Practice: Yield and Yield Spread Measures for Fixed-Rate Bonds
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Fixed IncomeYield and Yield Spread Measures for Fixed-Rate Bonds
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Question 1Exam level
A bond has a face value of $1,000, a coupon rate of 8% paid semi-annually, 5 years to maturity, and a current price of $920. Which of the following best describes the relationship between the bond's coupon rate, current yield, and yield to maturity?
How sure are you?
Correct: A. The bond trades at a discount (price $920 < par $1,000). For discount bonds: coupon rate < current yield < YTM. Current yield = $80/$920 = 8.70%. YTM must be higher than current yield because YTM also captures the capital gain from $920 to $1,000 at maturity. The ordering coupon rate < current yield < YTM always holds for discount bonds.
B. Choosing B might tempt you if you mistakenly believe the bond trades at a premium, but for a discount bond priced at $920, the YTM must be higher than the current yield to account for the capital gain to par value at maturity, thus violating the correct relationship where YTM is the highest.
C. You might be tempted by choice C if you think the YTM is lower than the current yield because the bond is at a discount, but this violates the principle that for discount bonds, the YTM must be higher than the current yield to account for the additional gain from the bond's price rising to par at maturity.
An investor buys a bond with a 6% annual coupon at a price of $108 per $100 face value. The bond matures in 4 years. The bond's current yield is closest to:
How sure are you?
Correct: A. Current yield = Annual coupon / Current price = $6 / $108 = 5.556%. Current yield does NOT account for the capital loss the investor will realize at maturity when the bond pays $100 but the investor paid $108. This is why YTM is lower than current yield for premium bonds: YTM incorporates the capital loss.
B. Choosing 6.00% might seem logical if you are thinking the coupon rate and current yield are the same, but this ignores the bond's premium price; the current yield is actually the annual coupon payment divided by the current price, making it lower than the coupon rate for a bond bought above par.
C. Choosing 6.48% might tempt you if you mistakenly divide the face value by the current price, but current yield is calculated by dividing the annual coupon payment by the current price, not the face value, making 6.48% incorrect.
A callable bond has a Z-spread of 180 basis points. If the estimated value of the embedded call option is 25 basis points, the bond's option-adjusted spread (OAS) is closest to:
How sure are you?
Correct: A. For a callable bond: OAS = Z-spread - Option cost = 180 - 25 = 155 bps. The call option benefits the issuer (hurts the investor), so the option cost is subtracted from the Z-spread to isolate the pure credit and liquidity spread. OAS is always less than Z-spread for callable bonds because Z-spread includes compensation for both credit risk AND the option the investor has written.
B. Choosing 180 bps might seem logical if you think the Z-spread and OAS are the same, but this ignores the need to subtract the value of the call option, which you have written, from the Z-spread to get the OAS for a callable bond.
C. Choosing 205 bps might tempt you if you mistakenly add the option cost to the Z-spread, but the OAS calculation for a callable bond actually subtracts the option cost to account for the embedded call option's benefit to the issuer, not add it.
A bond has a YTM of 7.2% on a semi-annual bond basis (BEY). The bond's effective annual yield (EAY) is closest to:
How sure are you?
Correct: A. EAY = (1 + BEY/2)^2 - 1 = (1 + 0.072/2)^2 - 1 = (1.036)^2 - 1 = 1.07330 - 1 = 7.33%. BEY is the nominal yield (stated as twice the semi-annual rate). EAY accounts for compounding and is always HIGHER than BEY for the same bond. The difference arises from the half-year reinvestment of the first coupon before the second coupon is paid.
B. You might use EAY = BEY/2 x 2 (no compounding), which gives 7.20%. The distractor at answer B. Always apply (1+r/m)^m - 1 to convert from nominal to effective.
C. You might be tempted to choose 7.41% if you incorrectly applied annual compounding instead of semi-annual, leading to an overestimation of the effective annual yield; remember, the effective annual yield (EAY) correctly accounts for semi-annual compounding, resulting in a lower figure than annual compounding would suggest.
Which of the following yield spread measures is MOST appropriate for comparing bonds with embedded options to option-free bonds?
How sure are you?
Correct: C. OAS removes the value of the embedded option from the spread, leaving only the spread attributable to credit risk and liquidity. G-spread and Z-spread include compensation for the embedded option, making cross-security comparisons misleading. OAS allows apples-to-apples comparison of callable bonds versus option-free bonds of the same issuer.
A. You might choose Z-spread because it sounds more 'sophisticated' than G-spread. Z-spread is better than G-spread for non-flat yield curves, but neither removes option value. Only OAS does.
B. You might choose Z-spread because it sounds more 'sophisticated' than G-spread. Z-spread is better than G-spread for non-flat yield curves, but neither removes option value. Only OAS does.
A 10-year government bond yields 3.5%. A 10-year corporate bond of equal maturity yields 5.2%. The 10-year swap rate is 3.8%. What is the corporate bond's G-spread and I-spread, respectively, most likely?
How sure are you?
Correct: A. G-spread = Corporate yield - Government benchmark yield = 5.2% - 3.5% = 1.70% = 170 bps. I-spread = Corporate yield - Swap rate = 5.2% - 3.8% = 1.40% = 140 bps. G-spread uses government bond yield as the risk-free benchmark. I-spread uses the swap rate (LIBOR/SOFR-based), which is slightly above government yields, producing a lower spread for the same bond.
B. You might be tempted to choose B if you mistakenly subtracted the swap rate from the government bond yield instead of the corporate bond yield for the G-spread, confusing the roles of the swap rate and government bond yield in calculating these spreads.
C. You might be tempted to think the G-spread and I-spread would be the same if you confuse the government bond yield and the swap rate as equivalent benchmarks, but the I-spread uses the swap rate of 3.8%, resulting in a lower spread of 140 bps compared to the G-spread using the government bond yield of 3.5%.
YTM assumes which of the following about a bond's cash flows, most likely?
How sure are you?
Correct: B. YTM is calculated assuming all coupon payments are reinvested at a rate equal to the YTM itself. This is the reinvestment assumption. In practice, reinvestment rates change over time (rates may be higher or lower than YTM when coupons are received), so the realized return almost never equals the YTM. The only bond for which YTM = realized return without reinvestment risk is a zero-coupon bond (no coupons to reinvest).
A. You might be tempted by the idea of reinvesting at the risk-free rate because it seems conservative and safe, but YTM specifically assumes coupons are reinvested at the YTM rate itself, not at the risk-free rate, to maintain consistency in the calculation.
C. Choosing C might seem logical if you think about immediate consumption, but YTM specifically assumes coupons are reinvested, not spent, directly contrasting with the assumption that coupons are reinvested at the YTM rate.
A bond with a 5% semi-annual coupon, $1,000 face value, and 10 years to maturity is priced at $1,050. Using a financial calculator, which of the following inputs correctly sets up the YTM calculation? The value is closest to:
How sure are you?
Correct: B. Semi-annual coupon bond: N = 10 years x 2 = 20 periods; PMT = 5% x $1,000 / 2 = $25 per period; PV = -$1,050 (negative because cash outflow for buyer); FV = $1,000. Solve for I/Y, then multiply by 2 for the BEY. Option A uses annual periods (N=10) and annual coupon ($50). Incorrect for semi-annual. Option C uses correct N=20 but annual coupon $50. The most common mistake.
A. Option A uses annual periods (N=10) and annual coupon ($50). Incorrect for semi-annual.
C. Option C uses correct N=20 but annual coupon $50. The most common mistake.
A bond is quoted with a bank discount yield of 4.8% on a 90-day Treasury bill with a face value of $1,000. The bill's price is closest to:
How sure are you?
Correct: A. Bank discount yield (BDY) uses face value as the base and a 360-day year. Price = Face x [1 - BDY x (days/360)] = $1,000 x [1 - 0.048 x (90/360)] = $1,000 x [1 - 0.012] = $1,000 x 0.988 = $988.00. True holding period yield or EAY would be higher.
B. You might be tempted by $987.69 if you mistakenly applied the money market yield formula instead of the bank discount yield formula, leading to a calculation that does not account for the face value base and 360-day year requirement of BDY.
C. You might be tempted by choice C if you incorrectly applied the formula for the holding period return instead of the bank discount yield, leading to an overly discounted price that does not reflect the BDY calculation based on a 360-day year.
For a premium bond, which ordering of yield measures is most likely correct?
How sure are you?
Correct: B. For a bond trading at a premium (price > par): coupon rate > current yield > YTM. Coupon rate is highest because it is based on par (a lower base than market price). Current yield = coupon/price, and since price > par, current yield < coupon rate. YTM is lowest because it incorporates the capital loss from paying premium price to receive only par at maturity. This reduces the total return below the current yield.
A. This reverses the entire ordering for a premium bond. Paying a market price above par means the bond's expected total return, the yield to maturity, falls below both the coupon rate and the current yield, since the investor loses money on the capital side at maturity. The correct order runs coupon rate first, then current yield, then yield to maturity, the opposite direction from what this choice states.
C. This puts current yield ahead of coupon rate, but for a premium bond current yield is the coupon divided by a price that is above par, which makes current yield lower than the coupon rate, not higher. The correct order is coupon rate first, then current yield, then yield to maturity at the bottom, reflecting the capital loss built into paying more than par for a bond that repays only par at maturity.
Which of the following most accurately describes the difference between a Z-spread and a G-spread, most likely?
How sure are you?
Correct: A. Z-spread (zero-volatility spread) adds a constant spread Z to each relevant spot rate on the benchmark zero-coupon yield curve so that the present value of cash flows equals the bond's price. G-spread simply subtracts the government benchmark bond's yield from the bond's YTM. A single-number subtraction using par yields. Z-spread is more accurate for non-flat yield curves because it respects the timing of each cash flow. G-spread uses a flat-curve approximation. Neither adjusts for option value. That is OAS.
B. You might be thinking that Z-spread accounts for option-adjusted values, but both Z-spread and G-spread do not adjust for embedded option values; that adjustment is actually done by the option-adjusted spread (OAS), not the Z-spread or G-spread.
C. You might think the G-spread uses spot rates for accuracy, but the G-spread actually relies on a single benchmark yield, making it less precise for non-flat yield curves compared to the Z-spread, which adds a constant spread to each spot rate.
A floating-rate note (FRN) resets its coupon every 6 months based on 6-month SOFR + 120 bps. If current 6-month SOFR is 4.5%, the current coupon rate on the FRN is closest to:
How sure are you?
Correct: A. FRN coupon = Reference rate + Quoted margin = 4.5% + 1.20% = 5.70%. For FRNs, the key yield measure is the quoted margin (QM) set at issuance and the discount margin (DM), which is the margin required by the market currently. If the bond trades at par, QM = DM. If credit quality deteriorates, DM > QM and the bond trades below par.
B. You might be tempted to choose 4.50% because it reflects the current 6-month SOFR rate, but this overlooks the additional quoted margin of 120 bps that must be added to the reference rate to determine the FRN coupon rate.
C. Choosing 1.20% might seem right if you mistakenly thought the quoted margin alone was the coupon rate, but the coupon rate for an FRN is the sum of the reference rate and the quoted margin, not just the margin itself.
Bond A has a G-spread of 150 bps over the interpolated government yield curve. Bond B has a Z-spread of 140 bps and an OAS of 90 bps, reflecting a meaningful embedded call option. Combining the definitions of G-spread, Z-spread, and OAS, an analyst comparing the credit and liquidity risk compensation embedded in the two bonds should most likely:
How sure are you?
Correct: B. The Z-spread includes compensation for ALL of a bond's risks, including any embedded option; the OAS specifically REMOVES the portion of the spread attributable to the option, leaving a cleaner measure of credit and liquidity compensation. When comparing an option-free bond's spread (like Bond A's G-spread, a reasonable option-free benchmark-relative spread) to a callable bond's spread, the OAS is the appropriate, apples-to-apples comparison, not the Z-spread, which still has the option's effect baked in.
A. G-spread and Z-spread are conceptually similar but not always numerically identical (G-spread uses a linearly interpolated government yield, Z-spread uses the full spot curve), and neither is the right comparison for a bond with an embedded option; comparing a Z-spread (with the option's effect still included) to an option-free spread mixes in the option's distorting effect on Bond B's numbers.
C. The comparison in this choice garbles the actual figures and the underlying logic; the correct comparison uses OAS (90 bps) for the option-embedded bond specifically because the raw Z-spread or a simple 'bigger number wins' comparison would be distorted by the value of Bond B's embedded call option, not a valid apples-to-apples risk comparison.
A floating-rate note has a quoted margin of 80 bps over the reference rate and a discount margin (DM), computed at the current price, of 120 bps. Combining the meaning of quoted margin with the meaning of discount margin, the FRN is most likely:
How sure are you?
Correct: B. The quoted margin is the FIXED spread over the reference rate set at issuance; the discount margin is the spread that equates the FRN's price (using its current market price) to its cash flows, reflecting the market's CURRENT required margin. When the market's required margin (DM, 120 bps) is higher than the note's fixed quoted margin (80 bps), it means the market now demands more compensation than the note pays, which can only be achieved by the note trading BELOW par (a discount), so that the extra price appreciation-to-par over time makes up the difference.
A. A discount margin higher than the quoted margin indicates the market requires MORE compensation than the note's fixed spread provides, which drives the price BELOW par, a discount, not a premium; a premium would instead occur if the discount margin were BELOW the quoted margin.
C. Quoted margin and discount margin are equal only when the FRN happens to be trading exactly at par; they are not equal by definition in general. The whole point of computing a separate discount margin is to reflect how the market's required spread may have diverged from the note's fixed quoted margin since issuance.