding period) = 3.2% x (365/180) = approximately 6.49%, converting the short-term instrument's holding period return to an annualized basis comparable to other fixed income yields quoted on a 365-day basis.

Correct answer: B) 7.08

Modified duration = Macaulay duration / (1 + YTM per period) = 7.5 / 1.06 = approximately 7.08, providing a more direct measure of the bond's approximate percentage price sensitivity to a small change in yield than Macaulay duration alone.

Correct answer: A) $920.15

The bond's price equals the present value of its coupon payments plus the present value of its face value, discounted at the 8% market yield: PV = 60/1.08 + 60/1.08^2 + 60/1.08^3 + 60/1.08^4 + 60/1.08^5 + 1,000/1.08^5 = approximately $920.15. This bond trades at a discount to face value because its 6% coupon is below the 8% market yield.